@article{2-s2.0-85184750118,

title = {Proton-polarized states in DNA},

author = { M.A. Pietruszka and M. Marzec},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85184750118&doi=10.1016%2fj.biosystems.2024.105125&partnerID=40&md5=81a9bceaf6e4ca6743ada0e70392fa58},

doi = {10.1016/j.biosystems.2024.105125},

issn = {03032647},

year  = {2024},

date = {2024-01-01},

journal = {BioSystems},

volume = {237},

publisher = {Elsevier Ireland Ltd},

abstract = {We observed signatures of a phase transition in the double-stranded DNA fragment of known length and sequences using a non-invasive semiconductor-electrolyte interface technique and statistical physics methods. Observations revealed a coherence peak in the electromotive force and a significant decline in calculated dynamic entropy at a critical temperature and pH. This behavior may arise from the dynamic interaction of proton (H+) pairs with opposite momentum and spin, carrying a charge q=2+ under critical conditions. © 2024},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-85146194949,

title = {Collective excitations of germinating pollen grains at critical points},

author = { M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85146194949&doi=10.1038%2fs41598-023-27754-6&partnerID=40&md5=7519e45459a56fa32f3608e387507bb2},

doi = {10.1038/s41598-023-27754-6},

issn = {20452322},

year  = {2023},

date = {2023-01-01},

journal = {Scientific Reports},

volume = {13},

number = {1},

publisher = {Nature Research},

abstract = {In plants, the germinating pollen grain (pollen tube) is a single, elongated cell that serves as a conduit through which gametes pass. Pollen tubes display a fast growth rate, which under certain conditions, changes periodically and is accompanied by ion exchange with the growth environment. Therefore, pollen tubes exposed to various abiotic conditions may adversely affect or improve their reproductive performance and fertility. We examined a collection of live pollen tubes of tobacco (Nicotiana tabacum L.) and hyacinth (Hyacinthus orientalis L.) using a non-invasive semiconductor–electrolyte interface technique in the vicinity of the germination temperature or optimum growth temperature of a pollen grains/tubes. The time series measurements and numerical calculations, performed using information theory methods, represent signatures of collective dynamics in living cells at critical—molecularly encoded—germination and growth temperatures. This method (and soil pH data) can facilitate assisted plant migrations from one ecosystem to another as the Earth faces climate change. © 2023, The Author(s).},

note = {1},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-85171476080,

title = {Phase coherent quasi-particle formation in biological systems},

author = { M.A. Pietruszka and M. Lipowczan},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85171476080&doi=10.1016%2fj.biosystems.2023.105020&partnerID=40&md5=68229d1d4e3f25db51dc0718a0497ece},

doi = {10.1016/j.biosystems.2023.105020},

issn = {03032647},

year  = {2023},

date = {2023-01-01},

journal = {BioSystems},

volume = {233},

publisher = {Elsevier Ireland Ltd},

abstract = {The problem of the origin of canonical and aberrant DNA mutations and the contribution of protons to genetic stability is an essential topic in molecular biology. Based on the empirical results, we reconsidered canonical and tautomeric mutations under the two-fluid model of quantum physics. We assumed that the pressure exerted by protons (H+) in the DNA environment, through changes in pH, could alter the concentration ratio of canonical and tautomeric base pairs, which were found to be different at and beyond the criticality level, respectively. We anticipate that the deviation of the cellular system from a specific (critical) temperature at which dynamic entropy reaches a minimum and a critical pH occurs could result in tautomerization and point mutations. © 2023 Elsevier B.V.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-85141980120,

title = {Collective excitations at non-equilibrium phase transition in metabolically active red blood cells},

author = { M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85141980120&doi=10.1016%2fj.biosystems.2022.104804&partnerID=40&md5=2e066cca614f6f222f510bda8d053866},

doi = {10.1016/j.biosystems.2022.104804},

issn = {03032647},

year  = {2023},

date = {2023-01-01},

journal = {BioSystems},

volume = {223},

publisher = {Elsevier Ireland Ltd},

abstract = {Collective excitations of superconductors and superfluids have been extensively studied in condensed matter physics, while recent experimental advances have made it possible to study the non-equilibrium dynamics of human blood. Here, we show that some dynamic quantitative metrics calculated for the ion fluxes of two isolated peripheral blood droplets that were spatially separated by the presence of a semiconductor exhibited the characteristic features of a quasi-particle (or collective excitation) at a critical point. In the experiment, the spontaneous peak, which indicates order, appeared at a physiological (hereafter: critical) temperature of 36 °C in the human blood. The ordering effect, which was still present in the weak magnetic field of 350 mT, disappeared above the critical magnetic field of approximately 500 mT, suggesting a dynamic Meissner effect in the system (henceforth “dynamic” means derived from the “time series” – a series of real numbers). Moreover, a superconducting gap ratio of approx. 2.91 was found below the upper limit (4) of the BCS theory for weak coupling. Both these effects indicate the existence of a “superconducting” (ion) environment that is conducive to the emergence of quasiparticles. While the dynamic structure of the time series is substantially isotropic at temperatures beyond the phase transition, the system undergoes symmetry breakdown and non-equilibrium phase transition at a critical state. The designated series of dynamic variables can be used in medicine, inter alia, in screening tests as new indicators describing the patient's health. © 2022},

note = {2},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-85111778439,

title = {Expansive Growth vs. pH Reflects a Poisson Point Process of Binding/Unbinding Events in Plant Cell Walls},

author = { M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85111778439&doi=10.1007%2fs00344-021-10459-3&partnerID=40&md5=f02c20c9dc7b939e1ff4e20489599008},

doi = {10.1007/s00344-021-10459-3},

issn = {07217595},

year  = {2022},

date = {2022-01-01},

journal = {Journal of Plant Growth Regulation},

volume = {41},

number = {6},

pages = {2543-2554},

publisher = {Springer},

abstract = {The paramount role of pH and temperature (T) in the expansive growth of a plant coleoptile/hypocotyl non-meristematic zone or plant and fungal cells was examined within the framework of the underlying chemical bond statistics in order to reproduce an experimental plot of growth vs. pH. Here, according to the definition},

note = {1},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-85119290501,

title = {Non-equilibrium phase transition at a critical point of human blood},

author = { M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85119290501&doi=10.1038%2fs41598-021-01909-9&partnerID=40&md5=c3c924a19d27e101d2936d1f440cbb21},

doi = {10.1038/s41598-021-01909-9},

issn = {20452322},

year  = {2021},

date = {2021-01-01},

journal = {Scientific Reports},

volume = {11},

number = {1},

publisher = {Nature Research},

abstract = {Blood is the basic medium in the existence, evolution and physiological balance of animals and represents the biochemical “Internet” of the body; at least human blood exhibit the presence of an emergent phase that is highly unusual. Homeostasis, the state of the optimal functioning of the body, is maintained in living organisms by many chemical and physical conditions, particularly temperature. However, no regulatory mechanism has been identified that has led to a predetermined (molecularly encoded) optimal, individually variable, very specific temperature of around 36 °C. Additionally, the homeostatic temperature range, which is kept within predetermined limits, is merely an empirical fact. In the following, I will show that the reference temperature that is necessary to achieve homeostasis can be established, and a preset homeostatic range can be determined, using an original experimental method and refined tools of mathematical physics related to the nonlinear measures of the complexity of human blood. Moreover, signatures of a macroscopic coherent state in a non-equilibrium system at a critical temperature are obtained. © 2021, The Author(s).},

note = {3},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-85103995019,

title = {Dynamic entropy of human blood},

author = { M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85103995019&doi=10.1038%2fs41598-021-87212-z&partnerID=40&md5=671b64d9a2699ab3164fb04dfe03d951},

doi = {10.1038/s41598-021-87212-z},

issn = {20452322},

year  = {2021},

date = {2021-01-01},

journal = {Scientific Reports},

volume = {11},

number = {1},

publisher = {Nature Research},

abstract = {Temperature control is a process that is used by biological systems to maintain a stable internal state for survival. People have an individually variable physiological temperature of about 36.6 °C, which can be modified by many undesirable factors. Based on an analysis of a time series of extracellular ionic fluxes that were obtained using the non-invasive solute-semiconductor interface technique, I show that this extremely specific (critical) temperature is encoded by a local minimum in the dynamic entropy of an isolated drop of human blood. Moreover, a dynamic zeroth-order normal fluid/“superfluid” nonequilibrium phase transition, which was reflected by a spontaneous symmetry breaking that occurred in the phase space, was revealed. The critical scaling of the dynamic measures for the covariates such as the spectral signature and Lyapunov exponent was also determined. © 2021, The Author(s).},

note = {4},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-85103067366,

title = {Application of time-series regularity metrics to ion flux data from a population of pollen tubes},

author = { M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85103067366&doi=10.1080%2f19420889.2021.1899574&partnerID=40&md5=3639c6952d62fd87ae2abf0bc91e28a7},

doi = {10.1080/19420889.2021.1899574},

issn = {19420889},

year  = {2021},

date = {2021-01-01},

journal = {Communicative and Integrative Biology},

volume = {14},

number = {1},

pages = {51-54},

publisher = {Bellwether Publishing, Ltd.},

abstract = {Detecting the presence of an irregularity/regularity or chaos in the ion flows of an evolving plant cell is an important task that can be unraveled by performing the analyses by different metrics. Here I show that the results of the advanced fluctuation estimation methods that are obtained from the time series that is generated by the extracellular ion fluxes of tobacco pollen tubes (Nicotiana tabacum L.) have long-range correlations at critical temperatures. Further experimental evidence has been found to support the claim that the autonomous growth organization of extreme plant cell expansion is accomplished by self-organizing criticality (SOC), which is an orchestrated instability that occurs in an optimally evolving cell. The temperature-induced synchronous action of the ionic fluxes that are manifested, inter alia, by minimal dynamic entropy enabled the molecularly encoded information about germination and optimal growth temperatures of tobacco pollen tubes to be determined. © 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.},

note = {2},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-85073957635,

title = {Chemical Potential-Induced Wall State Transitions in Plant Cell Growth},

author = { M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85073957635&doi=10.1007%2fs00344-019-10026-x&partnerID=40&md5=0aa05290a30a5fd42735a16d4507aca8},

doi = {10.1007/s00344-019-10026-x},

issn = {07217595},

year  = {2020},

date = {2020-01-01},

journal = {Journal of Plant Growth Regulation},

volume = {39},

number = {2},

pages = {841-866},

publisher = {Springer},

abstract = {The pH/T duality of acidic pH and temperature (T) action for the growth of grass shoots was examined in order to derive the phenomenological equation of wall properties for living plants. By considering non-meristematic growth as a dynamic series of state transitions (STs) in the extending primary wall, the critical exponents were identified, which exhibit a singular behaviour at a critical temperature, critical pH and critical chemical potential (μ) in the form of four power laws: fπ(τ) ∝ | τ| β - 1, fτ(π) ∝ | π| 1 - α, gμ(τ) ∝ | τ| - 2 - α + 2 β and gτ(μ) ∝ | μ| 2 - α. The indices α and β are constants, while π and τ represent a reduced pH and reduced temperature, respectively. The convexity relation α + β ≥ 2 for practical pH-based analysis and β ≡ 2 “mean-field” value in microscopic (μ) representation were derived. In this scenario, the magnitude that is decisive is the chemical potential of the H+ ions, which force subsequent STs and growth. Furthermore, observation that the growth rate is generally proportional to the product of the Euler beta functions of T and pH, allowed to determine the hidden content of the Lockhart constant Ф. It turned out that the pH-dependent time evolution equation explains either the monotonic growth or periodic extension that is usually observed—like the one detected in pollen tubes—in a unified account. © 2019, The Author(s).},

note = {4},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-85083362209,

title = {Extracellular ionic fluxes suggest the basis for cellular life at the 1/f ridge of extended criticality},

author = { M.A. Pietruszka and M. Olszewska},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85083362209&doi=10.1007%2fs00249-020-01430-3&partnerID=40&md5=82833762ce83f4f6eed8c2216a0d019b},

doi = {10.1007/s00249-020-01430-3},

issn = {01757571},

year  = {2020},

date = {2020-01-01},

journal = {European Biophysics Journal},

volume = {49},

number = {3-4},

pages = {239-252},

publisher = {Springer},

abstract = {Abstract: The criticality hypothesis states that a system may be poised in a critical state at the boundary between different types of dynamics. Previous studies have suggested that criticality has been evolutionarily selected, and examples have been found in cortical cell cultures and in the human nervous system. However, no one has yet reported a single- or multi-cell ensemble that was investigated ex vivo and found to be in the critical state. Here, the precise 1/f noise was found for pollen tube cells of optimum growth and for the physiological (“healthy”) state of blood cells. We show that the multi-scale processes that arise from the so-called critical phenomena can be a fundamental property of a living cell. Our results reveal that cell life is conducted at the border between order and disorder, and that the dynamics themselves drive a system towards a critical state. Moreover, a temperature-driven re-entrant state transition, manifest in the form of a Lorentz resonance, was found in the fluctuation amplitude of the extracellular ionic fluxes for the ensemble of elongating pollen tubes of Nicotiana tabacum L. or Hyacintus orientalis L. Since this system is fine-tuned for rapid expansion to reach the ovule at a critical temperature which results in fertilisation, the core nature of criticality (long-range coherence) offers an explanation for its potential in cell growth. We suggest that the autonomous organisation of expansive growth is accomplished by self-organised criticality, which is an orchestrated instability that occurs in an evolving cell. Graphic abstract: [Figure not available: see fulltext.] © 2020, The Author(s).},

note = {6},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-85063811711,

title = {Modified Bohm’s theory for abstruse measurements: Application to layer depth profiling using Auger spectroscopy},

author = { E. Rówiński and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85063811711&doi=10.24425%2famm.2019.126234&partnerID=40&md5=f08fa05c492eeb712c3dc45bc715eb90},

doi = {10.24425/amm.2019.126234},

issn = {17333490},

year  = {2019},

date = {2019-01-01},

journal = {Archives of Metallurgy and Materials},

volume = {64},

number = {1},

pages = {175-180},

publisher = {Polish Academy of Sciences},

abstract = {Modified Bohm’s formalism was applied to solve the problem of abstruse layer depth profiles measured by the Auger electron spectroscopy technique in real physical systems. The desorbed carbon/passive layer on an NiTi substrate and the adsorbed oxygen/ surface of an NiTi alloy were studied. It was shown that the abstruse layer profiles can be converted to real layer structures using the modified Bohm’s theory, where the quantum potential is due to the Auger electron effect. It is also pointed out that the stationary probability density predicts the multilayer structures of the abstruse depth profiles that are caused by the carbon desorption and oxygen adsorption processes. The criterion for a kind of break or “cut” between the physical and unphysical multilayer systems was found. We conclude with the statement that the physics can also be characterised by the abstruse measurement and modified Bohm’s formalism. © Institute of Metallurgy and Materials Science of Polish Academy of Sciences 2019. All rights reserved.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-85047242419,

title = {Single measurement detection of individual cell ionic oscillations using an n-type semiconductor - Electrolyte interface},

author = { M.A. Pietruszka and M. Olszewska and L. Machura and E. Rówiński},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85047242419&doi=10.1038%2fs41598-018-26015-1&partnerID=40&md5=4170de9d70b3c4138e965008544a5375},

doi = {10.1038/s41598-018-26015-1},

issn = {20452322},

year  = {2018},

date = {2018-01-01},

journal = {Scientific Reports},

volume = {8},

number = {1},

publisher = {Nature Publishing Group},

abstract = {Pollen tubes are used as models in studies on the type of tip-growth in plants. They are an example of polarised and rapid growth because pollen tubes are able to quickly invade the flower pistil in order to accomplish fertilisation. How different ionic fluxes are perceived, processed or generated in the pollen tube is still not satisfactorily understood. In order to measure the H+, K+, Ca2+ and Cl- fluxes of a single pollen tube, we developed an Electrical Lab on a Photovoltaic-Chip (ELoPvC) on which the evolving cell was immersed in an electrolyte of a germination medium. Pollen from Hyacinthus orientalis L. was investigated ex vivo. We observed that the growing cell changed the (redox) potential in the medium in a periodic manner. This subtle measurement was feasible due to the effects that were taking place at the semiconductor-liquid interface. The experiment confirmed the existence of the ionic oscillations that accompany the periodic extension of pollen tubes, thereby providing - in a single run - the complete discrete frequency spectrum and phase relationships of the ion gradients and fluxes, while all of the metabolic and enzymatic functions of the cell life cycle were preserved. Furthermore, the global 1/f α characteristic of the power spectral density, which corresponds to the membrane channel noise, was found. © 2018 The Author(s).},

note = {6},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-85052121015,

title = {Determination of selected dynamic quantities of growing intact seeds of maize},

author = { M. Olszewska and A. Haduch-Sendecka and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85052121015&doi=10.4149%2fgpb_2017058&partnerID=40&md5=94a9faa4daab00e76609739ff30ee0a2},

doi = {10.4149/gpb_2017058},

issn = {02315882},

year  = {2018},

date = {2018-01-01},

journal = {General Physiology and Biophysics},

volume = {37},

number = {4},

pages = {375-389},

publisher = {Slovak Academy of Sciences},

abstract = {Plant growth and intracellular H+ ion kinetics are known to be strictly correlated, although the history of this discovery, which is known as the acid-growth hypothesis, has faced many difficulties and provoked a long-lasting discussion. Simultaneous measurements of the plant cell extension and pH of the incubation medium helped to defend the theory and together with some of the newest physics-based models, offered a new insight at the molecular level. This article focuses on both the biological and physical aspects of plant growth in the presence of endogenous auxin. Our aim was to circumvent the experimental and conceptual pitfalls associated with the standard use of cut and/or abraded coleoptile segments. Therefore, we simultaneously investigated the growth of intact seedlings of maize (Zea mays L.) and pH of the incubation medium. The growth rates were measured by applying a non-invasive technique that records time-lapse images of the macroscopic elongation of the coleoptiles, while changes in the pH were monitored using a pH/Ion meter. In the experiments, we intentionally introduced growth stimulators: indole-3-acetic acid (IAA), fusicoccin (FC), gibberellic acid (GA3), and a growth inhibitor cadmium chloride (CdCl2), in order to analyse the resultant effect of both exogenous and endogenous factors. © 2018 Slovak Academy of Sciences. All rights reserved.},

note = {2},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-85032037787,

title = {Proton kinetics through the cuticle layer in maize},

author = { M. Olszewska and A. Konefał and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85032037787&doi=10.1007%2fs11738-017-2559-6&partnerID=40&md5=e8248ed18697d92c0076d030df95b0ae},

doi = {10.1007/s11738-017-2559-6},

issn = {01375881},

year  = {2017},

date = {2017-01-01},

journal = {Acta Physiologiae Plantarum},

volume = {39},

number = {12},

publisher = {Polish Academy of Sciences,Institute of Slavic Studies},

abstract = {A Monte Carlo simulation was used to determine the dependence between the thickness of the cuticle layer of coleoptiles and the spectra of the H+ ions (i.e., protons) passing through this layer, which is treated as a potential barrier. The apparently simplistic model of a walled cylinder filled with H+ ions propagating through the cuticle layer was solved in silico. We showed that the thickness of the cuticle layer clearly influences the intensity of the efflux of protons, which changes the pH of the surrounding solution. Then, diffusion and cross-correlation data for maize (Zea mays L.) coleoptile growth and H+ ion extrusion were probed in an experiment and compared with the Monte Carlo computation results. Ex vivo experiments for the control (APW), auxin (IAA) and fusicoccin (FC) were conducted. The transition from time-delayed pH—(abrasion time) cross-correlation to proton efflux that was not retarded was obtained, thus confirming the canvas that constitutes the acid growth hypothesis and the rationale that was accepted for the derivation of the ‘equation of state’ for plants. © 2017, The Author(s).},

note = {1},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-85029184821,

title = {Frequency-associated transition from single-cell asynchronous motion to monotonic growth},

author = { M. Lipowczan and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85029184821&doi=10.1007%2fs10867-017-9462-7&partnerID=40&md5=194868730293244768a4635f420772a1},

doi = {10.1007/s10867-017-9462-7},

issn = {00920606},

year  = {2017},

date = {2017-01-01},

journal = {Journal of Biological Physics},

volume = {43},

number = {4},

pages = {461-470},

publisher = {Springer Netherlands},

abstract = {This paper presents a Fourier analysis of the Ortega equation that examines the growth dynamics of plants, specifically the pollen tubes or non-meristematic zones of elongating coleoptiles. A frequency-induced transition from highly nonlinear (periodical) growth—like the one observed in pollen tubes—to monotonically ascending and asymptotically saturated (sigmoid-like) growth, which is anticipated within the framework of a ‘two-fluid model’, is shown. A dynamic phase diagram is calculated and presented in the form of a live video clip. © 2017, Springer Science+Business Media B.V.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-85025149317,

title = {Are water temperature anomalies conjugated to brain functions in microtubules?},

author = { M.A. Pietruszka and M. Lipowczan},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85025149317&doi=10.14704%2fnq.2017.15.1.984&partnerID=40&md5=b2b2f0290f907d1695cea70041597318},

doi = {10.14704/nq.2017.15.1.984},

issn = {13035150},

year  = {2017},

date = {2017-01-01},

journal = {NeuroQuantology},

volume = {15},

number = {1},

pages = {18-21},

publisher = {E-FLOW PDF NeuroQuantology},

abstract = {We considered a system of microtubule(s) (MTs) immersed in a water reservoir in order to investigate its thermodynamic properties and computation (processing) potential. We started with the “double frustration” concept for a single microtubule and next extended our considerations to an MT multi-cluster. We probed the influence of the physical anomalies of water in compressibility and the speed of sound, where acoustic phonons that are conjugated to the stress fluctuations that are produced by changes in symmetry, are possible carriers of information and the cause of ‘calculation’ enhancement at the physiological temperatures of human brain. We showed that the timing of the internal clock can be as high as 117 GHz and that the long-range coherence should be maintained for about 0.1 ms, which is a reasonable dynamical timescale. We advocated that some ‘local’, ‘intermediate’ and ‘extended states’ of our mind could be in relation to water temperature anomalies. We also suggested that the frustration scheme might introduce a direct link to the evolutionary survival paradigm in the case of the slow or fast computations that are performed by elementary systems able to perform basic calculations that can be identified with ‘thinking’. © 2017, E-FLOW PDF NeuroQuantology. All rights reserved.},

note = {3},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-84995794376,

title = {A quantitative report on the impact of chloride on the kinetic coefficients of auxin-induced growth: a numerical contribution to the “acid growth hypothesis”},

author = { M.A. Pietruszka and A. Haduch-Sendecka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84995794376&doi=10.1186%2fs40064-016-3626-y&partnerID=40&md5=48b0a7a75e53f355fece03a2a2e8aab5},

doi = {10.1186/s40064-016-3626-y},

issn = {21931801},

year  = {2016},

date = {2016-01-01},

journal = {SpringerPlus},

volume = {5},

number = {1},

publisher = {SpringerOpen},

abstract = {This work presents the application of several our own novel methods of analysing the kinetics of plant growth, which create, among others, a common platform for the comparison of experimental results. A relatively simple formula is used to parameterize the wide range of data that has been obtained for Zea mays L. in the literature, though it can also be used for different species. A biophysical/biochemical interpretation of the parameters was obtained from a theoretical model that is based on a modified Lockhart equation. The derived formula, which was extended for practical use in Zajdel et al. (Acta Physiol Plant 38:5; 2016), and which was implemented in the attached computer program (ibid.), allowed the data that was obtained from the growth-related problems to be parameterized in a simple way. As a working example that shows the robustness of our approach, we comment in detail on the qualitative assessments of the impact of chloride ions on auxin-induced growth. We note that calculated continuous curves (fits), which are rooted in the growth functional that was introduced by Pietruszka (J Theor Biol 315:119–127; 2012), were in a perfect agreement (R2 ~ 0.99998) with the raw experimental data that was published recently by Burdach et al. (Ann Bot 114:1023–1034; 2014). This fact justified the use of this strict technique, which allows for the determination of kinetic coefficients, to critically evaluate the results and suppositions (claims) therein. Moreover, we calculated the time-delay derivative of elongation growth—pH cross-correlations, and validated the “acid growth hypothesis” in figures by considering, amongst others, the magnitude of the H+-activity of elongation growth (per μm). An empirical constant (field strength), EH+ = Em/(log10 1/aH+ ∙ μm) = 0.157 ± 0.009 [V/mm] was obtained, where Em [mV] is the membrane potential in the perenchymal coleoptile cells of Zea mays L. When this relation is known, the membrane potential can not only be determined for intact growth, but also for different intervening substances exclusively from growth (or growth rate) and pH measurements, i.e. without performing electrophysiological measurements. However, the question of whether this constant is universal remains open. © 2016, The Author(s).},

note = {2},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-84992609793,

title = {Erratum to: Application of the effective formula of growth functional to quantitative description of growth of plant cells (Acta Physiol Plant, (2016), 38, (216), 10.1007/s11738-016-2233-4)},

author = { P. Zajdel and M.A. Pietruszka and A. Haduch-Sendecka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84992609793&doi=10.1007%2fs11738-016-2282-8&partnerID=40&md5=4b4ab2dbd095122bc51196dd56a0d7f4},

doi = {10.1007/s11738-016-2282-8},

issn = {01375881},

year  = {2016},

date = {2016-01-01},

journal = {Acta Physiologiae Plantarum},

volume = {38},

number = {11},

publisher = {Polish Academy of Sciences},

abstract = {In the “Conclusions” section an accidental erroneous occurrence of “influx rate” should be replaced by “efflux rate”. The corrected sentence reads: “Recently, the presented approach was successfully applied to quantitatively describe effective diffusion rates and correlations between growth and proton efflux rates in Zea mays L. (Pietruszka and Haduch-Sendecka 2016).”. © Franciszek Górski Institute of Plant Physiology, Polish Academy of Sciences, Kraków 2016.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-84981205624,

title = {Application of the effective formula of growth functional to quantitative description of growth of plant cells},

author = { P. Zajdel and M.A. Pietruszka and A. Haduch-Sendecka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84981205624&doi=10.1007%2fs11738-016-2233-4&partnerID=40&md5=683b910a7d36e1c682b3e62e7c731632},

doi = {10.1007/s11738-016-2233-4},

issn = {01375881},

year  = {2016},

date = {2016-01-01},

journal = {Acta Physiologiae Plantarum},

volume = {38},

number = {9},

publisher = {Polish Academy of Sciences},

abstract = {An effective formula describing expansive plant growth is derived from the modified Lockhart/Ortega-type equation. Its applicability is demonstrated on selected experimental data extracted from available literature. Quantitative information about the “diffusion rate” (k2) of the growth factors is obtained for two different model species in plant science: Arabidopsis thaliana L. belongs to the dicots and Zea mays L. belongs to the monocots. It is shown that the value of the diffusion rate may be useful in comparing different datasets and serve as a measure of reproducibility of standard measurements. Analysis of the formula and fits allows to identify and suggest a set of criteria for reporting future experiments, which would improve comparability and reproducibility of the results. © 2016, The Author(s).},

note = {4},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-84961353802,

title = {Effective diffusion rates and cross-correlation analysis of “acid growth” data},

author = { M.A. Pietruszka and A. Haduch-Sendecka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84961353802&doi=10.1007%2fs11738-016-2068-z&partnerID=40&md5=97238b47818a5e175b18a827047165a8},

doi = {10.1007/s11738-016-2068-z},

issn = {01375881},

year  = {2016},

date = {2016-01-01},

journal = {Acta Physiologiae Plantarum},

volume = {38},

number = {2},

pages = {1-17},

publisher = {Polish Academy of Sciences},

abstract = {We investigated the growth–temperature relationship in plants using a quantitative perspective of a recently derived growth functional. We showed that auxin-induced growth is achieved by the diffusion rate, which is almost constant or slowly ascending in temperature, while the diffusion rate of fusicoccin (FC)-induced growth increases monotonically with temperature for the entire temperature range (0–45) °C, although for some concentrations of indole-3-acetic acid (IAA), “super-diffusion” takes place for unperturbed growth. We also calculated the cross-correlations and the derivative of cross-correlations for elongation growth (rate) and pH as a function of time delay (lag) parameterised by temperature for artificial pond water (APW) control conditions (endogenous growth) and exogenous IAA and FC that were introduced into the medium. Dimensionality analysis revealed that discontinuities in the cross-correlation derivative corresponded to H+ ion kinetics, which attained definite numerical values that were approximately proportional to the (logarithm of) proton secretion rates (or relative buffer acidification). Furthermore, three types of experiments were compared: for abraded coleoptiles, coleoptile segments and intact growing seedlings. From the cross-correlation analysis, it was found that the timing of IAA and FC-induced proton secretion and growth matched well. Unambiguous results concerning the canvas constituting acid growth hypothesis were obtained by cross- and auto-correlation analysis: (1) for abraded coleoptiles, because of the lowering of the cuticle potential barrier, auxin-induced cell wall pH decreased simultaneously with the change in growth rate; no advancement or retardation of pH (proton efflux rate) or growth rate took place, (2) exogenous protons were able to substitute for auxin thus causing wall loosening and growth, (3) although the underlying molecular mechanisms differ vastly, a potent stimulator of proton secretion, the fungal toxin FC, promoted growth that was similar to auxin, although of an elevated intensity; as for auxin—no advancement or retardation took place. © 2016, The Author(s).},

note = {7},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-84957922508,

title = {Erratum: Ion frequency landscape in growing plants (PLoS ONE (2015) 10:10 (e0138839))},

author = { M.A. Pietruszka and A. Haduch-Sendecka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84957922508&doi=10.1371%2fjournal.pone.0143787&partnerID=40&md5=e253693bfd37f4816bc28e77897440c5},

doi = {10.1371/journal.pone.0143787},

issn = {19326203},

year  = {2015},

date = {2015-01-01},

journal = {PLoS ONE},

volume = {10},

number = {11},

publisher = {Public Library of Science},

abstract = {[No abstract available]},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-84948678986,

title = {Ion frequency landscape in growing plants},

author = { M.A. Pietruszka and A. Haduch-Sendecka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84948678986&doi=10.1371%2fjournal.pone.0138839&partnerID=40&md5=350e8f58ba2789404133ab3a1d96073e},

doi = {10.1371/journal.pone.0138839},

issn = {19326203},

year  = {2015},

date = {2015-01-01},

journal = {PLoS ONE},

volume = {10},

number = {10},

publisher = {Public Library of Science},

abstract = {It has been interesting that nearly all of the ion activities that have been analysed thus far have exhibited oscillations that are tightly coupled to growth. Here, we present discrete Fourier transform (DFT) spectra with a finite sampling of tip-growing cells and organs that were obtained from voltage measurements of the elongating coleoptiles of maize in situ. The electromotive force (EMF) oscillations (∼ 0.1 μV) were measured in a simple but highly sensitive resistor-inductor circuit (RL circuit), in which the solenoid was initially placed at the tip of the specimen and then was moved thus changing its position in relation to growth (EMF can be measured first at the tip; then at the sub-apical part and finally at the shank). The influx- and efflux-induced oscillations of Ca2+, along with H+, K+ and Cl- were densely sampled (preserving the Nyquist theorem in order to 'grasp the structure' of the pulse), the logarithmic amplitude of pulse spectrum was calculated, and the detected frequencies, which displayed a periodic sequence of pulses, were compared with the literature data. A band of life vital individual pulses was obtained in a single run of the experiment, which not only allowed the fundamental frequencies (and intensities of the processes) to be determined but also permitted the phase relations of the various transport processes in the plasma membrane and tonoplast to be established. A discrete (quantised) frequency spectrum was achieved for a growing plant for the first time, while all of the metabolic and enzymatic functions of the life cell cycle were preserved using this totally non-invasive treatment. © 2015 Pietruszka, Haduch-Sendecka.},

note = {3},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-84931040725,

title = {Pressure-induced wall thickness variations in multi-layered wall of a pollen tube and Fourier decomposition of growth oscillations},

author = { M.A. Pietruszka and A. Haduch-Sendecka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84931040725&doi=10.4149%2fgpb_2014035&partnerID=40&md5=b9d2d2f0f5515696a68cfc7b18d4a27e},

doi = {10.4149/gpb_2014035},

issn = {02315882},

year  = {2015},

date = {2015-01-01},

journal = {General physiology and biophysics},

volume = {34},

number = {2},

pages = {145-156},

abstract = {The augmented growth equation introduced by Ortega is solved for the apical portion of the pollen tube as an oscillating volume, which we approach in the framework of a two-fluid model in which the two fluids represent the constant pressure and the fluctuating features of the system. Based on routine Fourier analysis, we calculate the energy spectrum of the oscillating pollen tube, and discuss the resonant frequency problem of growth rate oscillations. We also outline a descriptive model for cell wall thickness fluctuations associated with small, yet regular variations (~ 0.01 MPa) observed in turgor pressure. We propose that pressure changes must lead to the sliding of wall layers, indirectly resulting in a wave of polarization of interlayer bonds. We conclude that pollen tube wall thickness may oscillate due to local variations in cell wall properties and relaxation processes. These oscillations become evident because of low amplitude/high frequency pressure fluctuations δP being superimposed on turgor pressure P. We also show that experimentally determined turgor pressure oscillates in a strict periodical manner. A solitary frequency f0 ≈ 0.066 Hz of these (~ 0.01 MPa in magnitude) oscillations for lily pollen tubes was established by the discrete Fourier transform and Lorentz fit.},

note = {5},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-84907454460,

title = {Check sum computing in doubly frustrated microtubule clusters},

author = { M.A. Pietruszka and M. Lipowczan},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84907454460&doi=10.14704%2fnq.2014.12.3.760&partnerID=40&md5=712b49290a0e8fc5c06b02b8f4c04082},

doi = {10.14704/nq.2014.12.3.760},

issn = {13035150},

year  = {2014},

date = {2014-01-01},

journal = {NeuroQuantology},

volume = {12},

number = {3},

pages = {344-349},

publisher = {E-FLOW PDF NeuroQuantology},

abstract = {The hitherto unexplained presence of 12 or 13 tubulin dimmers forming parallel protofilament subunits in microtubules (MTs) is supposed to ensure sum checking in the system of two MTs, each one being a potential computing ‘core’. The recently proposed, frustration – originated, double well potential is mapped, exclusively for modelling reasons, onto the Ising – type Hamiltonian acting in the rings with an intra-site nearest neighbours interaction. We infer that the final state of energetically favourable 12 qubit ‘calculation’ at physiological temperature is randomly ‘corrected’ by the conjugated nearest 13 qubit ‘core’ (via inter-site; as yet indeterminate; long-range interaction) in the double MT cluster. Helmholtz free energy is calculated to show that such computing cluster lowers the system demands for ATP energy while retaining the possibility of higher accuracy calculations. By performing calculation for two model systems, we find the frustration – originated energy enhancement at physiological temperatures of the human brain for the semi-classical system against the corresponding quantum one. Also, existing studies have not clearly dissociated the neural processes supporting short- and long-duration memories – we propose a possible localization of durable/flash memory in MTs, through introducing a double frustration concept. By extension to double frustration description it may be meaningful to make the next intuitive leap to the question of quantum computing and its possible function in the theory of consciousness. © 2014 NeuroQuantology. All rights reserved.},

note = {2},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-84904973135,

title = {Power spectrum, growth velocities and cross-correlations of longitudinal and transverse oscillations of individual Nicotiana tabacum pollen tube},

author = { A. Haduch-Sendecka and M.A. Pietruszka and P. Zajdel},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84904973135&doi=10.1007%2fs00425-014-2083-5&partnerID=40&md5=377e7dbc459942deb64a77a6869f3c36},

doi = {10.1007/s00425-014-2083-5},

issn = {00320935},

year  = {2014},

date = {2014-01-01},

journal = {Planta},

volume = {240},

number = {2},

pages = {263-276},

publisher = {Springer Verlag},

abstract = {We report on our results concerning growth rate and oscillation modes of the individual pollen tube apex. The observed volumetric growth and growth rate periodicity in the longitudinal (axial) direction are accompanied by transverse oscillations with similar frequencies but higher energies than the axial modes. Examination of the time-domain coherence between oscillations in mutually perpendicular directions revealed minimal energy dissipation in the unperturbed (isotonic) case, opposite to the two remaining cases (hypertonic; hypotonic) with notable correlations. We conjecture that the minimal energy loss is therefore optimal in the natural growth conditions. The longitudinal growth velocity is also found to be the fastest in the unperturbed case. As a result, the isolated system (pollen tube tip) is conserving energy by transforming it from elastic potential energy of extending apical wall to the kinetic energy of periodical motion. The energy dissipation is found to be about 20 % smaller in axial direction than in lateral one, indicating that the main energy consumption is dedicated to the elongation. We further observe that the hypertonic spectrum is shifted towards lower and the hypotonic towards higher frequencies with respect to the isotonic spectrum. In consequence, the turgor pressure inside the growing cell influences monotonically the frequency of both modes of oscillations. The calculated power spectrum seen as a measure of the overall energy efficiency of tip growth under hypertonic, hypotonic and isotonic conditions implies that the biochemistry has been fine tuned to be optimal under normal growth conditions, which is the developmental implication of this work. A simple theoretical extension of the Ortega equation is derived and analysed with respect to its contribution to power spectrum. We show that the plastic term, related to the effective turgor pressure, with maximum contribution at frequency f = 0 is responsible for the steady growth. In turn, the elastic contribution dependent on the time derivative of pressure fluctuations tends to move the system into oscillatory mode (f > 0). None of those mechanisms is privileged over another. The coupling mechanism is naturally generated through a convolution of those two terms and will decide about the overall character of the growth for each particular case. © 2014 The Author(s).},

note = {12},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-84896692074,

title = {Pressure-induced cell wall instability and growth oscillations in pollen tubes},

author = { M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84896692074&doi=10.1371%2fjournal.pone.0075803&partnerID=40&md5=2daadb13559028ed0d827d21b3155d75},

doi = {10.1371/journal.pone.0075803},

issn = {19326203},

year  = {2013},

date = {2013-01-01},

journal = {PLoS ONE},

volume = {8},

number = {11},

abstract = {In the seed plants, the pollen tube is a cellular extension that serves as a conduit through which male gametes are transported to complete fertilization of the egg cell. It consists of a single elongated cell which exhibits characteristic oscillations in growth rate until it finally bursts, completing its function. The mechanism behind the periodic character of the growth has not been fully understood. In this paper we show that the mechanism of pressure - induced symmetry frustration occurring in the wall at the transition-perimeter between the cylindrical and approximately hemispherical parts of the growing pollen tube, together with the addition of cell wall material, is sufficient to release and sustain mechanical self-oscillations and cell extension. At the transition zone, where symmetry frustration occurs and one cannot distinguish either of the involved symmetries, a kind of 'superposition state' appears where either single or both symmetry(ies) can be realized by the system. We anticipate that testifiable predictions made by the model (f ∝ √P) may deliver, after calibration, a new tool to estimate turgor pressure P from oscillation frequency f of the periodically growing cell. Since the mechanical principles apply to all turgor regulated walled cells including those of plant, fungal and bacterial origin, the relevance of this work is not limited to the case of the pollen tube. © 2013 Mariusz Pietruszka.},

note = {14},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-84873255927,

title = {Special Solutions to the Ortega Equation},

author = { M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84873255927&doi=10.1007%2fs00344-012-9280-x&partnerID=40&md5=c1356a009e250780c0c24d156e6deaed},

doi = {10.1007/s00344-012-9280-x},

issn = {07217595},

year  = {2013},

date = {2013-01-01},

journal = {Journal of Plant Growth Regulation},

volume = {32},

number = {1},

pages = {102-107},

publisher = {Springer Science and Business Media, LLC},

abstract = {The previously established augmented growth equation (Cosgrove; Plant Physiol 78:347-356; 1985; Ortega; Plant Physiol 79:318-320; 1985), suitable for description of pressure relationships in the growing plant cell, is revised with respect to the inclusion of changing cell wall properties hitherto represented by two constants, Φ and ε, connected with viscoelastic behavior. This phenomenological equation in the modified form is capable of appropriate description of volumetric extensibility, growth rate, and pressure changes in growing plant cells. This concerns deposition of new material in the polymer cell wall intercalation process, but it can also be used successfully for induced cell wall loosening, for example, by expansin EXPA (EXPB) proteins. In this context, a specific shape of the proposed equations, armed with a small number of physiologically explained parameters, opens up an experimental perspective for determining vital numbers connected with interactions at the nanoscale (polymer bonds "dilution" of an extending cell wall), or even at the molecular level in the cell wall (calculating numbers proportional to the expansin molecule's active surface area). A systematic survey of ready-to-use deterministic solutions originating from the Ortega equation, reporting on both reversible (elastic) and irreversible (plastic) features of a growing plant cell, is presented. These findings also provide a quantitative cytomechanical model able to account for the important role of mechanical properties of the cell wall in cellular growth processes. An important feature of the analytical approach is that all model equations, after calibrating on existing data, allow new results to be inferred without further experimental work. © 2012 Springer Science+Business Media, LLC.},

note = {9},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-84885799447,

title = {Conscious events as possible consequence of topological frustration in microtubules},

author = { M.A. Pietruszka and M. Lipowczan},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84885799447&doi=10.14704%2fnq.2013.11.3.680&partnerID=40&md5=1e47d7c260abd5fca0abf9e0b11b36dc},

doi = {10.14704/nq.2013.11.3.680},

issn = {13035150},

year  = {2013},

date = {2013-01-01},

journal = {NeuroQuantology},

volume = {11},

number = {3},

pages = {426-430},

publisher = {NeuroQuantology},

abstract = {The phenomenon of persistent frustration of pollen tubes led us to recognition of a new form of anharmonic potential, which after a simple transformation may yield a so called 'double well potential'. Because of possible links with conformational changes taking place in microtubules (MT) of human brain neuronal system, to start with, we have calculated the shift of energy levels of a double well potential with respect to the infinite square double well. We conjecture that the dynamic instability of MTs, which has not been elucidated yet, may be the effect of recently proposed mechanism of geometrical frustration, which can also be utilized in case of tubulin dimers forming parallel protofilament subunits in MTs and for modeling the cognitive brain processes.},

note = {2},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-84867086060,

title = {A biosynthesis/inactivation model for enzymatic WLFs or non-enzymatically mediated cell evolution},

author = { M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84867086060&doi=10.1016%2fj.jtbi.2012.09.016&partnerID=40&md5=7b34b740538ebbfc88bfe51edb19df5d},

doi = {10.1016/j.jtbi.2012.09.016},

issn = {00225193},

year  = {2012},

date = {2012-01-01},

journal = {Journal of Theoretical Biology},

volume = {315},

pages = {119-127},

abstract = {We perform the analysis of influence of a 'wall-loosening factor' (hereafter: WLF) activity in cases of isotropic or anisotropic growth of a plant cell/organ. We further explore a generalized form of the Lockhart/Ortega type of equation and make the 'extensibility' Φ (and the yield stress Y) a time and space dependent parameter, able to report on changing (location-dependent) viscoelastic cell wall properties. This procedure results in scalar and tensor equations, which model WLF-mediated isotropic/anisotropic loosening of polymers composing plant cell walls, thereby allowing pressure-driven polymer creep and plant cell expansion growth. An application to six empirical situations, which temporally and spatially vary the amount of WLFs in the cell wall, is anticipated. Combining the resulting explicit formulae with a curve fitting routine provides a new analytical tool that may relate to physiology and biochemistry of the growth process. It is shown, that the regression lines calculated for the derived growth functions perfectly fit (R2≅0.99998) the experimental data. © 2012 Elsevier Ltd.},

note = {10},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-84868353676,

title = {Persistent Symmetry Frustration in Pollen Tubes},

author = { M.A. Pietruszka and M. Lipowczan and A. Geitmann},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84868353676&doi=10.1371%2fjournal.pone.0048087&partnerID=40&md5=b002799cac5d40976d8b8661be86d8e6},

doi = {10.1371/journal.pone.0048087},

issn = {19326203},

year  = {2012},

date = {2012-01-01},

journal = {PLoS ONE},

volume = {7},

number = {11},

abstract = {Pollen tubes are extremely rapidly growing plant cells whose morphogenesis is determined by spatial gradients in the biochemical composition of the cell wall. We investigate the hypothesis (MP) that the distribution of the local mechanical properties of the wall, corresponding to the change of the radial symmetry along the axial direction, may lead to growth oscillations in pollen tubes. We claim that the experimentally observed oscillations originate from the symmetry change at the transition zone, where both intervening symmetries (cylindrical and spherical) meet. The characteristic oscillations between resonating symmetries at a given (constant) turgor pressure and a gradient of wall material constants may be identified with the observed growth-cycles in pollen tubes. © 2012 Pietruszka et al.},

note = {8},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-80053327359,

title = {The application of the Kedem-Katchalsky equations to membrane transport of ethyl alcohol and glucose},

author = { M. Jarzynska and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-80053327359&doi=10.1016%2fj.desal.2011.07.034&partnerID=40&md5=577044efb0b2e031358b0ebcc61dec9b},

doi = {10.1016/j.desal.2011.07.034},

issn = {00119164},

year  = {2011},

date = {2011-01-01},

journal = {Desalination},

volume = {280},

number = {1-3},

pages = {14-19},

abstract = {In the following paper we present the mathematical description of the volume flow (Jv) of aqueous solution of ethyl alcohol and glucose transported through a membrane. We consider three cases of the transport: the flow generated by the hydrostatic pressure difference δp, the osmotic pressure difference δΠ or by the simultaneous action of these two thermodynamical drives. The membrane transport is discussed within the frame of the Kedem-Katchalsky (K-K) equations, commonly used in the literature of this field. We present results obtained for the membrane filtration coefficient (Lp) in case of ethanol transport. This coefficient has been calculated based on the formula that accounts for the membrane properties, as well as the properties of the flowing liquid, namely the density and the viscosity of ethanol. The calculations of the volume flow (Jv) of the solution have been based on the original form of the K-K equations in the case when the solutions at both sides of the membrane are mechanically stirred. © 2011 Elsevier B.V.},

note = {16},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-79958057526,

title = {Solutions for a local equation of anisotropic plant cell growth: An analytical study of expansin activity},

author = { M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-79958057526&doi=10.1098%2frsif.2010.0552&partnerID=40&md5=89556dd4a18c8e896d60897a1da73098},

doi = {10.1098/rsif.2010.0552},

issn = {17425689},

year  = {2011},

date = {2011-01-01},

journal = {Journal of the Royal Society Interface},

volume = {8},

number = {60},

pages = {975-987},

abstract = {This paper presents a generalization of the Lockhart equation for plant cell/organ expansion in the anisotropic case. The intent is to take into account the temporal and spatial variation in the cell wall mechanical properties by considering the wall 'extensibility' (Φ), a time- and space-dependent parameter. A dynamic linear differential equation of a second-order tensor is introduced by describing the anisotropic growth process with some key biochemical aspects included. The distortion and expansion of plant cell walls initiated by expansins, a class of proteins known to enhance cell wall 'extensibility', is also described. In this approach, expansin proteins are treated as active agents participating in isotropic/anisotropic growth. Two-parameter models and an equation for describing α- and β-expansin proteins are proposed by delineating the extension of isolated wall samples, allowing turgor-driven polymer creep, where expansins weaken the non-covalent binding between wall polysaccharides. We observe that the calculated halftime (t1/2 = εΦ0 log 2) of stress relaxation due to expansin action can be described in mechanical terms. © 2011 The Royal Society.},

note = {12},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-77951652558,

title = {Exact analytic solutions for a global equation of plant cell growth},

author = { M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-77951652558&doi=10.1016%2fj.jtbi.2010.02.012&partnerID=40&md5=6b49cc665e2e1a4a7a9fb334be5c4cd3},

doi = {10.1016/j.jtbi.2010.02.012},

issn = {00225193},

year  = {2010},

date = {2010-01-01},

journal = {Journal of Theoretical Biology},

volume = {264},

number = {2},

pages = {457-466},

abstract = {A generalization of the Lockhart equation for plant cell expansion in isotropic case is presented. The goal is to account for the temporal variation in the wall mechanical properties-in this case by making the wall extensibility a time dependent parameter. We introduce a time-differential equation describing the plant growth process with some key biophysical aspects considered. The aim of this work was to improve prior modeling efforts by taking into account the dynamic character of the plant cell wall with characteristics reminiscent of damped (aperiodic) motion. The equations selected to encapsulate the time evolution of the wall extensibility offer a new insight into the control of cell wall expansion. We find that the solutions to the time dependent second order differential equation reproduce much of the known experimental data for long- and short-time scales. Additionally, in order to support the biomechanical approach, a new growth equation based on the action of expansin proteins is proposed. Remarkably, both methods independently converge to the same kind, sigmoid-shaped, growth description functional V(t)αexp(-exp(-t)), properly describing the volumetric growth and, consequently, growth rate as its time derivative. © 2010 Elsevier Ltd.},

note = {5},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-77952066579,

title = {Generalized phenomenological equation of plant growth},

author = { S. Lewicka and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-77952066579&doi=10.4149%2fgpb_2010_01_95&partnerID=40&md5=96dba290177df0384452a4e51be96e0b},

doi = {10.4149/gpb_2010_01_95},

issn = {02315882},

year  = {2010},

date = {2010-01-01},

journal = {General Physiology and Biophysics},

volume = {29},

number = {1},

pages = {95-105},

abstract = {Enlargement is one of the most fundamental activities of plants, and there are many simultaneous processes involved. Several could be temperature- dependent, like metabolic processes and cell wall sensitivity. A description of plant cell elongation was elaborated by Lockhart in the mid-60's of the last century in the form of time-dependent differential equation. However, the main disadvantage of this approach was the missing environmental temperature at which growth takes place, as well as the lack of representation of environmental factors influencing growth, like growth stimulators/inhibitors, external pressure or light. This absence has been merely covered in the series of our recent papers. Consequently, this manuscript attempts to construct a fairly complete, all-encompassing set of mathematical relationships which describe the basic process of cell/organ extension and the effects of modifying environmental perturbations. The output is provided in a form of composite equation supported by mathematical derivations. Starting with the generalized time- and temperature-dependent growth equation, we involve the action of phytohormones and toxic compounds, and especially of light (photocontrol of plant growth) onto the growth processes. All these external factors (treated as perturbations) are mapped onto the proper terms of temperature modified equation of growth thus giving a new theoretical tool to verify, interpret and draw conclusions concerning data originating from various kinds of plant-physiological experiments. It seems that this novel approach can provide a starting point for further experimentation especially on the plastic and elastic components of the growth process.},

note = {2},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-77349089718,

title = {Self-consistent equation of plant cell growth},

author = { M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-77349089718&doi=10.4149%2fgpb_2009_04_340&partnerID=40&md5=7f02696a6bab55a3633d1c9e1f360553},

doi = {10.4149/gpb_2009_04_340},

issn = {02315882},

year  = {2009},

date = {2009-01-01},

journal = {General Physiology and Biophysics},

volume = {28},

number = {4},

pages = {340-346},

abstract = {We introduce a transcendental equation, describing the subsequent stages of plant cell/organ growth. Starting from empirically verified conclusions originating from the central limit theorem we also insert the influence of temperature on elongation growth to receive a time-dependent equation of growth parameterized by temperature. This self-consistent equation evolves with time using three cardinal parameters: t0, T0 and V0. They represent the time of maximum expansion rate, the growth optimum temperature and the corresponding volume, respectively. Experimental determination of these cardinal values enables evaluation of the dynamic extensibility coefficient Φ= ΦT(t) in time and temperature domain.},

note = {2},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-58549092245,

title = {General proof of the validity of a new tensor equation of plant growth},

author = { M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-58549092245&doi=10.1016%2fj.jtbi.2008.11.001&partnerID=40&md5=ed0443bbdcb54f6731ac40d828d6ac52},

doi = {10.1016/j.jtbi.2008.11.001},

issn = {00225193},

year  = {2009},

date = {2009-01-01},

journal = {Journal of Theoretical Biology},

volume = {256},

number = {4},

pages = {584-585},

abstract = {Plant cell/organ growth may be partly described by a local tensor equation. We provide a mathematical proof that the Lockhart (global) equation is the diagonal component of this tensor equation. © 2008 Elsevier Ltd. All rights reserved.},

note = {4},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-77349098783,

title = {Simple method to estimate cell wall extensibility coefficient by using only two cardinal numbers},

author = { M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-77349098783&partnerID=40&md5=8ee34c879564a3471fc9c2c0ebb20610},

issn = {00016977},

year  = {2009},

date = {2009-01-01},

journal = {Acta Societatis Botanicorum Poloniae},

volume = {78},

number = {4},

pages = {269-270},

publisher = {Polish Botanical Society},

abstract = {In this short communication we consider the extensibility properties of the cell wall. This is accomplished by a heuristically motivated equation for the expanding volume of the cell. The experimentally determined characteristic time t0 and temperature T0 are the only numbers required for evaluating the effective yielding coefficient Φ(t; T) in the respective time and temperature domains.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-68949121122,

title = {Derivation of the formula for the filtration coefficient by application of poiseuille's law in membrane transport},

author = { M. Jarzynska and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-68949121122&partnerID=40&md5=ac933b5b7d59da2a71c40464a042a638},

issn = {00016977},

year  = {2009},

date = {2009-01-01},

journal = {Acta Societatis Botanicorum Poloniae},

volume = {78},

number = {2},

pages = {93-96},

publisher = {Polish Botanical Society},

abstract = {On the basis of Kedem-Katchalsky equations a mathematical analysis of volume flow (Jv) of a binary solution through a membrane (M) is presented. Two cases of transport generators have been considered: hydrostatic (Δp) as well as osmotic (ΔΠ) pressure difference. Based on the Poiseuille's law we derive the formula for the membrane filtration coefficient (Lp) which takes into account the membrane properties, kinetic viscosity and density of a solution flowing across the membrane. With use of this formula we have made model calculations of the filtration coefficient Lp and volume flow Jv for a polymer membrane in the case when the solutions on both sides of the membrane are mixed.},

note = {4},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-65649118996,

title = {Mathematical model for tissue stresses in growing plant cells and organs},

author = { S. Lewicka and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-65649118996&partnerID=40&md5=65cd646ed79fb226dbf32589e1da9eb0},

issn = {00016977},

year  = {2009},

date = {2009-01-01},

journal = {Acta Societatis Botanicorum Poloniae},

volume = {78},

number = {1},

pages = {19-23},

publisher = {Polish Botanical Society},

abstract = {In this study we propose a simple mathematical model based on the equilibrium equation for the materials deformed elastically. Owing to the turgor pressure of the cells, the peripheral walls of the outer tissue are under tension, while the extensible inner tissue is under compression. This well known properties of growing multicellular plant organs can be derived from the equation for equilibrium. The analytic solutions may serve as a good starting point for modeling the growth of a single plant cell or an organ.},

note = {1},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-50149113556,

title = {Effect of selenium on magnesium, iron, manganese, copper, and zinc accumulation in corn treated by indole-3-acetic acid},

author = { K. Pazurkiewicz-Kocot and A. Kita and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-50149113556&doi=10.1080%2f00103620802292343&partnerID=40&md5=a5d81050f83fdacffca1a1b27364b312},

doi = {10.1080/00103620802292343},

issn = {00103624},

year  = {2008},

date = {2008-01-01},

journal = {Communications in Soil Science and Plant Analysis},

volume = {39},

number = {15-16},

pages = {2303-2318},

abstract = {In this work, the relationship among accumulation of selenium, auxin, and some nutrient elements [magnesium (Mg2+); iron (Fe3+); manganese (Mn2+); copper (Cu2+); zinc (Zn2+)] in tissues of roots, mesocotyls, and leaves of Zea mays L. plants was studied. Seeds of maize were cultivated for 4 days in the darkness at 27°C on moist filter paper, then the individual seedlings were transferred into an aerated solution containing the macro- and microelements and were cultivated in a greenhouse for 12 h in the light and 12 h (12-h photoperiod) in the dark at 25°C. The seedlings were exposed to the solution containing sodium hydrogen selenite (NaHSeO3), indole-3 acetic acid (IAA), or IAA+NaHSeO3 for approximately 96 h before chemical analysis. The concentration of IAA in the external medium was 10-4 mol dm-3, concentration of selenite (NaHSeO3) was 10-6 mol dm-3, and the pH of the medium was 6.5. The accumulation of the probed elements in seedlings of maize was measured by inductively coupled plasma optical emission spectroscopy (ICP-OES). It was determined that the selenite and IAA, present in the external medium of growing plants, changed the uptake and accumulation of some cations in tissues of leaves, mesocotyls, and roots. The change of transport conditions of these nutrient elements is probably one of the first observed symptoms of selenium effects on plants. Copyright © Taylor & Francis Group, LLC.},

note = {26},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-60049096358,

title = {Central limit theorem and the short-term temperature response of coleoptile and hypocotyl elongation growth},

author = { S. Lewicka and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-60049096358&partnerID=40&md5=728235bcee33203a2c74bfa79e8e2fdb},

issn = {00016977},

year  = {2008},

date = {2008-01-01},

journal = {Acta Societatis Botanicorum Poloniae},

volume = {77},

number = {4},

pages = {289-292},

publisher = {Polish Botanical Society},

abstract = {In this contribution we deal with a new mathematical description of the response of short-term coleoptile/hypocotyl expansion growth to temperature. Although the interest of both the bio-mechanical basis of elongation growth and temperature responses has been studied in plant biology and biophysics for a long time, yet the question of the mode of actions of temperature is very relevant and still open. Here we introduce a simple idea that the normal distribution, due to the central limit theorem (CLT), is able to report on temperature-dependent elongation growth. The numerical fittings for temperature affected growth are in good agreement with empirical data. We suggest that the observation concerning a crossover effect occurring in temperature driven elongation together with CLT leads to the formulation of a hypothesis about the possible universal character of such a description, supposedly for many plant species and families. We conclude with the statement that properly constructed equations of temperature affected growth, should possibly include a specific term proportional to exp[-((T-T0)/T0)2] with T0 corresponding to the temperature of the optimum growth.},

note = {4},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-34250819263,

title = {Effect of temperature on plant elongation and cell wall extensibility},

author = { M.A. Pietruszka and S. Lewicka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-34250819263&partnerID=40&md5=7af82c5bb94e85fb86231e9557e177dd},

issn = {02315882},

year  = {2007},

date = {2007-01-01},

journal = {General Physiology and Biophysics},

volume = {26},

number = {1},

pages = {40-47},

abstract = {Lockhart equation was derived for explaining plant cell expansion where both cell wall extension and water uptake must occur concomitantly. Its fundamental contribution was to express turgor pressure explicitly in terms of osmosis and wall mechanics. Here we present a new equation in which pressure is determined by temperature. It also accounts for the role of osmosis and consequently the role of water uptake in growing cell. By adopting literature data, we also attempt to report theoretically the close relation between plant elongation and cell wall extensibility. This is accomplished by the modified equation of growth solved for various temperatures in case of two different species. The results enable to interpret empirical data in terms of our model and fully confirm its applicability to the investigation of the problem of plant cell extensibility in function of environmental temperature. Moreover, by separating elastic effects from growth process we specified the characteristic temperature common for both processes which corresponds to the resonance energy of biochemical reactions as well as to the rapid softening of the elastic modes toward the high temperature end where we encountered viscoelastic and/or plastic behavior as dominating. By introducing analytical formulae connected with growth and elastic properties of the cell wall, we conclude with the statement how these both processes contribute quantitatively to the resonance-like shape of the elongation curve. In addition, the tension versus temperature "phase diagram" for a living plant cell is presented.},

note = {8},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-33947534434,

title = {Temperature and the growth of plant cells},

author = { M.A. Pietruszka and S. Lewicka and K. Pazurkiewicz-Kocot},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-33947534434&doi=10.1007%2fs00344-006-0023-8&partnerID=40&md5=94f1b5d891f4f731fc2132479a49009a},

doi = {10.1007/s00344-006-0023-8},

issn = {07217595},

year  = {2007},

date = {2007-01-01},

journal = {Journal of Plant Growth Regulation},

volume = {26},

number = {1},

pages = {15-25},

abstract = {In cell elongation, the juvenile cell vacuolates, takes up water, and expands by irreversible extension of the growth-limiting primary walls. This process was elaborated analytically by Lockhart in the mid-1960s. His growth equation does not, however, include the influence of the environmental temperature at which cell growth takes place. In this article we consider a phenomenological model including temperature in the equation of growth. Also, by introducing the possible influence of growth regulators treated here as external perturbations, linear and nonlinear solutions are found. A comparison of experimental and theoretical results permits qualitative and quantitative conclusions concerning change in the magnitude of the cell wall yielding coefficient Φ as a function of both time and temperature (with or without external perturbations), which has acquired reasonable values throughout. © 2007 Springer Science+Business Media, Inc.},

note = {7},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-33845643558,

title = {Anisotropic plant growth due to phototropism},

author = { M.A. Pietruszka and S. Lewicka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-33845643558&doi=10.1007%2fs00285-006-0045-7&partnerID=40&md5=7c5e60c40bdac3097bc41754439d9f69},

doi = {10.1007/s00285-006-0045-7},

issn = {03036812},

year  = {2007},

date = {2007-01-01},

journal = {Journal of Mathematical Biology},

volume = {54},

number = {1},

pages = {45-55},

abstract = {Phototropism-the directional curvature of organs in response to lateral differences in light intensity and/or quality-represents one of the most rapid and visually obvious reaction of plants to changes in their light environment. It is a topic of fundamental interest to understand the mechanics of plants during growth. We propose a generalization of the scalar Lockhart model (1965) to three dimensional deformation, solve the new equation in two particular cases and compare results with empirical data. We believe that carefully designed experiments linked to our model will provide (by determining the active transport coefficient) a new method for qualitative description of auxin redistribution during phototropism. The proposed method supplements very recent investigations concerning specific auxin-influx and -efflux carriers (LAX and PIN proteins). © 2006 Springer-Verlag.},

note = {9},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-33845640480,

title = {Anisotropic plant cell elongation due to ortho-gravitropism},

author = { S. Lewicka and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-33845640480&doi=10.1007%2fs00285-006-0049-3&partnerID=40&md5=34d6108d776ce122eb63b5de28868d9b},

doi = {10.1007/s00285-006-0049-3},

issn = {03036812},

year  = {2007},

date = {2007-01-01},

journal = {Journal of Mathematical Biology},

volume = {54},

number = {1},

pages = {91-100},

abstract = {In this article we elucidate the well-known biological phenomenon (geotropism) as governed by physical mechanisms, resulting from internal biochemical reactions, in terms of mathematics. Gravitropism causes vertical orientation of plant's axis and in its special cases of positive (root) and negative (stem) geotropism together is called ortho-geotropism. It represents one of the most rapid and visually obvious response of plants to the influence of gravitational field. Seeking for approximate description for this phenomenon we confine to a single cell approach and we begin with the Lockhart equation considering a plant cell as a homogeneous one. In principle, the latter should also account for the existing anisotropies due to mechanical stresses (auxin redistribution). Hence, all global quantities like internal pressure or turgor threshold become direction dependent and consequently acquire tensor representation. Moreover, by involving explicitly time dependence the tensor differential equation becomes a dynamic one. In the context of ortho-geotropism, where gravitational field causes movement of phytohormones and mobile particles following gravity (statolith theory) a basic solution of our tensor equation is found and detailed step by step derivations are presented. By considering only positive (root) geotropism we may, however, extend our solution to the stem bending even though the biological mechanisms differ. Both solutions represent two possible empirical situations which have been probed and verified worldwide ever since. © 2006 Springer-Verlag.},

note = {6},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-33748352721,

title = {Theoretical search for the growth-temperature relationship in plants},

author = { S. Lewicka and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-33748352721&partnerID=40&md5=3f5de216b643411d8d8ab03ee167a076},

issn = {02315882},

year  = {2006},

date = {2006-01-01},

journal = {General Physiology and Biophysics},

volume = {25},

number = {2},

pages = {125-136},

abstract = {In this article we deal with the definition of a new phenomenological model with physical bases for the response of short-term cell expansion growth to temperature. Although the interest on both the biomechanical bases of elongation growth and on temperature responses has a long lasting development in plant biology and biophysics, yet the question of the mode of actions of temperature is a very relevant and still open one. The purpose of our paper was not to deal with all the complexity of the possible effects of temperature on a growing cell but to concentrate on two more focused questions: i) whether it is possible to specify an optimal temperature for growth responses all along development by defining some phenomenological equations for temperature response, ii) can we learn something from that on the temperature dependence of the cell wall expansion process using a minimal analytical modelling? To answer both questions we introduce (by extending Lockhart approach) the notion of temperature by simple thermodynamical reasoning. Assuming incompressibility of water (by the constant molar density n/V) we also accounted for the role of osmosis and consequently - the role of water uptake in growing cell. This approach allowed us (by comparing theoretical solutions and experimental results) not only to determine the specific (resonance) temperature (or corresponding absorption energy kBT*) of the optimal growth but also draw conclusions about the cell wall extensibility dependence on temperature and its evolution in time. A straightforward application of our method to determine optimum growth temperature for different plant species in a greenhouse practice (as its simple implication) can also be recommended.},

note = {8},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-33748343284,

title = {Thermodynamics of irreversible plant cell growth},

author = { M.A. Pietruszka and S. Lewicka and K. Pazurkiewicz-Kocot},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-33748343284&partnerID=40&md5=3cd8d7a9e79b98b674d69832bdc0f8b1},

issn = {00016977},

year  = {2006},

date = {2006-01-01},

journal = {Acta Societatis Botanicorum Poloniae},

volume = {75},

number = {3},

pages = {183-190},

publisher = {Polish Botanical Society},

abstract = {The time-irreversible cell enlargement of plant cells at a constant temperature results from two independent physical processes, e.g. water absorption and cell wall yielding. In such a model cell growth starts with reduction in wall stress because of irreversible extension of the wall. The water absorption and physical expansion are spontaneous consequences of this initial modification of the cell wall (the juvenile cell vacuolate; takes up water and expands). In this model the irreversible aspect of growth arises from the extension of the cell wall. Such theory expressed quantitatively by time-dependent growth equation was elaborated by Lockhart in the 60's. The growth equation omit however a very important factor, namely the environmental temperature at which the plant cells grow. In this paper we put forward a simple phenomenological model which introduces into the growth equation the notion of temperature. Moreover, we introduce into the modified growth equation the possible influence of external growth stimulator or inhibitor (phytohormones or abiotic factors). In the presence of such external perturbations two possible theoretical solutions have been found: the linear reaction to the application of growth hormones/abiotic factors and the non-linear one. Both solutions reflect and predict two different experimental conditions, respectively (growth at constant or increasing concentration of stimulator/inhibitor). The non-linear solution reflects a common situation interesting from an environmental pollution point of view e.g. the influence of increasing (with time) concentration of toxins on plant growth. Having obtained temperature modified growth equations we can draw further qualitative and, especially, quantitative conclusions about the mechanical properties of the cell wall itself. This also concerns a new and interesting result obtained in our model: We have calculated the magnitude of the cell wall yielding coefficient Φ(T) [m3 J -1·s-1] in function of temperature which has acquired reasonable numerical value throughout.},

note = {6},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-4644220874,

title = {Chemical potential induced phase transitions},

author = { M. Matlak and A. Molak and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-4644220874&doi=10.1002%2fpssb.200409039&partnerID=40&md5=e58aa79dd72f5b058119f1453e1eeaed},

doi = {10.1002/pssb.200409039},

issn = {03701972},

year  = {2004},

date = {2004-01-01},

journal = {Physica Status Solidi (B) Basic Research},

volume = {241},

number = {7},

pages = {R23-R26},

abstract = {A simple electrical set-up to detect phase transitions is proposed and applied to a series of investigated samples: Gd, Cr, TiNi and CuZnSn, all exhibiting different types of phase transitions. The sample is glued to a contact electrode (here Ag) and immersed into a thermostat. We measure the electrical resistivity of the contact electrode as function of temperature. Due to the fact that the chemical potentials of the sample and the contact electrode should be equal (μs = μe) the electron gas of the contact electrode "feels" a phase transition taking place in the investigated sample. Therefore we observe kinks in the resistivity plot of the contact electrode which easily localize the proper critical temperatures: TC (Gd), TN (Cr) and Tstruct (TiNi; CuZnSn). The proposed method visualizes the prevailing role of the chemical potential at phase transitions and provides a completely new ("remote") tool to detect critical points in solids. © 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.},

note = {11},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-1642477805,

title = {Phase transitions detection by means of a contact electrode},

author = { M. Matlak and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-1642477805&doi=10.1002%2fpssb.200301945&partnerID=40&md5=db011c1e5dc0f192616ea1a5c37de0a6},

doi = {10.1002/pssb.200301945},

issn = {03701972},

year  = {2004},

date = {2004-01-01},

journal = {Physica Status Solidi (B) Basic Research},

volume = {241},

number = {1},

pages = {163-169},

abstract = {We investigate theoretically and next experimentally a new possibility to detect critical temperatures of solids by means of a very simple electrical circuit consisting of an analyzed sample (exhibiting phase transitions) and a contact electrode (hereafter reference electrode) where the constant voltage is applied only to the latter one. The measured system is placed into a thermostat and the electric current flow through the reference electrode is measured as function of temperature. By assuming a model Hamiltonian for the probed sample describing ferromagnetic, superconducting or reentrant phase transitions and a one-band model for the contact electrode we calculate d.c. conductivity of the reference electrode. The temperature dependence of the conductivity of this electrode clearly indicates (in the form of kinks) the transition temperatures connected with phase transitions occurring in the investigated material. This is due to the fact that the chemical potential of the whole system in contact should equal at equilibrium. Our considerations suggest straightforward application of such a circuit in a direct laboratory praxis, especially because (beyond simplicity) the applied method possesses unlimited temperature range and can be considered as noninvasive with respect to the investigated sample. To verify the effect experimentally we have used as an investigated sample an antiferromagnetic Cr material and Cu as the reference electrode. The measurements of the resistivity R(Cr + Cu) and R(Cu) alone as functions of temperature made a possibility to plot the difference R(Cr + Cu) - R(Cu) vs temperature. This plot enabled to identify the critical Neel temperature of the Cr sample corresponding to the profound minimum in this curve. © 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.},

note = {13},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-0035151752,

title = {Comparative study of the specific heat and chemical potential at phase transitions},

author = { M. Matlak and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-0035151752&doi=10.1016%2fS0038-1098%2800%2900489-0&partnerID=40&md5=9abd0aae34329029f5b8f42b74c71d8a},

doi = {10.1016/S0038-1098(00)00489-0},

issn = {00381098},

year  = {2001},

date = {2001-01-01},

journal = {Solid State Communications},

volume = {117},

number = {7},

pages = {413-417},

publisher = {Elsevier Science Ltd, Exeter},

abstract = {The temperature dependence is studied of the specific heat and chemical potential using the model describing phase transitions from ferromagnet to paramagnet, from superconductor to normal system, as well as, combined reentrant phase transitions (normal ferromagnet-superconducting ferromagnet-paramagnetic superconductor-normal paramagnet). In the case of the phase transitions: ferromagnet-paramagnet or superconductor-normal system, the shapes of the temperature dependence of the specific heat and the temperature derivative of the chemical potential are similar with characteristic jump at the critical temperature. For the reentrant type phase transitions the upper superconducting critical temperature is hardly seen in the specific heat plot (exactly the same situation takes place in the experiment). The chemical potential temperature dependence locates, however, with ease this critical point. This observation can be widely utilized in the experimental praxis to locate precisely all critical points with the use of the chemical potential measurements, especially in such cases where other methods fail.},

note = {7},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-37649026793,

title = {Experimental method to detect phase transitions via the chemical potential},

author = { M. Matlak and M.A. Pietruszka and E. Rówiński},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-37649026793&doi=10.1103%2fPhysRevB.63.052101&partnerID=40&md5=c40e9609955a7301086920ac866bb036},

doi = {10.1103/PhysRevB.63.052101},

issn = {10980121},

year  = {2001},

date = {2001-01-01},

journal = {Physical Review B - Condensed Matter and Materials Physics},

volume = {63},

number = {5},

abstract = {We propose an experimental method to confirm theoretical predictions concerning the detection of phase transitions in solids via the measurement of the chemical potential as a function of temperature. Here, as experimental evidence of the validity of these predictions, we perform indirect measurements of the chemical potential vs temperature for Gd, Cr, and TiNi samples by means of an electrochemical experiment. This made it possible to easily localize all critical temperatures connected either with magnetic phase transitions [TC (Gd), TN (Cr)] or structural phase transformations in the shape-memory alloy NiTi. The values of the critical temperatures, obtained in this way remain in exceptionally good agreement with the results of the auxiliary heat flow measurements and the existing literature data concerning critical temperatures. We hope that further development of the experimental techniques, based on chemical potential measurements, can provide a new experimental tool in the search for phase transitions (induced by temperature, pressure, concentration, etc.) in real materials, regardless of the type of phase transitions and irrespective of the underlying mechanism. © 2001 The American Physical Society.},

note = {21},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-0033674145,

title = {The effect of lead on the photoelectric reaction of Zea mays L. plants},

author = { K. Pazurkiewicz-Kocot and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-0033674145&doi=10.1016%2fS1011-1344%2800%2900086-5&partnerID=40&md5=b288f4167d580318c144562b7f188bff},

doi = {10.1016/S1011-1344(00)00086-5},

issn = {10111344},

year  = {2000},

date = {2000-01-01},

journal = {Journal of Photochemistry and Photobiology B: Biology},

volume = {57},

number = {2-3},

pages = {119-122},

abstract = {We investigate the correlation between the concentrations of lead (10-6-10-2 mol dm-3 PbCl2) in the external medium and photoelectric reaction of Zea mays L. plants. The experiments were carried out on 8-10-day-old maize plants (Zea mays L. var. K33xF2) with the use of conventional electrophysiological technique. The results suggest that in plants treated with lead ions the photoelectric reaction is significantly reduced. The pH variation of the incubation medium including the green fragments of leaves showed that lead ions caused inhibition of light-induced external acidification. (C) 2000 Elsevier Science S.A. All rights reserved.},

note = {1},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-0034583319,

title = {Numerical investigation of action potential transmission in plants},

author = { M.A. Pietruszka and K. Pazurkiewicz-Kocot},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-0034583319&partnerID=40&md5=0eb7f6b3c1ac7e96c57942903ab16c80},

issn = {00016977},

year  = {2000},

date = {2000-01-01},

journal = {Acta Societatis Botanicorum Poloniae},

volume = {69},

number = {3},

pages = {181-184},

publisher = {Polish Botanical Society},

abstract = {In context of a fairly concise review of recent literature and well established experimental results we reconsider the problem of action potential propagating steadily down the plant cell(s). Having adopted slightly modified Hodgkin-Huxley set of differential equations for the action potential we carried out the numerical investigation of these equations in the course of time. We argue that the Hodgkin-Huxley-Katz model for the nerve impulse can be used to describe the phenomena which take place in plants - this point of view seems to be plausible since the mechanisms involving active ionic transport across membranes from the mathematical point of view are similar. Besides, we compare in a qualitative way our theoretical outcomes with typical experimental results for the action potential which arise as the reaction of plants to electrical mechanical and light stimuli. Moreover, we point out the relevance of the sequence of events during the pulse with the appropriate ionic fluxes.},

note = {1},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-0034248213,

title = {Critical behaviour of the chemical potential at phase transitions},

author = { M. Matlak and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-0034248213&doi=10.1016%2fS0921-4526%2899%2901406-4&partnerID=40&md5=e2d086a14f11a97825e652d5c50d782b},

doi = {10.1016/S0921-4526(99)01406-4},

issn = {09214526},

year  = {2000},

date = {2000-01-01},

journal = {Physica B: Condensed Matter},

volume = {291},

number = {1-2},

pages = {12-18},

publisher = {Elsevier Science Publishers B.V., Amsterdam},

abstract = {Investigating the thermodynamic properties of the generalized s-f model with intersite pairing in the context of magnetic, superconducting and reentrant-type phase transitions, as well as, structural phase transitions, we claim that all critical temperatures can easily be identified from the critical behaviour of the chemical potential and from the average occupation numbers (critical electron redistribution) of the electronic system. These quantities exhibit small but well-defined kinks at all critical temperatures as the evidence for phase transitions. The system undergoes a phase transition at such a critical temperature for which the chemical potential acquires its critical value. This new observation suggests a practical experimental application of the effect of how to find all critical temperatures when applied to real solids. The agreement between the calculated temperature dependence of the chemical potential, presented in our paper, and experimental measurement for high-temperature superconductor YBa2Cu3O7-δ entirely supports this point of view.},

note = {14},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-0033699909,

title = {On the new universal possibility to detect phase transitions in correlated electron systems},

author = { M. Matlak and M.A. Pietruszka and E. Gosławska and B. Grabiec and Kh. Eid},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-0033699909&doi=10.1080%2f01411590008224541&partnerID=40&md5=df39e7f1a51009fc28834fdbb64ec0d8},

doi = {10.1080/01411590008224541},

issn = {01411594},

year  = {2000},

date = {2000-01-01},

journal = {Phase Transitions},

volume = {71},

number = {2},

pages = {73-99},

publisher = {Gordon & Breach Science Publ Inc, Newark},

abstract = {We investigate temperature and concentration driven phase transitions (structural and reentrant phase transitions included) in magnetic and superconducting systems with the use of a wide class of model Hamiltonians applied to rare earth (Re) based compounds and alloys (integer and fluctuating valence systems). Studying the temperature or concentration dependence of the chemical potential we observe small but distinct and well localized kinks at all critical points as evidence for phase transitions. For systems with, at least, two kinds of interacting electrons the kinks at critical temperatures or concentrations occur also in the electronic average occupation numbers (critical electron redistribution). These observations suggest a direct and universal experimental application of the chemical potential as a detector of phase transitions for temperature and concentration driven phase transitions, as well as, for pressure- or external field- induced transitions in solids. The agreement between the calculated critical temperature behaviour of the chemical potential, presented in this paper, and experimental measurements for high-temperature superconductor YBa2Cu3O7-δ entirely supports these general observations.},

note = {14},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-0000769436,

title = {Chemical potential evidence for phase transitions in magnetic and superconducting compounds and alloys},

author = { M. Matlak and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-0000769436&doi=10.12693%2fAPhysPolA.97.253&partnerID=40&md5=b637095a5bd7b89899f21f533c0a821e},

doi = {10.12693/APhysPolA.97.253},

issn = {05874246},

year  = {2000},

date = {2000-01-01},

journal = {Acta Physica Polonica A},

volume = {97},

number = {1},

pages = {253-256},

publisher = {Polish Academy of Sciences},

abstract = {We announce that all phase transitions (induced by temperature or concentration) including structural ones and transitions between metastable or "exotic" states can be detected by the chemical potential critical behaviour, as well as, from the average occupation numbers of the electronic system (critical electron redistribution).},

note = {9},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-0033514771,

title = {Transport properties of the antiferromagnetic systems with fluctuating valence},

author = { M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-0033514771&doi=10.1016%2fS0304-8853%2898%2900623-4&partnerID=40&md5=7af67546e0090e73bd9cb3cee1139cc6},

doi = {10.1016/S0304-8853(98)00623-4},

issn = {03048853},

year  = {1999},

date = {1999-01-01},

journal = {Journal of Magnetism and Magnetic Materials},

volume = {192},

number = {3},

pages = {564-574},

publisher = {Elsevier},

abstract = {We present the calculation of the DC resistivity (conductivity) for the antiferromagnetic, two-band, extended s-f model. The influence on the finite bandwidth of the narrow 4f (5f) band on the transport properties of the model is investigated. We notice that the increase of the 4f (5f) bandwidth destroys the antiferromagnetic order and the system becomes paramagnetic in all temperatures. A systematic review of the DC resistivity (conductivity) is presented in the form of the 3D plots including different average occupation numbers of electrons per site (n=0.5, 0.75, 1, 1.25, 1.5, 1.75, 2), different relative positions of the 4f (5f) band and different 4f (5f) bandwidths. The calculated temperature dependence of the DC resistivity (conductivity) shows great similarities to the experimental results for many intermediate-valence rare-earth and actinide-based materials. © 1999 Elsevier Science B.V.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-0006149530,

title = {Chemical potential derivative as hallmark for phase transitions},

author = { M.A. Pietruszka and M. Matlak},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-0006149530&doi=10.12693%2fAPhysPolA.96.725&partnerID=40&md5=b95a511bdfe94b9b34b56378a0de0aa1},

doi = {10.12693/APhysPolA.96.725},

issn = {05874246},

year  = {1999},

date = {1999-01-01},

journal = {Acta Physica Polonica A},

volume = {96},

number = {6},

pages = {725-732},

publisher = {Polish Academy of Sciences},

abstract = {We study antiferromagnetic properties of the two-band extended s-f model with fluctuating valence in the context of two mutually bound new effects of chemical potential critical behaviour, as well as of critical electron redistribution. In order to exemplify both phenomena we build phase diagrams of the system displaying the dependence of the critical Néel temperatures (TN) of the system versus 4f (5f) level positions. The phase diagram consists of two different areas corresponding to antiferromagnetic and paramagnetic phases. We plot the magnetizations and the correlation functions of the system as functions of temperature. Next, we investigate the temperature dependence of the relative average occupation numbers Δnf(d) and the chemical potential Δμ for a given 4f (5f) level position Ef. Plotting this quantities along the Ef cross-section lines we observe small (of the order of 10-4-10-3) but well localized kinks exactly at the Néel temperature TN . Last but not least, we plot the first derivative of the chemical potential dμ/dT which, as it shows clearly visible jumps at TN, may turn out to be very accurate and sensitive (auxiliary) tool to find critical temperatures of the considered system. Moreover, we plot the difference μAF - μPARA where we subtract a chemical potential value of a reference paramagnetic sample from the actual value of the antiferromagnetic system. Also in this case we report the observation of discontinuous change in slope at TN. Our observations can be extended to point out to a new practical possibility of how to find experimentally the critical temperatures of the antiferromagnetic systems exclusively from the chemical potential measurements. We expect that the same type of measurement, according to our recent and present results, would also apply to all types of critical phenomena in real solids.},

note = {6},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-0000345111,

title = {Reentrant and nonreentrant properties of magnetic superconductors. Critical electron redistribution},

author = { M. Matlak and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-0000345111&doi=10.1016%2fS0921-4534%2898%2900621-2&partnerID=40&md5=038116af492353719e86dc13698faf03},

doi = {10.1016/S0921-4534(98)00621-2},

issn = {09214534},

year  = {1999},

date = {1999-01-01},

journal = {Physica C: Superconductivity and its Applications},

volume = {311},

number = {1-2},

pages = {151-162},

publisher = {Elsevier},

abstract = {We consider an array of magnetically ordered 4f ions forming s.c. lattice. In the center of each cube, we place one 'effective' nonmagnetic ion and we consider a model taking into account all necessary interactions of electrons belonging to both sorts of ions leading to a competition between ferromagnetism and superconductivity. Two kinds of solutions of the model can be found. One of them describes the reentrant superconductivity with three critical temperatures TS1, TS2 (lower and upper superconducting transition temperature) and TC (Curie temperature) which fulfil the relation TS1 < TC <TS2. The magnetizations due to 4f electrons, and net magnetization originating from two sorts of electrons (two different sorts of atoms) are all parallel in this case. Here, we observe a great similarity of the properties of the model to the observed properties of the real HoMo6S8 compound. The second kind of solutions of the model corresponds to the situation where the net magnetization originating from two sorts of electrons vanishes (antiparallel aligning of magnetic moments in different conduction subbands) and we observe the superconductivity in the temperature range T ∈ [0,TS2] (TS1 = 0) where TC < TS2 or TC > TS2 (coexistence of ferromagnetism and superconductivity of nonreentrant type). The latter situation seems to be similar to that observed in the real Y9Co7 compound. In all cases, we observe that the relative occupation numbers connected with two sorts of interacting electrons exhibit at critical temperatures small but distinctive kinks that give the evidence about the electron redistribution at critical temperatures (critical electron redistribution). Hence, we suggest that the secondary information about the critical temperatures of the real solids can be predicted from the experimental data providing that the temperature dependence of the density of states is available. © 1999 Elsevier Science B.V. All rights reserved.},

note = {14},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-2442565731,

title = {Time Evolution of the Action Potential in Plant Cells},

author = { M.A. Pietruszka and J. Stolarek and K. Pazurkiewicz-Kocot},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-2442565731&doi=10.1023%2fA%3a1005020826000&partnerID=40&md5=4ed80de89eba40cf6dc78ead7d9fb6a0},

doi = {10.1023/A:1005020826000},

issn = {00920606},

year  = {1997},

date = {1997-01-01},

journal = {Journal of Biological Physics},

volume = {23},

number = {4},

pages = {219-232},

publisher = {Springer Netherlands},

abstract = {In this paper we extend and reconsider a solitonic model of the action potential in biological membranes for the case of plant cells. Aiming to give at least a qualitative description of the K+, Cl- and Ca2+ driven process of propagation of the action potential along plant cells we put forward the hypothesis of three scalar fields φi(X)},

note = {8},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-3142639358,

title = {Effect of cadmium ions on the photoelectric potential of Zea mays L. plants},

author = { K. Pazurkiewicz-Kocot and M.A. Pietruszka and J. Stolarek},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-3142639358&partnerID=40&md5=f38484b6c154d586393e279fd3d72471},

issn = {12301485},

year  = {1996},

date = {1996-01-01},

journal = {Polish Journal of Environmental Studies},

volume = {5},

number = {3},

pages = {45-49},

abstract = {The relationship between the photoelectric reaction of Zea mays L. plants and concentrations of cadmium (10-2 M -10-6 M) in the external medium was investigated. The experiments were carried out by using the conventional electrophysiological technique. The effect of cadmium ions on the acidification of the external medium by fragments of leaves has also been studied. Our results suggest that the photoelectric reaction in plants treated with cadmium ions was significantly reduced. The effect of cadmium ions on the photoelectric reaction at low concentrations (10-6 M, 10-5 M and 10-4 M) was mainly quantitative. High sublethal concentrations of this metal (10-3 M and 10-2 M) induced strong inhibition on these reactions. Measurements of pH of the incubation medium showed that cadmium-decreased light induced acidification by Zea mays L. leave cells and that the H+ electrogenic proton pump probably participated in generation of the photoelectric response in the green plant cells. Moreover, the correlation between the electric potential value and decrease in chlorophyll content in mesophyll cells was studied.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-0030562335,

title = {Thermodynamics of intermediate-valence two-band ferromagnets: Magnetic susceptibility and dc resistivity},

author = { M. Matlak and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-0030562335&doi=10.1016%2f0304-8853%2895%2900527-7&partnerID=40&md5=a156c713e4132196626f202f86397508},

doi = {10.1016/0304-8853(95)00527-7},

issn = {03048853},

year  = {1996},

date = {1996-01-01},

journal = {Journal of Magnetism and Magnetic Materials},

volume = {153},

number = {3},

pages = {347-354},

publisher = {Elsevier},

abstract = {On the basis of the extended two-band s-f model we have calculated the temperature dependence of the magnetic susceptibility and dc resistivity (conductivity). A systematic review of the calculated quantities is presented in the form of 3D plots including different average occupation numbers of electrons per site n=1, 1.5, 2 and 2.5, different relative positions of the 4f (5f) band, and different 4f (5f) bandwidths. The calculated quantities exhibit great similarities to the experimentally measured curves for many intermediate-valence rare-earth and actinide-based materials.},

note = {2},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-0030084264,

title = {Thermodynamics of intermediate-valence two-band ferromagnets: Magnetic properties},

author = { M. Matlak and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-0030084264&doi=10.1016%2f0304-8853%2895%2900528-5&partnerID=40&md5=907578b91ea53d0a4442dee2bb922913},

doi = {10.1016/0304-8853(95)00528-5},

issn = {03048853},

year  = {1996},

date = {1996-01-01},

journal = {Journal of Magnetism and Magnetic Materials},

volume = {153},

number = {1-2},

pages = {115-123},

publisher = {Elsevier},

abstract = {We present the influence of the finite bandwidth of the 4f (5f) band and finite intrasite Coulomb repulsion on the magnetic properties of the generalized s-f model. The calculation of the Curie temperature TC shows that the increase of the 4f (5f) bandwidth suppress the magnetic phase and can completely destroy it. The increase in the Coulomb intrasite repulsion acts in the opposite direction. The mechanism of indirect exchange interaction is discussed in detail to explain the shapes of the TC dependence on different model parameters. The calculated TC dependence on the average occupation number or on the position of the 4f (5f) level shows great similarities to the experimentally measured TC curves versus applied pressure or dopant concentration in many intermediate-valence rare-earth or actinide compounds and alloys.},

note = {5},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-24544460208,

title = {On the φ4 field theoretical model for the action potential},

author = { M. Maśka and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-24544460208&doi=10.1007%2fBF00712346&partnerID=40&md5=5a4bf4f35596ed4d3aeedeeac97507db},

doi = {10.1007/BF00712346},

issn = {00920606},

year  = {1995},

date = {1995-01-01},

journal = {Journal of Biological Physics},

volume = {21},

number = {3},

pages = {211-222},

publisher = {Kluwer Academic Publishers},

abstract = {In this short letter we report on the possibility of a field-theoretical model of the action potential in biological membranes. In order to give a qualitative description of the (K+ and Na+ driven) process of propagation of the action potential we introduce two classical scalar fields φ and ψ representing Na+ and K+ ions, respectively. These fields are described by the Lagrangian densities {Mathematical expression} and {Mathematical expression}. Moreover, we add the interaction term {Mathematical expression} between the fields. The Lagrangian densities {Mathematical expression} and {Mathematical expression} include a double-well potential that leads to a spontaneous symmetry breaking (SSB) which may produce topologically non-trivial structures (i.e. structures with non-zero topological charge). In order to describe the transversal motion of K+ and Na+ ions we have to assume non-uniform solutions. Eventually, after deriving the Euler-Lagrange system of equations of motion we perform the Lorentz transformation (boost) on the static solution. © 1995 Kluwer Academic Publishers.},

note = {4},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-84989741886,

title = {The dose‐response curves for IAA induced elongation growth and acidification of the incubation medium of Zea mays coleoptile segments},

author = { W. Karcz and J. Stolarek and M.A. Pietruszka and E. Małkowski},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84989741886&doi=10.1111%2fj.1399-3054.1990.tb04405.x&partnerID=40&md5=3937e32beaddf84846928c2559f90f9c},

doi = {10.1111/j.1399-3054.1990.tb04405.x},

issn = {00319317},

year  = {1990},

date = {1990-01-01},

journal = {Physiologia Plantarum},

volume = {80},

number = {2},

pages = {257-261},

abstract = {The initial dose‐response curves for auxin‐induced elongation growth of Zea mays L. coleoptile segments and simultaneously measured changes of pH of the incubation medium were studied. It was found that these curves are bell‐shaped on all occasions and that at all IAA concentrations studied acidification of the incubation medium took place. The optimum response for IAA‐induced elongation growth and acidification of the incubation medium was 10−5 and 10−4M IAA, respectively. The regression curves and correlation coefficients between magnitude of the growth response and acidification of the incubation medium indicated a close relationship between these sets of data over a wide range of IAA concentrations. Copyright © 1990, Wiley Blackwell. All rights reserved},

note = {25},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-34250102085,

title = {Quasi-particle description of cross-over effects in two-band superconductors},

author = { J. Zieliński and P. Entel and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-34250102085&doi=10.1007%2fBF01311651&partnerID=40&md5=6128081a1326caac9b24d874beaf8a08},

doi = {10.1007/BF01311651},

issn = {07223277},

year  = {1987},

date = {1987-01-01},

journal = {Zeitschrift für Physik B Condensed Matter},

volume = {66},

number = {2},

pages = {161-166},

publisher = {Springer-Verlag},

abstract = {The possibility of singlet-like superconductivity in a hybridized two-band system is investigated. We reformulate the problem in terms of quasi-particle states originating from narrow f-like band and conduction band states. An effective BCS-like Hamiltonian for heavy and light quasi-particles is derived. The stability of these two types of Cooper pairs is studied by using the occupation number of heavy particles as an input parameter. Our results provide strong support for the assumption that in this kind of two-band system a cross-over effect can be observed. For large enough values of the input parameter superconductivity is mainly supported by heavy quasi-particles. By reducing the occupation number superconductivity is taken over by the light quasi-particles. The relevance of the results for heavy-fermion superconductors is discussed. © 1987 Springer-Verlag.},

note = {3},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-0023417952,

title = {On the phonon induced hybrid pairing in two band superconductors},

author = { J. Zieliński and M.A. Pietruszka},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-0023417952&doi=10.1016%2f0038-1098%2887%2990653-3&partnerID=40&md5=9ffa475cb5156048ca8d995930f9b957},

doi = {10.1016/0038-1098(87)90653-3},

issn = {00381098},

year  = {1987},

date = {1987-01-01},

journal = {Solid State Communications},

volume = {63},

number = {11},

pages = {1023-1025},

abstract = {The role of hybrid pairing originating from electron-phonon interaction has been investigated for a two band (f{hook} and d) superconductor at T = 0. This type of pairing seems to be less important than f{hook}-f{hook} pairing for the case of half-filled f{hook}-band when the latter type of Cooper pairs plays the dominating role. On the other hand, for the case of rather filled (or rather empty) f{hook}-band, the superconducting properties of the system are mainly determined by the formation of conduction electrons d-d pairs. © 1987.},

note = {3},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-34250114156,

title = {On the CPA treatment of Magnetic Disordered Hubbard model (II)},

author = { M.A. Pietruszka and W. Borgieł},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-34250114156&doi=10.1007%2fBF01307769&partnerID=40&md5=b6b8d6c71c46140b9cc14a8a8547beee},

doi = {10.1007/BF01307769},

issn = {07223277},

year  = {1985},

date = {1985-01-01},

journal = {Zeitschrift für Physik B Condensed Matter},

volume = {61},

number = {2},

pages = {147-152},

publisher = {Springer-Verlag},

abstract = {In this contribution we continue the treatment of the model based on the Hubbard hamiltonian in which the stochastic fields acting at the sites of the atoms can assume arbitrary directions and values due to accepted distribution. The averaging procedure introduced by Brandt and Gross to study the behaviour of the magnetically disordered system is used for a model with stochastically localized magnetic fields, resulting from magnetic moments, at the atomic sites, as previously in I. The coherent potential approximation-like method is employed. The selfconsistency problem is regarded as well as the thermodynamic consequences like density of states, localization function, magnetization, high temperature susceptibility and dc conductivity as functions of temperature are discussed. © 1985 Springer-Verlag.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2-s2.0-34250109819,

title = {On the CPA treatment of magnetic disordered Hubbard model (I)},

author = { M.A. Pietruszka and W. Borgieł},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-34250109819&doi=10.1007%2fBF01304260&partnerID=40&md5=5c95edd62357b85fdd8e5bb3bea7c327},

doi = {10.1007/BF01304260},

issn = {07223277},

year  = {1985},

date = {1985-01-01},

journal = {Zeitschrift für Physik B Condensed Matter},

volume = {58},

number = {2},

pages = {99-103},

publisher = {Springer-Verlag},

abstract = {We treat a model based on the Hubbard hamitonian where the stochastic fields acting at the sites of the atoms can assume arbitrary directions and values. The averaging procedure introduced by Brandt et al. to study the behaviour of the magnetically disordered system is used for a model with stochastically localized magnetic fields at the atomic sites. The coherent potential approximation (CPA)-like method is employed and the resulting new effects for the density of states, localization function and dc conductivity are demonstrated in two cases. © 1985 Springer-Verlag.},

note = {1},

keywords = {},

pubstate = {published},

tppubtype = {article}

}