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1

Diffusion of calcium in biological tissues and accompanying mechano-chemical effects

Peradzyński Z.

Archives of Mechanics

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2010

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Vol. 62, nr 6

423-440

EN

In this paper we consider the coupling between chemical and mechanical effects accompanying the diffusion of calcium, either in biological tissues or in a single long cell. The tissue is treated either as a 3-D, or as a quasi-2-D thin layer, of visco-elastic medium, whereas the cell is represented as a thin long cylinder. In particular, the influence of viscosity on the properties of calcium travelling waves is studied. In principle, we explore here the simplest model of calcium diffusion which is based on an effective diffusion coefficient, thus neglecting the details of the role played by buffers. The mechano-chemical coupling in the model is realized by the presence of a traction tensor, in addition to the viscoelastic stress tensor in the mechanical equations, and the strain tensor in the source term of the calcium diffusion equation, as proposed in [1–4]. Our aim is to provide a simple and effective theory, which can be useful in studying various effects influencing propagation of calcium waves. Since in the absence of viscosity the whole mechano-chemical system for calcium and buffers is easily reduced to the “chemical one”, i.e. it consists only of reaction diffusion equations, therefore we decided to perform expansion with respect to the viscosity. Treating, thus, viscous forces as a perturbation, we reduce the problem in each case to a single reaction diffusion equation for the calcium concentration. In this way we avoid the question of the existence of travelling wave solutions as for the so obtained models, their existence follows simply from already known theorems [5–9].

2

Fluid flows in narrow channels

Walenta Z. A., Kucaba-Piętal A., Peradzyński Z.

Journal of Technical Physics

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2009

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Vol. 50, no 1

65-70

EN

We present the results of some Direct Monte-Carlo Simulations of a simple, monoatomic gas flows and also some Molecular Dynamics simulations of the flows of water through very narrow channels (plane Poiseuille flows). The main conclusion from the results is that the roughness of the walls of such narrow channels, even if it is of molecular size, influences very strongly the flow of water, introducing large velocity fluctuations and sometimes even stopping the flow.

3

Molecular dynamics computer simulation of water flows in nanochannels

Kucaba-Piętal A., Walenta Z.A., Peradzyński Z.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2009

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Vol. 57, nr 1

55-61

EN

The work presents the results of the simulations of water flows through narrow channels (Poiseuille flows) performed using the molecular dynamics method, for two different channel widths (equal to 5 and 10 diameters of the water molecule) and for two different materials of the channel walls (copper and quartz). In the simulations, physical properties of the materials and their electrostatic interactions were considered. The obtained results are compared with the analytical solutions for a micropolar fluid flow taking account of the experimentally obtained rheological constants of water.

4

Current and plasma oscillation characterization in a PPS®-X000 Hall-effect thruster

Kurzyna J., Makowski K., Peradzyński Z., Lazurenko A., Mazouffre S., Coduti G., Dudeck M.

Journal of Technical Physics

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2008

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Vol. 49, no 3-4

267-282

EN

The correlations between local plasma oscillations and the discharge current or cathode potential variations are studied in a high-voltage Hall-effect thruster (HET). A set of electric probes is used to collect the signals. The probes are located in the exhaust region of the thruster, beyond its outer circumference. Measurements are performed for various probe positions and bias potentials, within a wide range of thruster operating conditions. The non-stationary signals are subsequently expanded into finite sets of intrinsic modes with the use of the Empirical Mode Decomposition (EMD) method. The Hilbert-Huang power spectra indicate characteristic bands in the low frequency (LF, tens of kHz), medium frequency (MF) and high frequency (HF, tens of MHz) range. However, the regular HF emission that has been observed in our previous low-voltage characterization of a PPS-100 thruster, is only observable in some particular operating conditions. When the supply voltage is low (e.g. 400 V), the known electrostatic drift wave propagating along the thruster azimuth is unambiguously identified in the probe signals. For higher voltages, HF spectra are usually broadband and do not highlight well the defined peaks. HF emission becomes very irregular or even seemingly random. On the other hand, when regular waves appear (intermittently or in series of bursts), frequencies in the ss 5-100 MHz band can be observed. The oscillations within the MF band that were previously weak in the PPS-100 thruster, appear now to dominate the discharge current spectrum when the thruster operates at the highest voltages. Intense oscillations in the MF range are identified with the use of positively biased probes and by examination of the cathode potential and discharge current variations. The correlations of all the mentioned signals are clear in this frequency band. Correlating the oscillations in the HF band with the MF discharge current wave, one can deduce that HF oscillations are periodically triggered by MF waves at high voltage, while at lower voltage they are triggered by the LF breathing mode, as previously observed in the case of the PPS-100 thruster.

5

Causality violation in analysis of Hall thruster plasma instabilities

Peradzyński Z., Barral S., Makowski K., Dudeck M.

Journal of Technical Physics

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2008

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Vol. 49, no 3-4

315-327

EN

Using the fluid equations of Hall thruster plasma we analyze the influence of the electron energy balance on the stability of ion sound modes. For sufficiently low frequencies (ω < 5 • 106^6 s-1 in the case of SPT-100) the gains and losses in the source term are approximately equal, thus the temperature can be in principle determined in terms of other dependent variables. This permits one to reduce the number of equations by one. It appears however, that the new system can have in some regions complex characteristics. This in turn implies instability of certain modes with frequencies lower than the critical frequency.

6

Cauchy problem for quasilinear hyperbolic systems with coefficients functionally dependent on solutions

Zdanowicz M., Peradzyński Z.

Archives of Mechanics

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2007

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Vol. 59, nr 2

173-197

EN

The cauchy problem for a quasilinear hyperbolic systems with coefficients functionally dependent on the solutions is studied. We assume that the coefficients are continuous nonlinear operators in the Banach space C1 (R) satisfying some additional assumptions. Under these assumptions we prove the uniqueness and existence of local in time C1 solutions, provided that the initial data are also of class C1.

7

Flows in microchannels

Kucaba-Piętal A., Walenta Z., Peradzyński Z.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2001

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Vol. 5, No 2

179-189

EN

The aim of this paper is to present a survey of the results for the flows of simple gases and liquids with substructure through narrow channels, obtained with the Direct Monte-Carlo and Molecular Dynamics Simulation methods.