Prof. Zbigniew Peradzyński, Ph.D., Dr. Habil. 

Doctoral thesis
1972  Inwarianty Riemanna w nieliniowym oddziaływaniu fal  zastosowanie w gazodynamice
 206 
Habilitation thesis
1981  Geometria nieliniowych oddziaływań w równaniach różniczkowych cząstkowych ze szczególnym uwzględnieniem równań dynamiki płynów 
Professor
1993  Title of professor 
Supervision of doctoral theses
1.  20071122  Zdanowicz Małgorzata  Analiza matematyczna równań modelujących plazmę w silniku jonowym  607  
2.  2003  Barral Serge  Numerical studies of Hall Thrusters based on fluid equations for plasma  
3.  1998  Lipniacki Tomasz  Wirowa warstwa przyścienna w dynamice nadciekłego helu. Turbulencja kwantowa  
4.  1993  Kurzyna Jacek  Numeryczne modelowanie plazmy podtrzymywanej promieniowaniem laserowym i porównanie z eksperymentem  
5.  1993  Owczarek Robert  Metody teorii pola w opisie cieczy kwantowych  
6.  1990  Kaźmierczak Bogdan  Warstwa przejściowa i asymptotyka rozwiązań nieliniowych cząstkowych równań różniczkowych typu reakcjidyfuzji. Zastosowanie w fizyce plazmy.  
7.  1987  Małyszko Ewa  Problem oddziaływania fal w hydrodynamice i magnetohydrodynamice 
Recent publications
1.  Kaźmierczak B., Peradzyński Z., Calcium waves with mechanochemical couplings, MATHEMATICAL BIOSCIENCES AND ENGINEERING, ISSN: 15471063, DOI: 10.3934/mbe.2013.10.743, Vol.10, pp.743759, 2013 Abstract: As follows from experiments, waves of calcium concentration in biological tissues can be easily excited by a local mechanical stimulation. Therefore the complete theory of calcium waves should also take into account coupling between mechanical and chemical processes. In this paper we consider the existence of travelling waves for buffered systems, as in [22], completed, however, by an equation for mechanical equilibrium and respective mechanochemical coupling terms. Thus the considered, coupled system consists of reactiondiffusion equations (for the calcium and buffers concentrations) and equations for the balance of mechanical forces. Keywords:Calcium waves, reactiondiffusion systems, mechanochemical coupling Affiliations:
 
2.  Zdanowicz M.^{♦}, Peradzyński Z.^{♦}, Propagation of weak discontinuities for quasilinear hyperbolic systems with coefficients functionally dependent on solutions, Annales Polonici Mathematici, ISSN: 00662216, DOI: 10.4064/ap10926, Vol.109,2, pp.177198, 2013 Abstract: The propagation of weak discontinuities for quasilinear systems with coefficients functionally dependent on the solution is studied. We demonstrate that, similarly to the case of usual quasilinear systems, the transport equation for the intensity of weak discontinuity is quadratic in this intensity. However, the contribution from the (nonlocal) functional dependence appears to be in principle linear in the jump intensity (with some exceptions). For illustration, several examples, including two hyperbolic systems (with functional dependence), the dispersive Maxwell equations and fluid equations of the Hall plasma thruster, are considered. Affiliations:
 
3.  Kaźmierczak B., Peradzyński Z., Calcium waves with fast buffers and mechanical effects, JOURNAL OF MATHEMATICAL BIOLOGY, ISSN: 03036812, DOI: 10.1007/s0028500903232, Vol.62, No.1, pp.138, 2011 Abstract: In the paper we consider the existence of calcium travelling waves for systems with fast buffers. We prove the convergence of the travelling waves to an asymptotic limit as the kinetic coefficients characterizing the interaction between calcium and buffers tend to infinity. To be more precise, we prove the convergence of the speeds as well as the calcium component concentration profile to the profile of the travelling wave of the reduced equation. Additionally, we take into account the effect of coupling between the mechanical and chemical processes and show the existence as well the monotonicity of the profiles of concentrations. This property guarantees their positivity. Keywords:Calcium waves, Reaction–diffusion systems, Mechanochemical coupling Affiliations:
 
4.  Barral S., Peradzyński Z.^{♦}, Ionization oscillations in Hall accelerators, PHYSICS OF PLASMAS, ISSN: 1070664X, DOI: 10.1063/1.3292645, Vol.17, pp.0145054, 2010 Abstract: The underlying mechanism of lowfrequency oscillations in Hall accelerators is investigated theoretically. It is shown that relaxation oscillations arise from a competition between avalancheionization and the advective transport of the working gas. The model derived recovers the slow progression and fast recession of the ionization front. Analytical approximations of the shape of current pulses and of the oscillation frequency are provided for the case of large amplitude oscillations. Affiliations:
 
5.  Peradzyński Z., Diffusion of calcium in biological tissues and accompanying mechanochemical effects, ARCHIVES OF MECHANICS, ISSN: 03732029, Vol.62, No.6, pp.117, 2010 Abstract: 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 3D, or as a quasi2D 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 mechanochemical 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 mechanochemical 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]. Keywords:calcium waves, reactiondiffusion systems, mechanochemical coupling Affiliations:
 
6.  KucabaPiętal A.^{♦}, Walenta Z.A., Peradzyński Z., Molecular dynamics computer simulation of water flows in nanochannels, BULLETIN OF THE POLISH ACADEMY OF SCIENCES: TECHNICAL SCIENCES, ISSN: 02397528, Vol.57, No.1, pp.5561, 2009 Abstract: 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). nanoflows, micropolar fluid, molecular dynamics simulation, nanochannels Affiliations:
 
7.  Walenta Z.A., KucabaPiętal A.^{♦}, Peradzyński Z., Fluid Flows in narrow channels, JOURNAL OF TECHNICAL PHYSICS, ISSN: 03248313, Vol.50, pp.6570, 2009  
8.  Peradzyński Z., Barral S., Makowski K., Dudeck M.^{♦}, Causality violation in analysis of Hall thruster plasma instabilities, JOURNAL OF TECHNICAL PHYSICS, ISSN: 03248313, Vol.49, pp.315327, 2009  
9.  Peradzyński Z., Barral S., Makowski K., Dudeck M.^{♦}, Causality violation in analysis of Hall thruster plasma instabilities, JOURNAL OF TECHNICAL PHYSICS, ISSN: 03248313, Vol.49, pp.315327, 2008  
10.  Peradzyński Z., Makowski K., Barral S., Kurzyna J., Dudeck M.^{♦}, The role of the electron energy balance in plasma thruster instabilities, AIP Conference Proceedings, ISSN: 0094243X, DOI: 10.1063/1.2909169, Vol.993, pp.435, 2008 Abstract: 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 frequencies lower than ωc = 107 s−1 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 to reduce the number of equations. It appears however, that the new system can have complex characteristics in some regions. This in turn implies instability of certain modes with frequencies lower than ωc. Keywords:Energy balance, Acoustic analysis, Fluid equations, Instability analysis, Plasma instabilities Affiliations:
 
11.  Kurzyna J., Makowski K., Peradzyński Z., Lazurenko A.^{♦}, Mazouffre S.^{♦}, Dudeck M.^{♦}, Where is the breathing mode? High voltage Hall effect thruster studies with EMD method, AIP Conference Proceedings, ISSN: 0094243X, DOI: 10.1063/1.2909172, Vol.993, pp.443, 2008 Abstract: Discharge current and local plasma oscillations are studied in a high voltage Hall effect thruster PPS®X000. Characteristic time scales that appear in different operating conditions are resolved with the use of HilbertHuang spectra (HHS) which display time dependenc of instantaneous frequency and power. Sets of intrinsic mode functions (imfs) that are used for HHS calculation result due to application of empirical mode decomposition method (EMD) to nonstationary multicomponent signals. In the experiment the signals are captured in the electric circuit of the thruster as well locally, in the vicinity of the thruster exhaust region. Classical electric probes spaced along the azimuth and/or thruster axis let us study correlations of signals which were captured in different locations. In this way azimuthal and axial propagation of disturbances is inspected. The discharge voltage is varied in the range of 200÷900 V while xenon mas flow rate of 5÷9 mg/s. LF, MF, and HF characteristic bands that are known from previous studies of PPS®100 thruster have been also detected here. However, expanding discharge current onto a set of intrinsic modes we can resolve MF mode more reliably than before. Moreover, for higher discharge voltages, this irregular mode turns into more regular waveform and tends to dominate in the discharge current masking almost completely the breathing mode (LF oscillations of the discharge current). In such a case triggering of HF oscillations is correlated with the phase of MF mode while in the case of PPS®100 thruster it was correlated with the appropriate phase of the breathing mode (LF band). Regular HF emission that can be unambiguously interpreted as azimuthal electrostatic wave now is observed only in the specific operating conditions of the thruster. However, even if irregular HF emission is observed the time delay of crosscorrelated signals which are captured in different azimuthal locations corresponds to the velocity of azimuthal electron drift in the field of magnetic barrier. Keywords:High voltage direct current transmission, Electrical circuits, Electrostatic discharges, Electrostatic waves, Plasma oscillations Affiliations:
 
12.  Barral S., Makowski K., Peradzyński Z., Dudeck M.^{♦}, Transit time instability in Hall Thruster, PHYSICS OF PLASMAS, ISSN: 1070664X, Vol.12, pp.7350419, 2005  
13.  Kurzyna J., Mazouffre S.^{♦}, Lazurenko A.^{♦}, Albarede L.^{♦}, Bonhomme G.^{♦}, Makowski K., Dudeck M.^{♦}, Peradzyński Z., Spectral analysis of Hall effect thruster plasma oscillations based on the empirical mode decomposition, PHYSICS OF PLASMAS, ISSN: 1070664X, DOI: 10.1063/1.2145020, Vol.12, pp.123506113, 2005 Abstract: Halleffect thruster plasma oscillations recorded by means of probes located at the channel exit are analyzed using the empirical mode decomposition (EMD) method. This selfadaptive technique permits to decompose a nonstationary signal into a set of intrinsic modes, and acts as a very efficient filter allowing to separate contributions of different underlying physical mechanisms. Applying the Hilbert transform to the whole set of modes allows to identify peculiar events and to assign them a range of instantaneous frequency and power. In addition to 25kHz breathingtype oscillations which are unambiguously identified, the EMD approach confirms the existence of oscillations with instantaneous frequencies in the range of 100–500kHz typical for ion transittime oscillations. Modeling of highfrequency modes (ν∼10MHz) resulting from EMD of measured wave forms supports the idea that highfrequency plasma oscillations originate from electrondensity perturbations propagating azimuthally with the electron drift velocity. Keywords:Plasma oscillations, Interplanetary magnetic fields, Plasma waves, Wavelets, High frequency discharges Affiliations:
 
14.  Peradzyński Z., Kaźmierczak B., On mechanochemical calcium waves, ARCHIVE OF APPLIED MECHANICS, ISSN: 09391533, DOI: 10.1007/s0041900503927, Vol.74, pp.827833, 2005 Abstract: The influence of mechanochemical coupling on calcium concentration waves is considered. The propagation of calcium waves is described by a reaction–diffusion equation with the reaction term dependent on the mechanical stress responsible for the release of calcium. Similarly the balance of mechanical forces is influenced by the calcium concentration through the socalled traction force. Keywords:Calcium waves, Reaction–diffusion systems, Mechanochemical coupling Affiliations:
 
15.  Szymański Z., Peradzyński Z., Kurzyna J., Hoffman J., Dudeck M.^{♦}, de Graaf M.^{♦}, Lago V.^{♦}, Spectroscopic study of a supersonic jet of laserheated argon plasma, JOURNAL OF PHYSICS DAPPLIED PHYSICS, ISSN: 00223727, DOI: 10.1088/00223727/30/6/013, Vol.30, No.6, pp.998, 1997 Abstract: A spectroscopic study of a lowpressure supersonic jet of laserheated argon plasma is presented. The experimental setup consisted of a highpressure convergent nozzle and a supersonic nozzle. The supersonic nozzle was placed just behind the convergent nozzle and was connected to a lowpressure chamber. A continuous wave laser with output power of 2 kW was used to maintain the plasma in the stream of argon gas flowing from the convergent nozzle. The plasma then expanded through the supersonic nozzle. Emission spectra from the lasersustained plasma and supersonic jet were measured with a 1.3 m focal length spectrograph and 1254 silicon intensified target (SIT) detector connected to an EG&G PARC optical multichannel analyser (OMA) III. We found that the supersonic stream of argon plasma had an electron density of  and a temperature of 6  7 kK. Affiliations:
 
16.  Szymański Z., Peradzyński Z., Kurzyna J., Free burning lasersustained plasma in a forced flow, JOURNAL OF PHYSICS DAPPLIED PHYSICS, ISSN: 00223727, DOI: 10.1088/00223727/27/10/014, Vol.27, No.10, pp.2074, 1994 Abstract: The boundaries of the existence of a lasersustained argon plasma in forced convective flow were investigated experimentally and numerically. The plasma was maintained by a cw CO2 laser with an output power of 2.5 kW and burnt in free space at atmospheric pressure. Flow velocities changed from 2.3 m s1 to 8 m s1. The f number was 8.8. The results show that a quasi2D model in which the axial flow is given by the relation rho u= rho 0u0( rho / rho 0)12/, where rho 0 and u0 are the density and velocity of the cold gas respectively, describes the observed phenomena fairly well. Affiliations:
 
17.  Peradzyński Z., Geometria nieliniowych oddziaływań w równaniach różniczkowych cząstkowych (Praca habilitacyjna), Prace IPPT  IFTR Reports, ISSN: 22993657, No.22, pp.1198, 1981 
Conference abstracts
1.  Peradzyński Z., Modeling calcium concentration waves in biological cells, III National Conference of Nano and Micromechanics, 20120704/0706, Warszawa (PL), pp.101, 2012 