M. Niemiec

Opole University, Oppein, Opole Voivodeship, Poland

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Publications (12)11.01 Total impact

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    ABSTRACT: A spherical growth process controlled by velocity fluctuations of particles of a saturated solution is investigated. Velocity fluctuations are modeled by a Gaussian random field. The interface evolution is determined by a Langevin-type equation with a multiplicative random field, which in the case of the quasi-homogeneous random Gaussian field is equivalent to Fokker–Planck dynamics. We analyze numerically the Fokker–Planck equation and compare growth kinetics in the case of noisy (i.e. space-independent) fluctuations. It is shown that for a large class of spatially correlated velocity fluctuations, the growth kinetics is universal, i.e. it does not depend on the details of statistics of fluctuations.
    International Journal of Bifurcation and Chaos 11/2011; 18(09). · 0.92 Impact Factor
  • I. J. Bifurcation and Chaos. 01/2008; 18:2673-2679.
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    M. Niemiec, W. Olchawa, J. Luczka
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    ABSTRACT: In the classical theory of diffusion limited growth, it is assumed that the concentration field of solution is described by the standard diffusion equation. It means that particles of the solution undergo a random walk described by the Wiener process. In turn, it means that the velocity of particles is a stochastic process being Gaussian white noise. In consequence, the velocity--velocity correlation function is the Dirac delta -function and velocity correlation time is zero. In many cases such modeling is insufficient and one should consider models in which velocity is correlated in space and/or time. The question is whether correlations of velocity can change the kinetics of growth, in particular, whether the long-time asymptotics of the growth kinetics displays the power-law time dependence with the classical exponent 1/2. How to model such processes is a subject of this paper.
    Acta Physica Polonica Series B 01/2005; 36. · 1.01 Impact Factor
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    J Luczka, M Niemiec, R Rudnicki
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    ABSTRACT: A model of the spherical (compact) growth process controlled by a fluctuating local convective velocity field of the fluid particles is introduced. It is assumed that the particle velocity fluctuations are purely noisy, Gaussian, of zero mean, and of various correlations: Dirac delta, exponential, and algebraic (power law). It is shown that for a large class of the velocity fluctuations, the long-time asymptotics of the growth kinetics is universal (i.e., it does not depend on the details of the statistics of fluctuations) and displays the power-law time dependence with the classical exponent 1/2 resembling the diffusion limited growth. For very slow decay of algebraic correlations of fluctuations asymptotically like t(-gamma), gamma in (0,1]), kinetics is anomalous and depends strongly on the exponent gamma. For the averaged radius of the crystal <R(t)> approximately t(1-gamma/2) for 0<gamma<1 or <R(t)> approximately (t ln t)1/2 for gamma=1.
    Physical Review E 05/2002; 65(5 Pt 1):051401. · 2.31 Impact Factor
  • M. Niemiec, A. Gadomski, J. Luczka
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    ABSTRACT: Kinetics of three-dimensional normal grain growth and related processes (e.g., soap froth evolutions) described by the Mulheran--Harding model is studied. The model is represented by a diffusion equation with the grain--size--dependent diffusion coefficient. The equation is solved for an arbitrary initial distribution of grain sizes. It is proved that asymptotic kinetics do not depend on the initial state.
    Acta Physica Polonica Series B 01/2001; 32. · 1.01 Impact Factor
  • T. Czernik, M. Niemiec, J. Luczka
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    ABSTRACT: Overdamped directed motion of Brownian motors in a spatially periodic system, induced by Poissonian fluctuations of various statistics and driven by thermal noise, is investigated. Two models of asymmetric as well as two models of symmetric Poissonian fluctuations are considered. Transport properties in dependence upon statistics of fluctuations imposed on the system are analyzed.
    Acta Physica Polonica Series B 01/2001; 32. · 1.01 Impact Factor
  • J Luczka, M Niemiec
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    ABSTRACT: An evolution equation for a reduced statistical operator of quantum systems driven by Poisson white noise is derived. It is applied to a simple system and compared with a counterpart driven by Gaussian white noise.
    Journal of Physics A General Physics 12/1998; 24(17):L1021.
  • J Luczka, M Niemiec, E Piotrowski
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    ABSTRACT: A linear process driven by additive Gaussian white noise, which is randomly interrupted by an exponentially correlated two-state (0,1) Markovian stochastic process, is considered. A characteristic function of the process is obtained using an approach based on conditional functionals for Markov processes. A single-event time dependent probability distribution is presented. Steady states are analysed in terms of stationary distributions and moments of the process. The deviation from Gaussianity (kurtosis) is investigated.
    Journal of Physics A General Physics 12/1998; 26(19):4849.
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    ABSTRACT: An analytical approach to the phase transformation in d-dimensional grains-containing complex systems is offered. It is based on considering the mechanism of surface material exchange among neighbouring grains as the so-called state-dependent diffusion process, where the diffusion function is related to the magnitude of the grain circumference. The approach proposed deals with the kinetics of that ensemble under circumstances of a volume increase of the new phase or microstructure. Probabilistic characteristics of the process are derived and analyzed. A comparison with 2d modelling of similar kind is presented for 3d case, and some possible practical realizations of the situation under study are discussed. 1 Introduction The world of phenomena called phase transformations (transitions) or phase changes remains, both, intriguing as well as a bid mysterious over many past decades of theoretical as well as practical investigations [1]. Among many aspects of knowledge on phase transformat...
    Physica A: Statistical Mechanics and its Applications 12/1997; · 1.68 Impact Factor
  • J Luczka, M Niemiec, P Hänggi
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    ABSTRACT: The mean-first-passage time (MFPT) of a non-Markovian process that switches randomly between deterministic flow and a Fokker-Planck process (i.e., randomly flashing diffusion) is considered. The problem is formulated in an extended phase space in which the corresponding process is Markovian. It is shown that (boundary and natural) conditions for integration of differential equations determining the MFPT depend strongly on the class of domains from which the process is to escape. Exact solutions are obtained for the MFPT of a linear flow driven by randomly flashing white noise. (c) 1995 The American Physical Society
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 01/1996; 52(6):5810-5816.
  • Jerzy Luczka, Mariusz Niemiec, Edward Piotrowski
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    ABSTRACT: An evolution equation of integro-differential type for a one-dimensional probability distribution of a linear process driven by additive randomly interrupted Gaussian white noise is exactly solved. A family of propagators for a probability distribution of the process is obtained. Selected examples of a time-dependent distribution are presented.
    Journal of Mathematical Physics 11/1993; 34(11). · 1.30 Impact Factor
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    J. Luczka, M. Niemiec, E. Piotrowski
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    ABSTRACT: Processes driven by Gaussian white noise, which is interrupted randomly by a two-state {0, 1} Markov stochastic process, are considered. An infinitesimal generator of the evolution operator for single-event probability distributions is constructed. It describes a non-local in space and non-local in time evolution of the system. It is shown that a stationary probability distribution is a solution of an ordinary differential equation of second order with two imposed conditions.
    Physics Letters A 01/1992; 167:475-478. · 1.77 Impact Factor