M. Niemiec

Opole University, Oppein, Opole Voivodeship, Poland

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Publications (13)14.23 Total impact

  • [Show abstract] [Hide abstract] 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.
    No preview · Article · Nov 2011 · International Journal of Bifurcation and Chaos
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    M. Niemiec · W. Olchawa · J. Luczka
    [Show abstract] [Hide abstract] 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.
    Preview · Article · May 2005 · Acta Physica Polonica Series B
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    J Luczka · M Niemiec · R Rudnicki
    [Show abstract] [Hide abstract] 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.
    Full-text · Article · May 2002 · Physical Review E
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    M. Niemiec · A. Gadomski · J. Łuczka
    [Show abstract] [Hide abstract] ABSTRACT: An analytical approach to the d-dimensional grain growth, which is a kind of the heterogeneous nucleation-and-growth phase transformation, is offered. The system is assumed to be driven by capillary forces. Another important operative assumption is that the system evolves under preservation of its hypervolume, which results in considering the process as a random walk in the space of grain sizes. A role of the initial condition imposed on the system behaviour, and how does the system behave upon a prescribed initial state, have been examined. A general conclusion appears, which states that this prescription does not affect the asymptotic system behavior, but may be of importance when inspecting the earlytime domain more carefully, cf. the Weibull-type initial distribution. This study is addressed to some analogous theoretical descriptions concerning polycrystals as well as bubbles-containing systems. Some comparison to another modelling, in which a crucial role of local material gradients (fluxes) was emphasized, has been attached.
    Full-text · Article · May 2001 · Acta Physica Polonica Series B
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    M. Niemiec · A. Gadomski · J. Luczka
    [Show abstract] [Hide abstract] 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.
    Full-text · Article · Jan 2001 · Acta Physica Polonica Series B
  • T. Czernik · M. Niemiec · J. Luczka
    [Show abstract] [Hide abstract] 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.
    No preview · Article · Jan 2001 · Acta Physica Polonica Series B
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    J Luczka · M Niemiec · E Piotrowski
    [Show abstract] [Hide abstract] 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.
    Preview · Article · Dec 1998 · Journal of Physics A General Physics
  • J Luczka · M Niemiec
    [Show abstract] [Hide abstract] 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.
    No preview · Article · Dec 1998 · Journal of Physics A General Physics
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    [Show abstract] [Hide abstract] 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...
    Full-text · Article · Dec 1997 · Physica A: Statistical Mechanics and its Applications
  • J Luczka · Mariusz Niemiec · Peter Hänggi
    [Show abstract] [Hide abstract] 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
    No preview · Article · Jan 1996 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
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    M. Niemiec · J. ŁUczka · A. Gadomski
    [Show abstract] [Hide abstract] ABSTRACT: A novel phenomenological approach to the microdomain structure formation or phase transformation in two-dimensional cooperative systems is proposed. The theory offered states that a new structure consists of pieces of islands, microdomains, germs, etc. and deals with modeling of the pattern formation process with increase of area of a new structure or phase. The kinetics of the process is studied. Probabilistic characteristics are obtained and first three moments of the process are analyzed.
    Full-text · Article · Jan 1996
  • Jerzy Luczka · Mariusz Niemiec · Edward Piotrowski
    [Show abstract] [Hide abstract] 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.
    No preview · Article · Nov 1993 · Journal of Mathematical Physics
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    J. Luczka · M. Niemiec · E. Piotrowski
    [Show abstract] [Hide abstract] 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.
    Full-text · Article · Aug 1992 · Physics Letters A