Publications (13)13.38 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 Langevintype equation with a multiplicative random field, which in the case of the quasihomogeneous 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. spaceindependent) 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.  [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 velocityvelocity 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 longtime asymptotics of the growth kinetics displays the powerlaw time dependence with the classical exponent 1/2. How to model such processes is a subject of this paper.  [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 longtime asymptotics of the growth kinetics is universal (i.e., it does not depend on the details of the statistics of fluctuations) and displays the powerlaw 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(1gamma/2) for 0<gamma<1 or <R(t)> approximately (t ln t)1/2 for gamma=1.  [Show abstract] [Hide abstract]
ABSTRACT: An analytical approach to the ddimensional grain growth, which is a kind of the heterogeneous nucleationandgrowth 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 Weibulltype initial distribution. This study is addressed to some analogous theoretical descriptions concerning polycrystals as well as bubblescontaining systems. Some comparison to another modelling, in which a crucial role of local material gradients (fluxes) was emphasized, has been attached.  [Show abstract] [Hide abstract]
ABSTRACT: Kinetics of threedimensional normal grain growth and related processes (e.g., soap froth evolutions) described by the MulheranHarding model is studied. The model is represented by a diffusion equation with the grainsizedependent 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.  [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.  [Show abstract] [Hide abstract]
ABSTRACT: A linear process driven by additive Gaussian white noise, which is randomly interrupted by an exponentially correlated twostate (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 singleevent 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.  [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. 
Article: Phase Transformation Kinetics in dDimensional GrainsContaining Systems: DiffusionType Model
[Show abstract] [Hide abstract]
ABSTRACT: An analytical approach to the phase transformation in ddimensional grainscontaining complex systems is offered. It is based on considering the mechanism of surface material exchange among neighbouring grains as the socalled statedependent 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...  [Show abstract] [Hide abstract]
ABSTRACT: The meanfirstpassage time (MFPT) of a nonMarkovian process that switches randomly between deterministic flow and a FokkerPlanck 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  [Show abstract] [Hide abstract]
ABSTRACT: A novel phenomenological approach to the microdomain structure formation or phase transformation in twodimensional 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.  [Show abstract] [Hide abstract]
ABSTRACT: An evolution equation of integrodifferential type for a onedimensional 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 timedependent distribution are presented. 
Article: Randomly interrupted diffusion
[Show abstract] [Hide abstract]
ABSTRACT: Processes driven by Gaussian white noise, which is interrupted randomly by a twostate {0, 1} Markov stochastic process, are considered. An infinitesimal generator of the evolution operator for singleevent probability distributions is constructed. It describes a nonlocal in space and nonlocal 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.
Publication Stats
85  Citations  
13.38  Total Impact Points  
Top Journals
Institutions

19972011

Opole University
 Institute of Physics
Oppein, Opole Voivodeship, Poland


1998

Silesian University of Technology
Gleiwitz, Silesian Voivodeship, Poland
