Tadeusz Kosztołowicz

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We propose a method to extract from experimental data the subdiffusion parameter alpha and subdiffusion coefficient D(alpha) which are defined by means of the relation x(2) = [2 D(alpha) /Gamma (1+alpha) ] t(alpha) where x(2) denotes the mean-square displacement of a random walker starting from x=0 at the initial time t=0 . The method exploits a membrane(More)
We propose a method to measure the subdiffusion parameter alpha and subdiffusion coefficient Dalpha which are defined by means of the relation chi2 = 2Dalpha / Gamma(1+alpha)(t alpha), where chi2 denotes a mean square displacement of a random walker starting from x = 0 at the initial time t = 0. The method exploits a membrane system where a substance of(More)
Subdiffusion with reaction A+B→B is considered in a system which consists of two homogeneous media joined together; the A particles are mobile, whereas B are static. Subdiffusion and reaction parameters, which are assumed to be independent of time and space variables, can be different in both media. Particles A move freely across the border between the(More)
We study both theoretically and experimentally a process of subdiffusion in a system with two thin membranes. The theoretical model uses Green's functions obtained for the membrane system by means of the generalized method of images. These Green's functions are combinations of the fundamental solutions to a fractional subdiffusion equation describing(More)
Using the quasistatic approximation, we show that in a subdiffusion-reaction system with arbitrary nonzero values of subdiffusion coefficients, the reaction front x_{f}(t) evolves in time as x_{f}(t)=Kt;{alpha2} , with alpha being the subdiffusion parameter and K being controlled by the subdiffusion coefficients. To check the correctness of our analysis, we(More)
We study the similarities and differences between different models concerning subdiffusion. More particularly, we calculate first passage time (FPT) distributions for subdiffusion, derived from Greens' functions of nonlinear equations obtained from Sharma-Mittal's, Tsallis's, and Gauss's nonadditive entropies. Then we compare these with FPT distributions(More)
Subdiffusion in a system in which mobile particles A can chemically react with static particles B according to the rule A+B→B is considered within a persistent random-walk model. This model, which assumes a correlation between successive steps of particles, provides hyperbolic Cattaneo normal diffusion or fractional subdiffusion equations. Starting with the(More)
We consider the subdiffusion-reaction process with reactions of a type A+B→B (in which particles A are assumed to be mobile, whereas B are assumed to be static) in comparison to the subdiffusion-reaction process with A→B reactions which was studied by Sokolov, Schmidt, and Sagués [Phys. Rev. E 73, 031102 (2006)]. In both processes a rule that reactions can(More)
We consider in this paper subdiffusion in a system with a thin membrane. The subdiffusion parameters are the same in both parts of the system separated by the membrane. Using the random walk model with discrete time and space variables the probabilities (Green's functions) P(x,t) describing a particle's random walk are found. The membrane, which can be(More)
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