Related papers: Diffusion in multiscale spacetimes
We present a series of results focused on the decay in time of solutions of classical and anomalous diffusive equations in a bounded domain. The size of the solution is measured in a Lebesgue space, and the setting comprises time-fractional…
Anomalous diffusion phenomena occur on length scales spanning from intracellular to astrophysical ranges. A specific form of decay at large argument of the probability density function of rescaled displacement (scaling function) is derived…
The Markovian diffusion theory in the phase space is generalized within the framework of the general theory of relativity. The introduction of moving orthonormal frame vectors both for the position as well the velocity space enables to…
The silo discharge process is studied by molecular dynamics simulations. The development of the velocity profile and the probability density function for the displacements in the horizontal and vertical axis are obtained. The PDFs obtained…
We investigate evolution equations for anomalous diffusion employing fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. Fractional diffusion equations…
The stochastic dynamics of colloidal particles with surface activity--in the form of catalytic reaction or particle release--and self-phoretic effects is studied analytically. Three different time scales corresponding to inertial effects,…
We study a process of anomalous diffusion, based on intermittent velocity fluctuations, and we show that its scaling depends on whether we observe the motion of many independent trajectories or that of a Liouville-like equation driven…
A generalized Fokker-Planck equation is derived to describe particle kinetics in specific situations when the probability transition function (PTF) has a long tail in momentum space. The equation is valid for an arbitrary value of the…
Convergence of stochastic processes with jumps to diffusion processes is investigated in the case when the limit process has discontinuous coefficients. An example is given in which the diffusion approximation of a queueing model yields a…
We study a quantum particle propagating through a ``quantum mechanically chaotic'' background, described by parametric random matrices with only short range spatial correlations. The particle is found to exhibit turbulent-like diffusion…
Multiparticle production processes provide valuable information about the mechanism of the conversion of the initial energy of projectiles into a number of secondaries by measuring their multiplicity distributions and their distributions in…
Fractional differential approach to cosmic ray physics problems is discussed. A short review in this field is given, some results are represented, analyzed and criticized. A new model called the bounded anomalous diffusion model is offered.…
The stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed. The particle is subjected to a stochastic stimulation obeying a general L\'evy stable statistics and experiences…
We define the notion of "diffusion algebras". They are quadratic Poincare-Birkhoff-Witt (PBW) algebras which are useful in order to find exact expressions for the probability distributions of stationary states appearing in one-dimensional…
Quantum diffusion is studied via dissipative Madelung hydrodynamics. Initially the wave packet spreads ballistically, than passes for an instant through normal diffusion and later tends asymptotically to a sub-diffusive law. It is shown…
Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…
Complex spatial and temporal structures are inherent characteristics of turbulent fluid flows and comprehending them poses a major challenge. This comprehesion necessitates an understanding of the space of turbulent fluid flow…
Anomalous diffusion is predicted for Brownian particles in inhomogeneous viscosity landscapes by means of scaling arguments, which are substantiated through numerical simulations. Analytical solutions of the related Fokker-Planck equation…
We answer to 72 frequently asked questions about theories of multifractional spacetimes. Apart from reviewing and reorganizing what we already know about such theories, we discuss the physical meaning and consequences of the very recent…
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…