Over the past two decades scientists have achieved a significant improvement of our understanding transport energetic particles across mean magnetic field. Due to test-particle simulations as well powerful non-linear analytical tools this type is almost complete. However, previously developed theories do not always agree perfectly with simulations. Therefore, correction factor $a^2$ was incorpo...

We revisit affine diffusion processes on general and on the canonical state space in particular. A detailed study of theoretic and applied aspects of this class of Markov processes is given. In particular, we derive admissibility conditions and provide a full proof of existence and uniqueness through stochastic invariance of the canonical state space. Existence of exponential moments and the fu...

We introduce a novel technique to find the asymptotic time behaviour of deterministic systems exhibiting anomalous diffusion. The procedure is tested for various classes of simple but physically relevant 1–D maps and possible relevance of our findings for more complicated problems is briefly discussed. In the last few years the phenomenon of deterministic diffusion has been widely investigated:...

Many important properties of granular fluids can be represented by a system of hard spheres with inelastic collisions. Traditional methods of nonequilibrium statistical mechanics are effective for analysis and description of the inelastic case as well. This is illustrated here for diffusion of an impurity particle in a fluid undergoing homogeneous cooling. An appropriate scaling of the Liouvill...

– We elucidate the mechanism underlying the continuous nonequilibrium phase transition of the Pair Contact Process with Diffusion (PCPD). We compute its scaling exponents to second order in an ε-expansion around the upper critical dimension dc = 2 within a simple functional renormalization group (RG) approach. In particular, we establish that the PCPD is not in the directed percolation universa...

The differential equations which describe the simultaneous diffusion of water and a salt in a cell model have been formulated and solved. The equations have been derived from the general laws which describe diffusion processes, thereby furnishing a physical interpretation for the constants which enter into the theory. The theoretical time curves for the two diffusing substances are in good agre...

We propose an alternative approach to self-diffusion in an atomic liquid. Our starting point is an oscillatory motion of a tagged particle in its first solvation shell ~cage!. Only after cage relaxation is taken into account is the tagged particle able to diffuse. This approach is suitable for describing liquids where the concept of binary collisions breaks down and the self-diffusion coefficie...