Persistent diffusion in one dimension, in which the velocity of the diffusing particle is a dichotomic Markov process, is considered. The flow is non-Markovian, but the position and the velocity together constitute a Markovian diffusion process. We solve the coupled forward Kolmogorov equations...

Using the replica technique, we calculate the maximum difference between test and generalization error for the ensemble of all perceptrons trained by a teacher perceptron. The result is compared with the bound provided by the Vapnik-Chervonenkis theorem.

A systematic development for a Multivariate Master Equation (MME), describing reaction diffusion systems, is presented along the same lines as the Chapman-Enskog development of kinetic gas theory. Diffusion, which occurs at a very fast rate, brings the system near a state of diffusional...

A dimer consisting of two coupled oscillators undergoing periodic parametric modulations with a phase difference θ reveals a rich panorama of stability–instability boundaries as a function of the system parameters. It was recently established that the instabilities observed in such dimers...

The eigenfunctions of the diffusion operator of the multivariate master equation, describing reaction diffusion systems, are calculated for various boundary conditions. This serves as a starting point for a systematic study of the general solution of the master equation. As a first application a...

The effect of harmonic forces on Brownian motion in linear shear flow is investigated including a short and intermediate time analysis. A diffusion regime exists for long times if the harmonic forces restrict the motion only in one direction. A series expansion for the effective longitudinal...

The time dependent longitudinal dispersion of Brownian particles, suspended in a fluid in unidirectional steady or oscillatory motion is calculated on the basis of the equivalence of Langevin and Fokker-Planck formalisms. In particular, a series expansion for the effective longitudinal diffusion...

We study the random walk of a particle in a random comb structure, both in the presence of a biasing field and an the field-free case. We show that the mean-field treatment of the quenched disorder can be exactly mapped on to a continuous time random walk (CTRW) on the backbone of the comb, with...

The diffusive motion of a particle within a spherical volume is analysed in detail, to provide insight into the recently observed non-Gaussian statistical properties of the displacements of particles in a dense colloidal suspension. The intermediate scattering function is evaluated and used as a...