This paper is a continuation of Part I 1 . In Section 3 of Part I, using the energy estimate and bootstrap arguments, the global existence of solutions for a Holling type III cross-diffusion predator-prey model with stage-structure has been discussed when the space dimension be less than 6. However, to obtain the L∞ estimate for the population density w of predator species, there is not cross-d...

We investigate the geometric properties displayed by the magnetic patterns developing on a twodimensional Ising system, when a diffusive thermal dynamics is adopted. Such a dynamics is generated by a random walker which diffuses throughout the sites of the lattice, updating the relevant spins. Since the walker is biased towards borders between clusters, the border-sites are more likely to be up...

Supernova remnants are expected to contain braided (or stochastic) magnetic fields, which are in some regions directed mainly perpendicular to the shock normal. For particle acceleration due to repeated shock crossings, the transport in the direction of the shock normal is crucial. The mean squared deviation along the shock normal is then proportional to the square root of the time. This kind o...

The authors address the problem of sampling double-ended diffusive paths. The ensemble of paths is expressed using a symmetric version of the Onsager-Machlup formula, which only requires evaluation of the force field and which, upon direct time discretization, gives rise to a symmetric integrator that is accurate to second order. Efficiently sampling this ensemble requires avoiding the well-kno...

We use an evolutionary approach to find “most appropriate” dispersal models for ecological applications. From a random walk with locally or nonlocally defined transition probabilities we derive a family of diffusion equations. We assume a monotonic dependence of its diffusion coefficient on the local population fitness and search for a model within this class that can invade populations with ot...