We investigate how a clean continuous phase transition is affected by spatiotemporal disorder, i.e., by an external perturbation that fluctuates in both space and time. We derive a generalization of the Harris criterion for the stability of the clean critical behavior in terms of the space-time correlation function of the external perturbation. As an application, we consider diffusive disorder,...

We present here a model for multivalent diffusive transport whereby central point-like hub is coupled to multiple feet, which bind complementary sites on two-dimensional landscape. The available number of binding interactions dependent the feet (multivalency) and their allowed distance from (span). Using Monte Carlo simulations that implement Gillespie algorithm, we simulate processes 100 disti...

In this paper the propagation of harmonic plane waves in a homogeneous anisotropic magneto-piezothermoelastic diffusive body with fractional order derivative is studied. The governing equations for a homogeneous transversely isotropic body in the context of the theory of thermoelasticity with diffusion given by Sherief et al. [1] are considered as a special case. It is found that three types of...

Diffuse photon density waves have lately been used both to characterize diffusive media and to locate and characterize hidden objects, such as tumors, in soft tissue. In practice, most biological media of medical interest consist of various layers with different optical properties, such as the fat layer in the breast or the different layers present in the skin. Also, most experimental setups co...

This paper is concerned with the Becker-Döring (BD) system of equations and their relationship to the Lifschitz-Slyozov-Wagner (LSW) equations. A diffusive version of the LSW equations is derived from the BD equations. Existence and uniqueness theorems for this diffusive LSW system are proved. The major part of the paper is taken up with proving that solutions of the diffusive LSW system conver...

In the framework of the statistical mechanics based on the Sharma-Taneja-Mittal entropy we derive a family of nonlinear Fokker-Planck equations characterized by the associated non-increasing Lyapunov functional. This class of equations describes kinetic processes in anomalous mediums where both super-diffusive and sub-diffusive mechanisms arise contemporarily and competitively. We classify the ...

Radiative transfer (RT) theory is often invoked to describe energy propagation in strongly scattering media. Fitting RT to measured wave field intensities is rather different at late times, when the transport is diffusive, than at intermediate times (around one extinction mean free time), when ballistic and diffusive behavior coexist. While there are many examples of late-time RT fits, we descr...

We present a domain decomposition theory on an interface problem for the linear transport equation between a diffusive and a non-diffusive region. To leading order, i.e. up to an error of the order of the mean free path in the diffusive region, the solution in the non-diffusive region is independent of the density in the diffusion region. However, the diffusive and the non-diffusive regions are...