We introduce a class of one dimensional deterministic models of energyvolume conserving interfaces. Numerical simulations show that these dynamics are genuinely super-diffusive. We then modify the dynamics by adding a conservative stochastic noise so that it becomes ergodic. System of conservation laws are derived as hydrodynamic limits of the modified dynamics. Numerical evidence shows these m...

Consider the steady neutron transport equation with diffusive boundary condition. In [17] and [18], it was discovered that geometric correction is necessary for the Milne problem of Knudsen-layer construction in a disk or annulus. In this paper, we establish diffusive limit for a 2D convex domain. Our contribution relies on novel weighted W 1,∞ estimates for the Milne problem with geometric cor...

As a function of the disorder strength in a mesoscopic system, the electron dynamics crosses over from the ballistic through the diffusive towards the localized regime. The ballistic and the localized situation correspond to integrable or regular behavior while diffusive conductors correspond to chaotic behavior. The chaotic or regular character of single wave functions can be inferred from pha...

For quantum particles, it is well known that static disorder would lead to Anderson localization (AL) while dynamic (evolving) disorder would destroy AL and facilitate the transport. In this article, we study the transport behavior of a quantum particle in weak dynamic disorder. Based on Wigner representation, we obtain the radiative transfer equation (a linear Boltzmann equation) in the weak d...

The diffusive (or semiconvection) regime of double-diffusive convection (DDC) is widespread in the polar oceans, generating ‘‘staircases’’ consisting of high-gradient interfaces of temperature and salinity separated by convectively mixed layers. Using two-dimensional direct numerical simulations, support is provided for a previous theory that rotation can influence DDC heat fluxes when the thic...

An analysis of diffusion in a supercooled liquid based solely in the density of diffusive directions and the value of energy barriers shows how the potential energy landscape (PEL) approach is capable of explaining the a and b relaxations and the fragility of a glassy system. We find that the b relaxation is directly related to the search for diffusive directions. Our analysis shows how in stro...

Phase-field-crystal (PFC) models constitute a field theoretical approach to solidification, melting, and related phenomena at atomic length and diffusive time scales. One of the advantages of these models is that they naturally contain elastic excitations associated with strain in crystalline bodies. However, instabilities that are diffusively driven towards equilibrium are often orders of magn...

A fractional time derivative is introduced into Burger’s equation to model losses of nonlinear waves. This term amounts to a time convolution product, which greatly penalizes the numerical modeling. A diffusive representation of the fractional derivative is adopted here, replacing this nonlocal operator by a continuum of memory variables that satisfy local-in-time ordinary differential equation...

The exchange of diffusive metabolites is known to control the spatial patterns formed by microbial populations, as revealed by recent studies in the laboratory. However, the matrices used, such as agarose pads, lack the structured geometry of many natural microbial habitats, including in the soil or on the surfaces of plants or animals. Here we address the important question of how such geometr...

In the present study, the onset of double diffusive reaction-convection in a uid layer with viscous fluid, heated and salted from below subject to chemical equilibrium on the boundaries, has been investigated. Linear and nonlinear stability analysis have been performed. For linear analysis normal mode technique is used and for nonlinear analysis minimal representation of truncated Fourier serie...