Related papers: Advection-Dispersion Across Interfaces
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
Nature is intrinsically heterogeneous, and remarkable phenomena can only be observed in the presence of intrinsically nonlinear heterogeneities. Spontaneous pattern formation in nature has fascinated humankind for centuries, and the…
We show global well-posedness and exponential stability of equilibria for a general class of nonlinear dissipative bulk-interface systems. They correspond to thermodynamically consistent gradient structure models of bulk-interface…
We analyze the role of the interplay between on-site interaction and inhomogeneous diffusion on the phenomenon of condensation in the zero-range process. We predict a universal phase diagram in the plane of two exponents, respectively…
Density functional theory calculations have been performed to study the structures and energetics of coherent and semicoherent TiC/Fe interfaces. A systematic method for determining the interfacial energy for the semicoherent interface with…
Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated…
The advection-diffusion equation is studied via a global Lagrangian coordinate transformation. The metric tensor of the Lagrangian coordinates couples the dynamical system theory rigorously into the solution of this class of partial…
Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electro-migration. Both continuous and stochastic dynamics are…
Elasticity theory provides an accurate description of the long-wavelength vibrational dynamics of homogeneous crystalline solids, and with supplemental boundary conditions on the displacement field can also be applied to abrupt…
This paper develops a scattering theory for the asymmetric transport observed at interfaces separating two-dimensional topological insulators. Starting from the spectral decomposition of an unperturbed interface Hamiltonian, we present a…
This paper is devoted to the interfacial behaviors of a class of backward forward diffusion convection equations. Under the assumption that the equations have classical solutions in one dimension, we prove that the backward region shrinks…
We consider the transport of conserved charges in spatially inhomogeneous quantum systems with a discrete lattice symmetry. We analyse the retarded two point functions involving the charge and the associated currents at long wavelengths,…
We consider the propagation of a single particle in a random chain, assisted by the coupling to dispersive bosons. Time evolution treated with rate equations for hopping between localized states reveals a qualitative difference between…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…
We consider a spatially homogeneous advection-diffusion equation in which the diffusion tensor and drift velocity are time-independent, but otherwise general. We derive asymptotic expressions, valid at large distances from a steady point…
This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the…
In this paper we study the dispersive properties related to a model of peridynamic evolution, governed by a non local initial value problem, in the cases of two and three spatial dimensions. The features of the wave propagation…
This paper studies spatial patterns formed by proximate population migration driven by real wage gradients and other idiosyncratic factors. The model consists of a tractable core-periphery model incorporating a quasi-linear log utility…
Insoluble surfactants adsorbed at liquid-liquid or gas-liquid interfaces alter interfacial tension, leading to variations in the normal stress jump and generating tangential Marangoni stresses that can dramatically affect the flow dynamics.…
The study of diffusion in Hamiltonian systems has been a problem of interest for a number of years. In this paper we explore the influence of self-consistency on the diffusion properties of systems described by coupled symplectic maps.…