Related papers: Material Barriers to Diffusive and Stochastic Tran…
The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The…
In an incoherent metal, transport is controlled by the collective diffusion of energy and charge rather than by quasiparticle or momentum relaxation. We explore the possibility of a universal bound $D \gtrsim \hbar v_F^2/(k_B T)$ on the…
Tortuosity is one of the key parameters describing the geometry and transport properties of porous media. It is defined either as an average elongation of fluid paths or as a retardation factor that measures the resistance of a porous…
We consider invertible linear maps with additive spherical bounded noise. We show that minimal attractors of such random dynamical systems are unique, strictly convex and have a continuously differentiable boundary. Moreover, we present an…
The general problem of two-phase transport in phase-field models is analyzed: the flux of a conserved quantity is driven by the gradient of a potential through a medium that consists of domains of two distinct phases which are separated by…
Chaotic deterministic dynamics of a particle can give rise to diffusive Brownian motion. In this paper, we compute analytically the diffusion coefficient for a particular two-dimensional stochastic layer induced by the kicked Harper map.…
We analyze the transport properties of a neutral tracer in a carrier fluid flowing through percolation-like porous media with spatial correlations. We model convection in the mass transport process using the velocity field obtained by the…
Charge transport in disordered two-dimensional (2D) systems showcases a myriad of unique phenomenologies that highlight different aspects of the underlying quantum dynamics. Electrons in such systems undergo a crossover from ballistic…
We investigate complex boundary conditions of the miscible displacement system in two and three space dimensions with the commonly-used Bear-Scheidegger diffusion-dispersion tensor, which describes, e.g., the porous medium flow processes in…
Thermal energy can be conducted by different mechanisms including by single particles or collective excitations. Thermal conductivity is system-specific and shows a richness of behaviors currently explored in different systems including…
Structures such as waves, jets, and vortices have a dramatic impact on the transport properties of a flow. Passive tracer transport in incompressible two-dimensional flows is described by Hamiltonian dynamics, and, for idealized structures,…
Surface incompressibility, also called inextensibility, imposes a zero-surface-divergence constraint on the velocity of a closed deformable material surface. The well-posedness of the mechanical problem under such constraint depends on an…
The resistivity scaling of metals is a crucial limiting factor for further downscaling of interconnects in nanoelectronic devices that affects signal delay, heat production, and energy consumption. Here, we generalize a commonly considered…
To characterize transport in a deterministic dynamical system is to compute exit time distributions from regions or transition time distributions between regions in phase space. This paper surveys the considerable progress on this problem…
Optimal transport has found widespread applications in signal processing and machine learning. Among its many equivalent formulations, optimal transport seeks to reconstruct a random variable/vector with a prescribed distribution at the…
In this work, a flexible higher-order space-time adaptive finite element approximation of convection-dominated transport with coupled fluid flow is developed and studied. Convection-dominated transport is a challenging subproblem in…
We study the diffusion of a tracer particle driven out-of-equilibrium by an external force and traveling in a dense environment of arbitrary density. The system evolves on a discrete lattice and its stochastic dynamics is described by a…
The flow of fluids within porous rocks is an important process with numerous applications in Earth sciences. Modeling the compaction-driven fluid flow requires the solution of coupled nonlinear partial differential equations that account…
Topological insulators are guaranteed to support metallic surface states on an insulating bulk, and one should thus expect that the electronic transport in these materials is dominated by the surfaces states. Alas, due to the high remaining…
Accurate determination of carrier transport properties in two-dimensional (2D) materials is critical for designing high-performance nano-electronic devices and quantum information platforms. While first-principles calculations effectively…