Related papers: Diffusion across semi-permeable barriers: spectral…
The distributions of the angular transmission coefficient and of the total transmission are calculated for multiple scattered waves. The calculation is based on a mapping to the distribution of eigenvalues of the transmission matrix. The…
To study the ballistic transport of charge carriers in nano-structured quantum devices, a highly efficient numerical technique is developed, which provides continuous transmission spectra for arbitrarily complex potential geometries in two…
We discuss a model in which a quantum particle passes through $\delta$ potentials arranged in an increasingly sparse way. For infinitely many barriers we derive conditions, expressed in terms ergodic properties of wave function phases,…
We present algorithms for solving spatially nonlocal diffusion models on the unit sphere with spectral accuracy in space. Our algorithms are based on the diagonalizability of nonlocal diffusion operators in the basis of spherical harmonics,…
Because the desire to explore opaque materials is ordinarily frustrated by multiple scattering of waves, attention has focused on the transmission matrix of the wave field. This matrix gives the fullest account of transmission and…
We use direct numerical simulations to compute turbulent transport coefficients for passive scalars in turbulent rotating flows. Effective diffusion coefficients in the directions parallel and perpendicular to the rotations axis are…
Vacancy-mediated diffusion in multi-principal element alloys (MPEAs) remains poorly understood. Existing computational methods face challenges in connecting electronic structure to macroscopic transport coefficients due to the large number…
We introduce a methodology for performing parameter inference in high-dimensional, non-linear diffusion processes. We illustrate its applicability for obtaining insights into the evolution of and relationships between species, including…
Diffusions are a fundamental class of models in many fields, including finance, engineering, and biology. Simulating diffusions is challenging as their sample paths are infinite-dimensional and their transition functions are typically…
We study molecular diffusion in linear nanopores with different types of roughness in the so-called Knudsen regime. Knudsen diffusion represents the limiting case of molecular diffusion in pores, where mutual encounters of the molecules…
Using an operator-theoretic framework in a Hilbert-space setting, we perform a detailed spectral analysis of the one-dimensional Laplacian in a bounded interval, subject to specific non-self-adjoint connected boundary conditions modelling a…
Marginal structural models are a popular method for estimating causal effects in the presence of time-varying exposures. In spite of their popularity, no scalable non-parametric estimator exist for marginal structural models with…
We develop an analytical framework and numerical approach to obtain the coefficient of self-diffusivity for the transport of a rarefied gas in channels in the limit of large Knudsen number. This framework provides a method for determining…
In this paper we study the problem of the numerical calculation (by Monte Carlo Methods) of the effective diffusivity for a particle moving in a periodic divergent-free velocity filed, in the limit of vanishing molecular diffusion. In this…
The equivalent permeability of a randomly cracked porous material is studied using a finite element program in which a four-nodes zero-thickness element is implemented for modelling the cracks. The numerical simulations are performed for…
The analysis of contagion-diffusion processes in metapopulations is a powerful theoretical tool to study how mobility influences the spread of communicable diseases. Nevertheless, many metapopulation approaches use indistinguishable agents…
Transport and acceleration of charged particles in turbulent media is a topic of great interest in space physics and interstellar astrophysics. These processes are dominated by the scattering of particles off magnetic irregularities. The…
We study a porous medium equation, with nonlocal diffusion effects given by an inverse fractional Laplacian operator. We pose the problem in n-dimensional space for all t>0 with bounded and compactly supported initial data, and prove…
The boundaries of waveguides and nanowires have drastic influence on their coherent scattering properties. Designing the boundary profile is thus a promising approach for transmission and band-gap engineering with many applications. By…
We report the first experimental realization of a rod diffusing in a two dimensional obstacle field following the single rod dynamics. We use a silver nanowire as our rod and two types of obstacles: repelling light beams and polymer…