Related papers: A Generalized Linear Transport Model for Spatially…
From Liouville's equation, a phase-space multi-scale transport equation is systematically derived. The proposed phase-space multi-scale transport equation based on the first principle indicates that the nonlinear stochastic transport is due…
The recently developed concept of spreadability, $\mathcal{S}(t)$, provides a direct link between time-dependent diffusive transport and the microstructure of two-phase media across length scales. We explicitly compute $\mathcal{S}(t)$ for…
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,…
Buoyancy-driven convection in porous media governs heat and mass transport in a wide range of natural and engineered systems, from groundwater aquifers and geothermal reservoirs to carbon storage in geological formations and flows through…
Diffusive transport is a universal phenomenon, throughout both biological and physical sciences, and models of diffusion are routinely used to interrogate diffusion-driven processes. However, most models neglect to take into account the…
In Bayesian applications, there is a huge interest in rapid and accurate estimation of the posterior distribution, particularly for high dimensional or hierarchical models. In this article, we propose to use optimization to solve for a…
This work considers the propagation of high-frequency waves in highly-scattering media where physical absorption of a nonlinear nature occurs. Using the classical tools of the Wigner transform and multiscale analysis, we derive semilinear…
We present a first numerical investigation of the accuracy of the recently proposed {\em non-classical transport equation}. This equation contains an extra independent variable (the path-length $s$), and models particle transport taking…
We study the concentration phenomenon for discrete-time random dynamical systems with an unbounded state space. We develop a heuristic approach towards obtaining exponential concentration inequalities for dynamical systems using an entirely…
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…
We develop the theory of strong stationary duality for diffusion processes on compact intervals. We analytically derive the generator and boundary behavior of the dual process and recover a central tenet of the classical Markov chain theory…
What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals $\tau$ distributed as a power-law $\sim \tau^{-(1+\alpha)};\alpha>0$? Modeling the stochastic process by diffusion and the…
Although one-dimensional systems that exhibit translational symmetry are generally believed to exhibit anomalous heat transport, previous work has shown that the model of coupled rotators on a one-dimensional lattice constitute a possible…
We investigate stochastic interpolation, a recently introduced framework for high dimensional sampling which bears many similarities to diffusion modeling. Stochastic interpolation generates a data sample by first randomly initializing a…
Very recent experiments have discovered that localized light in strongly absorbing media displays intriguing diffusive phenomena. Here we develop a first-principles theory of light propagation in open media with arbitrary absorption…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
Accretion occurs across a large range of scales and physical regimes. Despite this diversity in the physics, the observed properties show remarkably similarity. The theory of propagating fluctuations, in which broad-band variability within…
We discuss transport equations resulting from relativistic diffusions in the proper time. We show that a solution of the transport equation can be obtained from the solution of the diffusion equation by means of an integration over the…
In order to describe large transverse momentum ($p_T$) distributions observed in high energy nucleus-nucleus collisions, a stochastic model in the three dimensional rapidity space is introduced. The fundamental solution of the radial…
Trajectory prediction is a cornerstone in autonomous driving (AD), playing a critical role in enabling vehicles to navigate safely and efficiently in dynamic environments. To address this task, this paper presents a novel trajectory…