Related papers: Second-order diffusion limit for the phonon transp…
Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE, which in certain…
We theoretically study the optical properties of an InAs/GaAs quantum dot (QD) near the area of the second-order resonance between an electron confined in the QD and two longitudinal optical phonons. We present the absorption spectra of an…
This paper presents hybrid numerical techniques for solving the Boltzmann transport equation formulated by means of low-order equations for angular moments of the angular flux. The moment equations are derived by the projection operator…
We present a novel approach to solve the advection-diffusion equation under arbitrary transporting fields using a quantum-inspired 'Schrodingerisation' technique for Hamiltonian simulation. Although numerous methods exist for solving…
As more and more numerical and analytical solutions to the linear neutron transport equation become available, verification of numerical results is increasingly important. This presentation concerns the development of another benchmark for…
We study forward and inverse problems for a semilinear radiative transport model where the absorption coefficient depends on the angular average of the transport solution. Our first result is the well-posedness theory for the transport…
We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…
A solution is developed for a convection-diffusion equation describing chemical transport with sorption, decay, and production. The problem is formulated in a finite domain where the appropriate conservation law yields Robin conditions at…
Within a phonon-assisted resonance level model we develop a self-consistent procedure for calculating electron transport currents in molecular junctions with intermediate to strong electron-phonon interaction. The scheme takes into account…
Quantum diffusion of soliton microcombs has long been recognized as their fundamental noise limit. Here we surpass such limit by utilizing dispersive wave dynamics in multimode microresonators. Through the recoil force provided by these…
The radiation (reaction, Robin) boundary condition for the continuum diffusion equation is widely used in chemical and biological applications to express reactive boundaries. The underlying trajectories of the diffusing particles are…
We have investigated the effect on phonon energy transport in mesoscopic systems and the reduction in the thermal conductance in the quantum limit due to phonon scattering by surface roughness using full 3-dimensional elasticity theory for…
We calculate the electron-phonon interaction coefficients for surface acoustic waves and for phonons in free standing quantum wells. These are used to derive the inelastic current through a double quantum dot caused by spontaneous emission…
We revisit the instability properties of the recovery of the absorption coefficient for the radiative transfer equation in the diffusive regime. To this end, we develop a rather robust framework building on [Koch-R\"uland-Salo, 2021] which…
Raman spectra obtained by the inelastic scattering of light by crystalline solids contain contributions from first-order vibrational processes (e.g. the emission or absorption of one phonon, a quantum of vibration) as well as higher-order…
In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic…
Condition imposed on the nonlinear terms of a nonlinear diffusion equation with {R}obin boundary condition is the main focus of this paper. The degenerate parabolic equations, such as the {S}tefan problem, the {H}ele--{S}haw problem, the…
Transport of spherical Brownian particles of finite size possessing radii through narrow channels with varying cross-section area is considered. Applying the so-called Fick-Jacobs approximation, i.e. assuming fast equilibration in…
We consider the Robin problem for a uniformly elliptic divergence operator with measure data on the right-hand side of the equation and an absorption term on the boundary involving blowing up terms. We prove the existence of a positive…
This article presents a complete second order theory for a large class of geometric functionals on homogeneous Poisson input. In particular, the results don't require the existence of a radius of stabilisation. Hence they can be applied to…