Related papers: Characteristic Sweeps and Source Iteration for Cha…
This paper investigates the simultaneous identification of a spatially dependent potential and the initial condition in a subdiffusion model based on two terminal observations. The existence, uniqueness, and conditional stability of the…
The transport of sputtered aluminum inside a multi frequency capacitively coupled plasma chamber is simulated by means of a kinetic test multi-particle approach. A novel consistent set of scattering parameters obtained for a modified…
In this work, we propose an easy-to-implement fixed-point algorithm for reconstructing a space-time dependent source in a subdiffusion model from lateral boundary measurements. The numerical scheme combines a Galerkin finite element method…
While the Boltzmann transport equation can accurately model transport problems with highly forward-peaked scattering, obtaining its solution can become arbitrarily slow due to near-unity spectral radius associated with source iteration.…
The diagrammatic formalism and transport equation are conventionally considered as separate but complementary techniques to tackle the impurity scattering effect. To compare with the previous studies from the gauge-invariant kinetic…
We consider the problem of electron transport across a quasi-one-dimensional disordered multiply-scattering medium, and study the statistical properties of the electron density inside the system. In the physical setup that we contemplate,…
We consider point sources in hyperbolic equations discretized by finite differences. If the source is stationary, appropriate source discretization has been shown to preserve the accuracy of the finite difference method. Moving point…
We design a numerical scheme for transport equations with oscillatory periodic scattering coefficients. The scheme is asymptotic preserving in the diffusion limit as Knudsen number goes to zero. It also captures the homogenization limit as…
We present a stabilised finite element method for modelling proton transport in tissue, incorporating both inelastic energy loss and elastic angular scattering. A key innovation is a positivity-preserving formulation that guarantees…
For chaotic cavities with scattering leads attached, transport properties can be approximated in terms of the classical trajectories which enter and exit the system. With a semiclassical treatment involving fine correlations between such…
We show that by integrating out the electric field and incorporating proper boundary conditions, a semiclassical Boltzmann equation can describe electron transport properties, continuously from the diffusive to ballistic regimes. General…
We develop a theory of optimal transport for stationary random measures with a focus on stationary point processes and construct a family of distances on the set of stationary random measures. These induce a natural notion of interpolation…
Using the tools of random matrix theory we develop a statistical analysis of the transport properties of thermoelectric low-dimensional systems made of two electron reservoirs set at different temperatures and chemical potentials, and…
We derive iterative scaling algorithms of the Sinkhorn-Knopp (SK) type for constrained optimal transport. The constraints are in the form of prior-imposed zeroes in the transport plan. Based on classical Bregman arguments, we prove…
The chaotic scattering theory is here extended to obtain escape-rate expressions for the transport coefficients appropriate for a simple classical fluid, or for a chemically reacting system. This theory allows various transport coefficients…
A partial differential equation governing the global evolution of the joint probability distribution of an arbitrary number of local flow observations, drawn randomly from a control volume, is derived and applied to examples involving…
We derive the transport properties of a quantum dot subject to a source-drain bias voltage at zero temperature and magnetic field. Using the Scattering Bethe Anstaz, a generalization of the traditional Thermodynamic Bethe Ansatz to open…
In this paper we generalise our previous results [1] concerning scattering on the exterior of collapsing dust clouds to the charged case, including in particular the extremal case. We analyse the energy boundedness of solutions $\phi$ to…
We investigate nonlinear transport properties of quantum conductors in response to both electrical and thermal driving forces. Within scattering approach, we determine the nonequilibrium screening potential of a generic mesoscopic system…
Exact solutions of the Schr\"odinger equation for the Coulomb potential are used in the scope of both stationary and time-dependent scattering theories in order to find the parameters which define regularization of the Rutherford…