ﻻ يوجد ملخص باللغة العربية
Long-range interactions play a central role in electron transport. At the same time, they present a challenge for direct computer simulations, since sufficiently large portions of the bath have to be included in the computation to accurately compute the Coulomb potential. This article presents a reduced-order approach, by deriving an open quantum model for the reduced density-matrix. To treat the transient dynamics, the problem is placed in a reduced-order framework. The dynamics, described by the Liouville von Neumann equation, is projected to subspaces using a Petrov-Galerkin projection. In order to recover the global electron density profile as a vehicle to compute the Coulomb potential, we propose a domain decomposition approach, where the computational domain also includes segments of the bath that are selected using logarithmic grids. This approach leads to a multi-component self-energy that enters the effective Hamiltonian. We demonstrate the accuracy of the reduced model using a molecular junction built from a Lithium chains.
The Kolmogorov $n$-width of the solution manifolds of transport-dominated problems can decay slowly. As a result, it can be challenging to design efficient and accurate reduced order models (ROMs) for such problems. To address this issue, we propose
In this paper, we develop a simplified hybrid weighted essentially non-oscillatory (WENO) method combined with the modified ghost fluid method (MGFM) [28] to simulate the compressible two-medium flow problems. The MGFM can turn the two-medium flow pr
This paper proposes the use of a Spectral method to simulate diffusive moisture transfer through porous materials as a Reduced-Order Model (ROM). The Spectral approach is an a priori method assuming a separated representation of the solution. The met
Ill-posed linear inverse problems appear in many image processing applications, such as deblurring, super-resolution and compressed sensing. Many restoration strategies involve minimizing a cost function, which is composed of fidelity and prior terms
We propose a fast potential splitting Markov Chain Monte Carlo method which costs $O(1)$ time each step for sampling from equilibrium distributions (Gibbs measures) corresponding to particle systems with singular interacting kernels. We decompose the