Related papers: A Projection-based Reduced-order Method for Electr…
To describe non-equilibrium transport processes in a quantum device with infinite baths, we propose to formulate the problems as a reduced-order problem. Starting with the Liouville-von Neumann equation for the density-matrix, the…
This paper presents a reduced order approach for transient modeling of multiple moving objects in nonlinear crossflows. The Proper Orthogonal Decomposition method and the Galerkin projection are used to construct a reduced version of the…
We develop a linear theory of electron transport for a system of two identical quantum wires in a wide range of the wire length L, unifying both the ballistic and diffusive transport regimes. The microscopic model, involving the interaction…
In this work we focus on reduced order modelling for problems for which the resulting reduced basis spaces show a slow decay of the Kolmogorov $n$-width, or, in practical calculations, its computational surrogate given by the magnitude of…
This paper considers the reduction of the Langevin equation arising from bio-molecular models. To facilitate the construction and implementation of the reduced models, the problem is formulated as a reduced-order modeling problem. The…
While the vast majority of calculations reported on molecular conductance have been based on the static non-equilibrium Green's function formalism combined with density functional theory, in recent years a few time-depedent approaches to…
This work studies reduced order modeling (ROM) approaches to speed up the solution of variational data assimilation problems with large scale nonlinear dynamical models. It is shown that a key requirement for a successful reduced order…
In this paper, we present a numerical method, based on iterative Bregman projections, to solve the optimal transport problem with Coulomb cost. This is related to the strong interaction limit of Density Functional Theory. The first idea is…
This work addresses model order reduction for complex moving fronts, which are transported by advection or through a reaction-diffusion process. Such systems are especially challenging for model order reduction since the transport cannot be…
The evaluation of electrostatic energy for a set of point charges in a periodic lattice is a computationally expensive part of molecular dynamics simulations (and other applications) because of the long-range nature of the Coulomb…
We present a partitioned Model Order Reduction method for multiphysics problems, that is based on a semi-implicit treatment of the coupling conditions, and on a projection scheme. The proposed Reduced Order Method is based on the Proper…
By splitting the Coulomb interaction into long-range and short-range components, we decompose the energy of a quantum electronic system into long-range and short-range contributions. We show that the long-range part of the energy can be…
We study the connection between heat transport properties of systems coupled to different thermal baths in two separate regions and their underlying nonequilibrium dynamics. We consider classical systems of interacting particles that may…
Fluid-structure interactions are central to many bio-molecular processes, and they impose a great challenge for computational and modeling methods. In this paper, we consider the immersed boundary method (IBM) for biofluid systems, and to…
Reduced order models play an important role in the design, optimization and control of dynamical systems. In recent years, there has been an increasing interest in the application of data-driven techniques for model reduction that can…
In this work, we develop reduced order models (ROMs) to predict solutions to a multiscale kinetic transport equation with a diffusion limit under the parametric setting. When the underlying scattering effect is not sufficiently strong, the…
This work proposes an adaptive structure-preserving model order reduction method for finite-dimensional parametrized Hamiltonian systems modeling non-dissipative phenomena. To overcome the slowly decaying Kolmogorov width typical of…
A first-principles approach to describe electron dynamics in open quantum systems driven far from equilibrium via external time-dependent stimuli is introduced. Within this approach, the driven Liouville von Neumann methodology is used to…
We propose a new method for simulating electron dynamics in open quantum systems out of equilibrium, using a finite atomistic model. The proposed method is motivated by the intuitive and practical nature of the driven Liouville von-Neumann…
We develop a detailed theoretical investigation of the effect of Coulomb interaction on electron transport in arrays of chaotic quantum dots and diffusive metallic wires. Employing the real time path integral technique we formulate a new…