Related papers: Green's function-based control-oriented modeling o…
In this work we calculate the exact Green's function for arbitrary rectangular potentials. Specifically we focus on Green's function for rectangular quantum wells enlarging the knowledge of exact solutions for Green's functions and also…
We discuss a generalization of the dynamical mean field theory (DMFT) for strongly correlated systems close to a Mott transition based on a systematic approximation of the fully irreducible four-point vertex. It is an atomic-limit…
By computing a feedback control via the linear quadratic regulator (LQR) approach and simulating a non-linear non-autonomous closed-loop system using this feedback, we combine two numerically challenging tasks. For the first task, the…
With this paper we provide an effective method to solve a large class of problems related to the electromagnetic behavior of thin superconductors. Here all the problems are reduced to finding the weight functions for the Green integrals…
A key issue in the solution of partial differential equations via integral equation methods is the evaluation of possibly singular integrals involving the Green's function and its derivatives multiplied by simple functions over discretized…
The self-energy method for quantum impurity models expresses the correlation part of the self-energy in terms of the ratio of two Green's functions and allows for a more accurate calculation of equilibrium spectral functions than is…
Successful feedback control of small systems allows for the rectification of thermal fluctuations, converting them into useful energy; however, control itself requires work. This paper emphasizes the fact that the controller is a physical…
Green's function methods within many-body perturbation theory provide a general framework for treating electronic correlations in excited states. Here we investigate the cumulant form of the one-electron Green's function based on the…
We revise critically existing approaches to evaluation of thermodynamic potentials within the Green's function calculations at finite electronic temperatures. We focus on the entropy and show that usual technical problems related to the…
Force-aware grasping is an essential capability for most robots in practical applications. Especially for compliant grippers, such as Fin-Ray grippers, it still remains challenging to build a bidirectional mathematical model that mutually…
A simple transformation converts a solution of a partial differential equation with a Dirichlet boundary condition to a function satisfying a Robin (generalized Neumann) condition. In the simplest cases this observation enables the exact…
Using a conjecture that allows to approach separable-variables conductivity functions, the elements of the Modern Pseudoanalytic Function Theory are used, for the first time, to numerically solve the Dirichlet boundary value problem of the…
The Green's functions for the Laplace equation respectively satisfying the Dirichlet and Neumann boundary conditions on the upper side of an infinite plane with a circular hole are introduced and constructed. These functions enables…
When using boundary integral equation methods, we represent solutions of a linear partial differential equation as layer potentials. It is well-known that the approximation of layer potentials using quadrature rules suffer from poor…
This work presents a new approach to efficiently model the cathode in the moving boundary value problem of electrochemical machining. Until recently, the process simulation with finite elements had the drawback of remeshing required by the…
The aim of this paper is to show certain properties of the Green's functions related to the Hill's equation coupled with different two point boundary value conditions. We will obtain the expression of the Green's function of Neumann,…
This article is devoted to deduce the expression of the Green's function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional…
Neural operators, which learn mappings between the function spaces, have been applied to solve boundary value problems in various ways, including learning mappings from the space of the forcing terms to the space of the solutions with the…
This paper provides a rigorous analysis of boundary element methods for the magnetic field integral equation on Lipschitz polyhedra. The magnetic field integral equation is widely used in practical applications to model electromagnetic…
The objective of this research is to enable safety-critical systems to simultaneously learn and execute optimal control policies in a safe manner to achieve complex autonomy. Learning optimal policies via trial and error, i.e., traditional…