Related papers: Green's function-based control-oriented modeling o…
The electromagnetic Green's function is a crucial ingredient for the theoretical study of modern photonic quantum devices, but is often difficult or even impossible to calculate directly. We present a numerically efficient framework for…
We introduce a two-phase approximation method designed to resolve singularities in three-dimensional harmonic Dirichlet problems. The approach utilizes the classical Green's function representation, decomposing the function into its…
We discuss Euclidean Green functions on product manifolds P=NxM. We show that if M is compact then the Euclidean field on P can be approximated by its zero mode which is a Euclidean field on N. We estimate the remainder of this…
A new continuous contact force model for contacting problems with regular or irregular contacting surfaces and energy dissipations in multibody systems is presented and discussed in this work. The model is developed according to Hertz law…
Controlling the shape of deformable linear objects using robots and constraints provided by environmental fixtures has diverse industrial applications. In order to establish robust contacts with these fixtures, accurate estimation of the…
An accurate expression of the kinetic energy density of an electronic distribution in terms of the single particle reduced density matrix for atomic and molecular systems is a long-standing problem in electron structure theory. Existing…
In this paper, we consider the nonlinear doubly singular boundary value problems $(p(x)y'(x))'+ q(x)f(x,y(x))=0,~0<x<1$ with Dirichlet/Neumann boundary conditions at $x=0$ and Robin type boundary conditions at $x=1$. Due to the presence of…
We construct an expression for the Green function of a differential operator satisfying nonlocal, homogeneous boundary conditions starting from the fundamental solution of the differential operator. This also provides the solution to the…
We develop an immersed-boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a…
The Green-function technique, termed the irreducible Green functions (IGF) method, that is a certain reformulation of the equation-of motion method for double-time temperature dependent Green functions is presented. This method was…
We present functional forms allowing a broader range of analytic solutions to common economic equilibrium problems. These can increase the realism of pen-and-paper solutions or speed large-scale numerical solutions as computational…
This introduction to Green's functions is based on their role as kernels of differential equations. The procedures to construct solutions to a differential equation with an external source or with an inhomogeneity term are put together to…
We present a formulation of feedback in quantum systems in which the best estimates of the dynamical variables are obtained continuously from the measurement record, and fed back to control the system. We apply this method to the problem of…
This paper presents a mixed basis approach for Laplace eigenvalue problems, which treats the boundary as a perturbation of the free Laplace operator. The method separates the boundary from the volume via a generic function that can be…
The construction of feedback-like control fields for a kinetic model in phase space is investigated. The purpose of these controls is to drive an initial density of particles in the phase space to reach a desired cyclic trajectory and…
We derive the Green's functions (concentrated force and couple in an infinite space) for the isotropic planar relaxed micromorphic model. Since the relaxed micromorphic model particularises into the microstretch, Cosserat (micropolar),…
We derive an exact closed-form representation for the Euclidean thermal Green function of the two-dimensional (2D) free massless scalar field in coordinate space. This can be interpreted as the real part of a complex analytic function of a…
A simple model of noninteracting electrons with a separable one-body potential is used to discuss the possible pole structure of single particle Green's functions for fermions on unphysical sheets in the complex frequency plane as a…
This paper deals with the numerical computation of null controls for the linear heat equation. The goal is to compute approximations of controls that drive the solution from a prescribed initial state to zero at a given positive time. In…
A novel method for control of dynamical systems, proposed in the paper, ensures an output signal belonging to the given set at any time. The method is based on a special change of coordinates such that the initial problem with given…