Related papers: Full analysis of the Green's function for a singul…

Discrete Green's functions are the inverses or pseudo-inverses of combinatorial Laplacians. We present compact formulas for discrete Green's functions, in terms of the eigensystems of corresponding Laplacians, for products of regular graphs…

This study handles spatial three-dimensional solution of the nonlinear diffusion equation without particular initial conditions. The functional behavior of the equation and the concentration have been studied in new ways. An auxiliary…

We develop Green's function formalism to describe continuous multi-layered quasi-one-dimensional setups described by piece-wise constant single-particle Hamiltonians. The Hamiltonians of the individual layers are assumed to be quadratic…

The pointwise space-time behavior of the Green's function of the three-dimensional relativistic Boltzmann equation is studied in this paper. It is shown that the Green's function has a decomposition of the macroscopic diffusive waves and…

A stochastic method is described for estimating Green's functions (GF's), appropriate to linear advection-diffusion-reaction transport problems, evolving in arbitrary geometries. By allowing straightforward construction of approximate,…

In this work, we consider an extension to parabolic problems of the variational multiscale method with spectral approximation of the sub-scales. We first discretize in time using a finite difference scheme and second, apply the…

The two-dimensional elastodynamic Green tensor is the primary building block of solutions of linear elasticity problems dealing with nonuniformly moving rectilinear line sources, such as dislocations. Elastodynamic solutions for these…

We derive a closed-form expression for the Green function of linear evolution equations with the Dirichlet boundary condition for an arbitrary region, based on the singular perturbation approach to boundary problems.

We present a numerically efficient technique to evaluate the Green's function for extended two dimensional systems without relying on periodic boundary conditions. Different regions of interest, or `patches', are connected using self energy…

Reflection and transmission of waves in piecewise constant layered media are important in various imaging modalities and have been studied extensively. Despite this, no exact time domain formulas for the Green's functions have been…

The random motion of a Brownian particle confined in some finite domain is considered. Quite generally, the relevant statistical properties involve infinite series, whose coefficients are related to the eigenvalues of the diffusion…

An estimate on the operator norm of an abstract fermionic renormalization group map is derived. This abstract estimate is applied in another paper to construct the thermodynamic Green's functions of a two dimensional, weakly coupled fermion…

Based on a canonical approach and functional-integration techniques, a series expansion of Green's function of a scalar field, in the presence of a medium, is obtained. A series expansion for Lifshitz-energy, in finite-temperature, in terms…

We have calculated the asymptotics of Green's function of the differential equation of nonlinear diffusion in the microscopic range with strong porosity fluctuations in the problem of flow through irregular packed beds for arbitrary space…

These lectures aim to provide a basic introduction to dispersive methods and their modern applications to the phenomenology of the Standard Model at low energy. This approach exploits analyticity properties of Green functions and scattering…

The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…

We propose a finite difference scheme for the numerical solution of a two-dimensional singularly perturbed convection-diffusion partial differential equation whose solution features interacting boundary and interior layers, the latter due…

We introduce a technique to obtain pointwise upper and lower bounds for the Green's function of elliptic operators whose principal part is the Laplacian and that include a drift term diverging near the boundary like a power of the inverse…

We consider recurrent diffusive random walks on a strip. We present constructive conditions on Green functions of finite sub-domains which imply a Central Limit Theorem with polynomial error bound, a Local Limit Theorem, and mixing of…

Perturbation theory using self-consistent Green's functions is one of the most widely used approaches to study many-body effects in condensed matter. On the basis of general considerations and by performing analytical calculations for the…