Related papers: Localisation for a line defect in an infinite squa…
We examine theoretically and experimentally the localized %and extended electrical modes existing in a bi-inductive electrical lattice containing a bulk or a surface capacitive impurity. By means of the formalism of lattice Green's…
We study infinite resistor networks perturbed by line defects, in which the resistances are periodically modified along a single line. Using the Sherman-Morrison identity applied to the reciprocal-space representation of the lattice Green's…
Computing the atomic geometry of lattice defects--point defects, dislocations, crack tips, surfaces, or boundaries--requires an accurate coupling of the local strain field to the long-range elastic field. Periodic boundary conditions used…
This paper develops a finite-difference analogue of the boundary integral/element method for the numerical solution of two-dimensional exterior scattering from scatterers of arbitrary shapes. The discrete fundamental solution, known as the…
A high-frequency asymptotic scheme is generated that captures the motion of waves within discrete hexagonal and honeycomb lattices by creating continuum homogenised equations. The accuracy of these effective medium equations in describing…
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…
Efficient computation of lattice defect geometries such as point defects, dislocations, disconnections, grain boundaries, interfaces and free surfaces requires accurate coupling of displacements near the defect to the long-range elastic…
We deduce the dynamic frequency-domain-lattice Green's function of a linear chain with properties (masses and next-neighbor spring constants) of exponential spatial dependence. We analyze the system as discrete chain as well as the…
Geometrical disorder is present in many physical situations giving rise to eigenvalue problems. The simplest case of diffusion on a random lattice with fluctuating site connectivities is studied analytically and by exact numerical…
The capacitance between arbitrary nodes in perfect infinite networks of identical capacitors is studied. We calculate the capacitance between the origin and the lattice site (l,m)for an infinite linear chain, and for an infinite square…
We investigate the local density of states and Friedel oscillation in graphene around a well localized impurity in Born approximation. In our analytical calculations Green's function technique has been used taking into account both the…
Lattice Green functions appear in lattice gauge theories, in lattice models of statistical physics and in random walks. Here, space coordinates are treated as parameters and series expansions in the mass are obtained. The singular points in…
We analyze random resistor networks through a study of lattice Green's functions in arbitrary dimensions. We develop a systematic disorder perturbation expansion to describe the weak disorder regime of such a system. We use this formulation…
We examine a one-dimensional linear waveguide array containing a single saturable waveguide. By using the formalism of lattice Green functions, we compute in closed form the localized mode and the transmission across the impurity in closed…
Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…
Quenched disorder in a solid state system can result in Anderson localization, where electrons are exponentially localized and the system behaves like an insulator. By solving exactly a disordered electronic lattice model out of…
The asymptotic completeness of a set of the eigenmodes of an open system with increasing number of modes enables an accurate calculation of the system response in terms of these modes. Using the exact eigenmodes, such completeness is…
This paper examines the propagation of time-harmonic waves in a two-dimensional triangular lattice with a lattice constant $a = 1$. The sources are positioned along line segments within the lattice. Specifically, we investigate the discrete…
In this paper we derive general relations for the band-structure of an array of quantum dots and compute its transport properties when connected to two perfect leads. The exact lattice Green's functions for the perfect array and with an…
We use a lattice Green function approach to study the stationary modes of a linear/nonlinear (Kerr) impurity embedded in a periodic one-dimensional lattice where we replace the standard discrete Laplacian by a fractional one. The energies…