Related papers: Green's Functions For Random Resistor Networks
We develop a theoretical model to investigate wave propagation in media with random time-varying properties, where temporal fluctuations lead to complex scattering dynamics. Focusing on the ensemble-averaged field, we derive an exact…
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…
The past decade has witnessed the development and success of coarse-grained network models of proteins for predicting many equilibrium properties related to collective modes of motion. Curiously, the results are usually robust towards the…
We introduce a computational scheme for calculating the electronic structure of random alloys that includes electronic correlations within the framework of the combined density functional and dynamical mean-field theory. By making use of…
Complex networks have recently attracted much interest due to their prevalence in nature and our daily lives [1, 2]. A critical property of a network is its resilience to random breakdown and failure [3-6], typically studied as a…
This paper studies the observability radius of network systems, which measures the robustness of a network to perturbations of the edges. We consider linear networks, where the dynamics are described by a weighted adjacency matrix, and…
We generate the perturbative expansion of the single-particle Green's function and related self-energy for a half-filled single-band Hubbard model on a square lattice. We invoke algorithmic Matsubara integration to evaluate single-particle…
In realistic nanoelectronics, disordered impurities/defects are inevitable and play important roles in electron transport. However, due to the lack of effective quantum transport method to do disorder average, the important effects of…
A method to calculate exact Green's functions on lattices in various dimensions is presented. Expressions in terms of generalized hypergeometric functions in one or more variables are obtained for various examples by relating the resolvent…
Numerical calculations based on the recursive Green's functions method in the tight-binding approximation are performed to calculate the dimensionless conductance $g$ in disordered graphene nanoribbons with Gaussian scatterers. The…
Disordered soft materials, such as fibrous networks in biological contexts exhibit a nonlinear elastic response. We study such nonlinear behavior with a minimal model for networks on lattice geometries with simple Hookian elements with…
We elucidate the different mechanisms of wave localisation in disordered finite systems of subwavelength resonators, where the disorder is in the spatial arrangement of the resonators. To do so, we employ the capacitance matrix formalism…
This paper studies network resilience against structured additive perturbations to its topology. We consider dynamic networks modeled as linear time-invariant systems subject to perturbations of bounded energy satisfying specific sparsity…
An accurate simulation of Green's function and self-energy function of non-interacting electrons in disordered graphenes are performed. Fundamental physical quantities such as the elastic relaxation time {\tau}e, the phase velocity vp, and…
Studying the problem of wave propagation in media with resistive boundaries can be made by searching for "resonance modes" or free oscillations regimes. In the present article, a simple case is investigated, which allows one to enlighten…
We study estimates of the Green's function in $\mathbb{R}^d$ with $d \ge 2$, for the linear second order elliptic equation in divergence form with variable uniformly elliptic coefficients. In the case $d \ge 3$, we obtain estimates on the…
We introduce the notion of a network's conduciveness, a probabilistically interpretable measure of how the network's structure allows it to be conducive to roaming agents, in certain conditions, from one portion of the network to another.…
Recent studies have shown that modern deep neural network classifiers are easy to fool, assuming that an adversary is able to slightly modify their inputs. Many papers have proposed adversarial attacks, defenses and methods to measure…
The most profound effect of disorder on the elastic response of solids is the nonaffinity of local displacements whereby the atoms (particles, network junctions) do not simply follow the macroscopic strain, as they do in perfect crystals,…
The Green's function method is recognized to be a very powerful tool for modelling quantum transport in nanoscale electronic devices. As atomistic calculations are generally expensive, numerical methods and related algorithms have been…