Related papers: Lattice Green function for extended defect calcula…
In electromagnetic simulations of magnets and machines one is often interested in a highly accurate and local evaluation of the magnetic field uniformity. Based on local post-processing of the solution, a defect correction scheme is…
A continuum model of crystalline solid equilibrium is presented in which the underlying periodic lattice structure is taken explicitly into account. This model also allows for both point and line defects in the bulk of the lattice and at…
Latent force models (LFM) are principled approaches to incorporating solutions to differential equations within non-parametric inference methods. Unfortunately, the development and application of LFMs can be inhibited by their computational…
One-dimensional, boundary-driven lattice gases with local interactions are studied in the weakly interacting limit. The density profiles and the correlation functions are calculated to first order in the interaction strength for zero-range…
Green's function plays a significant role in both theoretical analysis and numerical computing of partial differential equations (PDEs). However, in most cases, Green's function is difficult to compute. The troubles arise in the following…
Herein we propose a new numerical technique for solving field theories: the large momentum frame (LMF). This technique combines several advantages of lattice gauge theory with the simplicity of front form quantisation. We apply the LMF on…
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…
We present a recursive method to generate the expansion of the lattice Green function of the d-dimensional face-centred cubic (fcc) lattice. We produce a long series for d =7. Then we show (and recall) that, in order to obtain the linear…
In systems removed from equilibrium, intrinsic microscopic fluctuations become correlated over distances comparable to the characteristic macroscopic length over which the external constraint is exerted. In order to investigate this…
In this contribution I discuss a recent proposal of a novel action for lattice gauge theory for finite systems, which accommodates non-periodic spatial boundary conditions. Drawing on the summation-by-parts formulation of finite differences…
We use computer simulation to study the layer-by-layer growth of particle structures in a lattice gas, taking the number of incorporated vacancies as a measure of the quality of the grown structure. By exploiting a dynamic scaling relation…
In this paper we obtain the explicit expression of the Green's function related to a general $n$ order differential equation coupled to non-local linear boundary conditions. In such boundary conditions, a $n$ dimensional parameter…
A major hurdle in understanding the phase diagram of twisted bilayer graphene (TBLG) are the roles of lattice relaxation and electronic structure on isolated band flattening near magic twist angles. In this work, the authors develop an…
Nonequilibrium electronic forces play a central role in voltage-driven phase transitions but are notoriously expensive to evaluate in dynamical simulations. Here we develop a machine learning framework for adiabatic lattice dynamics coupled…
We derive Griffith functionals in the framework of linearized elasticity from nonlinear and frame indifferent energies in brittle fracture via Gamma-convergence. The convergence is given in terms of rescaled displacement fields measuring…
A unique set of correction functions for Flux Reconstruction is presented, with there derivation stemming from proving the existence of energy stability in the Lebesgue norm. The set is shown to be incredibly arbitrary with the only union…
This paper is devoted to show a discrete adaptive finite element approximation result for the isotropic two-dimensional Griffith energy arising in fracture mechanics. The problem is addressed in the geometric measure theoretic framework of…
At high pressure electric discharges typically grow as thin, elongated filaments. In a numerical simulation this large aspect ratio should ideally translate into a narrow, cylindrical computational domain that envelops the discharge as…
The inverse design of nonlocal metasurfaces requires the precise optimization of lattice geometry to engineer spatial dispersion and high-Q resonances. However, gradient-based optimization is frequently bottle-necked by the evaluation of…
In this paper, we present details of the dual fermion (DF) method to study the non-local correction to single site DMFT. The DMFT two-particle Green's function is calculated using continuous time quantum monte carlo (CT-QMC) method. The…