Related papers: A dynamic high-frequency consistent continualizati…
In this paper, we propose a mass conservative semi-Lagrangian finite difference scheme for multi-dimensional problems without dimensional splitting. The semi-Lagrangian scheme, based on tracing characteristics backward in time from grid…
This study presents a comprehensive framework for constitutive modeling of a frame-invariant fractional-order approach to nonlocal thermoelasticity in solids. For this purpose, thermodynamic and mechanical balance laws are derived for…
We derive and analyze, analytically and numerically, two first-order continuum models to approximate the nonlinear dynamics of granular crystal lattices, focusing specifically on solitary waves, periodic waves, and dispersive shock waves.…
In this work we present a novel structure-preserving scheme for the discretization of the Godunov-Peshkov-Romenski (GPR) model of continuum mechanics written in Lagrangian form. This model admits an extra conservation law for the total…
We propose an experimentally relevant scheme to create stable solitons in a three-dimensional Bose-Einstein condensate confined by a one-dimensional optical lattice, using temporal modulation of the scattering length (through ac magnetic…
The statistical mechanical behavior of weakly nonlinear multimoded optical settings is attracting increased interest during the last few years. The main purpose of this work is to numerically investigate the main factors that affect the…
We apply standard, first-principles calculations to a complete treatment of lattice dynamics in the harmonic approximation. The algorithm makes use of the straightforward ``frozen-phonon'' approach to the calculation of vibrational spectra…
In this letter, we experimentally investigate the directional characteristics of propagating, finite-amplitude wave packets in lattice materials, with an emphasis on the functionality enhancement due to the nonlinearly-generated higher…
A key objective of computational solid state physics is to predict electronic properties of periodic materials. However, electronic structure simulations based on density functional theory fail to predict experimental results if…
Control over the physical properties of materials is ubiquitously required in many fields. One means by which this can be achieved is controlling the internal structure of multi-component materials with an eye to enhancing mechanical…
This paper introduces discrete-holomorphic Perfectly Matched Layers (PMLs) specifically designed for high-order finite difference (FD) discretizations of the scalar wave equation. In contrast to standard PDE-based PMLs, the proposed method…
Pairing between spinless fermions can generate Majorana fermion excitations that exhibit intriguing properties arising from non-local correlations. But simple models indicate that non-local correlation between Majorana fermions becomes…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
The aim of this paper is to show how rapidly decaying RBF Lagrange functions on the spheres can be used to create effective, stable finite difference methods based on radial basis functions (RBF-FD). For certain classes of PDEs this…
We present a simplified model for dynamical diffraction of particles through a periodic thick perfect crystal based on repeated application of a coherent beam splitting unitary at coarse-grained lattice sites. By demanding translational…
Phase separation in a complex fluid with lamellar order has been studied in the case of cold thermal fronts propagating diffusively from external walls. The velocity hydrodynamic modes are taken into account by coupling the…
We propose a compact and robust system architecture for soliton microcomb generation, based on two key techniques: direct fiber coupling using high numerical-aperture polarization-maintaining single-mode fibers (high-NA PMFs) and active…
Motivated by Lazer-Leach type results, we study the existence of periodic solutions for systems of functional-differential equations at resonance with an arbitrary even-dimensional kernel and linear deviating terms involving a general delay…
Multidimensional consistency has emerged as a key integrability property for partial difference equations (P$\Delta$Es) defined on the "space-time" lattice. It has led, among other major insights, to a classification of scalar affine-linear…
Lattice kinetic equations incorporating the effects of external/internal force fields via a shift of the local fields in the local equilibria, are placed within the framework of continuum kinetic theory. The mathematical treatment reveals…