相关论文: (In-)Stability and Stabilisation of QNL-Type Atomi…

We present a practical implementation of an energy-based atomistic-to-continuum (a/c) coupling scheme without ghost forces, and numerical tests evaluating its accuracy relative to other types of a/c coupling schemes.

This paper addresses the problem of consistent energy-based coupling of atomistic and continuum models of materials, limited to zero-temperature statics of simple crystals. It has been widely recognized that the most practical coupled…

In this paper we construct energy based numerical methods free of ghost forces in three dimensional lattices arising in crystalline materials. The analysis hinges on establishing a connection of the coupled system to conforming finite…

We present a comprehensive error analysis of two prototypical atomistic-to-continuum coupling methods of blending type: the energy-based and the force-based quasicontinuum methods. Our results are valid in two and three dimensions, for…

Inspired by the blending method developed by [P. Seleson, S. Beneddine, and S. Prudhome, \emph{A Force-Based Coupling Scheme for Peridynamics and Classical Elasticity}, (2013)] for the nonlocal-to-local coupling, we create a symmetric and…

We combine the ideas of atomistic/continuum energy blending and ghost force correction to obtain an energy-based atomistic/continuum coupling scheme which has, for a range of benchmark problems, the same convergence rates as optimal…

Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementing a consistent coupling energy. They are also the only known…

We present a new variant of the geometry reconstruction approach for the formulation of atomistic/continuum coupling methods (a/c methods). For multi-body nearest-neighbour interactions on the 2D triangular lattice, we show that patch test…

A sharp stability analysis of atomistic-to-continuum coupling methods is essential for evaluating their capabilities for predicting the formation and motion of lattice defects. We formulate a simple one-dimensional model problem and give a…

For a general class of atomistic-to-continuum coupling methods, coupling multi-body interatomic potentials with a P1-finite element discretisation of Cauchy--Born nonlinear elasticity, this paper adresses the question whether patch test…

We investigate the classical stability of two coupled scalar fields with opposite-sign kinetic terms evolving in 1+1 dimensional Minkowski spacetime. In the first part, we characterise unquenched ghostly interactions and present numerical…

We investigate the problems of ghosts and stability in the framework of asymptotical safe theory of gravity in the Minkowski background. Within one loop corrections, we obtain explicitly the constraints on the coupling parameters. Applying…

Ghost fields have reemerged in a handful of phenomenologically motivated cosmological and particle physics scenarios, and most recently in a cyclic mechanism to address the fine-tuning of gauge couplings in the standard model. We study the…

We present a new method to analytically prove global stability in ghost-ridden dynamical systems. Our proposal encompasses all prior results and consequentially extends them. In particular, we show that stability can follow from a conserved…

Very few works exist to date on development of a consistent energy-based coupling of atomistic and continuum models of materials in more than one dimension. The difficulty in constructing such a coupling consists in defining a coupled…

We formulate an atomistic-to-continuum coupling method based on blending atomistic and continuum forces. Our precise choice of blending mechanism is informed by theoretical predictions. We present a range of numerical experiments studying…

We explore the nonlinear dynamics of classical field theories containing ghost degrees of freedom, focusing on two coupled scalar fields with opposite kinetic terms in (1+1) and (2+1) dimensional Minkowski spacetime. Using a spacetime…

Atomistic/continuum coupling method is a class of multiscale computational method for the efficient simulation of crystalline defects. The recently developed blended ghost force correction (BGFC) method combines the efficiency of blending…

We review results on small-data global stability and highlight their applicability to classical interacting scalar fields with opposite-sign kinetic terms (ghosts). Further, we present a one-parameter family of numerical scattering…

The most essential concept in concurrent multiscale methods involving atomistic-continuum coupling is how to define the relation between atomistic and continuum regions. A well-known coupling method that has been frequently employed in…