Related papers: Atomistic-to-Continuum Coupling Approximation of a…
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…
We propose a toy-model theory, that mimics various characteristic features of quantum mechanics. Unlike the toy-models previously studied in the literature, our toy-model allows for an observer to have a full knowledge of a system's real…
We present a coupled atomistic-continuum method for the modeling of defects and interface dynamics of crystalline materials. The method uses atomistic models such as molecular dynamics near defects and interfaces, and continuum models away…
We investigate a number of simple toy models to explore interesting relationships between dynamics and typicality. We start with an infinite model that has been proposed as an illustration of how non-ergodic dynamics can produce interesting…
We extend our previous analysis of the toy model that mimics the mode coupling theory of supercooled liquids and glass transitions to the out of equilibrium dynamics. We derive a self-consistent set of equations for correlation and response…
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…
A toy model is proposed for four dimensional non-abelian gauge theories coupled to a large number of fermionic degrees of freedom. As the number of flavors is varied the gauge theory may be confining, walking or conformal. The toy model…
We study an atomistic model that describes the microscopic formation of material voids inside elastically stressed solids under an additional curvature regularization at the discrete level. Using a discrete-to-continuum analysis, by means…
Classical atomistic simulations based on interatomic potentials resolve lattice instabilities, defect nucleation, and microstructure evolution with high fidelity, but their accessible system sizes remain far below those required for…
We present a multiscale atomistic-to-continuum method for ionic crystals with defects. Defects often play a central role in ionic and electronic solids, not only to limit reliability, but more importantly to enable the functionalities that…
Atomistic-continuum multiscale modelling is becoming an increasingly popular tool for simulating the behaviour of materials due to its computational efficiency and reliable accuracy. In the case of ferromagnetic materials, the atomistic…
We present a comprehensive a priori error analysis of a practical energy based atomistic/continuum coupling method (Shapeev, arXiv:1010.0512) in two dimensions, for finite-range pair-potential interactions, in the presence of vacancy…
In order to better understand quantum field theory we present some toy models on finite dimensional Hilbert spaces. We discuss how these models converge to a discrete spacetime version of quantum field theory. We first define toy fermion,…
Models in which causation arises from higher level structures as well as from microdynamics may be relevant to unifying quantum theory with classical physics or general relativity. They also give a way of defining a form of panprotopsychist…
An exact solution of the problem of two-atom one- and two-mode Jaynes-Cummings model with intensity-dependent coupling is presented. Asymptotic solutions for system state vectors are obtained in the approximation of large initial coherent…
Cosmological models can be studied effectively using dynamical systems techniques. Starting from Brown's formulation of the variational principle for relativistic fluids, we introduce new types of couplings involving a perfect fluid, a…
A local, deterministic toy model for quantum mechanics is introduced and discussed. It is demonstrated that, when averaged over the hidden variables, the model produces the same predictions as quantum mechanics. In the model considered…
A new class of matching condition between the atomistic and continuum regions is presented for the multi-scale modeling of crystals. They ensure the accurate passage of large scale information between the atomistic and continuum regions and…
We discuss the properties of the effective dipolar interaction for two particles tightly confined along a one-dimensional tube, stressing the emergence of a single dipolar-induced resonance in a regime for which two classical dipoles would…
In this note we discuss a toy model in which the value of the effective cosmological constant is associated with a symmetry properties of the vacuum background solution and defined by the model parameter associated with a scalar field…