In a recent paper we constructed an integrable generalization of the Toda law on the square lattice. We construct other examples of integrable dynamics of Toda type on the square lattice, as well as on the triangular lattice, as nonlinear symmetries of the discrete Laplace equations on square and triangular lattices. We also construct the tau -function formulations and Darboux-Bäcklund transfor...

We develop an atomistic spin-lattice-dynamics model for simulating energy relaxation in magnetic materials. The model explicitly solves equations of motion for the atoms and spins, and includes interaction with electron excitations. We apply the model to simulate the dynamics of propagation of a compressive elastic wave in iron. We find that coupling between the lattice, spin, and electron degr...

We discuss the role and impact of lattice fluid dynamics, namely Lattice Gas Cellular Automata Boltzmann, on general framework Computational Fluid Dynamics.

Dynamics of the nonradiative transition in excited states of localized electrons is studied and clari ed. The nonradiative transition is induced by an o -diagonal interaction between the two states around the potential crossing region. We propose a model for the lattice relaxation by extending the quantum damping theory to a two level system and analyze the transition dynamics numerically. The ...

Discrete lattice systems have had a long and productive history in physics. Examples range from exact theoretical models studied in statistical mechanics to approximate numerical treatments of continuum models. There has, however, been relatively little attention paid to exact lattice models which obey an invertible dynamics: from any state of the dynamical system you can infer the previous sta...

In two previous letters [Velarde et al., 2005, 2006] a new form of electric conduction mediated by solitons was shown to be possible in an anharmonic one-dimensional (1D) lattice. In the first, a strictly classical approach was adopted hence treating the lattice dynamics classically and the electron-(ion) lattice interaction with classical electrodynamics. In the second, the electron-lattice in...

We have studied the dynamics of large vortex lattices in a dilute-gas Bose-Einstein condensate. While undisturbed lattices have a regular hexagonal structure, large-amplitude quadrupolar shape oscillations of the condensate are shown to induce a wealth of nonequilibrium lattice dynamics. When exciting an m=-2 mode, we observe shifting of lattice planes, changes of lattice structure, and sheetli...

We study fermions that are gauge coupled to a cavity mode via Raman-assisted hopping in a one-dimensional lattice. For an infinite lattice, we find a superradiant phase with an infinitesimal pumping threshold which induces a directed particle flow. We explore the fate of this flow in a finite lattice with boundaries, studying the nonequilibrium dynamics including fluctuation effects. The short-...

The current status of some nucleon isovector observables, the vector charge, gV , axial charge, gA, quark momentum fraction, 〈x〉u−d , and quark helicity fraction, 〈x〉∆u−∆d , calculated using recent RBC/UKQCD 2+1-flavor dynamical domain-wall fermions (DWF) lattice QCD ensembles are reported: with Iwasaki gauge action at inverse lattice spacing, a−1, of about 1.7 GeV, linear lattice extent, L, of...

We present a simplified lattice model to study calcium dynamics in the endoplasmic reticulum membrane. Calcium channels and calcium ions are placed in two interpenetrating square lattices which are connected in two ways: (i) via calcium release and (ii) because transitions between channel states are calcium dependent. The opening or closing of a channel is a stochastic process controlled by two...