相关论文: Chip-firing and energy minimization on M-matrices
We propose a kind of Bak-Sneppen dynamics as a general optimization technique to treat magnetic systems. The resulting dynamics shows self-organized criticality with power law scaling of the spatial and temporal correlations. An alternative…
The Maximum Energy Dissipation Principle (MEDP) for dynamics fracture, far from equilibrium, proposed by Slepyan was modified. This modification includes a decoupling between the injected and dissipated energy by adding of a time delay and…
We investigate the energy landscape of the mixed even $p$-spin model with Ising spin configurations. We show that for any given energy level between zero and the maximal energy, with overwhelming probability there exist exponentially many…
Hereditary chip-firing models generalize the Abelian sandpile model and the cluster firing model to an exponential family of games induced by covers of the vertex set. This generalization retains some desirable properties, e.g.…
Connections between the principle of stationary action and optimal control, and between established notions of minimax and viscosity solutions, are combined to describe trajectories of energy conserving systems as solutions of corresponding…
Power distribution in remote communities often depends on off-grid microgrids. In order to address the reliability challenges for these microgrids, we develop a mathematical model for topology design, capacity planning, and operation of…
When applying methods of optimal control to motion planning or stabilization problems, some theoretical or numerical difficulties may arise, due to the presence of specific trajectories, namely, singular minimizing trajectories of the…
We present and discuss a general density-matrix description of energy-dissipation and decoherence phenomena in open quantum systems, able to overcome the intrinsic limitations of the conventional Markov approximation. In particular, the…
We consider the hard-core model on a finite square grid graph with stochastic Glauber dynamics parametrized by the inverse temperature $\beta$. We investigate how the transition between its two maximum-occupancy configurations takes place…
We establish a set of nonequilibrium quantum phase transitions in the Lipkin-Meshkov-Glick model under monochromatic modulation of the inter-particle interaction. We show that the external driving induces a rich phase diagram that…
We study energy minimization for pair potentials among periodic sets in Euclidean spaces. We derive some sufficient conditions under which a point lattice locally minimizes the energy associated to a large class of potential functions. This…
Mixtures of bare atomic nuclei on a nearly uniform degenerate electron background are a realistic model of matter in the interior of white dwarfs. Despite tremendous progress in understanding their phase diagrams achieved mainly via…
We model the stabilization of clusters and lattices of cuboidal particles with long-ranged magnetic dipolar and short-ranged surface interactions. Two realistic systems were considered: one with magnetization orientated in the [001]…
Damped-driven systems are ubiquitous in engineering and science. Despite the diversity of physical processes observed in a broad range of applications, the underlying instabilities observed in practice have a universal characterization…
Sandier and Serfaty studied the one-dimensional Log-gas model, in particular they gave a crystallization result by showing that the one-dimensional lattice $\mathbb{z}$ is a minimizer for the so-called renormalized energy which they…
This article presents a new numerical scheme for the discretization of dissipative particle dynamics with conserved energy. The key idea is to reduce elementary pairwise stochastic dynamics (either fluctuation/dissipation or thermal…
Self-organised critical avalanche models are a class of cellular automata that, despite their simplicity, can be applied to the modeling of solar (and stellar) flares and generate robust power-law distributions in event size measures.…
We study the capacity of entanglement in the microcanonical ensemble for an effectively additive bipartite system. Using typicality and the block structure of the microcanonical reduced state, we show that in the thermodynamic regime the…
A two-dimensional atomic mass spring system is investigated for critical fracture loads and its crack path geometry. We rigorously prove that, in the discrete-to-continuum limit, the minimal energy of a crystal under uniaxial tension leads…
Particles interacting through long-range attraction and short-range repulsion given by power-laws have been widely used to model physical and biological systems, and to predict or explain many of the patterns they display. Apart from rare…