Related papers: Dynamics of one-dimensional spin models under the …
In this work, we study fast time scale dynamic interactions between inverters, synchronous machines, and transmission lines. The overlapping time scales between inverter controls and electromagnetic phenomena idfentified in recent years has…
We study the Lebwohl-Lasher model for systems in which spin are arranged on random graph lattices. At equilibrium our analysis follows the theory of spin-systems on random graphs which allows us to derive exact bifurcation conditions for…
Our understanding of the dynamics of complex networked systems has increased significantly in the last two decades. However, most of our knowledge is built upon assuming pairwise relations among the system's components. This is often an…
In this work we establish conditions which guarantee the existence of (strictly) positive steady states of a nonlinear structured population model. In our framework the steady state formulation amounts to recasting the nonlinear problem as…
We study the spin dynamics of quasi-one-dimensional F=1 condensates both at zero and finite temperatures for arbitrary initial spin configurations. The rich dynamical evolution exhibited by these non-linear systems is explained by…
The structure of interactions in most of animals and human societies can be best represented by complex hierarchical networks. In order to maintain close to optimal functioning both stability and adaptability are necessary. Here we…
We propose a new framework for the study of continuous time dynamical systems on networks. We view such dynamical systems as collections of interacting control systems. We show that a class of maps between graphs called graph fibrations…
We consider here the problem of a "giant spin", with spin quantum number S>>1, interacting with a set of microscopic spins. Interactions between the microscopic spins are ignored. This model describes the low-energy properties of magnetic…
Relaxational processes in ordered phases of one-dimensional Ising models with long-range interactions are investigated by Monte Carlo simulations. Three types of spin model, the pure ferromagnetic, the diluted ferromagnetic, and the spin…
Spin chains can be used to describe a wide range of platforms for quantum computation and quantum information. They enable the understanding, demonstration, and modeling of numerous useful phenomena, such as high fidelity transfer of…
We describe a method for simulating the dynamics of an $S_3$ cosmic string network. We use a lattice Monte Carlo to generate initial conditions for the network, which subsequently is allowed to relax continuously according to a simplified…
We determine limiting equations for large asymmetric `spin glass' networks. The initial conditions are not assumed to be independent of the disordered connectivity: one of the main motivations for this is that allows one to understand how…
We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined…
The evolution of stripe patterns in type-I superconductors subject to a rotating in-plane magnetic field is investigated magneto-optically. The experimental results reveal a very rich and interesting behavior of the patterns. For small…
The low-energy magnetic configurations of artificial frustrated spin chains are investigated using magnetic force microscopy and micromagnetic simulations. Contrary to most studies on two-dimensional artificial spin systems where…
This series of papers models the dynamics of a large set of interacting neurons within the framework of statistical field theory. The system is described using a two-field model. The first field represents the neuronal activity, while the…
The state of quantum systems, their energetics, and their time evolution is modeled by abstract operators. How can one visualize such operators for coupled spin systems? A general approach is presented which consists of several shapes…
We consider a Hubbard-like model of strongly-interacting spinless fermions and hardcore bosons on a square lattice, such that nearest neighbor occupation is forbidden. Stripes (lines of holes across the lattice forming antiphase walls…
Enabling robots to perform complex dynamic tasks such as picking up an object in one sweeping motion or pushing off a wall to quickly turn a corner is a challenging problem. The dynamic interactions implicit in these tasks are critical…
An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have…