Related papers: Stable Multi-Level Monotonic Eroders
The relativistic Vlasov-Maxwell system describes the evolution of a collisionless plasma. The problem of linear instability of this system is considered in two physical settings: the so-called "one and one-half" dimensional case, and the…
Uniaxial elastomers are characterized by five elastic constants. If their elastic modulus C_5 describing the energy of shear strains in planes containing the anisotropy axis vanishes, they are said to be soft. In spatial dimensions d less…
The asymmetric simple exclusion process (ASEP) is a paradigmatic nonequilibrium many-body system that describes the asymmetric random walk of particles with exclusion interactions in a lattice. Although the ASEP is recognized as an exactly…
We propose a correspondence between certain multiband linear cellular automata - models of computation widely used in the description of physical phenomena - and endomorphisms of certain algebraic unipotent groups over finite fields. The…
The spatial structure, fluctuations as well as all state probabilities of self-organized (steady) states of cellular automata can be found (almost) exactly and {\em explicitly} from their Markovian dynamics. The method is shown on an…
Electrostatic actuators are simple but important switching devices for MEMS applications. Due to the difficulties associated with the electrostatic nonlinearity, precise mathematical description is often hard to obtain for the dynamics of…
We investigate a system of harmonically coupled identical nonlinear constituents subject to noise in different spatial arrangements. For global coupling we find for infinitely many constituents the coexistence of several ergodic components…
The dynamics of rule 54 one-dimensional two-state cellular automaton (CA) are a discrete analog of a space-time dynamics of excitations in nonlinear active medium with mutual inhibition. A cell switches its state 0 to state 1 if one of its…
We are concerned with the nodal set of solutions to equations of the form \begin{equation*} -\Delta u = \lambda_+ \left(u^+\right)^{q-1} - \lambda_- \left(u^-\right)^{q-1} \quad \text{in $B_1$} \end{equation*} where $\lambda_+,\lambda_- >…
The positive rates conjecture states that a one-dimensional probabilistic cellular automaton (PCA) with strictly positive transition rates must be ergodic. The conjecture has been refuted by G\'acs, whose counterexample is a cellular…
We review some recent progresses in study of the 1D strongly correlated electron systems of long range hopping and exchange. The systems are completely integrable, with infinite number of constants of motions. The results of the physical…
Ergodicity breaking is observed in the blockade regime of Rydberg atoms arrays, in the form of low entanglement eigenstates known as scars, which fail to thermalize. The signature of these states persists in periodically driven systems,…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates a class of random dynamical systems, arising from perturbing a one-dimensional piecewise…
In this paper we study the dynamics of 1- and 2- dimensional cellular automata, using a 2-adic representation of the states, we give a simple graphical technique for finding periodic solutions. We also study the continuity properties of the…
The one-dimensional three-state cyclic cellular automaton is a simple spatial model with three states in a cyclic "rock-paper-scissors" prey-predator relationship. Starting from a random configuration, similar states gather in increasingly…
Dynamics of solitons is considered in an extended nonlinear Schr\"odinger equation, including a pseudo-stimulated-Raman-scattering (pseudo-SRS) term (scattering on damping low-frequency waves, third-order dispersion (TOD) and inhomogeneity…
We have developed a simple cellular automata model for nonlinearly coupled phase oscillators which can exhibit many important collective dynamical states found in other synchronizing systems. The state of our system is specified by a set of…
We study the cohesive energy and elastic properties as well as normal modes of the Wigner and bubble crystals of the two-dimensional electron system (2DES) in higher Landau levels. Using a simple Hartree-Fock approach, we show that the…
Electronic properties of amorphous or non-crystalline disordered solids are often modelled by one-particle Schroedinger operators with random potentials which are ergodic with respect to the full group of Euclidean translations. We give a…
An integrable system is a dynamic system characterized by the existence of constants of motion and the existence of algebraic invariants, having an origin in algebraic geometry. In the 1970s, Mumford introduced a new completely integrable…