Search results for " Pattern formation"
showing 10 items of 73 documents
Electromagnetically induced switching of ferroelectric thin films
2007
We analyze the interaction of an electromagnetic spike (one cycle) with a thin layer of ferroelectric medium with two equilibrium states. The model is the set of Maxwell equations coupled to the undamped Landau-Khalatnikov equation, where we do not assume slowly varying envelopes. From linear-scattering theory, we show that low-amplitude pulses can be completely reflected by the medium. Large-amplitude pulses can switch the ferroelectric. Using numerical simulations and analysis, we study this switching for long and short pulses, estimate the switching times, and provide useful information for experiments.
Weakly coupled map lattice models for multicellular patterning and collective normalization of abnormal single-cell states
2017
We present a weakly coupled map lattice model for patterning that explores the effects exerted by weakening the local dynamic rules on model biological and artificial networks composed of two-state building blocks (cells). To this end, we use two cellular automata models based on: (i) a smooth majority rule (model I) and (ii) a set of rules similar to those of Conway's Game of Life (model II). The normal and abnormal cell states evolve according with local rules that are modulated by a parameter $\kappa$. This parameter quantifies the effective weakening of the prescribed rules due to the limited coupling of each cell to its neighborhood and can be experimentally controlled by appropriate e…
Angular Pseudomomentum Theory for the Generalized Nonlinear Schr\"{o}dinger Equation in Discrete Rotational Symmetry Media
2009
We develop a complete mathematical theory for the symmetrical solutions of the generalized nonlinear Schr\"odinger equation based on the new concept of angular pseudomomentum. We consider the symmetric solitons of a generalized nonlinear Schr\"odinger equation with a nonlinearity depending on the modulus of the field. We provide a rigorous proof of a set of mathematical results justifying that these solitons can be classified according to the irreducible representations of a discrete group. Then we extend this theory to non-stationary solutions and study the relationship between angular momentum and pseudomomentum. We illustrate these theoretical results with numerical examples. Finally, we…
Experimental demonstration of phase bistability in a broad-area optical oscillator with injected signal
2015
We demonstrate experimentally that a broad-area laserlike optical oscillator (a nondegenerate photorefractive oscillator) with structured injected signal displays two-phase patterns. The technique [de Valc\'arcel and Staliunas, Phys. Rev. Lett. 105, 054101 (2010)] consists in spatially modulating the injection, so that its phase alternates periodically between two opposite values, i.e., differing by $\ensuremath{\pi}$.
Hysteretic nonequilibrium Ising-Bloch transition
2005
We show that a parametrically driven cubic-quintic complex Ginzburg-Landau equation exhibits a hysteretic nonequilibrium Ising-Bloch transition for large enough quintic nonlinearity. These results help to understand the recent experimental observation of this pheomenon [A. Esteban-Martin et al., Phys. Rev. Lett. 94, 223903 (2005)].
Dynamics of two competing species in the presence of Lévy noise sources
2010
We consider a Lotka-Volterra system of two competing species subject to multiplicative alpha-stable Lévy noise. The interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence both of a periodic driving term and an additive alpha-stable Lévy noise. We study the species dynamics, which is characterized by two different regimes, exclusion of one species and coexistence of both. We find quasi-periodic oscillations and stochastic resonance phenomenon in the dynamics of the competing species, analysing the role of the Lévy noise sources.
Parallelization of Cellular Automata for Surface Reactions
2002
We present a parallel implementation of cellular automata to simulate chemical reactions on surfaces. The scaling of the computer time with the number of processors for this parallel implementation is quite close to the ideal T/P, where T is the computer time used for one single processor and P the number of processors. Two examples are presented to test the algorithm, the simple A+B->0 model and a realistic model for CO oxidation on Pt(110). By using large parallel simulations, it is possible to derive scaling laws which allow us to extrapolate to even larger system sizes and faster diffusion coefficients allowing us to make direct comparisons with experiments.
Maxwell's equations approach to soliton excitations of surface plasmonic resonances
2012
We demonstrate that soliton-plasmon bound states appear naturally as propagating eigenmodes of nonlinear Maxwell's equations for a metal/dielectric/Kerr interface. By means of a variational method, we give an explicit and simplified expression for the full-vector nonlinear operator of the system. Soliplasmon states (propagating surface soliton-plasmon modes) can be then analytically calculated as eigenmodes of this non-selfadjoint operator. The theoretical treatment of the system predicts the key features of the stationary solutions and gives physical insight to understand the inherent stability and dynamics observed by means of finite element numerical modeling of the time independent nonl…
Pattern formation and spatial correlation induced by the noise in two competing species
2004
We analyze the spatio-temporal patterns of two competing species in the presence of two white noise sources: an additive noise acting on the interaction parameter and a multiplicative noise which affects directly the dynamics of the species densities. We use a coupled map lattice (CML) with uniform initial conditions. We find a nonmonotonic behavior both of the pattern formation and the density correlation as a function of the multiplicative noise intensity.
Nonmonotonic behavior of spatiotemporal pattern formation in a noisy Lotka-Volterra system
2004
The noise-induced pattern formation in a population dynamical model of three interacting species in the coexistence regime is investigated. A coupled map lattice of Lotka-Volterra equations in the presence of multiplicative noise is used to analyze the spatiotemporal evolution. The spatial correlation of the species concentration as a function of time and of the noise intensity is investigated. A nonmonotonic behavior of the area of the patterns as a function of both noise intensity and evolution time is found.