Showing papers in "Physica D: Nonlinear Phenomena in 2000"

TL;DR: In this article, the authors review 25 years of research on the Kuramoto model, highlighting the false turns as well as the successes, but mainly following the trail leading from Kuramoto's work to Crawford's recent contributions.

TL;DR: Specific as well as more general approaches to constrained randomisation, providing a full range of examples, and some implementational aspects of the realisation of these methods in the TISEAN software package are discussed.

TL;DR: In this paper, the authors apply the concept of phase synchronization of chaotic and/or noisy systems and the statistical distribution of the relative instantaneous phases to electroencephalograms (EEGs) recorded from patients with temporal lobe epilepsy.

TL;DR: In this paper, a Lagrangian definition for the boundaries of coherent structures in two-dimensional turbulence is introduced, defined as material lines that are linearly stable or unstable for longer times than any of their neighbors.

TL;DR: In this article, a two-dimensional frame-invariant phase field model of grain boundaries is developed, and one-dimensional analytical solutions for a stable grain boundary in a bicrystal are obtained, and equilibrium energies are computed.

TL;DR: In this article, it was shown that the velocity of a pulled front always relaxes algebraically like v. This front velocity is independent of the precise value of the front amplitude, which one tracks to measure the front position.

TL;DR: In this paper, the authors compare the spectra of the linearized evolution operators on unbounded and bounded domains for two classes of boundary conditions, namely, separated boundary conditions and periodic boundary conditions.

TL;DR: In this paper, conditions of existence and stability of solitons described by the fourth order nonlinear Schrodinger type equations in one, two and three dimensions with power-law nonlinearities are found.

TL;DR: In this article, a model of macroscopic friction was investigated using methods of dynamical systems analysis, focusing on the bifurcations associated with the appearance of stick friction.

TL;DR: The main result of this paper is to derive a simple and easily implementable set of reconstruction equations which close the system of ODEs produced by Galerkin projection.

TL;DR: The standard method seems to be the most efficient followed by the new method and the differential version of the standard method (in that order), as far as the CPU time for the computation of the Lyapunov spectra is concerned.

TL;DR: In this article, the authors describe the method of synchronizing slave to the master trajectory using intermittent coupling, where the information about master trajectory is limited only to the coordinates and timings of intersection points of that trajectory with the arbitrarily chosen Poincare section, making the coupling sporadic.

TL;DR: In this article, the authors extend the multi-phase field model to multi-stage alloys and provide a framework for describing and numerically simulating the solidification of both eutectic and peritectic systems.

TL;DR: In this article, a phase-field model for the solidification of a pure material that includes convection in the liquid phase is developed, which allows the interface to have an anisotropic surface energy, and allows a quasi-incompressible thermodynamic description in which the densities in the solid and liquid phases may each be uniform.

TL;DR: A practical measure for the complexity of sequences of symbols (“strings”) is introduced that is rooted in automata theory but avoids the problems of Kolmogorov‐Chaitin complexity, and is applied to tRNA sequence data.

TL;DR: Since the EPs are identified at the single stimulus level (without need of ensemble averaging), this will allow the calculation of better resolved averages and implementations in clinical settings are imaginable.

TL;DR: In this article, the behavior of trajectories of fluid particles in a compressible generalization of the Kraichnan ensemble of turbulent velocities was studied and it was shown that trajectories either explosively separate or implosively collapse.

TL;DR: In this paper, the authors present a detailed description of the main features of the classical Hill's problem, including a global description when the zero velocity curve (zvc) confines the motion.

TL;DR: A coherent method of analysis is presented that summarizes previous work and fills in some of the gaps as well as including some new results, and is applied to a number of examples, including surprising long and complex limit cycles involving sequences of hundreds of threshold transitions.

TL;DR: In this article, the utility of a discrete singular convolution (DSC) algorithm for the integration of the sine-Gordon equation is explored, where the initial values are chosen close to a homoclinic manifold for which previous methods have encountered significant numerical difficulties.

TL;DR: In this paper, a linear finite-dimensional output feedback control of the Kuramoto-Sivashinsky equation (KSE) with periodic boundary conditions is presented, under the assumption that the linearization of the KSE around the zero solution is controllable and observable.

TL;DR: In this paper, robust control theory has been examined as a technique by which effective control algorithms which are insensitive to a broad class of external disturbances may be developed for a wide variety of infinite-dimensional linear and nonlinear problems in fluid mechanics.

TL;DR: In this paper, a multiscale singular-spectrum analysis (SSA) was proposed for nonstationary time series, including the case where intermittency gives rise to the divergence of their variance.

TL;DR: In this paper, the authors describe the deterministic component of the long-time evolution of the perturbed system and define the metastable state for any initial point and for a given timescale.

TL;DR: In this article, the results obtained are modeled in terms of coupled oscillator systems and considered to represent the Wilson-cowan/Ermentrout-Cowan-model aspect of the unifying theory.

TL;DR: In this article, the authors consider the problem of thin film rupture driven by van der Waals forces and show that line and ring rupture are unstable and will generate axisymmetric rupture at isolated points.

TL;DR: In this paper, the generalized conditional symmetry approach is used to study the separation of variables of quasilinear diffusion equations with nonlinear source, and a complete list of canonical forms for such equations which admit the functionally separable solutions is obtained.

TL;DR: In this article, the dynamics of a relativistic charged particle in a uniform magnetic field and an electrostatic plane wave were studied, and the system was reduced to a two-degree-of-freedom Hamiltonian system with slow and fast variables.

TL;DR: In this paper, an ensemble of weakly interacting capillary waves on a free surface of deep ideal fluid is described statistically by methods of weak turbulence, and the Kolmogorov constant C is found analytically together with the interval of locality in K → -space.

TL;DR: An adaptive strategy for chaos synchronization is developed that allows the synchronization of high-order chaotic systems and only one tuning parameter is required to perform the chaos synchronization.