Showing papers in "Physica D: Nonlinear Phenomena in 1999"

TL;DR: In this article, the authors proposed a simpler method for estimating the delay time of a nonlinear time series using the correlation integral, which is known as the C-C method.

TL;DR: The proposed measure for characterizing statistical relationships between two time sequences is non-symmetric and provides information about the direction of interdependence and is closely related to recent attempts to detect generalized synchronization.

TL;DR: In this paper, the multiphase field method is reformulated by the use of interface fields, which allows for the decomposition of the nonlinear multiphases field interactions into pairwise interaction of interfaces, and removes some difficulties in the treatment of triple points or higher order interactions that occurred in the original model.

TL;DR: In this article, a simple neural network model with two delays is considered, and the Hopf bifurcation occurs when the sum of the two delays varies and passes a sequence of critical values.

TL;DR: In this article, the asymptotic behavior of solutions for parabolic non-linear evolution equations in R n is studied and the existence of the global attractor in L 2 (R n ) is established.

TL;DR: Formulae for estimating the errors on observed information entropies and mutual informations are derived using the standard error analysis familiar to physicists, and their validity is demonstrated by numerical experiment.

TL;DR: In this article, a new computational approach, CRCP, is proposed in which both the large-scale (LS) tropical dynamics and cloud-scale dynamics are captured explicitly by imbedding a 2D CS model in each column of the 3D LS model.

TL;DR: In this article, an unfolding of a degenerate reversible 1-1 resonance (or Hamiltonian-Hopf) bifurcation for four-dimensional systems of time reversible ODEs is considered.

TL;DR: In this paper, the dynamics near the collinear equilibrium points L 1, 2, 3 of the spatial Restricted Three Body Problem (RTBP) were studied and the Lindstedt-Poincare procedure was applied to explicitly compute the invariant tori contained in the center manifold.

TL;DR: In this article, Chen et al. provide a more detailed mathematical treatment of those equations for pipe flows which yield accurate predictions of turbulent flow profiles for very large Reynolds numbers, and a connection between the Camassa-Holm equations and turbulent flows in channels and pipes is discussed.

TL;DR: In this article, the utility of the recently proposed alpha equations in providing a subgrid model for fluid turbulence was explored, and the results showed that the large scale features, including statistics and structures, are preserved by the alpha models, even at coarser resolutions where the fine scales are not fully resolved.

TL;DR: In this paper, an efficient procedure for characterizing the solution of evolution equations with stochastic coefficients is presented, where the concepts of projection, orthogonality and weak convergence are exploited in a manner which directly mimics deterministic finite element solutions except that inner products refer to expectation operations.

TL;DR: In the presence of strong anomalous diffusion one does not have a unique exponent and therefore one has the failure of the usual scaling P(x,t)=t−νF(x/tν) of the probability density, which implies that the effective equation at large scale and long time for P( x,t), obeys neither the usual Fick equation nor other linear equations involving temporal and/or spatial fractional derivatives.

TL;DR: It is demonstrated that transient large-scale nonlinear entrainments by the epileptogenic region can be identified, this with or without epileptic activity, and raises the possibility that the cross-predictability analysis of interictal data may be used as a significant aid in locating epileptic foci.

TL;DR: In this article, the authors focus on the basic mechanism causing self-replicating patterns from a global bifurcational point of view and take their clues from two model systems including the Gray-Scott (GS) model.

TL;DR: In this article, the authors formulate equations for the slow time dynamics of fluid motion that self consistently account for the effects of the variability upon the mean, and introduce nonlinear dispersion that acts to spatially smooth the transport velocity of the mean flow relative to its circulation or momentum velocity, by the inversion of a Helmholtz operator whose length scale corresponds to the covariance of the fluctuations.

TL;DR: In this paper, the interaction between the fourth order regularization and the nonconvex flux was studied in the context of thin liquid films driven by the competing effects of a thermally induced surface tension gradient and gravity.

TL;DR: In this paper, the effect of time delay on the collective dynamics of coupled limit cycle oscillators at Hopf bifurcation was studied and the results showed significant changes in the stability boundaries of amplitude death, phase locked and incoherent regions.

TL;DR: In this article, the authors apply the theory of large deviations to a number of problems in statistical mechanics, such as deriving the form of the Gibbs state for a discrete ideal gas, describing probabilistically the phase transition in the Curie-Weiss model of a ferromagnet, and deriving variational formulas that describe the equilibrium macrostates in models of two-dimensional turbulence.

TL;DR: In this article, the authors explore the ability of nonoscillatory advection schemes to represent the effects of the unresolved scales of motion in numerical simulation of turbulent flows, and demonstrate that a non-oscillatorial fluid solver can accurately reproduce the dynamics of an atmospheric convective boundary layer.

TL;DR: In this article, the authors study the effects of an applied magnetic field on a superconductor and estimate the value of the upper critical magnetic field HC3 at which superconductivity can nucleate.

TL;DR: In this article, the influence of a homogeneous noise on the evolution of solitons for the Korteweg-de Vries equation was investigated using finite elements and least squares.

TL;DR: In this article, a new class of subgrid closures for large eddy simulation (LES) of turbulence is developed, based on the construction of synthetic, fractal subgrid-scale fields.

TL;DR: In this article, the authors study the coupled complex Ginzburg-Landau (CGL) equations for traveling wave systems, and show that sources and sinks are the important coherent structures that organize much of the dynamical properties of traveling wave system.

TL;DR: In this paper, the effects of the coefficient of the cubic nonlinear term can be either positive or negative for small-amplitude solitary wave transformation in a zone with a sign-variable coefficient for the quadratic non-linear term is studied in the framework of the variable-coefficient extended Kortewegde Vries equation.

TL;DR: In this article, the authors developed and analyzed a model for malignant invasion, brought about by a combination of proteolysis and haptotaxis, which admits a family of travelling waves which depend on two parameters, i.e. the tissue concentration of connective tissue and the rate of decay of the initial spatial profile of the invading cells.

TL;DR: In this article, the Fokker-Planck equation for the coupled Langevin system is reduced to a kinetic equation for oscillator distribution function, and the effect of a stochastic temporal variation in the frequencies is also included.

TL;DR: In this paper, the numerical integration in time of the equations of motion for mechanical systems subject to holonomic constraints is considered, and schemes are introduced for the direct treatment of a differential-algebraic form of equations that preserve the constraints, the total energy, and other integrals such as linear and angular momentum arising from affine symmetries.

TL;DR: In this paper, a class of velocity fields of the type u=(u1,u2,γ,u3,u4,u5,u6,u7,u8,u9,u10,u11,u12,u13,u14,u15,u16,u17,u18,u19,u20,u21,u22,u23,u24,u25,u26,u27,u28,u30,u31,u32,u33,u34,

TL;DR: Callahan et al. as mentioned in this paper used symmetry-breaking bifurcations on cubic lattices to make specific predictions about the formation of three-dimensional patterns in two models of the Turing instability, the Brusselator model and the Lengyel-Epstein model.