Showing papers in "Physica D: Nonlinear Phenomena in 2016"

TL;DR: A comprehensive survey of the field of dispersive hydrodynamics can be found in this paper, where the authors use Whitham's averaging theory as the primary mathematical tool and review the rich mathematical developments over the past fifty years with an emphasis on physical applications.

TL;DR: In this paper, a generalized Darboux transformation was used to construct the N-bright soliton solution in a compact determinant form, the N -breather solution including the Akhmediev breather and a general higher order rogue wave solution.

TL;DR: The tensorial formalism recently proposed to characterize and investigate this kind of complex topologies is relied on, and two well known random walk centrality measures, the random walk betweenness and closeness centrality are extended to interconnected multilayer networks.

TL;DR: In this article, the authors use persistent homology to build a quantitative understanding of large complex systems that are driven far-from-equilibrium; in particular, they analyze image time series of persistence diagrams from numerical simulations of two important problems in dynamics: Kolmogorov flow and Rayleigh-B enard convection.

TL;DR: In this article, the authors consider a network of identical weakly coupled dynamical systems that are close to a supercritical Hopf bifurcation and derive a generic normal form for a system of coupled phase oscillators with S N symmetry.

TL;DR: In this article, the authors explore the statistical power of the persistent homology rank functions and show that the rank functions from multiple simulations or experiments will lie in an affine subspace.

TL;DR: In this paper, an explicit generating function of correlations functions of an arbitrary tau-function of the KdV hierarchy is derived, and closed formulae of a new type for the generating series of intersection numbers of -classes as well as of mixed -classes in full genera.

TL;DR: In this article, the authors investigate surface gravity waves in a shallow water tank, in the limit of long wavelengths, and report the observation of non-stationary dispersive shock waves rapidly expanding over a 90 m flume.

TL;DR: In this paper, the authors formulate the inverse scattering transform (IST) for the defocusing nonlinear Schrodinger (NLS) equation with fully asymmetric nonzero boundary conditions (i.e., when the limiting values of the solution at space infinities have different non-zero moduli).

TL;DR: In this paper, a nonlinear tuned vibration absorber (NLTVA) is proposed for effective vibration mitigation, and a compact analytical formula for the nonlinear coefficient of the absorber is derived, valid for any polynomial nonlinearity in the primary system.

TL;DR: In this paper, the authors use trajectories from the classic Lorenz system to reconstruct the dynamics using the method of delays, then build a simplicial complex whose vertices are a small subset of the data: the witness complex.

TL;DR: In this paper, the authors developed a technique for proving existence of periodic solutions of nonlinear differential equations with non-polynomial nonlinearities using the radii polynomial approach.

TL;DR: In this paper, the authors focus on the existence of pseudohyperbolic attractors for 3D diffeomorphisms and show that three-dimensional maps may have only five different types of such attractors, which they call the discrete Lorenz, figure-8, double-figure-8 and super-Lorenz.

TL;DR: In this article, the authors study cascades on a two-layer multiplex network, with asymmetric feedback that depends on the coupling strength between the layers, and calculate the systemic risk measured by the final fraction of failed nodes on a reference layer.

TL;DR: In this article, the polar decomposition of the flow gradient is used as a diagnostic for elliptic invariant regions in non-autonomous dynamical systems, where the authors consider two-dimensional systems and derive explicit formulas using the singular values and vectors of flow gradient.

TL;DR: In this paper, the authors examined the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations and found that the power spectrum of the random wave broadens and takes exponential wings both in focusing and in defocusing regimes.

TL;DR: In this paper, it is shown that the number of state coordinates that need to be observed may even be significantly smaller than the total number of positive Lyapunov exponents of the underlying system.

TL;DR: The special issue on Dispersive Hydrodynamics as mentioned in this paper is dedicated to the memory and work of G.B.Whitham who was one of the pioneers in this field of physical applied mathematics.

TL;DR: In this article, the authors study the dynamics of the Schrodinger equation with a fractional Laplacian ( − Δ ) α, and the decoherence of the solution is observed.

TL;DR: The results indicate that the foreseen increase in the couplings between the grids has two competing effects: on the one hand, it increases the safety region where grids can operate without withstanding systemic failures; on the other hand,it increases the possibility of a joint systems’ failure.

TL;DR: In this article, a locally resonant granular material in the form of a precompressed Hertzian chain with linear internal resonators was studied and an effective nonlinear Schrodinger (NLS) modulation equation was derived.

TL;DR: A model in which agents with interrelated opinions, interacting on several layers representing different topics, tend to spread their own ideas to their neighborhood, strive to maintain internal coherence, and is demonstrated how mass media can be effectively used to favor the propagation of a chosen set of opinions, thus polarizing the consensus of an entire population.

TL;DR: In this article, the authors studied the problem of determining lower bounds for the number of isolated periodic orbits in planar piecewise linear differential systems defined in two zones, where the two linear zones are angular sectors of angles α and 2 π − α, respectively, for α ∈ ( 0, π ).

TL;DR: In this article, a goodness-of-fit statistical test is used to detect the breakdown of linear response given observations of deterministic dynamical systems, and it is shown that in order to reliably reject the linear response for typical observables sufficiently large data sets are needed.

TL;DR: In this article, the results of analytical study and molecular dynamics simulation of low energy nonlinear nonstationary dynamics of single-walled carbon nanotubes (CNTs) are presented.

TL;DR: In this article, a broad class of bounded potentials of the one-dimensional Schrodinger operator, called primitive potentials, are constructed as solutions of a system of singular integral equations, which can be efficiently solved numerically.

TL;DR: In this paper, the authors performed full-scale numerical simulation of instability of weakly nonlinear waves on the surface of deep fluid and showed that the instability development leads to chaotization and formation of wave turbulence.

TL;DR: In this article, a poroelastic model was proposed for the deformation waves in Physarum polycephalum by modeling and experiments, where active tension caused mechanochemical waves that were regulated by an inhibitor.

TL;DR: In this article, the authors proposed a generalization of the concept of assortativity based on the tensorial representation of multilayer networks, covering the definitions given in terms of Pearson and Spearman coefficients.

TL;DR: It is demonstrated that averaged persistence landscapes can be used to recover central system information in the Cahn-Hilliard theory of phase separation and shown that topological information of evolving microstructures alone suffices to accurately detect both concentration information and the actual decomposition stage of a data snapshot.