Showing papers in "Physica D: Nonlinear Phenomena in 2011"

TL;DR: In this article, a mathematical theory that clarifies the relationship between observable Lagrangian Coherent Structures (LCSs) and invariants of the Cauchy-Green strain tensor field is developed.

TL;DR: In this article, the authors provide an overview of early warning signs for critical transitions in dynamical systems and their application in a wide range of applications from ecosystems and climate change to medicine and finance.

TL;DR: In this article, a unification of the two approaches that have dominated theoretical climate dynamics since its inception in the 1960s: the nonlinear deterministic and the linear stochastic one is proposed.

TL;DR: It is argued that the spatio-temporal irregularity observed here describes a form of spatio -temporal chaos.

TL;DR: In this article, a continuum phase field theory and corresponding numerical solution methods are developed to describe deformation twinning in crystalline solids, where an order parameter is associated with the magnitude of twinning shear, i.e., the lattice transformation associated with twinning.

TL;DR: In this paper, the existence and uniqueness of both local martingale and local pathwise solutions of an abstract nonlinear stochastic evolution system were established and used to infer the local existence of strong, path-wise solutions to 3D primitive equations of the oceans and atmosphere forced by a nonlinear multiplicative white noise.

TL;DR: A metric that quantifies how far trajectories are from being ergodic with respect to a given probability measure is proposed and centralized feedback control laws for multi-agent systems are formulated so that agents trajectories sample aGiven probability distribution as uniformly as possible.

TL;DR: In this paper, the authors established an averaging principle for stochastic differential equations with non-Gaussian Levy noise and proved that the solutions to stochiastic systems with Levy noise can be approximated by solutions to averaged stochastically distributed differential equations in the sense of both convergence in mean square and convergence in probability.

TL;DR: In this article, the authors considered general heterogeneous ensembles of phase oscillators, sine coupled to arbitrary external fields, and obtained the description of the ensemble dynamics in terms of collective variables and constants of motion.

TL;DR: In this article, a variable order (VO) differential equation of motion for a spherical particle sedimenting in a quiescent viscous liquid was developed, and a new form for the history drag acting on the particle was proposed.

TL;DR: In this article, an approach based on Gronwall inequalities for the asymptotic complete phase-frequency synchronization of Kuramoto oscillators with finite inertia is presented, which leads to the complete phase and frequency synchronization.

TL;DR: In this article, discrete data assimilation for the Lorenz equations and the incompressible two-dimensional Navier-Stokes equations is studied and bounds on the time interval h between subsequent observations are obtained.

TL;DR: In this paper, the authors derived geometric, variational discretization of continuum theories arising in fluid dynamics, magnetohydrodynamics (MHD), and the dynamics of complex fluids.

TL;DR: In this paper, a geometrically derived discrete equations of motion for fluid dynamics from first principles in a purely Eulerian form were derived from a variational principle with nonholonomic constraints.

TL;DR: In this paper, the authors studied a rechargeable lithium-ion battery that uses a many-particle FePO4 electrode to reversibly store lithium atoms, which is accompanied by a phase transition and charging/discharging run along different paths, so that hysteretic behavior is observed.

TL;DR: In this paper, the Povzner equation is modified through a correction in the form of a nonlinear friction type operator to obtain a fluid dynamic description of a system of agents with weak dissipative interactions, with a coefficient of restitution that depends on their relative distance.

TL;DR: This work designs an Irreversible version of Metropolis–Hastings (IMH) and test it on an example of a spin cluster and constructs irreversible deformation of a given reversible algorithm capable of dramatic improvement of sampling from known distribution.

TL;DR: In this paper, the authors considered a Cahn-Hilliard model with non-permeable walls and proposed dynamic boundary conditions for weak solutions and showed the existence and uniqueness of weak solutions.

TL;DR: In this paper, the Ott-Antonsen ansatz is used to derive non-local differential equations which describe the network dynamics in the continuum limit, and the front and bump solutions of these equations are studied by either "freezing" them in a travelling coordinate frame or analysing them as homoclinic or heterocalic orbits.

TL;DR: In this paper, a modified Boussinesq hierarchy associated with the 3×3 matrix spectral problem is derived with the help of Lenard recursion equations based on the characteristic polynomial of Lax matrix for the modified boussineq hierarchy, and an algebraic curve is introduced, from which the associated Baker-Akhiezer function, meromorphic function and Dubrovin-type equations are derived.

TL;DR: The statistical techniques for this distance-based analysis of dynamical systems are presented, filling a gap in the literature, and their application is discussed in a few examples of datasets arising in physiology and neuroscience, and in the well-known Henon system.

TL;DR: In this article, a model for the flow of a mixture of two viscous and incompressible fluids in a two or three dimensional channel-like domain was considered, where the Navier-Stokes equations governing the fluid velocity coupled with a convective Cahn-Hilliard equation for the relative density of atoms of one of the fluids were considered.

TL;DR: In this article, the interaction properties of complex solitons are studied for the two U ( 1 ) -invariant integrable generalizations of the modified Korteweg-de Vries (mKdV) equation, given by the Hirota equation and the Sasa-Satsuma equation, which share the same traveling wave (single-soliton) solution having a sech profile characterized by constant speed and a constant phase angle.

TL;DR: The Functionalized Cahn-Hilliard (FCH) energy as mentioned in this paper is a negative multiple of the Cahn−Hilliard energy balanced against the square of its own variational derivative, as a finite width regularization of the sharp-interface Canham−Helfrich energy.

TL;DR: A single-formula Lyapunov function is given that covers the entire class of dynamics, which includes the replicator dynamic and the projection dynamic, as well as several new dynamics.

TL;DR: In this article, the authors considered spatially homogeneous locally rotationally symmetric solutions of the Einstein equations with a large class of anisotropic matter models including collisionless matter (Vlasov), elastic matter, and magnetic fields.

TL;DR: In this paper, the results of an experimental campaign developed with the aim of simulating sea-waves energy production by a parametric pendulum show that rotations exist in a region which is smaller than the theoretical one.

TL;DR: In this article, an analytical description of the non-stationary response of the forced Duffing oscillator near the 1:1 resonance is presented, where the authors exploit the concept of the limiting phase trajectories (LPTs) and derive an explicit asymptotic expression for the LPT.

TL;DR: In this paper, the existence of a boundary layer with thickness proportional to the square root of the Brinkman-Darcy number for the velocity field is established in both the L ∞ (H 1 ) norm (in 2 and 3 d).

TL;DR: A weakly nonlinear analysis of the dynamical states arising via primary instabilities of the asynchronous state is conducted to determine analytically how the nature and stability of these states depend on the choice of transfer function and connectivity.