Related papers: Polynomial chaos based uncertainty quantification …
Do nonlinear waves destroy Anderson localization? Computational and experimental studies yield subdiffusive nonequilibrium wave packet spreading. Chaotic dynamics and phase decoherence assumptions are used for explaining the data. We…
In this paper, we first investigate the well-posedness of a backward stochastic differential equation where the driver depends on the law of the solution conditioned to a common noise. Under standard assumptions, we show that existence and…
We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of…
We present an algorithm for computing sparse, least squares-based polynomial chaos expansions, incorporating both adaptive polynomial bases and sequential experimental designs. The algorithm is employed to approximate stochastic…
From a kinematical point of view, the geometrical information of hamiltonian chaos is given by the (un)stable directions, while the dynamical information is given by the Lyapunov exponents. The finite time Lyapunov exponents are of…
Incorporating probabilistic terms in mathematical models is crucial for capturing and quantifying uncertainties in real-world systems, especially when the solution is not unique or exhibits sudden qualitative changes as parameters vary.…
The chaotic diffusion for particles moving in a time dependent potential well is described by using two different procedures: (i) via direct evolution of the mapping describing the dynamics and ; (ii) by the solution of the diffusion…
We consider ray propagation in a waveguide with a designed sound-speed profile perturbed by a range-dependent perturbation caused by internal waves in deep ocean environments. The Hamiltonian formalism in terms of the action and angle…
Quantum chaos---the study of quantized nonintegrable Hamiltonian systems---is an extremely well-developed and sophisticated field. By contrast, very little work has been done in looking at quantum versions of systems which classically…
The effect of small nonlinear dissipation on the dynamics of system with stochastic web which is linear oscillator driven by pulses is studied. The scenario of coexisting attractors evolution with the increase of nonlinear dissipation is…
We show that the output of systems with time-varying delay can exhibit a new kind of chaotic behavior characterized by laminar phases, which are periodically interrupted by irregular bursts. Within each laminar phase the output intensity…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…
This paper deals with the problem of analytically computing the largest Lyapunov exponent for many degrees of freedom Hamiltonian systems. This aim is succesfully reached within a theoretical framework that makes use of a geometrization of…
A family of the billiard-type systems with zero Lyapunov exponent is considered as an example of dynamics which is between the regular one and chaotic mixing. This type of dynamics is called ``pseudochaos''. We demonstrate how the…
Uncertainty quantification techniques such as the time-dependent generalized polynomial chaos (TD-gPC) use an adaptive orthogonal basis to better represent the stochastic part of the solution space (aka random function space) in time.…
Investigating the possibility of applying techniques from linear systems theory to the setting of nonlinear systems has been the focus of many papers. The pseudo linear form representation of nonlinear dynamical systems has led to the…
We investigate chaotic dynamical systems for which the intensity of trajectories might grow unlimited in time. We show that (i) the intensity grows exponentially in time and is distributed spatially according to a fractal measure with an…
Coexistence of various ordered chaotic states in a Hamiltonian system is studied with the use of a symplectic coupled map lattice. Besides the clustered states for the attractive interaction, a novel chaotic ordered state is found for a…
We consider the unsteady regimes of an acoustically-driven jet that forces a recirculating flow through successive reflections on the walls of a square cavity. The specific question being addressed is to know whether the system can sustain…