Related papers: Polynomial chaos based uncertainty quantification …
For general dissipative dynamical systems we study what fraction of solutions exhibit chaotic behavior depending on the dimensionality $d$ of the phase space. We find that a system of $d$ globally coupled ODE's with quadratic and cubic…
Coupled problems with various combinations of multiple physics, scales, and domains can be found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled models is to…
This paper discusses a method enabling optimal control of nonlinear systems that are subject to parametric uncertainty. A stochastic optimal tracking problem is formulated that can be expressed in function of the first two stochastic…
We prove the holding of chaos in the sense of Li-Yorke for a family of four-dimensional discrete dynamical systems that are naturally associated to ODE systems describing coupled oscillators subject to an external non-conservative force,…
Compressive sensing has become a powerful addition to uncertainty quantification when only limited data is available. In this paper we provide a general framework to enhance the sparsity of the representation of uncertainty in the form of…
We demonstrate the presence of chaos in stochastic simulations that are widely used to study biodiversity in nature. The investigation deals with a set of three distinct species that evolve according to the standard rules of mobility,…
This paper tackles Hamiltonian chaos by means of elementary tools of Riemannian geometry. More precisely, a Hamiltonian flow is identified with a geodesic flow on configuration space-time endowed with a suitable metric due to Eisenhart.…
In this work we introduce a manifold learning-based surrogate modeling framework for uncertainty quantification in high-dimensional stochastic systems. Our first goal is to perform data mining on the available simulation data to identify a…
In this contribution, we discuss the construction of Polynomial Chaos surrogates for Monte Carlo radiation transport applications via non-intrusive spectral projection. This contribution focuses on improvements with respect to the approach…
The Chirikov resonance-overlap criterion predicts the onset of global chaos if nonlinear resonances overlap in energy, which is conventionally assumed to require a non-small magnitude of perturbation. We show that, for a time-periodic…
Dynamical chaos is a fundamental manifestation of gravity in astrophysical, many-body systems. The spectrum of Lyapunov exponents quantifies the associated exponential response to small perturbations. Analytical derivations of these…
In the particular case of a concave flux function, we are interested in the long time behaviour of the nonlinear process associated to the one-dimensional viscous scalar conservation law. We also consider the particle system obtained by…
We study the time evolution of perturbations in spatially extended chaotic systems in the presence of quenched disorder. We find that initially random perturbations tend to exponentially localize in space around static pinning centers that…
It is shown that the distributed chaos in the simple Hamiltonian (conservative) dynamical systems, such as the Nose-Hoover oscillator and double oscillator, can mimic the distributed chaos in the isotropic homogeneous turbulence. Direct…
Since the seminal work of Wiener, the chaos expansion has evolved to a powerful methodology for studying a broad range of stochastic differential equations. Yet its complexity for systems subject to the white noise remains significant. The…
A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of the system such that the stability of a set of periodic orbits changes (local…
Recently, the use of Polynomial Chaos Expansion (PCE) has been increasing to study the uncertainty in mathematical models for a wide range of applications and several extensions of the original PCE technique have been developed to deal with…
Polynomial chaos expansion is a popular way to develop surrogate models for stochastic systems with arbitrary random variables. Standard techniques such as Galerkin projection, stochastic collocation, and least squares approximation, are…
For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation may split into an initial exponential decrease, characterized by the maximal Lyapunov…
This work redefines the framework of chaos in dynamical systems by extending Devaney's definition to multiple mappings, emphasizing the pivotal role of nonlinearity. We propose a novel theorem demonstrating how nonlinear dynamics within a…