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The dynamics of escape from an attractive state due to random perturbations is of central interest to many areas in science. Previous studies of escape in chaotic systems have rather focused on the case of unbounded noise, usually assumed…
We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we…
Reliable optimal control is challenging when the dynamics of a nonlinear system are unknown and only infrequent, noisy output measurements are available. This work addresses this setting of limited sensing by formulating a Bayesian prior…
When complex systems are driven to extinction by some external factor, their non-stationary dynamics can present an intermittent behaviour between relative tranquility and burst of activity whose consequences are often catastrophic. To…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
We analyze situations where a saddle-node bifurcation occurs on a fractal basin boundary. Specifically, we are interested in what happens when a system parameter is slowly swept in time through the bifurcation. Such situations are known to…
Hypothesis: Surrounding fluids affect critically drop wetting dynamics in many applications involving viscous environments. Although macroscopic effects of outer fluid viscosity on contact line motion have been documented, the extent to…
We present evidence of the hysteretic nature of dissipation in unsteady turbulent flows. Wind tunnel experiments and direct numerical simulations in oscillating flows show that, at fixed mean Reynolds number, the dissipation constant is…
The control of wave scattering in complex non-Hermitian settings is an exciting subject -- often challenging the creativity of researchers and stimulating the imagination of the public. Successful outcomes include invisibility cloaks,…
The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject…
Stochastic dynamical systems arise as models for fluid particle motion in geophysical flows with random velocity fields. Escape probability (from a fluid domain) and mean residence time (in a fluid domain) quantify fluid transport between…
We study an influence of nonlinear dissipation and external perturbations onto transition scenarious to chaos in Lorenz-Haken system. It will be show that varying in external potential parameters values leads to parameters domain formation…
We use the H\'enon-Heiles system as a paradigmatic model for chaotic scattering to study the Lorentz factor effects on its transient chaotic dynamics. In particular, we focus on how time dilation occurs within the scattering region by…
The unsteady flow physics of wind-turbine wakes under dynamic forcing conditions are critical to the modeling and control of wind farms for optimal power density. Unsteady forcing in the streamwise direction may be generated by unsteady…
The nonlinear robustness of laminar plane Couette flow is considered under the action of in-phase spanwise wall oscillations by computing properties of the edge of chaos, i.e., the boundary of its basin of attraction. Three measures are…
We study the mean-field dynamics of a system of $N$ interacting bosons starting from an initially condensated state. For a broad class of mean-field Hamiltonians, including models with arbitrary bounded interactions and models with…
We provide deterministic controllability conditions that imply exponential mixing properties for randomly forced constrained dynamical systems with possibly unbounded state space. As an application, new ergodicity results are obtained for…
Using a system of two FitzHugh-Nagumo units, we demonstrate the occurrence of riddled basins of attraction in delay-coupled systems as the coupling between the units is increased. We characterize the riddled basin using the uncertainty…
In this article we present a general framework for non-concave robust stochastic control problems under model uncertainty in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent…
We carried out a fluid dynamical simulation for a forced dripping faucet system using a new algorithm that was recently developed. The simulation shows that periodic external forcing induces transitions from chaotic to periodic motion and…