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High-dimensional systems that have a low-dimensional dominant behavior allow for model reduction and simplified analysis. We use differential analysis to formalize this important concept in a nonlinear setting. We show that dominance can be…
This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation subject to a nonmonotone distributed damping. A well-posedness result is provided together with a precise characterization of the asymptotic…
Understanding mechanisms for energy dissipation from nanoparticles in contact with large samples is a central problem in describing friction microscopically. Calculation of the reduced density matrix appears to be the most suitable metho to…
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…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
In this work, we consider a system of two wave equations coupled by velocities in one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling…
Localized states in one-dimensional open disordered systems and their connection to the internal structure of random samples have been studied. It is shown that the localization of energy and anomalously high transmission associated with…
Based on first- and second-order perturbation theory, we present a numerical study of the temporal build-up and decay of unsteady acoustic fields and acoustic streaming flows actuated by vibrating walls in the transverse cross-sectional…
We study the evolution of diffuse elastodynamic spectral energy density under the influence of weak nonlinearity. It is shown that the rate of change of this quantity is given by a convolution of the linear energy at two frequencies.…
The influence of multiplicative white noise on the resonance capture of strongly nonlinear oscillatory systems under chirped-frequency excitations is investigated. It is assumed that the intensity of the perturbation decays polynomially…
The intensity distribution of electromagnetic polar waves in a chain of near-resonant weakly-coupled scatterers is investigated theoretically and supported by a numerical analysis. Critical scaling behavior is discovered for part of the…
We observe a crossover from strong to weak chaos in the spatiotemporal evolution of multiple site excitations within disordered chains with cubic nonlinearity. Recent studies have shown that Anderson localization is destroyed, and the wave…
One-dimensional chain of pointwise particles harmonically coupled with nearest neighbors and placed in six-order polynomial on-site potentials is considered. Power of the energy source in the form of single ac driven particles is calculated…
In this paper we provide a complete link between dissipation theory and a celebrated result on stability analysis with integral quadratic constraints. This is achieved with a new stability characterization for feedback interconnections…
In dense neutrino environments, such as provided by core-collapse supernovae or neutron-star mergers, neutrino angular distributions may be unstable to collective flavor conversions, whose outcome remains to be fully understood. These…
Strong frequency dependence is unlikely in diffusive or over-damped systems. When exceptions do occur, such as in the case of stochastic resonance, it signals an interesting underlying phenomenon. We find that such a case appears in the…
In this paper we consider second order evolution equations with bounded damping. We give a characterization of a non uniform decay for the damped problem using a kind of observability estimate for the associated undamped problem.
We consider N identical oscillators coupled to a single environment and show that the conditions for the existence of decoherence free subspaces are degeneracy of the oscillator frequencies and separability of the coupling with the…
Nonlinear dynamical systems possessing reflection symmetry have an invariant subspace in the phase space. The dynamics within the invariant subspace can be random or chaotic. As a system parameter changes, the motion transverse to the…
In weakly nonlinear dispersive wave systems, long-time dynamics are typically governed by time resonances, where wave phases evolve coherently due to exact frequency matching. Recent advances in spatio-temporal spectrum measurements,…