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We demonstrate that at long times the rate of passive scalar decay in a turbulent, or simply chaotic, flow is dominated by regions (in real space or in inverse space) where mixing is less efficient. We examine two situations. The first is…
The dissipative capacity as quantified by the nonlinear bandwidth measure of impulsively loaded primary structures (PSs) coupled to particle impact dampers (PIDs) is assessed. The considered PIDs are designed by initially placing different…
Instead of the infinitesimal extrinsic and intrinsic perturbations on strings, considered so far, we discuss the evolution and propagation of finite-amplitude perturbations. Those intrinsic perturbations may result in appearance of stable…
Dense granular flows are often unstable and form inhomogeneous structures. Although significant advances have been recently made in understanding simple flows, instabilities of such flows are often not understood. We present experimental…
Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…
We numerically investigate the properties of speckle patterns formed by nonlinear point scatterers. We show that, in the weak localization regime, dynamical instability appears, eventually leading to chaotic behavior of the system.…
Pinning and depinning of wave fronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators…
A theory for jammed granular materials is developed with the aid of a nonequilibrium steady-state distribution function. The approximate nonequilibrium steady-state distribution function is explicitly given in the weak dissipation regime by…
We propose a theoretical and computational approach to investigate temporal behavior of a nonlinear polarization in perturbative regime induced by an intense and ultrashort pulsed electric field. First-principles time-dependent density…
A model of the thin shell expanding into a uniform ambient medium is developed. Density perturbations are described using equations with linear and quadratic terms, and the linear and the nonlinear solutions are compared. We follow the time…
We present experimental data corresponding to a two dimensional dense granular flow, namely, the gravity-driven discharge of grains from a small opening in a silo. We study the microscopic velocity field with the help of particle tracking…
Propagating slow magneto-acoustic waves are often observed in polar plumes and active region fan loops. The observed periodicities of these waves range from a few minutes to few tens of minutes and their amplitudes were found to decay…
The propagation of weakly nonlinear dust--acoustic waves in a dusty plasma containing two ion species with different temperatures is explored. The nonlinear equations describing both the quadratic and cubic plasma nonlinearities are…
We study the propagation of few-cycle pulses in two-component medium consisting of nonlinear amplifying and absorbing two-level centers embedded into a linear and conductive host material. First we present a linear theory of propagation of…
Microwave pulses are used ubiquitously to control and measure qubits fabricated on superconducting circuits. Due to continual environmental coupling, the qubits undergo decoherence both when it is free and during its interaction with the…
The study of energy transport properties in heterogeneous materials has attracted scientific interest for more than a century, and it continues to offer fundamental and rich questions. One of the unanswered challenges is to extend Anderson…
Presented here is a study of well-posedness and asymptotic stability of a "degenerately damped" PDE modeling a vibrating elastic string. The coefficient of the damping may vanish at small amplitudes thus weakening the effect of the…
Shockwaves are violent nonlinear distortions of wave motion which have been reported in fluid waves and electromagnetic waves, while here we reveal that a shockwave can occur even in the quantum wave function of a single particle.…
We consider a chain of weakly harmonic coupled oscillators perturbed by a conservative noise. We show that by tuning accordingly the coupling constant energy can diffuse like a Brownian motion or superdiffuse like a maximally 3/2-stable…
We have used particle tracking methods to study the dynamics of individual balls comprising a granular flow in a small-angle two-dimensional funnel. We statistically analyze many ball trajectories to examine the mechanisms of shock…