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Linear response theory is a fundamental framework studying the macroscopic response of a physical system to an external perturbation. This paper focuses on the rigorous mathematical justification of linear response theory for Langevin…
Quasigeostrophic turbulence on a beta-plane with a finite deformation radius is studied nu- merically, with particular emphasis on frequency and combined wavenumber-frequency do- main analyses. Under suitable conditions, simulations with…
Motivated by current interest in the dynamics of trapped quantum gases, we study the microcanonical dynamics of a trapped one-dimensional gas of classical particles interacting via a finite-range repulsive force of tunable strength. We…
We show how pattern formation in Faraday waves may be manipulated by varying the harmonic content of the periodic forcing function. Our approach relies on the crucial influence of resonant triad interactions coupling pairs of critical…
Energy conservation in radiating processes requires, at the classical level, to take into account damping forces on the sources. These forces can be represented in terms of asymptotic data and lead to charges defined as integrals over the…
Strongly damped Doppler shift oscillations are observed frequently associated with flarelike events in hot coronal loops. In this paper, a review of the observed properties and the theoretical modeling is presented. Statistical measurements…
We discuss the linear response to low-frequency tidal forcing of fluid bodies that are slowly and uniformly rotating, are neutrally stratified and may contain a solid or fluid core. This problem may be regarded as a simplified model of…
During comprehensive study of weakly nonlinear interaction of surface capillary waves, processes of resonant and non-resonant interactions were considered both numerically and analytically: merging of two waves into one and waves on the…
A damped chain of particles with harmonic nearest-neighbor interactions in a spatially periodic, piecewise harmonic potential (Frenkel-Kontorova model) is studied numerically. One end of the chain is pulled slowly which acts as a weak…
In this study, we investigate the dynamics of the quantum kicked rotor in the near-resonant regime and observe distinct caustic structures, such as recurring cusps, cusp oscillations, and reticular cusp patterns in high-order resonant…
Resonantly forced spiral waves in excitable media drift in straight-line paths, their rotation centers behaving as point-like objects moving along trajectories with a constant velocity. Interaction with medium boundaries alters this…
Rapidly decaying slow magnetoacoustic waves are regularly observed in the solar coronal structures, offering a promising tool for a seismological diagnostics of the coronal plasma, including its thermodynamical properties. The effect of…
Periodic forcing of an oscillatory system produces frequency locking bands within which the system frequency is rationally related to the forcing frequency. We study extended oscillatory systems that respond to uniform periodic forcing at…
The longitudinal response of single semiflexible polymers to sudden changes in externally applied forces is known to be controlled by the propagation and relaxation of backbone tension. Under many experimental circumstances, realized, e.g.,…
We describe the relation between the dynamical properties of a quasiperiodically forced orientation-preserving circle homeomorphism and the behavior of the fibered rotation number with respect to strictly monotone perturbations. Despite the…
Starting from the random phase approximation for the weakly coupled multiband tightly-bounded electron systems, we calculate the dielectric matrix in terms of intraband and interband transitions. The advantages of this representation with…
The paper addresses the boundary control of a class of hyperbolic PDEs, based on an equivalent representation in terms of an integral-difference equation. The situation is considered where direct compensation of reflection terms induces a…
We investigate pattern formation in self-oscillating systems forced by an external periodic perturbation. Experimental observations and numerical studies of reaction-diffusion systems and an analysis of an amplitude equation are presented.…
Kinetic relations are required in order to characterize nonclassical undercompressive shock waves and formulate a well-posed initial value problem for nonlinear hyperbolic systems of conservation laws. Such nonclassical waves arise in weak…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…