Related papers: Short Time Angular Impulse Response of Rayleigh Be…
A recent large deflection cantilever model is considered. The principal nonlinear effects come through the beam's inextensibility---local arc length preservation---rather than traditional extensible effects attributed to fully restricted…
A model for the structure function constant associated with index of refraction fluctuations in Rayleigh-Benard turbulence is developed. The model is based upon the following assumptions: (1) the turbulence is homogeneous and isotropic at…
The Schr\"odinger equation is not frequently used in the framework of the classical mechanics, though historically this equation was derived as a simplified equation, which is equivalent to the classical Germain-Lagrange dynamic plate…
A continuum of excitations in interacting one-dimensional systems is bounded from below by a spectral edge that marks the lowest possible excitation energy for a given momentum. We analyse short-range interactions between Fermi particles…
The Euler-Bernoulli equation describing the deflection of a beam is a vital tool in structural and mechanical engineering. However, its derivation usually entails a number of intermediate steps that may confuse engineering or science…
The frequency-dependent linear response of a plasma is studied in the finite-temperature Thomas-Fermi approximation, with electron dynamics described using Bloch hydrodynamics. The variational framework of average-atoms in a plasma is used.…
This work presents theoretical and numerical models for the backscattering of two-dimensional Rayleigh waves by an elastic inclusion, with the host material being isotropic and the inclusion having arbitrary shape and crystallographic…
We investigate how Rayleigh waves interact with modulated resonators located on the free surface of a semi-infinite elastic medium. We begin by studying the dynamics of a single resonator with time-modulated stiffness. In particular, we…
We investigate the propagation of Rayleigh waves in a half-space coupled to a nonlinear metasurface. The metasurface consists of an array of nonlinear oscillators attached to the free surface of a homogeneous substrate. We describe,…
The present work attempts to present a consistent and efficient approach to piezoelectric laminated beams. The influence of hypotheses on three-dimensional sectional deformations and stress distributions on the estimate of the beam…
Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…
A class of three-dimensional initial data characterized by uniformly large vorticity is considered for the Euler equations of incompressible fluids. The fast singular oscillating limits of the Euler equations are studied for parametrically…
New corrections to the equation of motion and total collapsing time of an empty spherical cavity immersed in an infinite incompressible medium are proposed on the assumption of a non-uniform density. The dimensionless number quantifying the…
We numerically investigate the effects of fiber aspect ratio, roughness, flexibility, and flow inertia on the rheology of concentrated suspensions. We perform direct numerical simulations modeling the fibers, suspended in an incompressible…
Numerical simulations of the time-dependent Swift-Hohenberg equation are used to test predictions of Cross [Phys. Rev. A 25:1065-1076 (1982)] that Rayleigh-Benard convection in the form of straight rolls or of an array of dislocations may…
One of the fundamental ways of representing a droplet shape is through its Rayleigh-mode decomposition, in which each mode corresponds to a distinct surface-energy content. The influence of these modes on free oscillation dynamics has been…
We introduce Rayleigh functional for nonlinear systems. It is defined using the energy functional and the normalization properties of the variables of variation. The key property of the Rayleigh quotient for linear systems is preserved in…
In this paper a lower bound for solutions to the secular equation of the Schr\"odinger equation with basis functions discontinuous on boundaries of divided regions is given. If the functions do not have the discontinuity, the bound reduces…
The asymptotic analysis of kinetic models describing the behavior of particles interacting through alignment is performed. We will analyze the asymptotic regime corresponding to large alignment frequency where the alignment effects are…
Data-driven models for predicting dynamic responses of linear and nonlinear systems are of great importance due to their wide application from probabilistic analysis to inverse problems such as system identification and damage diagnosis. In…