Related papers: Nonlinear-damped Duffing oscillators having finite…
This work is focused on the doubly nonlinear equation, whose solutions represent the bending motion of an extensible, elastic bridge suspended by continuously distributed cables which are flexible and elastic with stiffness k^2. When the…
A modification of Coulomb's law of friction uses a variable coefficient of friction that depends on a power law in the energy of mechanical oscillation. Through the use of three different exponents: 0, 1/2 and 1; all commonly encountered…
The response of an oscillating granular damper to an initial perturbation is studied using experiments performed in microgravity and granular dynamics mulations. High-speed video and image processing techniques are used to extract…
We discuss algorithms applicable to the numerical solution of second-order ordinary differential equations by finite-differences. We make particular reference to the solution of the dissipative particle dynamics fluid model, and present…
A theoretical and experimental investigation is presented on the intermodal coupling between the flexural vibration modes of a single clamped-clamped beam. Nonlinear coupling allows an arbitrary flexural mode to be used as a self-detector…
We study how oscillations of a scalar field condensate are damped due to dissipative effects in a thermal medium. Our starting point is a non-linear and non-local condensate equation of motion descending from a 2PI-resummed effective action…
This paper is concerned with longtime dynamics of semilinear Lam\'e systems $$ \partial^2_t u - \mu \Delta u - (\lambda + \mu) \nabla {\rm div} u + \alpha \partial_t u + f(u) = 0, $$ defined in bounded domains of $\mathbb{R}^3$ with…
Recently, we have studied a delay differential equation which has a coefficient that is a linear function of time. The equation has shown the oscillatory transient dynamics appear and disappear as the delay is increased between zero to…
A new description of the dynamics of warped accretion discs is presented. A theory of fully nonlinear, slowly varying bending waves is developed, involving a proper treatment of viscous fluid dynamics but neglecting self-gravitation. The…
We study discrete time crystals (DTCs) in periodically driven quantum systems, in the presence of non-Markovian dissipation. In contrast to DTCs observed in earlier works in the presence of Markovian dynamics, using the open Dicke model in…
We show that any second order linear ordinary diffrential equation with constant coefficients (including the damped and undumped harmonic oscillator equation) admits an exact discretization, i.e., there exists a difference equation whose…
Finite-time coherent sets represent minimally mixing objects in general nonlinear dynamics, and are spatially mobile features that are the most predictable in the medium term. When the dynamical system is subjected to small parameter…
This article presents a new scheme for studying the dynamics of a quintic wave equation with nonlocal weak damping in a 3D smooth bounded domain. As an application, the existence and structure of weak, strong, and exponential attractors for…
According to the wave power rule, the second derivative of a function with respect to the variable t is equal to negative n times the function raised to the power of 2n-1. Solving the ordinary differential equations numerically results in…
Models of inviscid incompressible fluid are considered, with the kinetic energy (i.e., the Lagrangian functional) taking the form ${\cal L}\sim\int k^\alpha|{\bf v_k}|^2d^3{\bf k}$ in 3D Fourier representation, where $\alpha$ is a constant,…
We report a study of the rotational dynamics in double-walled nanotubes using molecular dynamics simulations and a simple analytical model reproducing very well the observations. We show that the dynamic friction is linear in the angular…
We present a microscopic theory of nonlinear damping and dephasing of low-frequency eigenmodes in nano- and micro-mechanical systems. The mechanism of the both effects is scattering of thermally excited vibrational modes off the considered…
Domino tilings have been studied extensively for both their statistical properties and their dynamical properties. We construct a subshift of finite type using matching rules for several types of dominos. We combine the previous results…
We prove the existence of nonlinear normal modes for general systems of two coupled nonlinear oscillators. Facilitating the comparison principle for ordinary differential equations it is shown that there exist exact solutions representing a…
The normal form and zero dynamics are powerful tools useful in analysis and control of both linear and nonlinear systems. There are no simple closed form solutions to the general zero dynamics problem for nonlinear systems. A few algorithms…