Related papers: Nonlinear Damping of the 'Linear' Pendulum

Recently, there has been great interest in connections between continuous-time dynamical systems and optimization methods, notably in the context of accelerated methods for smooth and unconstrained problems. In this paper we extend this…

The evolution of the interface separating a conduit of light, viscous fluid rising buoyantly through a heavy, more viscous, exterior fluid at small Reynolds numbers is governed by the interplay between nonlinearity and dispersion. Previous…

For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…

Nonlinearity in many systems is heavily dependent on component variation and environmental factors such as temperature. This is often overcome by keeping signals close enough to the device's operating point that it appears approximately…

A central challenge in neuroscience is understanding how neural system implements computation through its dynamics. We propose a nonlinear time series model aimed at characterizing interpretable dynamics from neural trajectories. Our model…

A mathematical model is derived for the dynamics of a cylinder, or wheel, rolling over a thin viscous film. The model combines the Reynolds lubrication equation for the fluid with an equation of motion for the wheel. Two asymptotic limits…

We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and…

The nonlinear sigma model (NLSM) epitomises a field-theoretical approach to (interacting) electrons in disordered media. These lectures are aimed at the audience who might have vaguely heard about its existence but know very little of what…

We analyze the dynamics of a driven, damped pendulum as used in mechanical clocks. We derive equations for the amplitude and phase of the oscillation, on time scales longer than the pendulum period. The equations are first order ODEs and…

The dynamics of viscous thin-film particle-laden flows down inclined surfaces are commonly modeled with one of two approaches: a diffusive flux model or a suspension balance model. The diffusive flux model assumes that the particles migrate…

The development of efficient and robust dynamic models is fundamental in the field of systems and control engineering. In this paper, a new formulation for the dynamic model of nonlinear mechanical systems, that can be applied to different…

A nonlinear inequality is formulated in the paper. An estimate of the rate of growth/decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can…

A vibrational model of transport properties of dense fluids assumes that solid-like oscillations of atoms around their temporary equilibrium positions dominate the dynamical picture. The temporary equilibrium positions of atoms do not form…

A non-perturbative nonlinear statistical approach is presented to describe turbulent magnetic systems embedded in a uniform mean magnetic field. A general formula in the form of an ordinary differential equation for magnetic field-line…

We consider binary mixtures of fluids with components having different temperatures. A new dynamical pressure term is associated with the difference of temperatures between components even if fluid viscosities are null. The non-equilibrium…

Propellant sloshing is a well-known, but not completely mastered phenomenon in space vehicles. It is particularly critical in both microgravity environments - such as interplanetary spacecraft requiring high pointing stability - and high-g…

We use the entropy method to analyze the nonlinear dynamics and stability of a continuum kinetic model of an active nematic suspension. From the time evolution of the relative entropy -- an energy-like quantity in the kinetic model -- we…

Using molecular dynamics simulations, we determine the linear and nonlinear viscoelastic properties of a model polymer melt in the unentangled regime. Several approaches are compared for the computation of linear moduli, including…

To circumvent the ill-posedness issues present in various models of continuum fluid mechanics, we present a dynamical systems approach aiming at selection of physically relevant solutions. Even under the presence of infinitely many…

Numerical simulations of the flow in an extrusion damper are performed using a finite volume method. The damper is assumed to consist of a shaft, with or without a spherical bulge, oscillating axially in a containing cylinder filled with a…