Related papers: Non-trivial solution to a simple problem
This paper concerns the dynamics of a layer of incompressible viscous fluid lying above a vertically oscillating rigid plane and with an upper boundary given by a free surface. We consider the problem with gravity and surface tension for…
We consider a single spike of ferrofluid, arising in a small cylindrical container, when a vertically oriented magnetic field is applied. The height of the spike as well as the surface topography is measured experimentally by two different…
An unconstrained, non-linearly elastic, semi-infinite solid is maintained in a state of large static plane strain. A power-law relation between the pre-stretches is assumed and it is shown that this assumption is well-motivated physically…
In this study, one-dimensional systems of masses connected by springs, i.e., spring-chain systems, are investigated numerically. The average kinetic energy of chain-end particles of these systems is larger than that of other particles,…
In this paper, we formulate a continuum theory of solidification within the context of finite-strain coupled thermoelasticity. We aim to fill a gap in the existing literature, as the existing studies on solidification typically decouple the…
This article concerns the stability of a model for mass-spring systems with positive damping and negative stiness. It is well known that when the coefficients are frozen in time the system is unstable. Here we find conditions on the…
We study a heavy piston of mass $M$ that separates finitely many ideal, unit mass gas particles moving in two or three dimensions. Neishtadt and Sinai previously determined a method for finding this system's averaged equation and showed…
We study the periodic motions of the coupled system $\mathscr S$, consisting of an incompressible Navier-Stokes fluid interacting with a structure formed by a rigid body subject to {\em undamped} elastic restoring forces and torque around…
The present work is essentially concerned with the development of statistical theory for the low temperature dislocation glide in concentrated solid solutions where atom-sized obstacles impede plastic flow. In connection with such a…
This paper presents a theoretical study of oscillatory and rotational instabilities of a solid spherical body, levitated electromagnetically in axisymmetric coils made of coaxial circular loops. We apply our previous theory to analyze the…
Spiral waves are a ubiquitous feature of the nonequilibrium dynamics of a great variety of excitable systems. In the limit of a large separation in timescale between fast excitation and slow recovery, one can reduce the spiral problem to…
A simple model for solid friction is analyzed. It is based on tangential springs representing interlocked asperities of the surfaces in contact. Each spring is given a maximal strain according to a probability distribution. At their maximal…
We consider conformation dynamics of a chain-like three-body bead-spring model, in which three point masses are connected in series by two springs and the conformation is defined by the bending angle between the two springs. Previous…
We solve several problems that involve imposing metrics on surfaces. The problem of a strip with a linear metric gradient is formulated in terms of a Lagrangean similar to those used for spin systems. We are able to show that the low energy…
The elastic response of mechanical, chemical, and biological systems is often modeled using a discrete arrangement of Hookean springs, either representing finite material elements or even the molecular bonds of a system. However, to date,…
The main purpose of this paper is to exhibit a simple variational setting for finding fully nontrivial solutions to the weakly coupled elliptic system (1.1). We show that such solutions correspond to critical points of a…
Two different methods are used to study the existence and stability of the (1+1)-dimensional $\Phi^4$ oscillon. The variational technique approximates it by a periodic function with a set of adiabatically changing parameters. An alternative…
The closed relativistic string carrying a point-like mass in the space with nontrivial geometry is considered. For rotational states of this system (resulting in non-trivial Regge trajectories) the stability problem is solved. It was shown…
We study the nonlinear behaviors of mass-spring systems damped by dry friction using simulation by a nonlinear LC circuit damped by anti-parallel diodes. We show that the differential equation for the electric oscillator is equivalent to…
A simple text book problem in mechanics\cite{klep}, describes a massive horizontal bar placed on two oppositely rotating rollers, kept at a fixed center to center distance. Subsequent motion is to be found out in presence of kinetic…