Related papers: On static equilibrium and balance puzzler
We prove that given a stress-free elastic body there exists, for sufficiently small values of the gravitational constant, a unique static solution of the Einstein equations coupled to the equations of relativistic elasticity. The solution…
The mathematical physics of mechanical systems in thermal equilibrium is a well studied, and relatively easy, subject, because the Gibbs distribution is in general an adequate guess for the equilibrium state. On the other hand, the…
Equilibrium thermodynamics describes the energy exchange of a body with its environment. Here, we describe the global energy exchange of an ideal gas in the Coutte flow in a thermodynamic-like manner. We derive a fundamental relation…
A conceptual framework for variational formulations of physical theories is proposed. Such a framework is displayed here just for statics, but it is designed to be subsequently adapted to variational formulations of static field theories…
We study equilibrium configurations of infinitely many identical particles on the real line or finitely many particles on the circle, such that the (repelling) force they exert on each other depends only on their distance. The main question…
Perturbative construction of the nonequilibrium steady state of a rotator under a stochastic forcing while subject to torque and friction
For a symmetric Hamiltonian system, lower bounds for the number of relative equilibria surrounding stable and formally unstable relative equilibria on nearby energy levels are given.
This paper provides a comprehensive analysis of stability and long-time behaviour of a coupled system constituted by two rigid bodies separated by a thin layer of lubricant. We show that permanent rotations of the whole system, with the…
A nonlinear parabolic differential equation is presented which has at least one equilibrium. This equilibrium is shown to have a negative definite linearization, but a spectrum which includes zero. An elementary construction shows that the…
The backbone of nonequilibrium thermodynamics is the stability structure, where entropy is related to a Lyapunov function of thermodynamic equilibrium. Stability is the background of natural selection: unstable systems are temporary, and…
In this paper the motion of two-phase, incompressible, viscous fluids with surface tension is investigated. Three cases are considered: (1) the case of heat-conducting fluids, (2) the case of isothermal fluids, and (3) the case of Stokes…
A new solution for a general half-plane contact in the steady state is presented. The contacting bodies are subject to a set of constant loads - normal force, shear force and bulk tension parallel with the interface - together with an…
We consider a rate-independent system with nonconvex energy under discontinuous external loading. The underlying space is finite dimensional and the loads are functions in $BV([0,T];\mathbb{R}^d)$. We investigate the stability of various…
In his treatise on floating bodies Archimedes determines the equilibrium positions of a floating paraboloid segment, but only in the case when the basis of the segment is either completely outside of the fluid or completely submerged. Here…
We consider the Lotka-Volterra system and provide necessary conditions for an equilibrium to be stable. Our results naturally complement earlier fundamental results by N. Adachi, Y. Takeuchi, and H. Tokumaru, who, in a series of papers,…
The stability of a system of $N$ equal sized mutually gravitating spheres resting on each other in a straight line and rotating in inertial space is considered. This is a generalization of the "Euler Resting" configurations previously…
The question of the stability of unstable states of dynamical systems that do not explicitly contain a small parameter, chaos and bifurcations in them has attracted attention ever since [1-14]. This is due to the fact that this problem…
We examine the stability of the "coast" motion of fish, that is to say, the motion of a neutrally buoyant fish at constant speed in a straight line. The forces and moments acting on the fish body are thus perfectly balanced. The fish motion…
We consider the multiverse in the intrinsically quantum mechanical framework recently proposed in Refs. [1,2]. By requiring that the principles of quantum mechanics are universally valid and that physical predictions do not depend on the…
Stability is a fundamental concept that refers to a system's ability to return close to its original state after disturbances. The minimal conditions for stability when system parameters vary in time, though common in physics, have been…