Related papers: On static equilibrium and balance puzzler
We consider a rigid body acted upon by two forces, a constant force and the collective force of interaction with a continuum of particles. We assume that some of the particles that collide with the body reflect elastically (specularly),…
From the axiom of the unrestricted repeatability of all experiments, Bondi and Gold argued that the universe is in a stable, self-perpetuating equilibrium state. This concept generalizes the usual cosmological principle to the perfect…
We determine and study the steady state of two independent two-level systems weakly coupled to a stationary non-equilibrium environment. Whereas this bipartite state is necessarily uncorrelated if the splitting energies of the two-level…
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system coupling operator. A general stability result is given for a class of perturbations to the system…
The question of the allowed signs for the static dielectric function for exactly homogeneous ground states in many body systems is further analyzed. The discussion is restricted to zero temperature situation. Firstly, it is argued that the…
The stability of a special class of equilibria for the free rigid body on $\mathfrak{so}(5)$ is discussed. An instability region and two stability regions are established. The list of constants of motion which assure the complete…
Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a…
One of the main aspects of switched affine systems that makes their stabilizability study intricate is the existence of (generally) infinitely many equilibrium points in the state space. Thus, prior to designing the switched control, the…
An equilibrium statistical system is known to be stable if the fluctuations of global observables are normal, when their dispersions are proportional to the number of particles, or to the system volume. A general theorem is rigorously…
By using a physically-relevant and theory independent definition of measurement-based equilibration, we show quantitatively that equilibration is easier for quantum systems than for classical systems, in the situation where the initial…
We study the static equilibrium of an elastic sphere held in a rigid groove by gravity and frictional contacts, as determined by contact mechanics. As a function of the opening angle of the groove and the tilt of the groove with respect to…
The Einstein static universe has played a central role in a number of emergent scenarios recently put forward to deal with the singular origin of the standard cosmological model. Here we study the existence and stability of the Einstein…
We consider the problem of constructing static, elastic, many-body systems in Einstein gravity. The solutions constructed are deformations of static many-body configurations in Newtonian gravity. No symmetry assumptions are made.
In this talk I will introduce the principle of stochastic stability and discussing its consequences both at equilibrium and off-equilibrium.
We demonstrate existence in the ``large" and uniqueness in the ``small" of equilibrium configurations for the coupled system consisting of a Navier-Stokes fluid interacting with a rigid body subjected to spring forces and restoring moments.…
Voltage instability is a major threat in power system operation. The growing presence of constant power loads significantly aggravates this issue, hence motivating the development of new analysis methods for both existence and stability of…
When modelling driven steady states of matter, it is common practice either to choose transition rates arbitrarily, or to assume that the principle of detailed balance remains valid away from equilibrium. Neither of those practices is…
A century ago, the foundations of equilibrium statistical mechanics were laid. For a system in equilibrium with a thermal bath, much is understood through the Boltzmann factor, exp{-H[C]/kT}, for the probability of finding the system in any…
Any control law for aircraft asymptotic stabilization requires the existence of an equilibrium condition, also called trim flight condition. At a constant velocity flight, for instance, there must exist an aircraft orientation such that…
Legged locomotion has received increasing attention from the robotics community. In this respect, contact stability plays a critical role in ensuring that robots maintain balance, and it is a key element for balancing and walking…