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In the present paper we consider convection and cracking instabilities as well as their interplay. We develop a simple criterion to identify equations of state unstable to convection, and explore the influence of buoyancy on cracking (or…
The evolution of small perturbations around rotating black branes and strings, which are low energy solutions of string theory, are investigated. For simplicity, we concentrate on the Kerr solution times transverse flat extra dimensions,…
We give a topological classification of stable and unconfined massive particles and strings (and some instantons) in worldvolume theories of M5-branes and their dimensional reductions, generalizing Witten's classification of strings in SYM.…
The quark mass dependence of the energy spectrum in the Nambu--Goto string with point--like masses (quarks) at its ends is analyzed. To this end, linearized equations of motion and boundary conditions in this model are considered. It is…
In the spatial circular restricted three-body problem librational motion around the Lagrangian points $L_4$ and $L_5$ exists up to high inclinations of the massless object. We report the results of numerical investigations on the stability…
The steady states of an isotone electric system are described by an isotone function with respect to the componentwise order. When there are steady states, we highlight a dominant steady state and we study its domain of attraction for the…
In previous work we analyzed the linear stability of non-relativistic $\ell$-boson stars with respect to radial modes and showed that ground state configurations are stable with respect to these modes, whereas excited states are unstable.…
It is possible to condense a macroscopic number of bosons into a single mode. Adding interactions the question arises whether the condensate is stable. For repulsive interaction the answer is positive with regard to the ground-state, but…
We study macroscopic entanglement of various pure states of a one-dimensional N-spin system with N>>1. Here, a quantum state is said to be macroscopically entangled if it is a superposition of macroscopically distinct states. To judge…
We present an equation of state for elastic matter which allows for purely longitudinal elastic waves in all propagation directions, not just principal directions. The speed of these waves is equal to the speed of light whereas the…
The motion of a point mass in the J2 problem is generalized to that of a rigid body in a J2 gravity field. Different with the original J2 problem, the gravitational orbit-rotation coupling of the rigid body is considered in this generalized…
The Cauchy problem for the attraction-repulsion chemotaxis system in the whole $n$-dimensional space has uncountable constant steady states. In the attraction chemotaxis system, each positive constant steady state is stable if it is in a…
Neutron stars are among the densest known objects in the universe and an ideal laboratory for the strange physics of super-condensed matter. While the simultaneously measurements of mass and radius of non-rotating neutron stars may impose…
We discuss stability of Q-balls interacting with fermions in theory with small coupling constant g. We argue that for configurations with large global U(1)-charge Q the problem of classical stability becomes more subtle. For example, in…
The planetary restricted three-body problem (RTBP) is considered. The primary mass M is much more than another masses mj, i=1..N, which revolve around M. The massless probe particle m moves on elliptic orbit, is perturbed by mj. It is well…
We extend our earlier work, regarding the perturbative stability of string configurations used for computing the interaction potential of heavy quarks within the gauge/gravity correspondence, to cover a more general class of gravity duals.…
We discuss the existence and stability of circular orbits of a relativistic point particle moving in a central force field. The stability condition is somewhat more restrictive in Special Relativity. In the particular case of attractive…
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…
We describe the dynamics of a stream of equally spaced macroscopic particles in orbit around a central body (e.g. a planet or star). A co-orbital configuration of small bodies may be subject to gravitational instability, which takes the…
Equilibrium states of a closed semiflexible polymer binding to a cylinder are described. This may be either by confinement or by constriction. Closed completely bound states are labeled by two integers: the number of oscillations, $n$, and…