Related papers: Unstable Rotational States of Closed String with M…
In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed…
We consider the problem of boundary control for a vibrating string with $N$ interior point masses. We assume the control is at the left end, and the string is fixed at the right end. Singularities in waves are "smoothed" out to one order as…
We ask whether a stationary lattice in dimension $d$ whose points are shifted by identically distributed but possibly dependent perturbations remains hyperuniform. When $d = 1$ or $2$, we show that it is the case when the perturbations have…
We introduce multi-soliton sets in the two-dimensional medium with the second-harmonic-generating nonlinearity subject to spatial modulation in the form of a triangle of singular peaks. Various families of symmetric and asymmetric sets are…
We review, critique, and extend results related to the problem of closed loop shape equilibria of a string shooter, a type of catenary consisting of steady, axially moving configurations of an inertial, inextensible, perfectly flexible…
We consider the motion of point masses given by a natural extension of Newtonian gravitation to spaces of constant positive curvature. Our goal is to explore the spectral stability of tetrahedral orbits of the corresponding 4-body problem…
Scalar, spherically symmetric, radially excited boson stars were previously shown to be stabilized, against spherical dynamics, by sufficiently strong self-interactions. Here, we further test their stability now in a full 3+1D evolution. We…
We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and non-uniform stability of the closed-loop system. We apply the…
We consider a simple model for multidimensional cone-wise linear dynamics around cusp-like equilibria. We assume that the local linear evolution is either $\mathbf{v}^\prime=\mathbb{A}\mathbf{v}$ or $\mathbb{B}\mathbf{v}$ (with…
We consider a one dimensional elastic string as a set of massless beads interacting through springs characterized by anisotropic elastic constants. The string, driven by an external force, moves in a medium with quenched disorder. We…
Assuming that the Casimir scaling hypothesis is well verified in QCD, masses of glueballs and hybrid gluelumps (gluon with a point-like $c\bar c$ pair) are computed within the rotating string formalism. In our model, two gluons are attached…
Gauged boson stars are exotic compact objects that can potentially mimic black holes or magnetized neutron stars in both their gravitational and electromagnetic signatures, offering a compelling new description or even an alternative…
We show that the electroweak $Z-$string can be stabilized by the presence of bound states of a complex scalar field. We argue that fermions coupled to the scalar field of the string can also make the string stable and discuss the physical…
We investigate the collective motion of magnetic rotors suspended in a viscous fluid under an uniform rotating magnetic field. The rotors are positioned on a square lattice, and low Reynolds hydrodynamics is assumed. For a $3 \times 3$…
This paper deals with the problem of string stability of interconnected systems with double-integrator open loop dynamics (e.g.~acceleration-controlled vehicles). We analyze an asymmetric bidirectional linear controller, where each vehicle…
The stability of the multiple equilibrium states of a hexagram ring with six curved sides is investigated. Each of the six segments is a rod having the same length and uniform natural curvature. These rods are bent uniformly in the plane of…
Hadron bubbles that nucleate with radius $R_{nuc}$ in a quark sea (if the phase transition is first order) are shown to be unstable to the growth of nonspherical structure when the bubble radii exceed a critical size of $20 - 10^3$…
We analyze stability of a thin inextensible elastic rod which has non-vanishing spontaneous generalized torsions in its stress-free state. Two classical problems are studied, both involving spontaneously twisted rods: a rectilinear beam…
In this paper we have examined the linear stability of triangular equilibrium points in the generalised photogravitational restricted three body problem with Poynting-Robertson drag. We have found the position of triangular equilibrium…
Rotations on the circle by irrational numbers give rise to uniquely ergodic Sturm dynamical systems. We show that rotations by badly approximable irrationals have the property of fast ergodicity. It was shown recently that any Sturmian…