Related papers: Stability of $\mathbb{Z}^2$ configurations in 3D
Observational surveys show that at least ~ 30% of short-period multiplanetary systems host tightly packed planets, some of which are locked in stable chains of mean-motion resonances. Despite recent progress, the dynamical stability of…
There are at least three fundamental states of matter, depending upon temperature and pressure: gas, liquid, and solid (crystal). These states are separated by first-order phase transitions between them. In both gas and liquid phases the…
We study the stability of the circular orbits of the electromagnetic two-body problem of classical electrodynamics. We introduce the concept of resonant dissipation, i.e. a motion that radiates the center-of-mass energy while the…
Compatibility conditions are investigated for planar network structures consisting of nodes and connecting bars; these conditions restrict the elongations of bars and are analogous to the compatibility conditions of deformation in continuum…
We consider a special case of the three dimensional Vlasov-Poisson system where the particles are restricted to a plane, a situation that is used in astrophysics to model extremely flattened galaxies. We prove the existence of steady states…
Defects are crucial in determining a variety of material properties especially in low dimensions. In this work, we study point defects in monolayer alpha-phase Ruthenium (III) chloride (alpha-RuCl3), a promising candidate to realize quantum…
The aim of this work is to study the dynamics and stability of soft shape-morphing configurations and specifically the modes of interaction between the front and rear airfoil segments. Initially we present several steady-state solutions,…
Self-assembly of colloidal particles is a promising avenue to control the shape and dynamics of larger aggregates. However, achieving the necessary fine control over the dynamics and specificity of the bonds between such particles remains a…
A geometrical analysis of the stability of nuclei against deformations is presented. In particular, we use Catastrophe Theory to illustrate discontinuous changes in the behavior of nuclei with respect to deformations as one moves in the N -…
We use inverse methods of statistical mechanics to explore trade-offs associated with designing interactions to stabilize self-assembled structures against changes in density or temperature. Specifically, we find isotropic,convex-repulsive…
In this paper, we establish a general setup for studying incidence-preserving motions of projective geometric configurations of points and lines via a "projective rigidity matrix". The spaces of infinitesimal motions of a point-line…
We consider a three-component Fermi gas that has SU(3) symmetry and is confined to two dimensions (2D). For realistic cold atomic gas experiments, we show that the phase diagram of the quasi-2D system can be characterized using two 2D…
In the paper we have developed a theory of stability preserving structural transformations of systems of second-order ordinary differential equations (ODEs), i.e., the transformations which preserve the property of Lyapunov stability. The…
The relative equilibria for the spherical, finite density 3 body problem are identified. Specifically, there are 28 distinct relative equilibria in this problem which include the classical 5 relative equilibria for the point-mass 3-body…
We consider $n$-component fixed-length order parameter interacting with a weak random field in $d=1,2,3$ dimensions. Relaxation from the initially ordered state and spin-spin correlation functions have been studied on lattices containing…
Three quantum particles with on-site repulsion and nearest-neighbour attraction on a one-dimensional lattice are considered. The three-body Schroedinger equation is reduced to a set of single-variable integral equations. Energies of…
We reconsider both the global and local stability of solutions of continuously evolving dynamical systems from a geometric perspective. We clarify that an unambiguous definition of stability generally requires the choice of additional…
The homology groups of a simplicial complex reveal fundamental properties of the topology of the data or the system and the notion of topological stability naturally poses an important yet not fully investigated question. In the current…
We survey our recent results on stability of 3D crystals in the Schr\"odinger-Poisson-Newton model. We establish orbital stability for the ground state in the case of finite crystal and linear stability for infinite crystals under novel…
This work deals with the presence of topological structures in models of two real scalar fields in the two-dimensional spacetime. The subject concerns the presence of a geometric constriction, which appears with a modification of the…