Related papers: Static self-gravitating Newtonian elastic balls
In this thesis we investigate the stationary properties and formation process of a class of nontopological solitons, namely Q-balls. We explore both the quantum-mechanical and classical stability of Q-balls that appear in polynomial,…
The application of variational principles for analyzing problems in the physical sciences is widespread. Cantilever-like problems, where one end is fixed and the other end is free, have received less attention in terms of their stability…
We investigate the dynamics of $U(1)$ gauged Q-balls using fully three-dimensional numerical simulations. We consider two different scenarios: first, the classical stability of gauged Q-balls with respect to generic three-dimensional…
The explicit relationship is determined between the interior properties of a static cylindrical matter distribution and the metric of the exterior space-time according to Einstein gravity for space-time dimensionality larger or equal to…
We consider the problem of the motion of $N$ bodies in a self-gravitating system in two spacetime dimensions. We point out that this system can be mapped onto the quantum-mechanical problem of an N-body generalization of the problem of the…
This work focuses on the stability analysis of an Euler Bernoulli cantilever beam with a tip mass at the free end, subject to a follower force. This can serve as a viable model for analysis of elastic instability occurring due to…
We consider the system of two material points that interact by elastic forces according to Hooke's law and their motion is restricted to certain curves lying on the plane. The nonintegrability of this system and idea of the proof are…
The theory presented in this monograph establishes the first mathematically rigorous result on the global nonlinear stability of self-gravitating matter under small perturbations of an asymptotically flat, spacelike hypersurface of…
The relativistic theory of elasticity is reviewed within the spherically symmetric context with a view towards the modeling of star interiors possessing elastic properties such as theones expected in neutron stars. Emphasis is placed on…
This study considers the stability of a non-inflectional elastica under a conservative end force subject to the Dirichlet, mixed, and Neumann boundary conditions. It is demonstrated that the non-inflectional elastica subject to the…
A perfectly elastic beam is situated on top of a two dimensional fluid canister. The beam is deforming in accordance to an interaction with a Navier-Stokes fluid. Hence a hyperbolic equation is coupled to the Navier-Stokes equation. The…
We study the statics and dynamics of a stable, mobile, three-dimensional matter-wave spherical quantum ball created in the presence of an attractive two-body and a very small repulsive three-body interaction. The quantum ball can propagate…
The aim of this short note is to give a synthetic presentation of the mathematical elements that are used to solve the elastic wave system of equations in a bounded anisotropic elastic body, in a general framework. In particular, the proof…
In this work we deal with nontopological solutions of the Q-ball type in two spacetime dimensions. We study models of current interest, described by a Higgs-like and other, similar potentials which unveil the presence of exact solutions. We…
Although fully elastic when static, granular media become transiently elastic when being slowly sheared -- during which both the elastic energy and stress relax. Starting from this observation, we cogently derive the framework for granular…
A generalization of the Euler's elastic problem, i.e., finding a stationary configuration (planar elastica) of the Bernoulli's thin ideal elastic rod with boundary conditions defined through fixed endpoints and/or tangents at the endpoints,…
This article is a description of elasticity theory for readers with mathematical background. The first sections are an abridgment of parts of the book by Marsden and Hughes, including a compact identification of the equations of motion as…
We consider the system of N (\ge 2) elastically colliding hard balls with masses m_1,..., m_N, radius r, moving uniformly in the flat torus T_L^{\nu}= R^\nu/L \cdot Z^\nu, \nu \ge 2. It is proved here that the relevant Lyapunov exponents of…
We show that the vibrational response of a glassy liquid at finite frequencies can be described by continuum mechanics despite the vast degeneracy of the vibrational ground state; standard continuum elasticity assumes a unique ground state.…
Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations of motion of Newtonian type ("acceleration equals forces") which determine the motion of points in the complex plane. These…