相关论文: Relativistic elastic membranes: rotating disks and…

We show that the equation of motion for a rigid one-dimensional elastic body (i.e. a rod or string whose speed of sound is equal to the speed of light) in a two-dimensional spacetime is simply the wave equation. We then solve this equation…

The dynamics of a membrane is a coupled system comprising a moving elastic surface and an incompressible membrane fluid. We will consider a reduced elastic surface model, which involves the evolution equations of the moving surface, the…

The buckling instabilities of core-shell systems, comprising an interior elastic sphere, attached to an exterior shell, have been proposed to underlie myriad biological morphologies. To fully discuss such systems, however, it is important…

We study the interaction between gravitational waves and elastic bodies within the framework of relativistic elasticity. Starting from the Lagrangian formulation of relativistic elasticity, we derive the linearized equations governing the…

The elasticity difference tensor, used in [1] to describe elasticity properties of a continuous medium filling a space-time, is here analysed from the point of view of the space-time connection. Principal directions associated with this…

The paper studies the equilibrium configurations of inextensible elastic membranes exhibiting lateral fluidity. Using a continuum description of the membrane's motions based on the surface Navier--Stokes equations with bending forces, the…

We use the image solution technique to compute the leading order frequency-dependent self-mobility function of a small solid particle moving perpendicular to the surface of a spherical capsule whose membrane possesses shearing and bending…

We study the dynamics of an elastic body whose shape and position evolve due to the gravitational forces exerted by a pointlike planet. The main result is that, if all the deformations of the satellite dissipate some energy, then under a…

Intrinsic nonlinear elasticity deals with the deformations of elastic bodies as isometric immersions of Riemannian manifolds into the Euclidean spaces (see Ciarlet [9,10]). In this paper, we study the rigidity and continuity properties of…

After briefly reviewing the theory of relativistic elasticity, we expand a general elastic Lagrangian to quadratic order and compute the main parameters for the linear elasticity of relativistic solids: the longitudinal and transverse…

We generalize recent study of the stability of isotropic (spherical) rotating membranes to the anisotropic ellipsoidal membrane. We find that while the stability persists for deformations of spin $l=1$, the quadrupole and higher spin…

The effects of viscoelasticity have been shown to manifest themselves via symmetry breaking. In this investigation, we show a novel phenomenon that arises from this idea. We observe that when a dense sphere is rotated near a wall (the…

There are many different formulations of relativistic elasticity. Most of them are only concerned with formal questions rather than questions regarding the PDE point of view. The aim of this thesis is to obtain various local existence…

The foundation of continuum elasticity theory is based on two general principles: (i) the force felt by a small volume element from its surrounding acts only through its surface (the Cauchy principle, justified by the fact that interactions…

We formulate and solve by semi-analytic means the axisymmetric equilibria of relativistic self-similar disks of infinitesimal vertical thickness. These disks are supported in the horizontal directions against their self-gravity by a…

We study the shapes of elastic membranes under the simultaneous exertion of tensile and compressive forces when the translational symmetry along the tension direction is broken. We predict a multitude of novel morphological phases in…

We study the axisymmetric impact of a rigid sphere onto an elastic membrane theoretically and experimentally. We derive governing equations from first principles and impose natural kinematic and geometric constraints for the coupled motion…

The purpose of this review it to present a renewed perspective of the problem of self-gravitating elastic bodies under spherical symmetry. It is also a companion to the papers [Phys. Rev. D105, 044025 (2022)], [Phys. Rev. D106, L041502…

Rotation is ubiquitous in the Universe, and recent kinematic surveys have shown that early type galaxies and globular clusters are no exception. Yet the linear response of spheroidal rotating stellar systems has seldom been studied. This…

We study the behaviour of a specific system of relativistic elasticity in its own gravitational field: a static, spherically symmetric shell whose wall is of arbitrary thickness consisting of hyperelastic material. We give the system of…