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We initiate the development of a theory of the elasticity of nanoscale objects based upon new physical concepts which remain properly defined on the nanoscale. This theory provides a powerful way of understanding nanoscale elasticity in…
We consider the linear equation of state for matter distributions that may be applied to strange stars with quark matter. In our general approach the compact relativistic body allows for anisotropic pressures in the presence of the…
Some compact stars may contain deconfined quark matter, forming hybrid stars or quark stars. If the quark matter forms an inhomogeneous condensate in the crystalline color superconducting phase, its rigidity may be high enough to noticeably…
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…
Almost all available results in elasticity on curved topographies are obtained within either a small curvature expansion or an empirical covariant generalization that accounts for screening between Gaussian curvature and disclinations. In…
Amongst a number of modified theories of gravity, the Rastall theory has been propounded to address some shortcomings of the standard theory of general relativity. Our purpose is to investigate this framework's capacity to analyse stellar…
We shall consider some common models in linear thermo-elasticity within a common structural framework. Due to the flexibility of the structural perspective we will obtain well-posedness results for a large class of generalized models…
We consider static massive thin cylindrical shells (tubes) as the sources in Einstein's equations. They correspond to $\dl$- and $\dl'$-function type energy-momentum tensors. The corresponding metric components are found explicitly. They…
We derive the equations of motion for relativistic elastic membranes, that is, two-dimensional elastic bodies whose internal energy depends only on their stretching, starting from a variational principle. We show how to obtain conserved…
We study the elastic scattering of quantum particles based on a real Hilbert space approach to quaternionic quantum mechanics ($\mathbbm H$QM) and derive expression for the wave function, the phase shifts, as well as the optical theorem for…
We prove existence of solutions for an elastic body interacting with itself through its Newtonian gravitational field. Our construction works for configurations near one given by a self-gravitating ball of perfect fluid. We use an implicit…
The modeling of the elastic properties of disordered or nanoscale solids requires the foundations of the theory of elasticity to be revisited, as one explores scales at which this theory may no longer hold. The only cases for which…
We make use of continuum elasticity theory to investigate the collective modes that propagate along the edge of a two-dimensional electron liquid or crystal in a magnetic field. An exact solution of the equations of motion is obtained with…
Finite plasticity theories are still a subject of controversy and lively discussions. Among the approaches to finite elastoplasticity two became especially popular. The first, implemented in the commercial finite element codes, is based on…
This work develops the dynamics of perfectly elastic solid model for application to the outer crust of a magnetised neutron star. Particular attention is given to the Noether identities responsible for energy-momentum conservation, using a…
The purpose of this paper is to present a new mathematical model for the dynamics of thin Cosserat elastic plates. Our approach, which is based on a generalization of the classical Reissner-Mindlin plate theory, takes into account the…
We first review the phenomenology of viscous liquids and the standard models used for explaining the non-Arrhenius average relaxation time. Then the focus is turned to the so-called elastic models, arguing that these models are all…
We construct time independent configurations of two gravitating elastic bodies. These configurations either correspond to the two bodies moving in a circular orbit around their center of mass or strictly static configurations.
A macroscopic theory for the dynamics of elastic, isotropic matter in presence of electromagnetic fields is proposed here. We avail of Gordon's general relativistic derivation of Abraham's electromagnetic energy tensor as starting point.…
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…