Related papers: On self-gravitating polytropic elastic balls
The symmetries of the general Euler equations of fluid dynamics with polytropic exponent are determined using the Kaluza-Klein type framework of Duval et $\it{al}$. In the standard polytropic case the recent results of O'Raifeartaigh and…
The plasma of quarks and gluons created in ultrarelativistic heavy-ion collisions turns out to be paramagnetic. In the presence of a background magnetic field, this paramagnetism thus leads to a pressure anisotropy, similar to anisotropies…
Non-ideal fluids are generally subject to the occurrence of non-isotropic pressure tensors, whose determination is fundamental in order to characterize their dynamical and thermodynamical properties. This requires the implementation of…
There is introduced a class of barotropic equations of state (EOS) which become polytropic of index $n = 5$ at low pressure. One then studies asymptotically flat solutions of the static Einstein equations coupled to perfect fluids having…
Elastomers filled with liquid inclusions -- as opposed to conventional solid fillers -- are a recent trend in the soft matter community because of their unique range of mechanical and physical properties. Such properties stem, in part, from…
Polytropic stars are useful tools for learning about stellar structure without the complexity of comprehensive stellar models. These models rely on a certain power-law correlation between the star's pressure and density. This paper proposes…
We have previously introduced the parameter `alpha' as an indicator of stability to m=2 nonaxisymmetric modes in rotating, self-gravitating, axisymmetric, gaseous and stellar systems. This parameter can be written as a function of the total…
We develop a new formalism to study the dynamics of fluid polytropes in three dimensions. The stars are modeled as compressible ellipsoids and the hydrodynamic equations are reduced to a set of ordinary differential equations for the…
We propose a nonlinear elasto-plastic model, for which a specific class of hyperbolic elasticity arises as a straight consequence of the yield criterion invariance on the plasticity level. We superimpose this nonlinear elastic (or…
The Lagrangian fluid description is employed to solve the initial value problem for one-dimensional, compressible fluid flows represented by the Euler-Poisson system. Exact nonlinear and time-dependent solutions are obtained, which exhibit…
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…
We argue that an arbitrary general relativistic static anisotropic fluid sphere, (static and spherically symmetric but with transverse pressure not equal to radial pressure), can nevertheless be successfully mimicked by suitable linear…
We introduce a class of continuum mechanical models aimed at describing the behaviour of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant…
We study a spherical, self-gravitating fluid model, which finds applications in cosmic structure formation. We argue that since the system features nonlinearity and gravity-induced dispersion, the emergence of solitons becomes possible. We…
In this work we evaluate the physical acceptability of relativistic anisotropic spheres modeled by two polytropic equations of state -- with the same newtonian limit -- commonly used to describe compact objects in General Relativity. We…
Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to nonlinear mechanics and nontrivial geometrical effects. While numeric approaches are successful, analytic tools and…
The process of gravitational accretion of initially homogeneous gas onto a solid ball is studied with methods of fluid dynamics. The fluid partial differential equations for polytropic flow can be solved exactly in an early stage, but this…
We study the statistical mechanics of the self-gravitating gas at thermal equilibrium with two kinds of particles. We start from the partition function in the canonical ensemble which we express as a functional integral over the densities…
We propose a new discrete element method supporting general polyhedral meshes. The method can be understood as a lowest-order discontinuous Galerkin method parametrized by the continuous mechanical parameters (Young's modulus and Poisson's…
The large deflections of cantilevered beams and plates are modeled and discussed. Traditional nonlinear elastic models (e.g., that of von Karman) employ elastic restoring forces based on the effect of stretching on bending, and these are…