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The analysis and the simulation of fluid extruded out of a die opening are of great importance in different industrial applications. Mathematical modeling and experimental studies of extrusion out of a constant die gap has been the subject…
Though extensively studied, hardness, defined as the resistance of a material to deformation, still remains a challenging issue for a formal theoretical description due to its inherent mechanical complexity. The widely applied Teter's…
The study aims at a derivation of generalized \RH relations, especially that for the entropy, for the case of different upstream/downstream polytropic indices and their implications. We discuss the solar/stellar wind interaction with the…
Gravitational instability is a key process that may lead to fragmentation of gaseous structures (sheets, filaments, haloes) in astrophysics and cosmology. We introduce here a method to derive analytic expressions for the growth rate of…
Calculating the primordial bispectrum predicted by a model of inflation and comparing it to what we see in the sky is very computationally intensive, necessitating layers of approximations and limiting the models which can be constrained.…
We discuss the standard Lane-Emden formalism as well as the one related to the slowly rotating objects. It is preceded by a brief introduction of different forms of the polytropic equation of state. This allows to study a wide class of…
We propose several descriptive measures to characterize the arrangements of planetary masses, periods, and mutual inclinations within exoplanetary systems. These measures are based in complexity theory and capture the global, system-level…
In this work, we investigate astrophysical systems in a Newtonian regime using anisotropic matter. For this purpose, we considered that both radial and tangential pressures satisfy a generalized Chaplygin-type equation of state. Using this…
In this paper, we propose a numerical method for computing solutions to Biot's fully dynamic model of incompressible saturated porous media [Biot;1956]. Our spatial discretization scheme is based on the three-field formulation (u-w-p) and…
Hyperuniform particle arrangements are characterized by a local number variance that grows more slowly than the volume of the observation window. We generalize this concept to describe particle systems in which particles carry weights:…
In an inflationary regime driven by a free massive inflaton we derive within a genuinely gauge invariant approach the backreaction effects due to long wavelength scalar fluctuations on the effective Hubble factor and equation of state with…
We propose finite element methods for compressible barotropic Stokes systems. We state convergence results for these methods and outline their proofs. The principal tools of the proofs are higher integrability estimates for the discrete…
We present an algorithm to generalize a plethora of well-known solutions to Einstein field equations describing spherically symmetric relativistic fluid spheres by relaxing the pressure isotropy condition on the system. By suitably fixing…
We extend our theory of amorphous packings of hard spheres to binary mixtures and more generally to multicomponent systems. The theory is based on the assumption that amorphous packings produced by typical experimental or numerical…
Solar-type stars generate spherical winds, which are pressure driven flows, that start subsonic, reach the sound speed at the sonic point and transition to supersonic flows. The sonic point, mathematically corresponds to a singularity of…
The early Universe inflation is well known as a promising theory to explain the origin of large scale structure of the Universe, a causal theory for the origin of primordial density fluctuations which may explain the observed density…
A density scaled diffusivity function for viscous liquids derived earlier [Phys. Rev. E 79, 032501 (2009)] is revisited, based on an improved equation of state assuming that the isothermal bulk modulus increases linearly with pressure.…
Spherically symmetric relativistic stars with the polytropic equation of state, which possess the local pressure anisotropy, are considered in the context of general relativity. The modified Lane-Emden equations are derived for the special…
We propose new construction of dependent variables for equations of an ideal barotropic fluid. This construction is based on a direct generalization of the known connection between Schroedinger equation and a system of Euler-type equations.…
An analytical solution in a closed form is obtained for the three-dimensional elastic strain distribution in an unlimited medium containing an inclusion with a coordinate-dependent lattice mismatch (an eigenstrain). Quantum dots consisting…