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We derived here in a systematic way, and for a large class of scaling regimes, asymptotic models for the propagation of internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid…
I present a generalization of the Ehrenfest urn model that is aimed at simulating the approach to equilibrium in a dilute gas. The present model differs from the original one in two respects: 1) the two boxes have different volumes and are…
The motion of a compressible inviscid radiative flow can be described by the radiative Euler equations, which consists of the Euler system coupled with a Poisson equation for the radiative heat flux through the energy equation. Although…
The maximum complexity momentum distribution for an isolated monodimensional ideal gas out of equilibrium is derived analytically. In a first approximation, it consists of a double non-overlapping Gaussian distribution. In good agreement…
Supernova can be polarized by an asymmetry in the explosion process, an off-center source of illumination, scattering in an envelope distorted by rotation or a binary companion, or scattering by the circumstellar dust. Careful polarimetry…
After decades of one-dimensional nucleosynthesis calculations, the growth of computational resources has meanwhile reached a level, which for the first time allows astrophysicists to consider performing routinely realistic multidimensional…
A fundamental two-fluid model for describing dynamics of a plasma is the Euler-Poisson system, in which compressible ion and electron fluids interact with their self-consistent electrostatic force. Global smooth electron dynamics were…
The concepts of symmetry and its breakdown are investigated in two different terms according to whether the resulting asymmetry is universal or only obtained for a special configuration: we shall illustrate this by considering in the first…
The numerical simulation of turbulence in stars has led to a rich set of possibilities regarding stellar pulsations, asteroseismology, thermonuclear yields, and formation of neutron stars and black holes. The breaking of symmetry by…
We analyse the evolution of cosmological perturbations which leads to the formation of large voids in the distribution of galaxies. We assume that perturbations are spherical and all components of the Universe - radiation, matter and dark…
We review the general theory of duality rotations which, in four dimensions, exchange electric with magnetic fields. Necessary and sufficient conditions in order for a theory to have duality symmetry are established. A nontrivial example is…
The study of spherically symmetric motion is important for the theory of explosion waves. In this paper, we construct rigorously self-similar solutions to the Riemann problem of the spherically symmetric Euler equations for general…
When density fluctuations collapse gravitationally out of the expanding cosmological background universe to form galaxies, the secondary energy release which results can affect their subsequent evolution profoundly. We focus here on the…
We study non-linear integrable partial differential equations naturally arising as bi-Hamiltonian Euler equations related to the looped cotangent Virasoro algebra. This infinite-dimensional Lie algebra (constructed in \cite{OR}) is a…
The formation of a singularity in a compressible gas, as described by the Euler equation, is characterized by the steepening, and eventual overturning of a wave. Using a self-similar description in two space dimensions, we show that the…
A higher dimensional modified gravity theory with an action that includes dimensionally continued Euler-Poincar\'e forms up to second order in curvatures is considered. The variational field equations are derived. Matter in the universe at…
In the literature, for semidynamical systems in infinite dimensional phase spaces, different topological structures are used (Hilbert, Banach, Sobolev, locally convex, Hausdorf topology etc.). That is because there are neither set rules nor…
One of the central problems in supernova theory is the question how massive stars explode. Understanding the physical processes that drive the explosion is crucial for linking the stellar progenitors to the final remnants and for predicting…
We use ideal hydrodynamics to investigate clustering in a gas of inelastically colliding spheres. The hydrodynamic equations exhibit a new type of finite-time density blowup, where the gas pressure remains finite. The density blowups signal…
We investigate the qualitative dynamics of smooth solutions to the radially symmetric isentropic compressible Euler equations, focusing specifically on the evolution of rarefactive and compressive wave characters across three distinct…