Related papers: Boyle's law and gravitational instability
Boyle's 1662 observation that the volume of a gas is, at constant temperature, inversely proportional to pressure, offered a prototypical example of how an equation of state (EoS) can succinctly capture key properties of a many-particle…
Rigorous results on the nonlinear dynamics of a dilute Bose gas with a negative scattering length in an harmonic magnetic trap are presented and sufficient conditions for the collapse of the system are formulated. By using the virial…
This study investigates the steady Boltzmann equation in one spatial variable for a polyatomic single-component gas in a half-space. Inflow boundary conditions are assumed at the half-space boundary, where particles entering the half-space…
Consider the dynamics of a gas bubble in an inviscid, compressible liquid with surface tension. Kinematic and dynamic boundary conditions couple the bubble surface deformation dynamics with the dynamics of waves in the fluid. This system…
Hard sphere systems in two dimensions are examined for arbitrary density. Simulation results are compared to the theoretical predictions for both the low and the high density limit, where the system is either disordered or ordered,…
We use computational methods to determine the minimal yield-stress required in order to hold static a buoyant bubble in a yield-stress liquid. The static limit is governed by the bubble shape, the dimensionless surface tension ($\gamma$)…
To be a formation mechanism of such large-scale structures as giant molecular clouds (GMCs) and HI superclouds, the classical Parker instability driven by external gravity has to overcome three major obstacles: The convective motion…
We complete the existing literature on the structure and stability of polytropic gas spheres reported in the classical monograph of Chandrasekhar (1942). For isolated polytropes with index $1<n<5$, we provide a new, alternative, proof that…
We use holography to study the spinodal instability of a four-dimensional, strongly-coupled gauge theory with a first-order thermal phase transition. We place the theory on a cylinder in a set of homogeneous, unstable initial states. The…
A steady state of a granular gas with homogeneous granular temperature, no mass flow, and nonzero heat flux is studied. The state is created by applying an external position--dependent force or by enclosing the grains inside a curved…
Cold gas entering the central $1$ to $10^2$ pc of a galaxy fragments and condenses into clouds. The stability of the clouds determines whether they will be turned into stars or can be delivered to the central supermassive black hole (SMBH)…
We show that the self-gravitating gas at thermal equilibrium has an infinite volume limit in the three ensembles (GCE, CE, MCE) when (N, V) -> infty, keeping N/V^{1/3} fixed, that is, with eta = G m^2 N/[ V^{1/3} T] fixed. We develop…
We present an analytical model of the relation between the surface density of gas and star formation rate in galaxies and clouds, as a function of the presence of supersonic turbulence and the associated structure of the interstellar…
The thermodynamic equilibrium conditions for compact structures composed by mass varying particles are discussed assuming that the so-called dynamical mass behaves like an additional extensive thermodynamic degree of freedom. It then…
We discuss the statistical mechanics of rotating self-gravitating systems by allowing properly for the conservation of angular momentum. We study analytically the case of slowly rotating isothermal spheres by expanding the solutions of the…
We employ hydrodynamic equations to follow the clustering instability of a freely cooling dilute gas of inelastically colliding spheres into a well-developed nonlinear regime. We simplify the problem by dealing with a one-dimensional…
A rotating continuum of particles attracted to each other by gravity may be modeled by the Euler-Poisson system. The existence of solutions is a very classical problem. Here it is proven that a curve of solutions exists, parametrized by the…
We examine the linear stability of a filamentary cloud permeated by a perpendicular magnetic field. The initial magnetic field is assumed to be uniform and perpendicular to the cloud axis. The model cloud is assumed to have a Plummer-like…
We study the interplay between the anisotropy of the dipole-dipole interaction and confinement in a curved geometry by means of the extended Gross-Pitaevskii equation, which allows us to characterize the ground state of a dipolar Bose gas…
We consider a self-gravitating collisionless gas as described by the Vlasov-Poisson or Einstein-Vlasov system or a self-gravitating fluid ball as described by the Euler-Poisson or Einstein-Euler system. We give a simple proof for the finite…