Collisionless Gas Research Articles

Accurate solution of the boundary problem for collisionless gas in the field of a plane gravitational wave

An accurate solution of the Cauchy problem is found for a general-relativity collisionless kinetic equation against the background of the metric of a nonlinear plane gravitational field with an arbitrary law of gas-particle reflection from a boundary of any specified form. It is shown that in the field of a gravitational wave, interaction of the gas with the boundary necessarily leads to the appearance of shock waves.

Relativistic Stellar Dynamics on the Computer - Part Two - Physical Applications

This is the second of a series of papers on the numerical solution of Einstein's equations for the dynamical evolution of a collisionless gas of particles in general relativity. This paper deals mainly with applications to sphericcal star clusters. Previous studies were restricted to static equilibria and linear perturbations. We bring together the tools of numerical relativity and N-body particle simulation to follow the full nonlinear evolution of such dynamical systems.

Relativistic stellar dynamics on the computer. I - Motivation and numerical method

view Abstract Citations (79) References (34) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Relativistic stellar dynamics on the computer. I - Motivation and numerical method Shapiro, S. L. ; Teukolsky, S. A. Abstract In the first part of the present work on the numerical solution of the Einstein (1939) equations for the dynamical evolution of a collisionless gas of particles in general relativity, in the case of spherically symmetric systems with arbitrarily strong gravitational field and particle velocities approaching the speed of light, the Vlasov equation is solved in general relativity by particle simulation. The gravitational field is integrated by means of the 3 + 1 formalism of Arnowitt et al. (1962). The method is found to be extremely accurate, even in the case of black hole formation. In the second part, the method is applied to spherical star clusters with attention to the stability of equilibrium configurations. Strong numerical evidence is obtained to the effect that, as in the case of fluid stars, the binding energy maximum along an equilibrium sequence signals the onset of dynamical instability. Unstable clusters, Newtonian polytropic clusters, and violent relaxation in the relativistic domain are also explored. Publication: The Astrophysical Journal Pub Date: November 1985 DOI: 10.1086/163587 Bibcode: 1985ApJ...298...34S Keywords: Astrodynamics; Black Holes (Astronomy); Computerized Simulation; Many Body Problem; Relativity; Star Clusters; Astronomical Models; Dynamical Systems; Gravitation Theory; Numerical Analysis; Astrophysics full text sources ADS |

Spatially homogeneous cosmological models with a collisionless gas

The authors pose problems of finding the simultaneous solutions of Vlasov's equation and Einstein's equations for all types of spatially homogeneous cosmological models and substantiate the method of counterflowing beams in the case of strong anistropy. The solutions obtained can be used in studying the question of the emergence of some anistropic solutions into Friedmann's regime. In this case, the anisotropy is small and the structure of the energy-momentum tensor is substantially simplified.

The self-similar evolution of holes in an Einstein-de Sitter universe

view Abstract Citations (176) References (46) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The self-similar evolution of holes in an Einstein-de Sitter universe Bertschinger, E. Abstract Similarity solutions have been found for the nonlinear evolution of spherical holes in an Einstein-de Sitter universe. A negative perturbation grows until it becomes a hole, which expands in a self-similar fashion, in most cases sweeping up and compressing the matter around it into a thin, dense shell. Holes compensated by an overdense shell are considered, and it is shown that the Einstein-de Sitter-Sedov solution for a cosmological blast wave gives the self-similar adiabatic flow of a collisional gas around such a hole. The corresponding solution for a collisionless gas is given, followed by a solution for a collisional gas with omega much less than one. Uncompensated holes are treated, giving solutions for a collisionless gas, a collisional gas, and for a mixture where the collisionless gas dominates. The possibility that holes may form naturally from the growth of fluctuations in a hierarchical clustering model is examined. Several processes modifying the similarity solutions are discussed. Publication: The Astrophysical Journal Supplement Series Pub Date: May 1985 DOI: 10.1086/191027 Bibcode: 1985ApJS...58....1B Keywords: Cosmology; Galactic Clusters; Galactic Evolution; Hydrodynamics; Relativity; Shock Waves; Collisional Plasmas; Collisionless Plasmas; Density Distribution; Hubble Constant; Nonlinear Equations; Perturbation Theory; Similarity Theorem; Astrophysics full text sources ADS |

Formation of difference in distribution between visible and invisible matters in the expanding universe

The visible and invisible matters in the universe have rather different density distributions. The formar is obvious clustered on the scales of galaxies, clusters and superclusters, while the latter is rather more uniform. Here we discuss the possibility of this difference forming during the stage of Jeans clustering. For a two-component universe, so long as the growth and decay time-scales of gravitational perturbation satisfy a certain relation, the perturbation will grow in one component and decay in the other. Specific calculations are made for the development of inhomogeneity in a universe consisting of two collisionless gases. It is found that as long as the densities of the Jeans lengths of the two components satisfy the relations ϱ 1 ⪡ ϱ 2 λ 1 j ⪡ λ 2 j , then, whether the initial perturbation is in component 1 or component 2, the result will be component 1 having a large degree of inhomogeneity and component 2, a small one. If the invisible matter is mainly neutrino with a finite rest-mass, then the above result can be used to explain the quasi-uniform distribution of the invisible matter.

Gauge-invariant density fluctuations in a cold dark matter universe

Adiabatic density fluctuations of a cold collisionless gas in a radiation background are examined using a gauge-invariant formalism. Particular attention is paid to fluctuations which cross the horizon during the radiation-dominated era. The resulting density spectrum invalidates previous arguments that a Zel'dovich primordial fluctuation spectrum is not consistent with an axion-dominated universe.

Initial and boundary value problems in kinetic theory part I: The knudsen gas

Abstract This paper provides a general description of reflection laws in kinetic theory including all reflection laws of interest. Solutions of the corresponding initial and boundary value problem for a collisionless gas confined in a bounded region areconstructed and analyzed. We, inaddition, provide conditions guaranteeing the uniqueness of solutions and the conservation o f mass.

The stochastic, one-dimensional inertial equation, the inviscid Burger’s model, and the surface intersection problem

A collisionless (rarefied) gas with an initial velocity in one dimension is discussed. It is shown that this inertial problem, the problem of the multiple intersections of a line of sight with a random surface, and the inviscid Burger’s model all have the same solutions. Kahng earlier used the full Wiener–Hermite expansion and guessed a solution to the stochastic problem. It is shown, using a constructive functional derivative procedure, that this solution is a linear combination of the occurring multiple solutions, with alternating signs. It is also shown that such an alternating sum of any moment is conserved, so that the initial, marginal distribution is invariant for this forceless problem. Kahng’s later-time energy spectrum for one example, which for large k was found to be k−3, is shown to be the correct result because of square root irregularities appearing at later times for solutions of the inertial equation. Further it is shown that any Gaussian process with arbitrary initial spectrum approaches k−3 for k large, with the initial dissipation length as its characteristics length. Finally a new technique is used to obtain the Wiener–Hermite expansion for physically reasonable fields in the collisionless gas problem.

The effect of low-velocity, low-mass intruders (collisionless gas) on the dynamical evolution of a binary system

More than 20,000 computer-simulated encounters between low-mass (compared to the binary components) intruders and binary systems have been made. These calculations were made in the important (and difficult) limit where the intruder velocity is small compared to the orbital velocity of the binary. The dependence of the encounters on orbital eccentricity, on the mass ratios of the binary components, and on the impact parameter was found. These encounters increase the binding energy of the binary. At zero impact parameter, the average increase in the binding energy is proportional to the square of the binary orbital eccentricity. However, the increase in the binding energy decreases much faster with increasing impact parameter as the eccentricity increases. The net result is that the total cross section for increasing the binding energy of a binary through encounters with low-mass intruders is independent of the orbital eccentricity of the binary. The average increase in the binding energy per encounter is directly proportional to the mass of the intruder (in the limit where its mass is small compared to the binary mass). If the binary components are equally massive, the probability that the intruder is captured into a long-lived orbit which persists for at least 1.5more » x 10/sup 5/ integration steps or about 700 revolutions of the original binary is only about 1% at zero impact parameter. However, the probability of long-term capture climbs rapidly for encounters in which the closest approach, R/sub min/, of the intruder to the binary is greater than 0.5 of the semimajor axis a/sub 0/ of the orbit. It climbs to about 20% at R/sub min//a/sub 0/ = 1.9 and then falls off rapidly at larger R/sub min/. Here the capture is due to the tidal field of the binary. The probability of long-term capture increases as the orbital eccentricity increases. 14 references, 9 figures, 4 tables.« less

Shear flow in the presence of 'strong rotation'. I. Exact free-molecular solution

Plane Couette flow of a gas in a strong pseudo-centrifugal field can mimic an interesting problem arising in gas centrifuges. Here, the exact distribution function for this situation is obtained for a collisionless gas, assuming diffuse-plus-specular reflection at boundaries. The flow is found to differ greatly from its force-free zero value.

The flow of a non-adsorbed, collisionless gas through linked spheres — a model for zeolite diffusion

We calculate the flux of non-adsorbed, collisionless molecules which follow linear trajectories and obey the cosine law, through spheres of radius R, linked by windows of radius r, formed by removing two spherical caps from each sphere and arranged in a linear sequence. Two methods of calculation have been used; in the first, the molecular path tracing (MPT) method, no assumptions, other than those mentioned above, were introduced. The expression for the flux is obtained in the form of an integral which has been evaluated numerically. In the second method, a radiating disc theorem was employed which does not take account of flux variation over a cross section, but which leads to a very simple analytical result which shows similar behaviour to that predicted by the MPT method. A simple empirical correction has been calculated to provide an accurate analytical equation. The second method can also be readily extended to a network of linked spheres and, augmented by the empirical correction, leads to a model for the description of the flow of a very dilute, weakly adsorbed gas in a system of this kind. The relationship between geometrical structure and flow is discussed with reference to another similar model and to zeolitic networks.

The peculiar velocity field in flattened superclusters

The linear growth rate of small transverse perturbations in a self-gravitating, collisionless gas that is undergoing a one-dimensional collapse is strongly influenced by the nonlinear flow of the background. In the collapse plane, smaller Hubble flow deviations and infall velocities are obtained than in the simple linear theory. Application of this theory to the kinematics of galaxies in a flat supercluster shows that the usual linear approximation may seriously underestimate Omega, the density parameter of the universe, if there is a strong deviation from spherical symmetry. Furthermore, dissipative separation of baryonic matter from collisionless dark material (such as hypothesized massive neutrinos) enhances this effect, leading to apparent Omega values of 0.2-0.3 for a wide range of separation parameters in an Einstein-de Sitter (Omega = 1) model.

Relativistic collisionless particles and the evolution of cosmological perturbations

view Abstract Citations (26) References (23) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Relativistic collisionless particles and the evolution of cosmological perturbations Vishniac, E. T. Abstract The paper considers the evolution of cosmological perturbations in an Einstein-de Sitter universe filled with the usual perfect gas plus a relativistic collisionless gas. On scales smaller than the horizon the collisionless gas undergoes rapid phase mixing and tends to a uniform distribution. However, on larger scales the ability of the collisionless gas to support a stress leads to altered growth rates for all perturbation modes except the nondecaying tensor and scalar modes. If the fraction of the total energy contained in the collisionless gas exceeds 5/16, then all the affected modes display oscillatory behavior. Also presented are the results of a numerical integration of the evolution of adiabatic perturbations as they cross the horizon, including the effect of massless neutrinos. The sound waves that result are lowered in amplitude by approximately 20% relative to their amplitudes in a neutrino-free cosmology. Publication: The Astrophysical Journal Pub Date: June 1982 DOI: 10.1086/160004 Bibcode: 1982ApJ...257..456V Keywords: Collisionless Plasmas; Cosmology; Perturbation Theory; Relativistic Particles; Relativity; Adiabatic Flow; Astronomical Models; Baryons; Neutrinos; Scalars; Sound Waves; Tensors; Astrophysics full text sources ADS |

Heat conduction in a nearly collisionless molecular gas

Transport phenomena in molecular gases and the respective field effects have so far been analyzed in the hydrodynamic and Knudsen regimes. In between there is a rather large gap covered by the transition regime. For the case of heat conduction through a diatomic diamagnetic gas between parallel plates an attempt is made to partially bridge the gap by the beginning of a density expansion derived through iteration of an integral form of the Boltzmann equation. Second-order perturbation in non-sphericity of both intermolecular and gas-wall interactions is applied to determine the effect of a magnetic field. Explicit expressions are derived for a simple model.

Bianchi type I anisotropic cosmological model with a collisionless gas

The self-consistent system of Einstein-Vlasov equations is investigated in a class of homogeneous spaces. The Bianchi Type I anisotropic cosmological model with orthogonal Killing vectors is considered in detail. It is shown that the energymomentum tensor of a collisionless gas is spatially anisotropic. Exact solutions of the Einstein-Vlasov equations are found in the case of strong anisotropy. The behavior of small perturbations is investigated for a mixture of an ideal fluid and a collisionless gas as well as for a nonrelativistic collisionless gas.

Transport phenomena in molecular Knudsen gas

Transport properties of a collisionless molecular gas between plane-parallel plates are influenced by a magnetic field because of precession of the molecules after polarization by surface collisions. A systematic analysis of phenomena of this kind is attempted by considering mass flow in two directions and heat flow in three directions, together with the five conjugate thermodynamic forces. For the case of diamagnetic linear rigid molecules, the phenomenological coefficients are expressed by matrix elements involving the surface scattering operator. Explicit expressions are derived for a simple model of that operator.

Free Molecular Flow through a Long Circular Tube

This paper concerns the flow of collisionless gas through a circular tube from a reservoir to a vacuum. The case of a very long tube is studied by developing an asymptotic theory. A formula is given for the flux of molecules through the tube,which is valid up to O ( A -3 ), where A is the ratio of the tube length to its diameter. The distribution of the impact density along the tube wall is also calculated.

Flow past a massive object and the gravitational drag

The gravitational interaction between a massive object and ambient gas is considered. We give a description of subsonic and supersonic flows past a massive, mass ejecting object in nonviscous gas, including an estimate of the maximum density enhancements near the shock-front. The drag and the associated gas heating rates are calculated and compared with results for motion through collisionless gas.

Calculation of the “surface flow” of a dilute gas in model pores from first principles. I. Calculation of free molecule flow in an adsorbent force field by two methods

An ab initio calculation of the flow of a dilute (i.e., collisionless) gas, through a channel in which a force field due to the walls acts on the flowing molecules, can be carried out either by a molecular path tracing (MPT) method or by a Monte Carlo (MC) method. The latter yields diffusion coefficients both from transmission probabilities and also by a direct application of random walk theory. The two methods are described here as applied to a two-dimensional slit in which the adsorbate-adsorbent potential is represented by a triangular well. Although highly simplified, this model retains the essential features of a more realistic system. It is shown that discrepancies between the MPT method as usually applied and the MC method can be attributed to “end-effects” and a previously described procedure which corrects for these in MPT calculations is verified here by the MC results. The significance of end-effects in the wider context of model porous materials is briefly discussed.