18,226 research outputs found
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Alligator mississippiensis
Number of Pages: 14Integrative BiologyGeological Science
The rich behavior of the Boltzmann equation for dissipative gases
Within the framework of the homogeneous non-linear Boltzmann equation, we
present a new analytic method, without the intrinsic limitations of existing
methods, for obtaining asymptotic solutions. This method permits extension of
existing results for Maxwell molecules and hard spheres to large classes of
particle interactions, from very hard spheres to softer than Maxwell molecules,
as well as to more general forcing mechanisms, beyond free cooling and white
noise driving. By combining this method with numerical solutions, obtained from
the Direct Simulation Monte Carlo (DSMC) method, we study a broad class of
models relevant for the dynamics of dissipative fluids, including granular
gases. We establish a criterion connecting the stability of the non-equilibrium
steady state to an exponentially bound form for the velocity distribution ,
which varies depending on the forcing mechanism. Power laws arise in marginal
stability cases, of which several new cases are reported. Our results provide a
minimal framework for interpreting large classes of experiments on driven
granular gases
Boltzmann equation for dissipative gases in homogeneous states with nonlinear friction
Combining analytical and numerical methods, we study within the framework of
the homogeneous non-linear Boltzmann equation, a broad class of models relevant
for the dynamics of dissipative fluids, including granular gases. We use the
new method presented in a previous paper [J. Stat. Phys. 124, 549 (2006)] and
extend our results to a different heating mechanism, namely a deterministic
non-linear friction force. We derive analytically the high energy tail of the
velocity distribution and compare the theoretical predictions with high
precision numerical simulations. Stretched exponential forms are obtained when
the non-equilibrium steady state is stable. We derive sub-leading corrections
and emphasize their relevance. In marginal stability cases, power-law behaviors
arise, with exponents obtained as the roots of transcendental equations. We
also consider some simple BGK (Bhatnagar, Gross, Krook) models, driven by
similar heating devices, to test the robustness of our predictions
Recommended from our members
Crocodylus acutus
Number of Pages: 17Integrative BiologyGeological Science
Velocity Tails for Inelastic Maxwell Models
We study the velocity distribution function for inelastic Maxwell models,
characterized by a Boltzmann equation with constant collision rate, independent
of the energy of the colliding particles. By means of a nonlinear analysis of
the Boltzmann equation, we find that the velocity distribution function decays
algebraically for large velocities, with exponents that are analytically
calculated.Comment: 4 pages, 2 figure
Encounters and impressions during more than half a century.1
God had ordained that I had to live in and serve many countries in every continent; but more especially Europe and South East Asia. My life experiences of more than a half-century have taught me the absolute need for the European, with his higher culture and way of life, to live incomplete separation or “apartheid” from the natives of Asiatic and African countries; not because they are black or brown or yellow, but because the environment in which they have grown up has produced types of a lower standard of morality and culture
Transport calculation of dilepton production at ultrarelativistic energies
Dilepton spectra are calculated within the microscopic transport model UrQMD
and compared to data from the CERES experiment. The invariant mass spectra in
the region 300 MeV < M < 600 MeV depend strongly on the mass dependence of the
meson decay width which is not sufficiently determined by the Vector
Meson Dominance model. A consistent explanation of both the recent Pb+Au data
and the proton induced data can be given without additional medium effects
Partitioning of energy in highly polydisperse granular gases
A highly polydisperse granular gas is modeled by a continuous distribution of
particle sizes, a, giving rise to a corresponding continuous temperature
profile, T(a), which we compute approximately, generalizing previous results
for binary or multicomponent mixtures. If the system is driven, it evolves
towards a stationary temperature profile, which is discussed for several
driving mechanisms in dependence on the variance of the size distribution. For
a uniform distribution of sizes, the stationary temperature profile is
nonuniform with either hot small particles (constant force driving) or hot
large particles (constant velocity or constant energy driving). Polydispersity
always gives rise to non-Gaussian velocity distributions. Depending on the
driving mechanism the tails can be either overpopulated or underpopulated as
compared to the molecular gas. The deviations are mainly due to small
particles. In the case of free cooling the decay rate depends continuously on
particle size, while all partial temperatures decay according to Haff's law.
The analytical results are supported by event driven simulations for a large,
but discrete number of species.Comment: 10 pages; 5 figure
The Computational Complexity of the Lorentz Lattice Gas
The Lorentz lattice gas is studied from the perspective of computational
complexity theory. It is shown that using massive parallelism, particle
trajectories can be simulated in a time that scales logarithmically in the
length of the trajectory. This result characterizes the ``logical depth" of the
Lorentz lattice gas and allows us to compare it to other models in statistical
physics.Comment: 9 pages, LaTeX, to appear in J. Stat. Phy
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