523 research outputs found
Derivation of the Lattice Boltzmann Model for Relativistic Hydrodynamics
A detailed derivation of the Lattice Boltzmann (LB) scheme for relativistic
fluids recently proposed in Ref. [1], is presented. The method is numerically
validated and applied to the case of two quite different relativistic fluid
dynamic problems, namely shock-wave propagation in quark-gluon plasmas and the
impact of a supernova blast-wave on massive interstellar clouds. Close to
second order convergence with the grid resolution, as well as linear dependence
of computational time on the number of grid points and time-steps, are
reported
On the hyperbolicity and causality of the relativistic Euler system under the kinetic equation of state
We show that a pair of conjectures raised in [11] concerning the construction
of normal solutions to the relativistic Boltzmann equation are valid. This
ensures that the results in [11] hold for any range of positive temperatures
and that the relativistic Euler system under the kinetic equation of state is
hyperbolic and the speed of sound cannot overcome .Comment: 6 pages. Abridged version; full version to appear in Commun. Pure
Appl. Ana
Linking the hydrodynamic and kinetic description of a dissipative relativistic conformal theory
We use the entropy production variational method to associate a one particle
distribution function to the assumed known energy-momentum and entropy currents
describing a relativistic conformal fluid. Assuming a simple form for the
collision operator we find this one particle distribution function explicitly,
and show that this method of linking the hydro and kinetic description is a non
trivial generalization of Grad's ansatz. The resulting constitutive relations
are the same as in the conformal dissipative type theories discussed in J.
Peralta-Ramos and E. Calzetta, Phys. Rev. D {\bfseries 80}, 126002 (2009). Our
results may prove useful in the description of freeze-out in ultrarelativistic
heavy-ion collisions.Comment: v2: 23 pages, no figures, accepted in Phys. Rev.
Semitoric integrable systems on symplectic 4-manifolds
Let M be a symplectic 4-manifold. A semitoric integrable system on M is a
pair of real-valued smooth functions J, H on M for which J generates a
Hamiltonian S^1-action and the Poisson brackets {J,H} vanish. We shall
introduce new global symplectic invariants for these systems; some of these
invariants encode topological or geometric aspects, while others encode
analytical information about the singularities and how they stand with respect
to the system. Our goal is to prove that a semitoric system is completely
determined by the invariants we introduce
Macroscopic Equations of Motion for Two Phase Flow in Porous Media
The established macroscopic equations of motion for two phase immiscible
displacement in porous media are known to be physically incomplete because they
do not contain the surface tension and surface areas governing capillary
phenomena. Therefore a more general system of macroscopic equations is derived
here which incorporates the spatiotemporal variation of interfacial energies.
These equations are based on the theory of mixtures in macroscopic continuum
mechanics. They include wetting phenomena through surface tensions instead of
the traditional use of capillary pressure functions. Relative permeabilities
can be identified in this approach which exhibit a complex dependence on the
state variables. A capillary pressure function can be identified in equilibrium
which shows the qualitative saturation dependence known from experiment. In
addition the new equations allow to describe the spatiotemporal changes of
residual saturations during immiscible displacement.Comment: 15 pages, Phys. Rev. E (1998), in prin
On the relativistic Lattice Boltzmann method for quark-gluon plasma simulations
In this paper, we investigate the recently developed lattice Boltzmann model
for relativistic hydrodynamics. To this purpose, we perform simulations of
shock waves in quark-gluon plasma in the low and high viscosities regime, using
three different computational models, the relativistic lattice Boltzmann (RLB),
the Boltzmann Approach Multi-Parton Scattering (BAMPS), and the viscous sharp
and smooth transport algorithm (vSHASTA). From the results, we conclude that
the RLB model departs from BAMPS in the case of high speeds and high
temperature(viscosities), the departure being due to the fact that the RLB is
based on a quadratic approximation of the Maxwell-J\"uttner distribution, which
is only valid for sufficiently low temperature and velocity. Furthermore, we
have investigated the influence of the lattice speed on the results, and shown
that inclusion of quadratic terms in the equilibrium distribution improves the
stability of the method within its domain of applicability. Finally, we assess
the viability of the RLB model in the various parameter regimes relevant to
ultra-relativistic fluid dynamics.Comment: 10 pages, 16 Figure
Conservation of energy and momenta in nonholonomic systems with affine constraints
We characterize the conditions for the conservation of the energy and of the
components of the momentum maps of lifted actions, and of their `gauge-like'
generalizations, in time-independent nonholonomic mechanical systems with
affine constraints. These conditions involve geometrical and mechanical
properties of the system, and are codified in the so-called
reaction-annihilator distribution
The enigmatic nature of the circumstellar envelope and bow shock surrounding Betelgeuse as revealed by Herschel. I. Evidence of clumps, multiple arcs, and a linear bar-like structure
Context. The interaction between stellar winds and the interstellar medium
(ISM) can create complex bow shocks. The photometers on board the Herschel
Space Observatory are ideally suited to studying the morphologies of these bow
shocks. Aims. We aim to study the circumstellar environment and wind-ISM
interaction of the nearest red supergiant, Betelgeuse. Methods. Herschel PACS
images at 70, 100, and 160 micron and SPIRE images at 250, 350, and 500 micron
were obtained by scanning the region around Betelgeuse. These data were
complemented with ultraviolet GALEX data, near-infrared WISE data, and radio 21
cm GALFA-HI data. The observational properties of the bow shock structure were
deduced from the data and compared with hydrodynamical simulations. Results.
The infrared Herschel images of the environment around Betelgeuse are
spectacular, showing the occurrence of multiple arcs at 6-7 arcmin from the
central target and the presence of a linear bar at 9 arcmin. Remarkably, no
large-scale instabilities are seen in the outer arcs and linear bar. The dust
temperature in the outer arcs varies between 40 and 140 K, with the linear bar
having the same colour temperature as the arcs. The inner envelope shows clear
evidence of a non-homogeneous clumpy structure (beyond 15 arcsec), probably
related to the giant convection cells of the outer atmosphere. The
non-homogeneous distribution of the material even persists until the collision
with the ISM. A strong variation in brightness of the inner clumps at a radius
of 2 arcmin suggests a drastic change in mean gas and dust density some 32 000
yr ago. Using hydrodynamical simulations, we try to explain the observed
morphology of the bow shock around Betelgeuse. Conclusions: [abbreviated]Comment: 26 page
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