50 research outputs found
Smoothed Particle Hydrodynamics for Relativistic Heavy Ion Collisions
The method of smoothed particle hydrodynamics (SPH) is developped
appropriately for the study of relativistic heavy ion collision processes. In
order to describe the flow of a high energy but low baryon number density
fluid, the entropy is taken as the SPH base. We formulate the method in terms
of the variational principle. Several examples show that the method is very
promising for the study of hadronic flow in RHIC physics.Comment: 14 pages, 8figure
Dynamics and delocalisation transition for an interface driven by a uniform shear flow
We study the effect of a uniform shear flow on an interface separating the
two broken-symmetry ordered phases of a two-dimensional system with
nonconserved scalar order parameter. The interface, initially flat and
perpendicular to the flow, is distorted by the shear flow. We show that there
is a critical shear rate, \gamma_c, proportional to 1/L^2, (where L is the
system width perpendicular to the flow) below which the interface can sustain
the shear. In this regime the countermotion of the interface under its
curvature balances the shear flow, and the stretched interface stabilizes into
a time-independent shape whose form we determine analytically. For \gamma >
\gamma_c, the interface acquires a non-zero velocity, whose profile is shown to
reach a time-independent limit which we determine exactly. The analytical
results are checked by numerical integration of the equations of motion.Comment: 5 page
Hydrodynamic obstruction to bubble expansion
We discuss a hydrodynamic obstruction to bubble wall acceleration during a
cosmological first-order phase transition. The obstruction results from the
heating of the plasma in the compression wave in front of the phase transition
boundary. We provide a simple criterion for the occurrence of the obstruction
at subsonic bubble wall velocity in terms of the critical temperature, the
phase transition temperature, and the latent heat of the model under
consideration. The criterion serves as a sufficient condition of subsonic
bubble wall velocities as required by electroweak baryogenesis.Comment: 18 pages, 4 figures; comments and reference added, published versio
Method for Generating Additive Shape Invariant Potentials from an Euler Equation
In the supersymmetric quantum mechanics formalism, the shape invariance
condition provides a sufficient constraint to make a quantum mechanical problem
solvable; i.e., we can determine its eigenvalues and eigenfunctions
algebraically. Since shape invariance relates superpotentials and their
derivatives at two different values of the parameter , it is a non-local
condition in the coordinate-parameter space. We transform the shape
invariance condition for additive shape invariant superpotentials into two
local partial differential equations. One of these equations is equivalent to
the one-dimensional Euler equation expressing momentum conservation for
inviscid fluid flow. The second equation provides the constraint that helps us
determine unique solutions. We solve these equations to generate the set of all
known -independent shape invariant superpotentials and show that there
are no others. We then develop an algorithm for generating additive shape
invariant superpotentials including those that depend on explicitly,
and derive a new -dependent superpotential by expanding a Scarf
superpotential.Comment: 1 figure, 4 tables, 18 page
The stochastic gravitational wave background from turbulence and magnetic fields generated by a first-order phase transition
We analytically derive the spectrum of gravitational waves due to
magneto-hydrodynamical turbulence generated by bubble collisions in a
first-order phase transition. In contrast to previous studies, we take into
account the fact that turbulence and magnetic fields act as sources of
gravitational waves for many Hubble times after the phase transition is
completed. This modifies the gravitational wave spectrum at large scales. We
also model the initial stirring phase preceding the Kolmogorov cascade, while
earlier works assume that the Kolmogorov spectrum sets in instantaneously. The
continuity in time of the source is relevant for a correct determination of the
peak position of the gravitational wave spectrum. We discuss how the results
depend on assumptions about the unequal-time correlation of the source and
motivate a realistic choice for it. Our treatment gives a similar peak
frequency as previous analyses but the amplitude of the signal is reduced due
to the use of a more realistic power spectrum for the magneto-hydrodynamical
turbulence. For a strongly first-order electroweak phase transition, the signal
is observable with the space interferometer LISA.Comment: 46 pages, 17 figures. Replaced with revised version accepted for
publication in JCA
Kinetic models of heterogeneous dissipation
We suggest kinetic models of dissipation for an ensemble of interacting
oriented particles, for example, moving magnetized particles. This is achieved
by introducing a double bracket dissipation in kinetic equations using an
oriented Poisson bracket, and employing the moment method to derive continuum
equations for magnetization and density evolution. We show how our continuum
equations generalize the Debye-Hueckel equations for attracting round
particles, and Landau-Lifshitz-Gilbert equations for spin waves in magnetized
media. We also show formation of singular solutions that are clumps of aligned
particles (orientons) starting from random initial conditions. Finally, we
extend our theory to the dissipative motion of self-interacting curves.Comment: 28 pages, 2 figures. Submitted to J. Phys.
Acceleration, streamlines and potential flows in general relativity: analytical and numerical results
Analytical and numerical solutions for the integral curves of the velocity
field (streamlines) of a steady-state flow of an ideal fluid with
equation of state are presented. The streamlines associated with an accelerate
black hole and a rigid sphere are studied in some detail, as well as, the
velocity fields of a black hole and a rigid sphere in an external dipolar field
(constant acceleration field). In the latter case the dipole field is produced
by an axially symmetric halo or shell of matter. For each case the fluid
density is studied using contour lines. We found that the presence of
acceleration is detected by these contour lines. As far as we know this is the
first time that the integral curves of the velocity field for accelerate
objects and related spacetimes are studied in general relativity.Comment: RevTex, 14 pages, 7 eps figs, CQG to appea
Energy Budget of Cosmological First-order Phase Transitions
The study of the hydrodynamics of bubble growth in first-order phase
transitions is very relevant for electroweak baryogenesis, as the baryon
asymmetry depends sensitively on the bubble wall velocity, and also for
predicting the size of the gravity wave signal resulting from bubble
collisions, which depends on both the bubble wall velocity and the plasma fluid
velocity. We perform such study in different bubble expansion regimes, namely
deflagrations, detonations, hybrids (steady states) and runaway solutions
(accelerating wall), without relying on a specific particle physics model. We
compute the efficiency of the transfer of vacuum energy to the bubble wall and
the plasma in all regimes. We clarify the condition determining the runaway
regime and stress that in most models of strong first-order phase transitions
this will modify expectations for the gravity wave signal. Indeed, in this
case, most of the kinetic energy is concentrated in the wall and almost no
turbulent fluid motions are expected since the surrounding fluid is kept mostly
at rest.Comment: 36 pages, 14 figure
Quantum Revivals in a Periodically Driven Gravitational Cavity
Quantum revivals are investigated for the dynamics of an atom in a driven
gravitational cavity. It is demonstrated that the external driving field
influences the revival time significantly. Analytical expressions are presented
which are based on second order perturbation theory and semiclassical secular
theory. These analytical results explain the dependence of the revival time on
the characteristic parameters of the problem quantitatively in a simple way.
They are in excellent agreement with numerical results
All electromagnetic form factors
The electromagnetic form factors of spin-1/2 particles are known, but due to
historical reasons only half of them are found in many textbooks. Given the
importance of the general result, its model independence, its connection to
discrete symmetries and their violations we made an effort to derive and
present the general result based only on the knowledge of Dirac equation. We
discuss the phenomenology connected directly with the form factors, and spin
precession in external fields including time reversal violating terms. We apply
the formalism to spin-flip synchrotron radiation and suggest pedagogical
projects.Comment: Latex, 22 page