2,113 research outputs found
Relativistic magnetohydrodynamics in one dimension
We derive a number of solution for one-dimensional dynamics of relativistic
magnetized plasma that can be used as benchmark estimates in relativistic
hydrodynamic and magnetohydrodynamic numerical codes.
First, we analyze the properties of simple waves of fast modes propagating
orthogonally to the magnetic field in relativistically hot plasma. The magnetic
and kinetic pressures obey different equations of state, so that the system
behaves as a mixture of gases with different polytropic indices. We find the
self-similar solutions for the expansion of hot strongly magnetized plasma into
vacuum.
Second, we derive linear hodograph and Darboux equations for the relativistic
Khalatnikov potential, which describe arbitrary one-dimensional isentropic
relativistic motion of cold magnetized plasma and find their general and
particular solutions. The obtained hodograph and Darboux equations are very
powerful: system of highly non-linear, relativistic, time dependent equations
describing arbitrary (not necessarily self-similar) dynamics of highly
magnetized plasma reduces to a single linear differential equation.Comment: accepted by Phys. Rev.
Can one count the shape of a drum?
Sequences of nodal counts store information on the geometry (metric) of the
domain where the wave equation is considered. To demonstrate this statement, we
consider the eigenfunctions of the Laplace-Beltrami operator on surfaces of
revolution. Arranging the wave functions by increasing values of the
eigenvalues, and counting the number of their nodal domains, we obtain the
nodal sequence whose properties we study. This sequence is expressed as a trace
formula, which consists of a smooth (Weyl-like) part which depends on global
geometrical parameters, and a fluctuating part which involves the classical
periodic orbits on the torus and their actions (lengths). The geometrical
content of the nodal sequence is thus explicitly revealed.Comment: 4 pages, 1 figur
Gravitational wave generation from bubble collisions in first-order phase transitions: an analytic approach
Gravitational wave production from bubble collisions was calculated in the
early nineties using numerical simulations. In this paper, we present an
alternative analytic estimate, relying on a different treatment of
stochasticity. In our approach, we provide a model for the bubble velocity
power spectrum, suitable for both detonations and deflagrations. From this, we
derive the anisotropic stress and analytically solve the gravitational wave
equation. We provide analytical formulae for the peak frequency and the shape
of the spectrum which we compare with numerical estimates. In contrast to the
previous analysis, we do not work in the envelope approximation. This paper
focuses on a particular source of gravitational waves from phase transitions.
In a companion article, we will add together the different sources of
gravitational wave signals from phase transitions: bubble collisions,
turbulence and magnetic fields and discuss the prospects for probing the
electroweak phase transition at LISA.Comment: 48 pages, 14 figures. v2 (PRD version): calculation refined; plots
redone starting from Fig. 4. Factor 2 in GW energy spectrum corrected. Main
conclusions unchanged. v3: Note added at the end of paper to comment on the
new results of 0901.166
A direct proof of Kim's identities
As a by-product of a finite-size Bethe Ansatz calculation in statistical
mechanics, Doochul Kim has established, by an indirect route, three
mathematical identities rather similar to the conjugate modulus relations
satisfied by the elliptic theta constants. However, they contain factors like
and , instead of . We show here that
there is a fourth relation that naturally completes the set, in much the same
way that there are four relations for the four elliptic theta functions. We
derive all of them directly by proving and using a specialization of
Weierstrass' factorization theorem in complex variable theory.Comment: Latex, 6 pages, accepted by J. Physics
Distortions Of The Phase Space Behavior Of A Particle During one-third integral Resonance Extraction
Symplectic tracking using point magnets and a reference orbit made of circular arcs and straight lines
Symplectic tracking of beam particles using point magnets is achieved using a
reference orbit made of circular arcs and straight lines that join smoothly
with each other. For this choice of the reference orbit, results are given for
the transfer functions, transfer matrices, and the transit times of the magnets
and drift spaces. These results provide a symplectic integrator, and allow the
linear orbit parameters to be computed by multiplying transfer matrices. It is
shown that this integrator is a second-order integrator, and that the transfer
functions can be derived from a hamiltonian.Comment: 16 pages, PDF fil
Mixed Hyperbolic - Second-Order Parabolic Formulations of General Relativity
Two new formulations of general relativity are introduced. The first one is a
parabolization of the Arnowitt, Deser, Misner (ADM) formulation and is derived
by addition of combinations of the constraints and their derivatives to the
right-hand-side of the ADM evolution equations. The desirable property of this
modification is that it turns the surface of constraints into a local attractor
because the constraint propagation equations become second-order parabolic
independently of the gauge conditions employed. This system may be classified
as mixed hyperbolic - second-order parabolic. The second formulation is a
parabolization of the Kidder, Scheel, Teukolsky formulation and is a manifestly
mixed strongly hyperbolic - second-order parabolic set of equations, bearing
thus resemblance to the compressible Navier-Stokes equations. As a first test,
a stability analysis of flat space is carried out and it is shown that the
first modification exponentially damps and smoothes all constraint violating
modes. These systems provide a new basis for constructing schemes for long-term
and stable numerical integration of the Einstein field equations.Comment: 19 pages, two column, references added, two proofs of well-posedness
added, content changed to agree with submitted version to PR
Generalization of Einstein-Lovelock theory to higher order dilaton gravity
A higher order theory of dilaton gravity is constructed as a generalization
of the Einstein-Lovelock theory of pure gravity. Its Lagrangian contains terms
with higher powers of the Riemann tensor and of the first two derivatives of
the dilaton. Nevertheless, the resulting equations of motion are quasi-linear
in the second derivatives of the metric and of the dilaton. This property is
crucial for the existence of brane solutions in the thin wall limit. At each
order in derivatives the contribution to the Lagrangian is unique up to an
overall normalization. Relations between symmetries of this theory and the
O(d,d) symmetry of the string-inspired models are discussed.Comment: 18 pages, references added, version to be publishe
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