1,429 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.
Stable splitting of bivariate spline spaces by Bernstein-Bézier methods
We develop stable splitting of the minimal determining sets for the spaces of bivariate C1 splines on triangulations, including a modified Argyris space, Clough-Tocher, Powell-Sabin and quadrilateral macro-element spaces. This leads to the stable splitting of the corresponding bases as required in Böhmer's method for solving fully nonlinear elliptic PDEs on polygonal domains
Linear and multiplicative 2-forms
We study the relationship between multiplicative 2-forms on Lie groupoids and
linear 2-forms on Lie algebroids, which leads to a new approach to the
infinitesimal description of multiplicative 2-forms and to the integration of
twisted Dirac manifolds.Comment: to appear in Letters in Mathematical Physic
Potentials for which the Radial Schr\"odinger Equation can be solved
In a previous paper, submitted to Journal of Physics A -- we presented an
infinite class of potentials for which the radial Schr\"odinger equation at
zero energy can be solved explicitely. For part of them, the angular momentum
must be zero, but for the other part (also infinite), one can have any angular
momentum. In the present paper, we study a simple subclass (also infinite) of
the whole class for which the solution of the Schr\"odinger equation is simpler
than in the general case. This subclass is obtained by combining another
approach together with the general approach of the previous paper. Once this is
achieved, one can then see that one can in fact combine the two approaches in
full generality, and obtain a much larger class of potentials than the class
found in ref. We mention here that our results are explicit, and when
exhibited, one can check in a straightforward manner their validity
A note on the wellposedness of scalar brane world cosmological perturbations
We discuss scalar brane world cosmological perturbations for a 3-brane world
in a maximally symmetric 5D bulk. We show that Mukoyama's master equations
leads, for adiabatic perturbations of a perfect fluid on the brane and for
scalar field matter on the brane, to a well posed problem despite the "non
local" aspect of the boundary condition on the brane. We discuss in relation to
the wellposedness the way to specify initial data in the bulk.Comment: 14 pages, one figure, v2 minor change
Proof that the Hydrogen-antihydrogen Molecule is Unstable
In the framework of nonrelativistic quantum mechanics we derive a necessary
condition for four Coulomb charges ,
where all masses are assumed finite, to form the stable system. The obtained
stability condition is physical and is expressed through the required minimal
ratio of Jacobi masses. In particular this provides the rigorous proof that the
hydrogen-antihydrogen molecule is unstable. This is the first result of this
sort for four particles.Comment: Submitted to Phys.Rev.Let
Radiation reaction and four-momentum conservation for point-like dyons
We construct for a system of point-like dyons a conserved energy-momentum
tensor entailing finite momentum integrals, that takes the radiation reaction
into account.Comment: 12 pages, no figure
Dressed-State Approach to Population Trapping in the Jaynes-Cummings Model
The phenomenon of atomic population trapping in the Jaynes-Cummings Model is
analysed from a dressed-state point of view. A general condition for the
occurrence of partial or total trapping from an arbitrary, pure initial
atom-field state is obtained in the form of a bound to the variation of the
atomic inversion. More generally, it is found that in the presence of initial
atomic or atom-field coherence the population dynamics is governed not by the
field's initial photon distribution, but by a `weighted dressedness'
distribution characterising the joint atom-field state. In particular,
individual revivals in the inversion can be analytically described to good
approximation in terms of that distribution, even in the limit of large
population trapping. This result is obtained through a generalisation of the
Poisson Summation Formula method for analytical description of revivals
developed by Fleischhauer and Schleich [Phys. Rev. A {\bf 47}, 4258 (1993)].Comment: 24 pages, 5 figures, to appear in J. Mod. Op
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