385 research outputs found
Negative Specific Heat of a Magnetically Self-Confined Plasma Torus
It is shown that the thermodynamic maximum entropy principle predicts
negative specific heat for a stationary magnetically self-confined
current-carrying plasma torus. Implications for the magnetic self-confinement
of fusion plasma are considered.Comment: 10p., LaTeX, 2 eps figure file
Integrals of motion and the shape of the attractor for the Lorenz model
In this paper, we consider three-dimensional dynamical systems, as for
example the Lorenz model. For these systems, we introduce a method for
obtaining families of two-dimensional surfaces such that trajectories cross
each surface of the family in the same direction. For obtaining these surfaces,
we are guided by the integrals of motion that exist for particular values of
the parameters of the system. Nonetheless families of surfaces are obtained for
arbitrary values of these parameters. Only a bounded region of the phase space
is not filled by these surfaces. The global attractor of the system must be
contained in this region. In this way, we obtain information on the shape and
location of the global attractor. These results are more restrictive than
similar bounds that have been recently found by the method of Lyapunov
functions.Comment: 17 pages,12 figures. PACS numbers : 05.45.+b / 02.30.Hq Accepted for
publication in Physics Letters A. e-mails : [email protected] &
[email protected]
An approximate self-consistent theory of the magnetic field of fluted penumbrae
A self-consistent mathematical description of the magnetic field of fluted
sunspot penumbrae is presented. This description is based on an expansion of
the nonlinear force-free magnetohydrostatic equations written in cylindrical
coordinates. The lowest order solutions are mathematically equivalent to
laminated force-free equilibria in Cartesian geometry. The lowest order
solutions have no toroidal component of the magnetic field and the magnetic
pressure does not vary with azimuth but the solutions allow arbitrary
variations of the magnetic field components with azimuth. Explicit solutions
are presented which have a realistic radial profile of the magnetic field
strength and reproduce the basic features of the observations.Comment: 8 pages, 4 figures, accepted for publication in Astronomy and
Astrophysic
2D stationary resistive MHD flows: borderline to magnetic reconnection solutions
We present the basic equations for stationary, incompressible resistive MHD
flows in two dimensions. This leads to a system of differential equations for
two flux functions, one elliptic partial differential equation
(Grad-Shafranov-like) for the magnetic flux function and one for the stream
function of the flow. In these equations two potentials appear: one potential
is a generalized pressure. The second potential couples the magnetic and the
flow shear components of the system. With the restriction to flux or at least
line conserving flows one has to solve a modified Ohm's law. For the two
dimensional case these are two coupled differential equations, which represent
the borderline between the resistive but flux conserving (or line conserving)
case, and that of reconnective solutions. We discuss some simplified solutions
of these equations.Comment: 5 pages, 2 figures, Advances in Space Research (in press
Arbitrarily large families of spaces of the same volume
In any connected non-compact semi-simple Lie group without factors locally
isomorphic to SL_2(R), there can be only finitely many lattices (up to
isomorphism) of a given covolume. We show that there exist arbitrarily large
families of pairwise non-isomorphic arithmetic lattices of the same covolume.
We construct these lattices with the help of Bruhat-Tits theory, using Prasad's
volume formula to control their covolumes.Comment: 9 pages. Syntax corrected; one reference adde
On higher congruences between cusp forms and Eisenstein series
In this paper we present several finite families of congruences between cusp
forms and Eisenstein series of higher weights at powers of prime ideals. We
formulate a conjecture which describes properties of the prime ideals and their
relation to the weights. We check the validity of the conjecture on several
numerical examples.Comment: 20 page
Representations of integers by certain positive definite binary quadratic forms
We prove part of a conjecture of Borwein and Choi concerning an estimate on
the square of the number of solutions to n=x^2+Ny^2 for a squarefree integer N.Comment: 8 pages, submitte
Reconnection at the Heliopause
In this MHD-model of the heliosphere, we assume a Parker-type flow, and a
Parker-type spiral magnetic field, which is extrapolated further downstream
from the termination shock to the heliopause. We raise the question whether the
heliopause nose region may be leaky with respect to fields and plasmas due to
nonideal plasma dynamics, implying a breakdown of the magnetic barrier. We
analyse some simple scenarios to find reconnection rates and circumstances,
under which the heliosphere can be an "open" or a "closed" magnetosphere. We do
not pretend to offer a complete solution for the heliosphere, on the basis of
nonideal MHD theory, but present a prescription to find such a solution on the
basis of potential fields including the knowledge of neutral points. As an
example we imitate the Parker spiral as a monopole with a superposition of
homogeneous asymptotical boundary conditions. We use this toy model for x < -R
where R = 100 AU is the distance of the termination shock to describe the
situation in the nose region of the heliopause.Comment: 12 pages, 3 figures, Advances in Space Research (in press
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