545 research outputs found
Global Birkhoff coordinates for the periodic Toda lattice
In this paper we prove that the periodic Toda lattice admits globally defined
Birkhoff coordinates.Comment: 32 page
Hydromagnetic Instability in plane Couette Flow
We study the stability of a compressible magnetic plane Couette flow and show
that compressibility profoundly alters the stability properties if the magnetic
field has a component perpendicular to the direction of flow. The necessary
condition of a newly found instability can be satisfied in a wide variety of
flows in laboratory and astrophysical conditions. The instability can operate
even in a very strong magnetic field which entirely suppresses other MHD
instabilities. The growth time of this instability can be rather short and
reach shear timescales.Comment: 6 pages, 5 figures. To appear on PR
Mapping the phase diagram of strongly interacting matter
We employ a conformal mapping to explore the thermodynamics of strongly
interacting matter at finite values of the baryon chemical potential .
This method allows us to identify the singularity corresponding to the critical
point of a second-order phase transition at finite , given information
only at . The scheme is potentially useful for computing thermodynamic
properties of strongly interacting hot and dense matter in lattice gauge
theory. The technique is illustrated by an application to a chiral effective
model.Comment: 5 pages, 3 figures; published versio
Inverting the Sachs-Wolfe Formula: an Inverse Problem Arising in Early-Universe Cosmology
The (ordinary) Sachs-Wolfe effect relates primordial matter perturbations to
the temperature variations in the cosmic microwave background
radiation; can be observed in all directions around us. A standard
but idealised model of this effect leads to an infinite set of moment-like
equations: the integral of with respect to k ()
is equal to a given constant, , for . Here, P is the
power spectrum of the primordial density variations, is a spherical
Bessel function and y is a positive constant. It is shown how to solve these
equations exactly for ~. The same solution can be recovered, in
principle, if the first ~m equations are discarded. Comparisons with classical
moment problems (where is replaced by ) are made.Comment: In Press Inverse Problems 1999, 15 pages, 0 figures, Late
Conformal Mapping on Rough Boundaries II: Applications to bi-harmonic problems
We use a conformal mapping method introduced in a companion paper to study
the properties of bi-harmonic fields in the vicinity of rough boundaries. We
focus our analysis on two different situations where such bi-harmonic problems
are encountered: a Stokes flow near a rough wall and the stress distribution on
the rough interface of a material in uni-axial tension. We perform a complete
numerical solution of these two-dimensional problems for any univalued rough
surfaces. We present results for sinusoidal and self-affine surface whose slope
can locally reach 2.5. Beyond the numerical solution we present perturbative
solutions of these problems. We show in particular that at first order in
roughness amplitude, the surface stress of a material in uni-axial tension can
be directly obtained from the Hilbert transform of the local slope. In case of
self-affine surfaces, we show that the stress distribution presents, for large
stresses, a power law tail whose exponent continuously depends on the roughness
amplitude
Hydromagnetic Instability in Differentially Rotating Flows
We study the stability of a compressible differentially rotating flows in the
presence of the magnetic field, and we show that the compressibility profoundly
alters the previous results for a magnetized incompressible flow. The necessary
condition of newly found instability can be easily satisfied in various flows
in laboratory and astrophysical conditions and reads where and are the radial and azimuthal components of
the magnetic field, with being the cylindrical
radius. Contrary to the well-known magnetorotational instability that occurs
only if decreases with , the instability considered in this paper
may occur at any sign of . The instability can operate even in a very
strong magnetic field which entirely suppresses the standard magnetorotational
instability. The growth time of instability can be as short as few rotation
periods.Comment: 5 pages, 3 figure
On Kaluza's sign criterion for reciprocal power series
T. Kaluza has given a criterion for the signs of the power series of a
function that is the reciprocal of another power series. In this note the
sharpness of this condition is explored and various examples in terms of the
Gaussian hypergeometric series are given. A criterion for the monotonicity of
the quotient of two power series due to M. Biernacki and J. Krzy\.z is applied.Comment: 13 page
The Szemeredi-Trotter Theorem in the Complex Plane
It is shown that points and lines in the complex Euclidean plane
determine point-line incidences. This
bound is the best possible, and it generalizes the celebrated theorem by
Szemer\'edi and Trotter about point-line incidences in the real Euclidean plane
.Comment: 24 pages, 5 figures, to appear in Combinatoric
Even perturbations of self-similar Vaidya space-time
We study even parity metric and matter perturbations of all angular modes in
self-similar Vaidya space-time. We focus on the case where the background
contains a naked singularity. Initial conditions are imposed describing a
finite perturbation emerging from the portion of flat space-time preceding the
matter-filled region of space-time. The most general perturbation satisfying
the initial conditions is allowed impinge upon the Cauchy horizon (CH), whereat
the perturbation remains finite: there is no ``blue-sheet'' instability.
However when the perturbation evolves through the CH and onto the second future
similarity horizon of the naked singularity, divergence necessarily occurs:
this surface is found to be unstable. The analysis is based on the study of
individual modes following a Mellin transform of the perturbation. We present
an argument that the full perturbation remains finite after resummation of the
(possibly infinite number of) modes.Comment: Accepted for publication in Physical Review D, 27 page
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