451 research outputs found
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
The structure of atomic nitrogen adsorbed on Fe(100)
Nitrogen atoms adsorbed on a Fe(100) surface cause the formation of an ordered c(2 Ă 2) overlayer with coverage 0.5. A structure analysis was performed by comparing experimental LEED IâV spectra with the results of multiple scattering model calculations. The N atoms were found to occupy fourfold hollow sites, with their plane 0.27 Ă
above the plane of the surface Fe atoms. In addition, nitrogen adsorption causes an expansion of the two topmost Fe layers by 10% (= 0.14 Ă
). The minimum r-factor for this structure analysis is about 0.2 for a total of 16 beams. The resulting atomic arrangement is similar to that in the (002) plane of bulk Fe4N, thus supporting the view of a âsurface nitrideâ and providing a consistent picture of the structural and bonding properties of this surface phase
Texture and shape of two-dimensional domains of nematic liquid crystal
We present a generalized approach to compute the shape and internal structure
of two-dimensional nematic domains. By using conformal mappings, we are able to
compute the director field for a given domain shape that we choose from a rich
class, which includes drops with large and small aspect ratios, and sharp
domain tips as well as smooth ones. Results are assembled in a phase diagram
that for given domain size, surface tension, anchoring strength, and elastic
constant shows the transitions from a homogeneous to a bipolar director field,
from circular to elongated droplets, and from sharp to smooth domain tips. We
find a previously unaccounted regime, where the drop is nearly circular, the
director field bipolar and the tip rounded. We also find that bicircular
director fields, with foci that lie outside the domain, provide a remarkably
accurate description of the optimal director field for a large range of values
of the various shape parameters.Comment: 12 pages, 10 figure
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
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
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
Boundaries of Siegel Disks: Numerical Studies of their Dynamics and Regularity
Siegel disks are domains around fixed points of holomorphic maps in which the maps are locally linearizable (i.e., become a rotation under an appropriate change of coordinates which is analytic in a neighborhood of the origin). The dynamical behavior of the iterates of the map on the boundary of the Siegel disk exhibits strong scaling properties which have been intensively studied in the physical and mathematical literature. In the cases we study, the boundary of the Siegel disk is a Jordan curve containing a critical point of the map (we consider critical maps of different orders), and there exists a natural parametrization which transforms the dynamics on the boundary into a rotation. We compute numerically this parameterization and use methods of harmonic analysis to compute the global Holder regularity of the parametrization for different maps and rotation numbers. We obtain that the regularity of the boundaries and the scaling exponents are universal numbers in the sense of renormalization theory (i.e., they do not depend on the map when the map ranges in an open set), and only depend on the order of the critical point of the map in the boundary of the Siegel disk and the tail of the continued function expansion of the rotation number. We also discuss some possible relations between the regularity of the parametrization of the boundaries and the corresponding scaling exponents. (C) 2008 American Institute of Physics.NSFMathematic
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
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