21,029 research outputs found
Scalar--flat K\"ahler metrics with conformal Bianchi V symmetry
We provide an affirmative answer to a question posed by Tod \cite{Tod:1995b},
and construct all four-dimensional Kahler metrics with vanishing scalar
curvature which are invariant under the conformal action of Bianchi V group.
The construction is based on the combination of twistor theory and the
isomonodromic problem with two double poles. The resulting metrics are
non-diagonal in the left-invariant basis and are explicitly given in terms of
Bessel functions and their integrals. We also make a connection with the LeBrun
ansatz, and characterise the associated solutions of the SU(\infty) Toda
equation by the existence a non-abelian two-dimensional group of point
symmetries.Comment: Dedicated to Maciej Przanowski on the occasion of his 65th birthday.
Minor corrections. To appear in CQ
Averaging of Nonlinearity Management with Dissipation
Motivated by recent experiments in optics and atomic physics, we derive an
averaged nonlinear partial differential equation describing the dynamics of the
complex field in a nonlinear Schroedinger model in the presence of a periodic
nonlinearity and a periodically-varying dissipation coefficient. The
incorporation of dissipation is motivated by experimental considerations. We
test the numerical behavior of the derived averaged equation by comparing it to
the original nonautonomous model in a prototypical case scenario and observe
good agreement between the two
Particle Impact Analysis of Bulk Powder During Pneumatic Conveyance
Fragmentation of powders during transportation is a common problem for manufacturers of food and pharmaceutical products. We illustrate that the primary cause of breakage is due to inter-particle collisions, rather than particle-wall impacts, and provide a statistical mechanics model giving the number of collisions resulting in fragmentation
Solitons and admissible families of rational curves in twistor spaces
It is well known that twistor constructions can be used to analyse and to
obtain solutions to a wide class of integrable systems. In this article we
express the standard twistor constructions in terms of the concept of an
admissible family of rational curves in certain twistor spaces. Examples of of
such families can be obtained as subfamilies of a simple family of rational
curves using standard operations of algebraic geometry. By examination of
several examples, we give evidence that this construction is the basis of the
construction of many of the most important solitonic and algebraic solutions to
various integrable differential equations of mathematical physics. This is
presented as evidence for a principal that, in some sense, all soliton-like
solutions should be constructable in this way.Comment: 15 pages, Abstract and introduction rewritten to clarify the
objectives of the paper. This is the final version which will appear in
Nonlinearit
Mirror symmetry breaking as a problem in dynamical critical phenomena
The critical properties of the Frank model of spontaneous chiral synthesis
are discussed by applying results from the field theoretic renormalization
group (RG). The long time and long wavelength features of this microscopic
reaction scheme belong to the same universality class as multi-colored directed
percolation processes. Thus, the following RG fixed points (FP) govern the
critical dynamics of the Frank model for d<4: one unstable FP that corresponds
to complete decoupling between the two enantiomers, a saddle-point that
corresponds to symmetric interspecies coupling, and two stable FPs that
individually correspond to unidirectional couplings between the two chiral
molecules. These latter two FPs are associated with the breakdown of mirror or
chiral symmetry. In this simplified model of molecular synthesis, homochirality
is a natural consequence of the intrinsic reaction noise in the critical
regime, which corresponds to extremely dilute chemical systems.Comment: 9 pages, 3 figure
Neutron scattering in a d_{x^2-y^2}-wave superconductor with strong impurity scattering and Coulomb correlations
We calculate the spin susceptibility at and below T_c for a d_{x^2-y^2}-wave
superconductor with resonant impurity scattering and Coulomb correlations. Both
the impurity scattering and the Coulomb correlations act to maintain peaks in
the spin susceptibility, as a function of momentum, at the Brillouin zone edge.
These peaks would otherwise be suppressed by the superconducting gap. The
predicted amount of suppression of the spin susceptibility in the
superconducting state compared to the normal state is in qualitative agreement
with results from recent magnetic neutron scattering experiments on
La_{1.86}Sr_{0.14}CuO_4 for momentum values at the zone edge and along the zone
diagonal. The predicted peak widths in the superconducting state, however, are
narrower than those in the normal state, a narrowing which has not been
observed experimentally.Comment: 24 pages (12 tarred-compressed-uuencoded Postscript figures), REVTeX
3.0 with epsf macros, UCSBTH-94-1
Husimi Maps in Lattices
We build upon previous work that used coherent states as a measurement of the
local phase space and extended the flux operator by adapting the Husimi
projection to produce a vector field called the Husimi map. In this article, we
extend its definition from continuous systems to lattices. This requires making
several adjustments to incorporate effects such as group velocity and multiple
bands. Several phenomena which uniquely occur in lattice systems, like
group-velocity warping and internal Bragg diffraction, are explained and
demonstrated using Husimi maps. We also show that scattering points between
bands and valleys can be identified in the divergence of the Husimi map
The Influence of Magnetic Imperfections on the Low Temperature Properties of D-wave Superconductors
We consider the influence of planar ``magnetic" imperfections which destroy
the local magnetic order, such as Zn impurities or vacancies, on the
low temperature properties of the cuprate superconductors. In the unitary
limit, at low temperatures, for a pairing state such
imperfections produce low energy quasiparticles with an anistropic spectrum in
the vicinity of the nodes. We find that for the system, one
is in the {\em quasi-one-dimensional} regime of quasiparticle scattering,
discussed recently by Altshuler, Balatsky, and Rosengren, for impurity
concentrations in excess of whereas YBCO appears likely to be
in the true 2D scattering regime for Zn concentrations less than . We
show the neutron scattering results of Mason et al. \cite{Aeppli} on
provide strong evidence for ``dirty d-wave"
superconductivity in their samples. We obtain simple expressions for the
dynamic spin susceptibility and spin-lattice relaxation time,
, in the superconducting state.Comment: 10 pages; revtex; Los Alamos preprint LA-UR-94-53
Why do some intermediate polars show soft X-ray emission? A survey of XMM-Newton spectra
We make a systematic analysis of the XMM-Newton X-ray spectra of intermediate
polars (IPs) and find that, contrary to the traditional picture, most show a
soft blackbody component. We compare the results with those from AM Her stars
and deduce that the blackbody emission arises from reprocessing of hard X-rays,
rather than from the blobby accretion sometimes seen in AM Hers. Whether an IP
shows a blackbody component appears to depend primarily on geometric factors: a
blackbody is not seen in those that have accretion footprints that are always
obscured by accretion curtains or are only visible when foreshortened on the
white-dwarf limb. Thus we argue against previous suggestions that the blackbody
emission characterises a separate sub-group of IPs which are more akin to AM
Hers, and develop a unified picture of the blackbody emission in these stars.Comment: 9 pages, 6 figures. Accepted for publication in Ap
- …