766 research outputs found
A certain class of Laplace transforms with applications to reaction and reaction-diffusion equations
A class of Laplace transforms is examined to show that particular cases of
this class are associated with production-destruction and reaction-diffusion
problems in physics, study of differences of independently distributed random
variables and the concept of Laplacianness in statistics, alpha-Laplace and
Mittag-Leffler stochastic processes, the concepts of infinite divisibility and
geometric infinite divisibility problems in probability theory and certain
fractional integrals and fractional derivatives. A number of applications are
pointed out with special reference to solutions of fractional reaction and
reaction-diffusion equations and their generalizations.Comment: LaTeX, 12 pages, corrected typo
Homology and K--Theory Methods for Classes of Branes Wrapping Nontrivial Cycles
We apply some methods of homology and K-theory to special classes of branes
wrapping homologically nontrivial cycles. We treat the classification of
four-geometries in terms of compact stabilizers (by analogy with Thurston's
classification of three-geometries) and derive the K-amenability of Lie groups
associated with locally symmetric spaces listed in this case. More complicated
examples of T-duality and topology change from fluxes are also considered. We
analyse D-branes and fluxes in type II string theory on with torsion flux and demonstrate in details
the conjectured T-duality to with no flux. In the
simple case of , T-dualizing the circles reduces to
duality between with
flux and with no flux.Comment: 27 pages, tex file, no figure
Yang-Mills theory for bundle gerbes
Given a bundle gerbe with connection on an oriented Riemannian manifold of
dimension at least equal to 3, we formulate and study the associated Yang-Mills
equations. When the Riemannian manifold is compact and oriented, we prove the
existence of instanton solutions to the equations and also determine the moduli
space of instantons, thus giving a complete analysis in this case. We also
discuss duality in this context.Comment: Latex2e, 7 pages, some typos corrected, to appear in J. Phys. A:
Math. and Ge
Anti-ferromagnetic ordering in arrays of superconducting pi-rings
We report experiments in which one dimensional (1D) and two dimensional (2D)
arrays of YBa2Cu3O7-x-Nb pi-rings are cooled through the superconducting
transition temperature of the Nb in various magnetic fields. These pi-rings
have degenerate ground states with either clockwise or counter-clockwise
spontaneous circulating supercurrents. The final flux state of each ring in the
arrays was determined using scanning SQUID microscopy. In the 1D arrays,
fabricated as a single junction with facets alternating between alignment
parallel to a [100] axis of the YBCO and rotated 90 degrees to that axis,
half-fluxon Josephson vortices order strongly into an arrangement with
alternating signs of their magnetic flux. We demonstrate that this ordering is
driven by phase coupling and model the cooling process with a numerical
solution of the Sine-Gordon equation. The 2D ring arrays couple to each other
through the magnetic flux generated by the spontaneous supercurrents. Using
pi-rings for the 2D flux coupling experiments eliminates one source of disorder
seen in similar experiments using conventional superconducting rings, since
pi-rings have doubly degenerate ground states in the absence of an applied
field. Although anti-ferromagnetic ordering occurs, with larger negative bond
orders than previously reported for arrays of conventional rings, long-range
order is never observed, even in geometries without geometric frustration. This
may be due to dynamical effects. Monte-Carlo simulations of the 2D array
cooling process are presented and compared with experiment.Comment: 10 pages, 15 figure
Subordination model of anomalous diffusion leading to the two-power-law relaxation responses
We derive a general pattern of the nonexponential, two-power-law relaxation
from the compound subordination theory of random processes applied to anomalous
diffusion. The subordination approach is based on a coupling between the very
large jumps in physical and operational times. It allows one to govern a
scaling for small and large times independently. Here we obtain explicitly the
relaxation function, the kinetic equation and the susceptibility expression
applicable to the range of experimentally observed power-law exponents which
cannot be interpreted by means of the commonly known Havriliak-Negami fitting
function. We present a novel two-power relaxation law for this range in a
convenient frequency-domain form and show its relationship to the
Havriliak-Negami one.Comment: 5 pages; 3 figures; corrected versio
Effective descriptions of branes on non-geometric tori
We investigate the low-energy effective description of non-geometric
compactifications constructed by T-dualizing two or three of the directions of
a T^3 with non-vanishing H-flux. Our approach is to introduce a D3-brane in
these geometries and to take an appropriate decoupling limit. In the case of
two T-dualities, we find at low energies a non-commutative T^2 fibered
non-trivially over an S^1. In the UV this theory is still decoupled from
gravity, but is dual to a little string theory with flavor. For the case of
three T-dualities, we do not find a sensible decoupling limit, casting doubt on
this geometry as a low-energy effective notion in critical string theory.
However, by studying a topological toy model in this background, we find a
non-associative geometry similar to one found by Bouwknegt, Hannabuss, and
Mathai.Comment: 22 pages, 4 figures, references adde
Kinematics and dynamics of freely rising spheroids at high Reynolds numbers
We experimentally investigate the effect of geometrical anisotropy for
buoyant ellipsoidal particles rising in a still fluid. All other parameters,
such as the Galileo number and the particle density ratio
are kept constant. The geometrical aspect ratio, ,
of the particle is varied systematically from = 0.2 (oblate) to 5
(prolate). Based on tracking all degrees of particle motion, we identify six
regimes characterised by distinct rise dynamics. Firstly, for , increased rotational dynamics are observed and the particle flips
over semi-regularly in a "tumbling"-like motion. Secondly, for oblate particles
with , planar regular "zig-zag" motion is observed,
where the drag coefficient is independent of . Thirdly, for the most
extreme oblate geometries () a "flutter"-like behaviour is
found, characterised by precession of the oscillation plane and an increase in
the drag coefficient. For prolate geometries, we observed two coexisting
oscillation modes that contribute to complex trajectories: the first is related
to oscillations of the pointing vector and the second corresponds to a motion
perpendicular to the particle's symmetry axis. We identify a "longitudinal"
regime (), where both modes are active and a different
one, the "broadside"-regime (), where only the second mode is
present. Remarkably, for the most prolate particles (), we observe an
entirely different "helical" rise with completely unique features.Comment: 46 pages, 20 figure
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