947 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
Discrete Morse Theory and Extended L2 Homology
AbstractA brief overview of Forman's discrete Morse theory is presented, from which analogues of the main results of classical Morse theory can be derived for discrete Morse functions, these being functions mapping the set of cells of a CW complex to the real numbers satisfying some combinatorial relations. The discrete analogue of the strong Morse inequality was proved by Forman for finite CW complexes using a Witten deformation technique. This deformation argument is adapted to provide strong Morse inequalities for infinite CW complexes which have a finite cellular domain under the free cellular action of a discrete group. The inequalities derived are analogous to the L2 Morse inequalities of Novikov and Shubin and the asymptotic L2 Morse inequalities of an inexact Morse 1-form as derived by Mathai and Shubin. We also obtain quantitative lower bounds for the Morse numbers whenever the spectrum of the Laplacian contains zero, using the extended category of Farber
Josephson (001) tilt grain boundary junctions of high temperature superconductors
We calculate the critical current across in-plane (001) tilt grain
boundary junctions of high temperature superconductors. We solve for the
electronic states corresponding to the electron-doped cuprates, two slightly
different hole-doped cuprates, and an extremely underdoped hole-doped cuprate
in each half-space, and weakly connect the two half-spaces by either specular
or random quasiparticle tunneling. We treat symmetric, straight, and fully
asymmetric junctions with s-, extended-s-, or d-wave order
parameters. For symmetric junctions with random grain boundary tunneling, our
results are generally in agreement with the Sigrist-Rice form for ideal
junctions that has been used to interpret ``phase-sensitive'' experiments
consisting of such in-plane grain boundary junctions. For specular grain
boundary tunneling across symmetric juncitons, our results depend upon the
Fermi surface topology, but are usually rather consistent with the random facet
model of Tsuei {\it et al.} [Phys. Rev. Lett. {\bf 73}, 593 (1994)]. Our
results for asymmetric junctions of electron-doped cuparates are in agreement
with the Sigrist-Rice form. However, ou resutls for asymmetric junctions of
hole-doped cuprates show that the details of the Fermi surface topology and of
the tunneling processes are both very important, so that the
``phase-sensitive'' experiments based upon the in-plane Josephson junctions are
less definitive than has generally been thought.Comment: 13 pages, 10 figures, resubmitted to PR
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
Type I D-branes in an H-flux and twisted KO-theory
Witten has argued that charges of Type I D-branes in the presence of an
H-flux, take values in twisted KO-theory. We begin with the study of real
bundle gerbes and their holonomy. We then introduce the notion of real bundle
gerbe KO-theory which we establish is a geometric realization of twisted
KO-theory. We examine the relation with twisted K-theory, the Chern character
and provide some examples. We conclude with some open problems.Comment: 23 pages, Latex2e, 2 new references adde
"Candidatus Rickettsia kellyi," India
We report the first laboratory-confirmed human infection due to a new rickettsial genotype in India, "Candidatus Rickettsia kellyi," in a 1-year-old boy with fever and maculopapular rash. The diagnosis was made by serologic testing, polymerase chain reaction detection, and immunohistochemical testing of the organism from a skin biopsy specimen
Trapping reactions with subdiffusive traps and particles characterized by different anomalous diffusion exponents
A number of results for reactions involving subdiffusive species all with the
same anomalous exponent gamma have recently appeared in the literature and can
often be understood in terms of a subordination principle whereby time t in
ordinary diffusion is replaced by t^gamma. However, very few results are known
for reactions involving different species characterized by different anomalous
diffusion exponents. Here we study the reaction dynamics of a (sub)diffusive
particle surrounded by a sea of (sub)diffusive traps in one dimension. We find
rigorous results for the asymptotic survival probability of the particle in
most cases, with the exception of the case of a particle that diffuses normally
while the anomalous diffusion exponent of the traps is smaller than 2/3.Comment: To appear in Phys. Rev.
The target problem with evanescent subdiffusive traps
We calculate the survival probability of a stationary target in one dimension
surrounded by diffusive or subdiffusive traps of time-dependent density. The
survival probability of a target in the presence of traps of constant density
is known to go to zero as a stretched exponential whose specific power is
determined by the exponent that characterizes the motion of the traps. A
density of traps that grows in time always leads to an asymptotically vanishing
survival probability. Trap evanescence leads to a survival probability of the
target that may be go to zero or to a finite value indicating a probability of
eternal survival, depending on the way in which the traps disappear with time
Operator algebra quantum homogeneous spaces of universal gauge groups
In this paper, we quantize universal gauge groups such as SU(\infty), as well
as their homogeneous spaces, in the sigma-C*-algebra setting. More precisely,
we propose concise definitions of sigma-C*-quantum groups and sigma-C*-quantum
homogeneous spaces and explain these concepts here. At the same time, we put
these definitions in the mathematical context of countably compactly generated
spaces as well as C*-compact quantum groups and homogeneous spaces. We also
study the representable K-theory of these spaces and compute it for the quantum
homogeneous spaces associated to the universal gauge group SU(\infty).Comment: 14 pages. Merged with [arXiv:1011.1073
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