1,132 research outputs found
Extended Reaction Rate Integral as Solutions of Some General Differential Equations
Here an extended form of the reaction rate probability integral, in the case
of nonresonant thermonuclear reactions with the depleted tail and the right
tail cut off, is considered. The reaction rate integral then can be looked upon
as the inverse of the convolution of the Mellin transforms of Tsallis type
statistics of nonextensive statistical mechanics and stretched exponential as
well as that of superstatistics and stretched exponentials. The differential
equations satisfied by the extended probability integrals are derived. The idea
used is a novel one of evaluating the extended integrals in terms of some
special functions and then by invoking the differential equations satisfied by
these special functions. Some special cases of limiting situations are also
discussed.Comment: 9 pages, LaTe
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
Parametrised strict deformation quantization of C*-bundles and Hilbert C*-modules
In this paper, we use the parametrised strict deformation quantization of
C*-bundles obtained in a previous paper, and give more examples and
applications of this theory. In particular, it is used here to classify
H_3-twisted noncommutative torus bundles over a locally compact space. This is
extended to the case of general torus bundles and their parametrised strict
deformation quantization. Rieffel's basic construction of an algebra
deformation can be mimicked to deform a monoidal category, which deforms not
only algebras but also modules. As a special case, we consider the parametrised
strict deformation quantization of Hilbert C*-modules over C*-bundles with
fibrewise torus action.Comment: 13 page
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
Translational and rotational dynamics of a large buoyant sphere in turbulence
We report experimental measurements of the translational and rotational dynamics of a large buoyant sphere in isotropic turbulence. We introduce an efficient method to simultaneously determine the position and (absolute) orientation of a spherical body from visual observation. The method employs a minimization algorithm to obtain the orientation from the 2D projection of a specific pattern drawn onto the surface of the sphere. This has the advantages that it does not require a database of reference images, is easily scalable using parallel processing, and enables accurate absolute orientation reference. Analysis of the sphere’s translational dynamics reveals clear differences between the streamwise and transverse directions. The translational autocorrelations and PDFs provide evidence for periodicity in the particle’s dynamics even under turbulent conditions. The angular autocorrelations show weak periodicity. The angular accelerations exhibit wide tails, however without a directional dependence
Wake-Driven Dynamics of Finite-Sized Buoyant Spheres in Turbulence
Particles suspended in turbulent flows are affected by the turbulence and at
the same time act back on the flow. The resulting coupling can give rise to
rich variability in their dynamics. Here we report experimental results from an
investigation of finite-sized buoyant spheres in turbulence. We find that even
a marginal reduction in the particle's density from that of the fluid can
result in strong modification of its dynamics. In contrast to classical spatial
filtering arguments and predictions of particle models, we find that the
particle acceleration variance increases with size. We trace this reversed
trend back to the growing contribution from wake-induced forces, unaccounted
for in current particle models in turbulence. Our findings highlight the need
for improved multi-physics based models that account for particle wake effects
for a faithful representation of buoyant-sphere dynamics in turbulence.Comment: 5 pages, 4 figures,
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.12450
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
Random matrix theory within superstatistics
We propose a generalization of the random matrix theory following the basic
prescription of the recently suggested concept of superstatistics. Spectral
characteristics of systems with mixed regular-chaotic dynamics are expressed as
weighted averages of the corresponding quantities in the standard theory
assuming that the mean level spacing itself is a stochastic variable. We
illustrate the method by calculating the level density, the
nearest-neighbor-spacing distributions and the two-level correlation functions
for system in transition from order to chaos. The calculated spacing
distribution fits the resonance statistics of random binary networks obtained
in a recent numerical experiment.Comment: 20 pages, 6 figure
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