1,312 research outputs found
Fractional Hamilton formalism within Caputo's derivative
In this paper we develop a fractional Hamiltonian formulation for dynamic
systems defined in terms of fractional Caputo derivatives. Expressions for
fractional canonical momenta and fractional canonical Hamiltonian are given,
and a set of fractional Hamiltonian equations are obtained. Using an example,
it is shown that the canonical fractional Hamiltonian and the fractional
Euler-Lagrange formulations lead to the same set of equations.Comment: 8 page
Fractional conservation laws in optimal control theory
Using the recent formulation of Noether's theorem for the problems of the
calculus of variations with fractional derivatives, the Lagrange multiplier
technique, and the fractional Euler-Lagrange equations, we prove a Noether-like
theorem to the more general context of the fractional optimal control. As a
corollary, it follows that in the fractional case the autonomous Hamiltonian
does not define anymore a conservation law. Instead, it is proved that the
fractional conservation law adds to the Hamiltonian a new term which depends on
the fractional-order of differentiation, the generalized momentum, and the
fractional derivative of the state variable.Comment: The original publication is available at http://www.springerlink.com
Nonlinear Dynamic
Reaction-diffusion systems and nonlinear waves
The authors investigate the solution of a nonlinear reaction-diffusion
equation connected with nonlinear waves. The equation discussed is more general
than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results
are presented in a compact and elegant form in terms of Mittag-Leffler
functions and generalized Mittag-Leffler functions, which are suitable for
numerical computation. The importance of the derived results lies in the fact
that numerous results on fractional reaction, fractional diffusion, anomalous
diffusion problems, and fractional telegraph equations scattered in the
literature can be derived, as special cases, of the results investigated in
this article.Comment: LaTeX, 16 pages, corrected typo
Renormalization of the mass gap
The full gluon propagator relevant for the description of the truly
non-perturbative QCD dynamics, the so-called intrinsically non-perturbative
gluon propagator has been derived in our previous work. It explicitly depends
on the regularized mass gap, which dominates its structure at small gluon
momentum. It is automatically transversal in a gauge invariant way. It is
characterized by the presence of severe infrared singularities at small gluon
momentum, so the gluons remain massless, and this does not depend on the gauge
choice. In this paper we have shown how precisely the renormalization program
for the regularized mass gap should be performed. We have also shown how
precisely severe infrared singularities should be correctly treated. This
allowed to analytically formulate the exact and gauge-invariant criteria of
gluon and quark confinement. After the renormalization program is completed,
one can derive the gluon propagator applicable for the calculation of physical
observables processes, etc., in low-energy QCD from first principles.Comment: 16 pages, no figures, no tables, some minor changes are introduce
Solution of generalized fractional reaction-diffusion equations
This paper deals with the investigation of a closed form solution of a
generalized fractional reaction-diffusion equation. The solution of the
proposed problem is developed in a compact form in terms of the H-function by
the application of direct and inverse Laplace and Fourier transforms.
Fractional order moments and the asymptotic expansion of the solution are also
obtained.Comment: LaTeX, 18 pages, corrected typo
Measurement of the tensor analyzing power T20 in the dd->^3Hen and dd->^3Hp at intermediate energies and at zero degree
The data on the tensor analyzing power T20 in the dd->^3Hen and dd-> ^3Hp
reactions at 140, 200 and 270 MeV of the deuteron kinetic energy and at zero
degree obtained at RIKEN Accelerator Research Facility are presented. The
observed positive sign of T20 clearly demonstrates the sensitivity to the D/S
wave ratios in the ^3He and ^3H in the energy domain of the measurements. The
T20 data for the ^3He-n and ^3H-p channels are in agreement within experimental
accuracy.Comment: 9 pages, 3 figures, submitted in Phys.Lett.
Fractional reaction-diffusion equations
In a series of papers, Saxena, Mathai, and Haubold (2002, 2004a, 2004b)
derived solutions of a number of fractional kinetic equations in terms of
generalized Mittag-Leffler functions which provide the extension of the work of
Haubold and Mathai (1995, 2000). The subject of the present paper is to
investigate the solution of a fractional reaction-diffusion equation. The
results derived are of general nature and include the results reported earlier
by many authors, notably by Jespersen, Metzler, and Fogedby (1999) for
anomalous diffusion and del-Castillo-Negrete, Carreras, and Lynch (2003) for
reaction-diffusion systems with L\'evy flights. The solution has been developed
in terms of the H-function in a compact form with the help of Laplace and
Fourier transforms. Most of the results obtained are in a form suitable for
numerical computation.Comment: LaTeX, 17 pages, corrected typo
Schottky barrier heights at polar metal/semiconductor interfaces
Using a first-principle pseudopotential approach, we have investigated the
Schottky barrier heights of abrupt Al/Ge, Al/GaAs, Al/AlAs, and Al/ZnSe (100)
junctions, and their dependence on the semiconductor chemical composition and
surface termination. A model based on linear-response theory is developed,
which provides a simple, yet accurate description of the barrier-height
variations with the chemical composition of the semiconductor. The larger
barrier values found for the anion- than for the cation-terminated surfaces are
explained in terms of the screened charge of the polar semiconductor surface
and its image charge at the metal surface. Atomic scale computations show how
the classical image charge concept, valid for charges placed at large distances
from the metal, extends to distances shorter than the decay length of the
metal-induced-gap states.Comment: REVTeX 4, 11 pages, 6 EPS figure
High-statistics measurement of the pion form factor in the rho-meson energy range with the CMD-2 detector
We present a measurement of the pion form factor based on e+e- annihilation
data from the CMD-2 detector in the energy range 0.6<sqrt(s)<1.0 GeV with a
systematic uncertainty of 0.8%. A data sample is five times larger than that
used in our previous measurement.Comment: 18 pages, 10 figures. Added comparison with KLOE measurement, minor
updates. Accepted by PL
Star cluster formation and star formation: the role of environment and star-formation efficiencies
“The original publication is available at www.springerlink.com”. Copyright Springer. DOI: 10.1007/s10509-009-0088-5By analyzing global starburst properties in various kinds of starburst and post-starburst galaxies and relating them to the properties of the star cluster populations they form, I explore the conditions for the formation of massive, compact, long-lived star clusters. The aim is to determine whether the relative amount of star formation that goes into star cluster formation as opposed to field star formation, and into the formation of massive long-lived clusters in particular, is universal or scales with star-formation rate, burst strength, star-formation efficiency, galaxy or gas mass, and whether or not there are special conditions or some threshold for the formation of star clusters that merit to be called globular clusters a few billion years later.Peer reviewe
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