15,634 research outputs found
Analytical results for long time behavior in anomalous diffusion
We investigate through a Generalized Langevin formalism the phenomenon of
anomalous diffusion for asymptotic times, and we generalized the concept of the
diffusion exponent. A method is proposed to obtain the diffusion coefficient
analytically through the introduction of a time scaling factor . We
obtain as well an exact expression for for all kinds of diffusion.
Moreover, we show that is a universal parameter determined by the
diffusion exponent. The results are then compared with numerical calculations
and very good agreement is observed. The method is general and may be applied
to many types of stochastic problem
Gravitation and Duality Symmetry
By generalizing the Hodge dual operator to the case of soldered bundles, and
working in the context of the teleparallel equivalent of general relativity, an
analysis of the duality symmetry in gravitation is performed. Although the
basic conclusion is that, at least in the general case, gravitation is not dual
symmetric, there is a particular theory in which this symmetry shows up. It is
a self dual (or anti-self dual) teleparallel gravity in which, due to the fact
that it does not contribute to the interaction of fermions with gravitation,
the purely tensor part of torsion is assumed to vanish. The ensuing fermionic
gravitational interaction is found to be chiral. Since duality is intimately
related to renormalizability, this theory may eventually be more amenable to
renormalization than teleparallel gravity or general relativity.Comment: 7 pages, no figures. Version 2: minor presentation changes,
references added. Accepted for publication in Int. J. Mod. Phys.
The influence of statistical properties of Fourier coefficients on random surfaces
Many examples of natural systems can be described by random Gaussian
surfaces. Much can be learned by analyzing the Fourier expansion of the
surfaces, from which it is possible to determine the corresponding Hurst
exponent and consequently establish the presence of scale invariance. We show
that this symmetry is not affected by the distribution of the modulus of the
Fourier coefficients. Furthermore, we investigate the role of the Fourier
phases of random surfaces. In particular, we show how the surface is affected
by a non-uniform distribution of phases
Primordial magnetic fields constrained by CMB anisotropies and dynamo cosmology
Magneto-curvature stresses could deform magnetic field lines and this would
give rise to back reaction and restoring magnetic stresses [Tsagas, PRL
(2001)]. Barrow et al [PRD (2008)] have shown in Friedman universe the
expansion to be slow down in spatial section of negative Riemann curvatures.
From Chicone et al [CMP (1997)] paper, proved that fast dynamos in compact 2D
manifold implies negatively constant Riemannian curvature, here one applies the
Barrow-Tsagas ideas to cosmic dynamos. Fast dynamo covariant stretching of
Riemann slices of cosmic Lobachevsky plane is given. Inclusion of advection
term on dynamo equations [Clarkson et al, MNRAS (2005)] is considered. In
absence of advection a fast dynamo is also obtained. Viscous and restoring
forces on stretching particles decrease, as magnetic rates increase. From COBE
data (), one computes stretching
.
Zeldovich et al has computed the maximum magnetic growth rate as
. From COBE data one computes
a lower growth rate for the magnetic field as
, well-within Zeldovich et al
estimate. Instead of the Harrison value one obtains the
lower primordial field which yields the
at the Big Bang time.Comment: Dept of theoretical physics-UERJ-Brasi
Memory effects on the statistics of fragmentation
We investigate through extensive molecular dynamics simulations the
fragmentation process of two-dimensional Lennard-Jones systems. After
thermalization, the fragmentation is initiated by a sudden increment to the
radial component of the particles' velocities. We study the effect of
temperature of the thermalized system as well as the influence of the impact
energy of the ``explosion'' event on the statistics of mass fragments. Our
results indicate that the cumulative distribution of fragments follows the
scaling ansatz , where is
the mass, and are cutoff parameters, and is a scaling
exponent that is dependent on the temperature. More precisely, we show clear
evidence that there is a characteristic scaling exponent for each
macroscopic phase of the thermalized system, i.e., that the non-universal
behavior of the fragmentation process is dictated by the state of the system
before it breaks down.Comment: 5 pages, 8 figure
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