733,839 research outputs found
Non-Gaussianity of the density distribution in accelerating universes
According to recent observations, the existence of the dark energy has been
considered. Even though we have obtained the constraint of the equation of the
state for dark energy () as by combining WMAP
data with other astronomical data, in order to pin down , it is necessary to
use other independent observational tools. For this purpose, we consider the
dependence of the non-Gaussianity of the density distribution generated by
nonlinear dynamics. To extract the non-Gaussianity, we follow a semi-analytic
approach based on Lagrangian linear perturbation theory, which provides an
accurate value for the quasi-nonlinear region. From our results, the difference
of the non-Gaussianity between and is about 4% while that
between and is about . For the highly non-linear
region, we estimate the difference by combining this perturbative approach with
N-body simulation executed for our previous paper. From this, we can expect the
difference to be more enhanced in the low- region, which suggests that the
non-Gaussianity of the density distribution potentially plays an important role
for extracting the information of dark energy.Comment: 15 pages, 4 figures, accepted for publication in JCAP; v2: smoothing
scale has been change
Polarization fluctuations in vertical cavity surface emitting lasers: a key to the mechanism behind polarization stability
We investigate the effects of the electron-hole spin dynamics on the
polarization fluctuations in the light emitted from a vertical cavity surface
emitting laser (VCSEL). The Langevin equations are derived based on a rate
equation model including birefringence, dichroism, and two carrier density
pools seperately coupled to right and left circular polarization. The results
show that the carrier dynamics phase lock the polarization fluctuations to the
laser mode. This is clearly seen in the difference between fluctuations in
ellipticity and fluctuations in polarization direction. Seperate measurements
of the polarization fluctuations in ellipticity and in polarization direction
can therefore provide quantitative information on the non-linear contribution
of the carrier dynamics to polarization stability in VCSELs.Comment: 6 pages RevTex and 3 figures, to be published in Quantum and
Semiclassical Optics, minor changes to the discussion of timescale
Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations
The global attractor of a skew product semiflow for a non-autonomous
differential equation describes the asymptotic behaviour of the model. This attractor is usually characterized as the union, for all the parameters in the base space, of the associated cocycle attractors in the product space. The continuity of the cocycle attractor in the parameter is usually a difficult question. In this paper we develop in detail a 1D non-autonomous linear differential equation and show the richness of non-autonomous dynamics by focusing on the continuity, characterization and chaotic dynamics of the cocycle attractors. In particular, we analyse the sets of continuity and discontinuity for the parameter of the attractors, and relate them with the eventually forward behaviour of the processes. We will also find chaotic behaviour on the attractors in the Li-Yorke and Auslander-Yorke senses. Note that they hold for linear 1D equations, which shows a crucial difference with respect to the presence of chaotic dynamics in autonomous systems.Fondo Europeo de Desarrollo RegionalMinisterio de Economía y CompetitividadJunta de AndalucíaBrazilian-European partnership in Dynamical Systems (BREUDS)Junta de Castilla y Leó
Fractional Dynamics of Network Growth Constrained by aging Node Interactions
In many social complex systems, in which agents are linked by non-linear
interactions, the history of events strongly influences the whole network
dynamics. However, a class of "commonly accepted beliefs" seems rarely studied.
In this paper, we examine how the growth process of a (social) network is
influenced by past circumstances. In order to tackle this cause, we simply
modify the well known preferential attachment mechanism by imposing a time
dependent kernel function in the network evolution equation. This approach
leads to a fractional order Barabasi-Albert (BA) differential equation,
generalizing the BA model. Our results show that, with passing time, an aging
process is observed for the network dynamics. The aging process leads to a
decay for the node degree values, thereby creating an opposing process to the
preferential attachment mechanism. On one hand, based on the preferential
attachment mechanism, nodes with a high degree are more likely to absorb links;
but, on the other hand, a node's age has a reduced chance for new connections.
This competitive scenario allows an increased chance for younger members to
become a hub. Simulations of such a network growth with aging constraint
confirm the results found from solving the fractional BA equation. We also
report, as an exemplary application, an investigation of the collaboration
network between Hollywood movie actors. It is undubiously shown that a decay in
the dynamics of their collaboration rate is found, - even including a sex
difference. Such findings suggest a widely universal application of the so
generalized BA model.Comment: 13 pages; 5 figures; 71 references; as prepared for submission to
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Aging phenomena in the two-dimensional complex Ginzburg-Landau equation
The complex Ginzburg-Landau equation with additive noise is a stochastic
partial differential equation that describes a remarkably wide range of
physical systems which include coupled non-linear oscillators subject to
external noise near a Hopf bifurcation instability and spontaneous structure
formation in non-equilibrium systems, e.g., in cyclically competing populations
or oscillatory chemical reactions. We employ a finite-difference method to
numerically solve the noisy complex Ginzburg-Landau equation on a
two-dimensional domain with the goal to investigate its non-equilibrium
dynamics when the system is quenched into the "defocusing spiral quadrant". We
observe slow coarsening dynamics as oppositely charged topological defects
annihilate each other, and characterize the ensuing aging scaling behavior. We
conclude that the physical aging features in this system are governed by
non-universal aging scaling exponents. We also investigate systems with control
parameters residing in the "focusing quadrant", and identify slow aging
kinetics in that regime as well. We provide heuristic criteria for the
existence of slow coarsening dynamics and physical aging behavior in the
complex Ginzburg-Landau equation.Comment: 7 pages, 3 figures, to appear in EPL (Europhys. Lett.
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