35 research outputs found
Interaction Properties of the Periodic and Step-like Solutions of the Double-Sine-Gordon Equation
The periodic and step-like solutions of the double-Sine-Gordon equation are
investigated, with different initial conditions and for various values of the
potential parameter . We plot energy and force diagrams, as functions
of the inter-soliton distance for such solutions. This allows us to consider
our system as an interacting many-body system in 1+1 dimension. We therefore
plot state diagrams (pressure vs. average density) for step-like as well as
periodic solutions. Step-like solutions are shown to behave similarly to their
counterparts in the Sine-Gordon system. However, periodic solutions show a
fundamentally different behavior as the parameter is increased. We
show that two distinct phases of periodic solutions exist which exhibit
manifestly different behavior. Response functions for these phases are shown to
behave differently, joining at an apparent phase transition point.Comment: 17pages, 15 figure
Kinks in the Presence of Rapidly Varying Perturbations
Dynamics of sine-Gordon kinks in the presence of rapidly varying periodic
perturbations of different physical origins is described analytically and
numerically. The analytical approach is based on asymptotic expansions, and it
allows to derive, in a rigorous way, an effective nonlinear equation for the
slowly varying field component in any order of the asymptotic procedure as
expansions in the small parameter , being the frequency
of the rapidly varying ac driving force. Three physically important examples of
such a dynamics, {\em i.e.}, kinks driven by a direct or parametric ac force,
and kinks on rotating and oscillating background, are analysed in detail. It is
shown that in the main order of the asymptotic procedure the effective equation
for the slowly varying field component is {\em a renormalized sine-Gordon
equation} in the case of the direct driving force or rotating (but phase-locked
to an external ac force) background, and it is {\em the double sine-Gordon
equation} for the parametric driving force. The properties of the kinks
described by the renormalized nonlinear equations are analysed, and it is
demonstrated analytically and numerically which kinds of physical phenomena may
be expected in dealing with the renormalized, rather than the unrenormalized,
nonlinear dynamics. In particular, we predict several qualitatively new effects
which include, {\em e.g.}, the perturbation-inducedComment: New copy of the paper of the above title to replace the previous one,
lost in the midst of the bulletin board. RevTeX 3.
Localization of electromagnetic waves in a two dimensional random medium
Motivated by previous investigations on the radiative effects of the electric
dipoles embedded in structured cavities, localization of electromagnetic waves
in two dimensions is studied {\it ab initio} for a system consisting of many
randomly distributed two dimensional dipoles. A set of self-consistent
equations, incorporating all orders of multiple scattering of the
electromagnetic waves, is derived from first principles and then solved
numerically for the total electromagnetic field. The results show that
spatially localized electromagnetic waves are possible in such a simple but
realistic disordered system. When localization occurs, a coherent behavior
appears and is revealed as a unique property differentiating localization from
either the residual absorption or the attenuation effects
Diffusive and localization behavior of electromagnetic waves in a two-dimensional random medium
In this paper, we discuss the transport phenomena of electromagnetic waves in
a two-dimensional random system which is composed of arrays of electrical
dipoles, following the model presented earlier by Erdogan, et al. (J. Opt. Soc.
Am. B {\bf 10}, 391 (1993)). A set of self-consistent equations is presented,
accounting for the multiple scattering in the system, and is then solved
numerically. A strong localization regime is discovered in the frequency
domain. The transport properties within, near the edge of and nearly outside
the localization regime are investigated for different parameters such as
filling factor and system size. The results show that within the localization
regime, waves are trapped near the transmitting source. Meanwhile, the
diffusive waves follow an intuitive but expected picture. That is, they
increase with travelling path as more and more random scattering incurs,
followed by a saturation, then start to decay exponentially when the travelling
path is large enough, signifying the localization effect. For the cases that
the frequencies are near the boundary of or outside the localization regime,
the results of diffusive waves are compared with the diffusion approximation,
showing less encouraging agreement as in other systems (Asatryan, et al., Phys.
Rev. E {\bf 67}, 036605 (2003).)Comment: 8 pages 9 figure
Active Brownian Particles. From Individual to Collective Stochastic Dynamics
We review theoretical models of individual motility as well as collective
dynamics and pattern formation of active particles. We focus on simple models
of active dynamics with a particular emphasis on nonlinear and stochastic
dynamics of such self-propelled entities in the framework of statistical
mechanics. Examples of such active units in complex physico-chemical and
biological systems are chemically powered nano-rods, localized patterns in
reaction-diffusion system, motile cells or macroscopic animals. Based on the
description of individual motion of point-like active particles by stochastic
differential equations, we discuss different velocity-dependent friction
functions, the impact of various types of fluctuations and calculate
characteristic observables such as stationary velocity distributions or
diffusion coefficients. Finally, we consider not only the free and confined
individual active dynamics but also different types of interaction between
active particles. The resulting collective dynamical behavior of large
assemblies and aggregates of active units is discussed and an overview over
some recent results on spatiotemporal pattern formation in such systems is
given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte
Black hole thermodynamical entropy
As early as 1902, Gibbs pointed out that systems whose partition function
diverges, e.g. gravitation, lie outside the validity of the Boltzmann-Gibbs
(BG) theory. Consistently, since the pioneering Bekenstein-Hawking results,
physically meaningful evidence (e.g., the holographic principle) has
accumulated that the BG entropy of a black hole is
proportional to its area ( being a characteristic linear length), and
not to its volume . Similarly it exists the \emph{area law}, so named
because, for a wide class of strongly quantum-entangled -dimensional
systems, is proportional to if , and to if
, instead of being proportional to (). These results
violate the extensivity of the thermodynamical entropy of a -dimensional
system. This thermodynamical inconsistency disappears if we realize that the
thermodynamical entropy of such nonstandard systems is \emph{not} to be
identified with the BG {\it additive} entropy but with appropriately
generalized {\it nonadditive} entropies. Indeed, the celebrated usefulness of
the BG entropy is founded on hypothesis such as relatively weak probabilistic
correlations (and their connections to ergodicity, which by no means can be
assumed as a general rule of nature). Here we introduce a generalized entropy
which, for the Schwarzschild black hole and the area law, can solve the
thermodynamic puzzle.Comment: 7 pages, 2 figures. Accepted for publication in EPJ