arXiv
(422,153 recursos)
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Mostrando recursos 41 - 60 de 13,166
41.
Limit Cycle and Conserved Dynamics - Zhu, X. -M.; Yin, L.; Ao, P.
We demonstrate that a potential coexists with limit cycle. Here the potential
determines the final distribution of population. Our demonstration consists of
three steps: We first show the existence of limit from a typical physical
sciences setting: the potential is a type of Mexican hat type, with the
strength of a magnetic field scale with the strength the potential gradient
near the limit cycle, and the friction goes to zero faster than the potential
near the limit cycle. Hence the dynamics at the limit cycle is conserved. The
diffusion matrix is nevertheless finite at the limit cycle. Secondly, we
construct the potential in the dynamics with limit cycle...
42.
Scarring in a driven system with wave chaos - Virovlyansky, A. L.; Zaslavsky, G. M.
We consider acoustic wave propagation in a model of a deep ocean acoustic
waveguide with a periodic range-dependence. Formally, the wave field is
described by the Schrodinger equation with a time-dependent Hamiltonian. Using
methods borrowed from the quantum chaos theory it is shown that in the driven
system under consideration there exists a "scarring" effect similar to that
observed in autonomous quantum systems.
43.
Long Tailed Maps as a Representation of Mixed Mode Oscillatory Systems - Raghavan, Rajesh; Ananthakrishna, G.
Mixed mode oscillatory (MMO) systems are known to exhibit some generic
features such as the reversal of period doubling sequences and crossover to
period adding sequences as bifurcation parameters are varied. In addition, they
exhibit a nearly one dimensional unimodal Poincare map with a longtail. We
recover these common features from a general class of two parameter family of
one dimensional maps with a unique critical point that satisfy a few general
constraints that determine the nature of the map. We derive scaling laws that
determine the parameter widths of the dominant windows of periodic orbits
sandwiched between two successive states of RL^k sequence. An example of a...
44.
Gurevich-Zybin system - Pavlov, Maxim
We present three different linearizable extensions of the Gurevich-Zybin
system. Their general solutions are found by reciprocal transformations. In
this paper we rewrite the Gurevich-Zybin system as a Monge-Ampere equation. By
application of reciprocal transformation this equation is linearized.
Infinitely many local Hamiltonian structures, local Lagrangian representations,
local conservation laws and local commuting flows are found. Moreover, all
commuting flows can be written as Monge-Ampere equations similar to the
Gurevich-Zybin system. The Gurevich-Zybin system describes the formation of a
large scale structures in the Universe. The second harmonic wave generation is
known in nonlinear optics. In this paper we prove that the Gurevich-Zybin
system is equivalent to a degenerate case...
45.
The symmetries of the Fokker - Planck equation in one dimension - Tanski, Igor A.
We calculate all point symmetries of the Fokker - Planck equation in
one-dimensional Euclidean space. General expression of symmetry group action on
arbitrary solution of Fokker - Planck equation is presented. We propose new
notation for the group-theoretic analysis of PDE. The Lie prolongation formula
is derived as an example of the new notation.
46.
Chaos and Control in Nonlinear Bloch System - Rakshit, B.; Saha, P.; Chowdhury, A. Roy.
The dynamics of two nonlinear Bloch systems is studied from the viewpoint of
bifur- cation and a particular parameter space has been explored for the
stability analysis based on stability criterion. This enables the choice of the
desired unstable periodic orbit from the numerous unstable ones present within
the attractor through the pro- cess of closed return pairs. A generalized
active control method have been discussed for two Bloch systems arising from di
erent initial conditions.
47.
The large-scale structure of passive scalar turbulence - Celani, Antonio; Seminara, Agnese
We investigate the large-scale statistics of a passive scalar transported by
a turbulent velocity field. At scales larger than the characteristic
lengthscale of scalar injection, yet smaller than the correlation length of the
velocity, the advected field displays persistent long-range correlations due to
the underlying turbulent velocity. These induce significant deviations from
equilibrium statistics for high-order scalar correlations, despite the absence
of scalar flux.
48.
The symmetries of the Fokker - Planck equation in two dimensions - Tanski, Igor A.
We calculate all point symmetries of the Fokker - Planck equation in
two-dimensional Euclidean space. General expression of symmetry group action on
arbitrary solution of Fokker - Planck equation is presented.
49.
Dynamics of distributed sources - Novikov, E. A.
The dynamics of distributed sources is described by nonlinear partial
differential equations. Lagrangian analytical solutions of these (and
associated) equations are obtained and discussed in the context of Lagrangian
modeling - from the Lagrangian invariants to dynamics. Possible applications of
distributed sources and sinks to geophysical fluid dynamics and to the
cosmology are indicated.
50.
The symmetries of the Fokker - Planck equation in three dimensions - Tanski, Igor A.
We calculate all point symmetries of the Fokker - Planck equation in
three-dimensional Euclidean space. General expression of symmetry group action
on arbitrary solution of Fokker - Planck equation is presented.
51.
Polymer dynamics in chaotic flows with strong shear component - Turitsyn, K. S.
We consider the internal dynamics of the polymer molecule which is injected
in the chaotic flow with strong mean shear component. The flow geometry
corresponds to the recent experiments on the elastic turbulence (Groisman,
Steinberg 2000). The passive polymer in such flows experiences aperiodic
tumbling. We present a detailed study of the statistical properties of such
polymer dynamics. First we obtain the stationary probability distribution
function of the polymer orientation. Secondly we find the distribution of the
time periods between consequent events of tumbling, and finally we find the
tails of the polymer size distribution.
52.
Optical Vortices and Vortex Solitons - Desyatnikov, Anton S.; Torner, Lluis; Kivshar, Yuri S.
Optical vortices are phase singularities nested in electromagnetic waves that
constitute a fascinating source of phenomena in the physics of light and
display deep similarities to their close relatives, quantized vortices in
superfluids and Bose-Einstein condensates. We present a brief overview of the
major advances in the study of optical vortices in different types of nonlinear
media, with emphasis on the properties of {\em vortex solitons}. Self-focusing
nonlinearity leads, in general, to the azimuthal instability of a
vortex-carrying beam, but it can also support novel types of stable or
meta-stable self-trapped beams carrying nonzero angular momentum, such as
ring-like solitons, necklace beams, and soliton clusters. We describe vortex
solitons created...
53.
A new self-synchronizing stream cipher - Wang, Shihong; Lv, Huaping; Hu, Gang
A new self-synchronizing stream cipher (SSSC) is proposed based on one-way
and nearest neighbor coupled integer maps. Some ideas of spatiotemporal chaos
synchronization and chaotic cryptography are applied in this new SSSC system.
Several principles of constructing optimal SSSC are discussed, and the methods
realizing these principles are specified. This SSSC is compared with several
SSSC systems in security by applying chosen-ciphertext attacks. It is shown
that our new system can provide SSSC with high security and fairly fast
performance.
54.
On complex adaptive systems and terrorism - Ahmed, E.; Elgazzar, A. S.; Hegazi, A. S.
Complex adaptive systems (CAS) are ubiquitous in nature. They are basic in
social sciences. An overview of CAS is given with emphasize on the occurrence
of bad side effects to seemingly wise decisions. Hence application to terrorism
is given. Some conclusions on how to deal with this phenomena are proposed.
55.
Universal Scaling in Saddle-Node Bifurcation Cascades (I) - San-Martín, Jesús
A saddle-node bifurcation cascade is studied in the logistic equation, whose
bifurcation points follow an expression formally identical to the one given by
Feigenbaum for period doubling cascade. The Feigenbaum equation is generalized
because it rules several objects, which do not have to be orbits. The outcome
is that an attractor of attractors appears, and information about the birth,
death and scaling of windows is obtained.
56.
Reconnection of Stable/Unstable Manifolds of the Harper Map - Ajisaka, Shigeru; Tasaki, Shuichi
The Harper map is one of the simplest chaotic systems exhibiting reconnection
of invariant manifolds. The method of asymptotics beyond all orders (ABAO) is
used to construct stable/unstable manifolds of the Harper map. When the
parameter changes to the reconnection threshold, the stable/unstable manifolds
are shown to acquire new oscillatory portion corresponding to the heteroclinic
tangle after the reconnection.
57.
Laws of Energy Gradient for Instabilities - Dou, Hua-Shu
Transition to turbulence is due to the instability of a laminar flow subject
to a disturbance. This complicated problem can be explained using a new
proposed energy gradient theory in our previous study. This theory is extended
to the instability of fluid material systems in this study. The instability of
fluid material systems may lead to the evolution of natural environments and
the occurrence of catastrophic events in the world. To better describe these
phenomena and to understand the physical mechanism behind them are very
important. In order to more generally describe the instability of fluid
material systems, laws of energy gradient are summarized for static and motion
systems,...
58.
Flow Transition in Plane Couette Flow - Dou, Hua-Shu; Khoo, Boo Cheong; Yeo, Khoon Seng
The energy gradient theory has been proposed with the aim of better
understanding the mechanism of flow transition from laminar flow to turbulent
flow. In this theory, it is suggested that the transition to turbulence depends
on the relative magnitudes of the energy gradient amplifying the disturbance
and the viscous friction damping that disturbance. For a given flow geometry
and fluid properties, when the maximum of K (the ratio of the energy gradient
in the transverse direction to that in the streamwise direction) in the flow
field is larger than a certain critical value, it is expected that instability
would occur for some initial disturbances. In this paper,...
59.
Discrete peakons - Comech, A.; Cuevas, J.; Kevrekidis, P. G.
We demonstrate for the first time the possibility for explicit construction
in a discrete Hamiltonian model of an exact solution of the form $\exp(-|n|)$,
i.e., a discrete peakon. These discrete analogs of the well-known, continuum
peakons of the Camassa-Holm equation [Phys. Rev. Lett. {\bf 71}, 1661 (1993)]
are found in a model different from their continuum siblings. Namely, we
observe discrete peakons in Klein-Gordon-type and nonlinear Schr\"odinger-type
chains with long-range interactions. The interesting linear stability
differences between these two chains are examined numerically and illustrated
analytically. Additionally, inter-site centered peakons are also obtained in
explicit form and their stability is studied. We also prove the global
well-posedness for the discrete...
60.
Nonlinear dual-core photonic crystal fiber couplers - Salgueiro, Jose R.; Kivshar, Yuri S.
We study nonlinear modes of dual-core photonic crystal fiber couplers made of
a material with the focusing Kerr nonlinearity. We find numerically the
profiles of symmetric, antisymmetric, and asymmetric nonlinear modes, and
analyze all-optical switching based on instability of the symmetric mode. We
also describe elliptic spatial solitons controlled by the waveguide boundaries.
41.
