arXiv
(422,153 recursos)
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Mostrando recursos 181 - 200 de 13,166
181.
Hamiltonization of nonholonomic systems - Borisov, A. V.; Mamaev, I. S.
We consider some issues of the representation in the Hamiltonian form of two
problems of nonholonomic mechanics, namely, the Chaplygin's ball problem and
the Veselova problem. We show that these systems can be written as generalized
Chaplygin systems and can be integrated by the method of reducing multiplier.
We also indicate the algebraic form of the Poisson brackets of these systems
(after the time substitution). Generalizations of the problems are considered
and new realizations of nonholonomic constraints are presented. Some
nonholonomic systems with an invariant measure and a sufficient number of first
integrals are indicated, for which the question of the representation in the
Hamiltonian form is still open,...
182.
1D spirals: is multi stability essential? - Bhattacharyay, A.
The origin of 1D spirals or antisymmetric 1D pulses is explaind so far on the
basis of multistability of spatially inhomogeneous and temporally oscillatory
phases and so called nonvariational effects. Thus, coupled amplitude equations
which are valid near a co-dimention 2 point and provides with the necessary
multistable environment are commonly in use in the numerical calculations to
generate such structures. In the present work we analytically show that a
complex Ginzburg-Landau type amplitude equation which is valid in the Hopf
region of phase space near an instability threshold admits solutions like
antisymmetric pulses traveling in alternate directions from a core. The pulses
can have well defined spatial profile...
183.
Vortices, circumfluence, symmetry groups and Darboux transformations of
the Euler equations - Lou, S. Y.; Tang, X. Y.; Jia, M.; Huang, F.
The Euler equation (EE) is one of the basic equations in many physical fields
such as the fluids, plasmas, condense matters, astrophysics, oceanic and
atmospheric dynamics. A new symmetry group theorem of the two dimensional EE is
obtained via a simple direct method and the theorem is used to find \em exact
analytical \rm vortex and circumfluence solutions. Some types of Darboux
transformations (DTs) for the both two and three dimensional EEs are obtained
for \em arbitrary spectral parameters \rm which indicates that the EEs are
integrable and the Navier-Stockes (NS) equations with large Renoyed number are
nearly integrable, i.e, they are singular perturbations of the integrable EEs.
The...
184.
Turning light into a liquid via atomic coherence - Michinel, Humberto; Alonso, Maria J. Paz; Perez-Garcia, Victor M.
We study a four level atomic system with electromagnetically induced
transparency with giant $\chi^{(3)}$ and $\chi^{(5)}$ susceptibilities of
opposite signs. This system would allow to obtain multidimensional solitons and
light condensates with surface tension properties analogous to those of usual
liquids.
187.
Integrability of $q$-oscillator lattice model - Sergeev, S.
A simple formulation of an exactly integrable $q$-oscillator model on two
dimensional lattice (in 2+1 dimensional space-time) is given. Its
interpretation in the terms of 2d quantum inverse scattering method and nested
Bethe Ansatz equations is discussed.
188.
Solitary Waves in Discrete Media with Four Wave Mixing - Horne, R. L.; Kevrekidis, P. G.; Whitaker, N.
In this paper, we examine in detail the principal branches of solutions that
arise in vector discrete models with nonlinear inter-component coupling and
four wave mixing. The relevant four branches of solutions consist of two single
mode branches (transverse electric and transverse magnetic) and two mixed mode
branches, involving both components (linearly polarized and elliptically
polarized). These solutions are obtained explicitly and their stability is
analyzed completely in the anti-continuum limit (where the nodes of the lattice
are uncoupled), illustrating the supercritical pitchfork nature of the
bifurcations that give rise to the latter two, respectively, from the former
two. Then the branches are continued for finite coupling constructing a...
189.
On asymptotic properties of some complex Lorenz-like systems - Panchev, Stoicho; vitanov, Nikolay K.
The classical Lorenz lowest order system of three nonlinear ordinary
differential equations, capable of producing chaotic solutions, has been
generalized by various authors in two main directions: (i) for number of
equations larger than three (Curry1978) and (ii) for the case of complex
variables and parameters. Problems of laser physics and geophysical fluid
dynamics (baroclinic instability, geodynamic theory, etc. - see the references)
can be related to this second aspect of generalization. In this paper we study
the asymptotic properties of some complex Lorenz systems, keeping in the mind
the physical basis of the model mathematical equations.
190.
Lyapunov Modes and Time-Correlation Functions for Two-Dimensional Systems - Taniguchi, Tooru; Morriss, Gary P.
The relation between the Lyapunov modes (delocalized Lyapunov vectors) and
the momentum autocorrelation function is discussed in two-dimensional hard-disk
systems. We show numerical evidence that the smallest time-oscillating period
of the Lyapunov modes is twice as long as the time-oscillating period of
momentum autocorrelation function for both square and rectangular
two-dimensional systems with hard-wall boundary conditions.
191.
Ten Questions about Emergence - Fromm, Jochen
Self-Organization is of growing importance for large distributed computing
systems. In these systems, a central control and manual management is
exceedingly difficult or even impossible. Emergence is widely recognized as the
core principle behind self-organization. Therefore the idea to use both
principles to control and organize large-scale distributed systems is very
attractive and not so far off.
Yet there are many open questions about emergence and self-organization,
ranging from a clear definition and scientific understanding to the possible
applications in engineering and technology, including the limitations of both
concepts. Self-organizing systems with emergent properties are highly
desirable, but also very challenging. We pose ten central questions about
emergence, give preliminary...
192.
Amplitude death in coupled chaotic oscillators - Prasad, Awadhesh
Amplitude death can occur in chaotic dynamical systems with time-delay
coupling, similar to the case of coupled limit cycles. The coupling leads to
stabilization of fixed points of the subsystems. This phenomenon is quite
general, and occurs for identical as well as nonidentical coupled chaotic
systems. Using the Lorenz and R\"ossler chaotic oscillators to construct
representative systems, various possible transitions from chaotic dynamics to
fixed points are discussed.
193.
Distribution of the spacing between two adjacent avoided crossings - Machida, Manabu; Saito, Keiji
We consider the frequency at which avoided crossings appear in an energy
level structure when an external field is applied to a quantum chaotic system.
The distribution of the spacing in the parameter between two adjacent avoided
crossings is investigated. Using a random matrix model, we find that the
distribution of these spacings is well fitted by a power-law distribution for
small spacings. The powers are 2 and 3 for the Gaussian orthogonal ensemble and
Gaussian unitary ensemble, respectively. We also find that the distributions
decay exponentially for large spacings. The distributions in concrete quantum
chaotic systems agree with those of the random matrix model.
194.
Noise Stabilized Random Attractor - Finn, J. M.; Tracy, E. R.; Cooke, W. E.; Richardson, A. S.
A two dimensional flow model is introduced with deterministic behavior
consisting of bursts which become successively larger, with longer interburst
time intervals between them. The system is symmetric in one variable x and
there are bursts on either side of x = 0, separated by the presence of an
invariant manifold at x = 0. In the presence of arbitrarily small additive
noise in the x direction, the successive bursts have bounded amplitudes and
interburst intervals. This system with noise is proposed as a model for edge
localized modes in tokamaks. Further, the bursts can switch from positive to
negative x and vice-versa. The probability distribution of burst...
195.
Bifurcations in nonlinear models of fluid-conveying pipes supported
at both ends - Nikolic, Mladen; Rajkovic, Milan
Stationary bifurcations in several nonlinear models of fluid conveying pipes
fixed at both ends are analyzed with the use of Lyapunov-Schmidt reduction and
singularity theory. Influence of gravitational force, curvature and vertical
elastic support on various properties of bifurcating solutions are
investigated. In particular the conditions for occurrence of supercritical and
subcritical bifurcations are presented for the models of Holmes, Thurman and
Mote, and Paidoussis.
196.
Nonlinear elastic polymers in random flow - Afonso, M. Martins; Vincenzi, D.
Polymer stretching in random smooth flows is investigated within the
framework of the FENE dumbbell model. The advecting flow is Gaussian and
short-correlated in time. The stationary probability density function of
polymer extension is derived exactly. The characteristic time needed for the
system to attain the stationary regime is computed as a function of the
Weissenberg number and the maximum length of polymers. The transient relaxation
to the stationary regime is predicted to be exceptionally slow in the proximity
of the coil-stretch transition.
197.
A 2 - Component or N=2 Supersymmetric Camassa - Holm Equation - Popowicz, Ziemowit
The extended N=2 supersymmetric Camasa - Holm equation is presented. It is
accomplishe by formulation the supersymmeytric version of the Fuchssteiner
method. In this framework we use two supersymmetric recursion operators of the
N=2, $\alpha=-2,4$ Korteweg - de Vries equation and constructed two different
version of the supersymmetric Camassa - Holm equation. The bosonic sector of
N=2, $\alpha=4$ supersymmetric Camassa - Holm equation contains two component
generalization of this equation considered by Chen, Liu and Zhang and as a
special case two component generalized Hunter - Saxton equation considered by
Aratyn, Gomes and Zimerman, As a byproduct of our analysis we defined the N=2
supersymmetric Hunter - Saxton equation....
198.
Random matrix description of decaying quantum systems - Gorin, T.
This contribution describes a statistical model for decaying quantum systems
(e.g. photo-dissociation or -ionization). It takes the interference between
direct and indirect decay processes explicitely into account. The resulting
expressions for the partial decay amplitudes and the corresponding cross
sections may be considered a many-channel many-resonance generalization of
Fano's original work on resonance lineshapes [Phys. Rev 124, 1866 (1961)].
A statistical (random matrix) model is then introduced. It allows to describe
chaotic scattering systems with tunable couplings to the decay channels. We
focus on the autocorrelation function of the total (photo) cross section, and
we find that it depends on the same combination of parameters, as the
Fano-parameter distribution....
199.
Interaction between Kirchhoff vortices and point vortices in an ideal
fluid - Borisov, Alexey V.; Mamaev, Ivan S.
We consider the interaction of two vortex patches (elliptic Kirchhoff
vortices) which move in an unbounded volume of an ideal incompressible fluid. A
moment second-order model is used to describe the interaction. The case of
integrability of a Kirchhoff vortex and a point vortex by the variable
separation method is qualitatively analyzed. A new case of integrability of two
Kirchhoff vortices is found. A reduced form of equations for two Kirchhoff
vortices is proposed and used to analyze their regular and chaotic behavior.
200.
A Systems-Based Approach to Multiscale Computation: Equation-Free
Detection of Coarse-Grained Bifurcations - Siettos, C. I.; Rico-Martinez, R.; kevrekidis, I. G.
We discuss certain basic features of the equation-free (EF) approach to
modeling and computation for complex/multiscale systems. We focus on links
between the equation-free approach and tools from systems and control theory
(design of experiments, data analysis, estimation, identification and
feedback). As our illustrative example, we choose a specific numerical task
(the detection of stability boundaries in parameter space) for stochastic
models of two simplified heterogeneous catalytic reaction mechanisms. In the
equation-free framework the stochastic simulator is treated as an experiment
(albeit a computational one). Short bursts of fine scale simulation (short
computational experiments) are designed, executed, and their results processed
and fed back to the process, in integrated protocols...
181.
