arXiv
(422,153 recursos)
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Mostrando recursos 161 - 180 de 13,166
161.
The restricted two-body problem in constant curvature spaces - Borisov, Alexey V.; Mamaev, Ivan S.
We perform the bifurcation analysis of the Kepler problem on $S^3$ and $L^3$.
An analogue of the Delaunay variables is introduced. We investigate the motion
of a point mass in the field of the Newtonian center moving along a geodesic on
$S^2$ and $L^2$ (the restricted two-body problem). When the curvature is small,
the pericenter shift is computed using the perturbation theory. We also present
the results of the numerical analysis based on the analogy with the motion of
rigid body.
162.
Reduction and chaotic behavior of point vortices on a plane and a sphere - Borisov, A. V.; Kilin, A. A.; Mamaev, I. S.
We offer a new method of reduction for a system of point vortices on a plane
and a sphere. This method is similar to the classical node elimination
procedure. However, as applied to the vortex dynamics, it requires substantial
modification. Reduction of four vortices on a sphere is given in more detail.
We also use the Poincare surface-of-section technique to perform the reduction
a four-vortex system on a sphere.
163.
Motion of vortex sources on a plane and a sphere - Borisov, Alexey V.; Mamaev, Ivan S.
The Equations of motion of vortex sources (examined earlier by Fridman and
Polubarinova) are studied, and the problems of their being Hamiltonian and
integrable are discussed. A system of two vortex sources and three
sources-sinks was examined. Their behavior was found to be regular. Qualitative
analysis of this system was made, and the class of Liouville integrable systems
is considered. Particular solutions analogous to the homothetic configurations
in celestial mechanics are given.
164.
Synchronization in delayed discrete-time complex networks - Sun, Weigang; Li, Changpin; Fan, Zhengping
In this paper, we study synchronization in the delayed discrete-time complex
networks. Several criterions of synchronization stability for such networks are
established. And illustrative examples are presented. The numerical simulations
coincide with the theoretical analysis.
165.
Asymptotic Calculation of Discrete Nonlinear Wave Interactions - Kevrekidis, P. G.; Khare, Avinash; Saxena, A.; Bena, I.; Bishop, A. R.
We illustrate how to compute asymptotic interactions between discrete
solitary waves of dispersive equations, using the approach proposed by Manton
[Nucl. Phys. B 150, 397 (1979)]. We also discuss the complications arising due
to discreteness and showcase the application of the method in nonlinear
Schrodinger, as well as in Klein-Gordon lattices, finding excellent agreement
with direct numerical computations.
166.
Scattering fidelity in elastodynamics - Gorin, T.; Seligman, T. H.; Weaver, R. L.
The recent introduction of the concept of scattering fidelity, causes us to
revisit the experiment by Lobkis and Weaver [Phys. Rev. Lett. 90, 254302
(2003)]. There, the ``distortion'' of the coda of an acoustic signal is
measured under temperature changes. This quantity is in fact the negative
logarithm of scattering fidelity. We re-analyse their experimental data for two
samples, and we find good agreement with random matrix predictions for the
standard fidelity. Usually, one may expect such an agreement for chaotic
systems only. While the first sample, may indeed be assumed chaotic, for the
second sample, a perfect cuboid, such an agreement is more surprising. For the
first sample,...
167.
Asymptotic properties of mathematical models of excitability - Biktasheva, I. V.; Simitev, R. D.; Suckley, R.; Biktashev, V. N.
We analyse small parameters in selected models of biological excitability,
including Hodgkin-Huxley (1952) model of nerve axon, Noble (1962) model of
heart Purkinje fibres, and Courtemanche et al. (1998) model of human atrial
cells. Some of the small parameters are responsible for differences in the
characteristic timescales of dynamic variables, as in the traditional singular
perturbation approaches. Others appear in a way which makes the standard
approaches inapplicable. We apply this analysis to study the behaviour of
fronts of excitation waves in spatially-extended cardiac models. Suppressing
the excitability of the tissue leads to a decrease in the propagation speed,
but only to a certain limit; further suppression blocks active...
168.
The sixth Painleve equation as similarity reduction of gl_3 hierarchy - Kakei, Saburo; Kikuchi, Tetsuya
Scaling symmetry of gl_n-type Drinfel'd-Sokolov hierarchy is investigated.
Applying similarity reduction to the hierarchy, one can obtain the Schlesinger
equation with (n+1) regular singularities. Especially in the case of n=3, the
hierarchy contains the three-wave resonant system and the similarity reduction
gives the generic case of the Painleve VI equation. We also discuss Weyl group
symmetry of the hierarchy.
169.
Resonance- and Chaos-Assisted Tunneling - Schlagheck, Peter; Eltschka, Christopher; Ullmo, Denis
We consider dynamical tunneling between two symmetry-related regular islands
that are separated in phase space by a chaotic sea. Such tunneling processes
are dominantly governed by nonlinear resonances, which induce a coupling
mechanism between ``regular'' quantum states within and ``chaotic'' states
outside the islands. By means of a random matrix ansatz for the chaotic part of
the Hamiltonian, one can show that the corresponding coupling matrix element
directly determines the level splitting between the symmetric and the
antisymmetric eigenstates of the pair of islands. We show in detail how this
matrix element can be expressed in terms of elementary classical quantities
that are associated with the resonance. The validity...
170.
Coupled KdV equations derived from atmospherical dynamics - Lou, S. Y.; Tong, Bin; Hu, Heng-chun; Tang, Xiao-yan
Some types of coupled Korteweg de-Vries (KdV) equations are derived from an
atmospheric dynamical system. In the derivation procedure, an unreasonable
$y$-average trick (which is usually adopted in literature) is removed. The
derived models are classified via Painlev\'e test. Three types of
$\tau$-function solutions and multiple soliton solutions of the models are
explicitly given by means of the exact solutions of the usual KdV equation. It
is also interesting that for a non-Painlev\'e integrable coupled KdV system
there may be multiple soliton solutions.
171.
Separating the influence of Brain Signals from the Dynamics of Heart - Vaidya, P G
ECG signals appear to be quite complex. In this paper, we present results,
which show that a normal ECG signal, which is a function of time can be
transformed into a relatively simpler signal by stretching the time in a
predetermined way. Before such a transformation, if you were to analyze various
packets of the data for the Trans-Spectral Coherence (TSC) you could confirm
that the signal indeed is very complicated. This is because the TSC gives us an
idea of how various harmonics in a spectrum are related to one another. The
coherence dramatically improved once we found an intermediate variable..
However, there was one hurdle. To...
172.
Computation of Spiral Spectra - Wheeler, P.; Barkley, D.
A computational linear stability analysis of spiral waves in a
reaction-diffusion equation is performed on large disks. As the disk radius R
increases, eigenvalue spectra converge to the absolute spectrum predicted by
Sandstede and Scheel. The convergence rate is consistent with 1/R, except
possibly near the edge of the spectrum. Eigenfunctions computed on large disks
are compared with predicted exponential forms. Away from the edge of the
absolute spectrum the agreement is excellent, while near the edge computed
eigenfunctions deviate from predictions, probably due to finite-size effects.
In addition to eigenvalues associated with the absolute spectrum, computations
reveal point eigenvalues. The point eigenvalues and associated eigenfunctions
responsible for both core...
173.
Instability of solitary waves on Euler's elastica - Il'ichev, A.
Stability of solitary waves in a thin inextensible and unshearable rod of
infinite length is studied. Solitary-wave profile ofthe elastica of such a rod
without torsion has the form of a planar loop and its speed depends on a
tension in the rod. The linear instability of a solitary-wave profile subject
to perturbations escaping from the plane of the loop is established for a
certain range of solitary-wave speeds. It is done using the properties of the
Evans function, an analytic function on the right complex half-plane, that has
zeroes if and only if there exist the unstable modes of the linearization
around a solitary-wave solution. The result...
174.
Numerical study of polymer tumbling in linear shear flows - Puliafito, A.; Turitsyn, K.
We investigate numerically the dynamics of a single polymer in a linear shear
flow. The effects of thermal fluctuations and randomly fluctuating velocity
gradients are both analyzed. Angular, elongation and tumbling time statistics
are measured numerically. We perform analytical calculations and numerical
simulations for a linear single-dumbbell polymer model comparing the results
with previous theoretical and experimental studies. For thermally driven
polymers the balance between relaxation and thermal fluctuations plays a
fundamental role, whereas for random velocity gradients the ratio between the
intensity of the random part and the mean shear is the most relevant quantity.
In the low-noise limit, many universal aspects of the motion of a polymer...
175.
A note on the forced Burgers equation - Eule, S.; Friedrich, R.
We obtain the exact solution for the Burgers equation with a time dependent
forcing, which depends linearly on the spatial coordinate. For the case of a
stochastic time dependence an exact expression for the joint probability
distribution for the velocity fields at multiple spatial points is obtained. A
connection with stretched vortices in hydrodynamic flows is discussed.
176.
Period tripling accumulation point for complexified Henon map - Isaeva, O. B.; Kuznetsov, S. P.
Accumulation point of period-tripling bifurcations for complexified Henon map
is found. Universal scaling properties of parameter space and Fourier spectrum
intrinsic to this critical point is demonstrated.
177.
Soliton mobility in nonlocal optical lattices - Xu, Zhiyong; Kartashov, Yaroslav V.; Torner, Lluis
We address the impact of nonlocality in the physical features exhibited by
solitons supported by Kerr-type nonlinear media with an imprinted optical
lattice. We discover that nonlocality of nonlinear response can profoundly
affect the soliton mobility, hence all the related phenomena. Such behavior
manifests itself in significant reductions of the Peierls-Nabarro potential
with increase of the degree of nonlocality, a result that opens the rare
possibility in nature of almost radiationless propagation of highly localized
solitons across the lattice.
178.
Lax Representation of WZNW-Like Systems - Balandin, A. V.; Pakhareva, O. N.
The Lax representation and Backlund transformations for the systems similar
to WZNW (Wess-Zumino-Novicov-Witten) systems and non-abelian affine Toda models
are obtained in present paper. One of these systems is a new integrable
extension of well known sine-Gordon equation.
179.
Stackel systems: bi-Hamiltonian property and systematic construction - Blaszak, Maciej
It is shown that separation conditions (separation curves) are fundamental
objects of separability theory. They are used for the classification of certain
clases of separable systems, for the proof of bi-Hamiltonian property and
finally they allow to construct new separable systems from known ones.
180.
Integrable Equations on Time Scales - Gurses, Metin; Guseinov, Gusein Sh.; Silindir, Burcu
Integrable systems are usually given in terms of functions of continuous
variables (on ${\mathbb R}$), functions of discrete variables (on ${\mathbb
Z}$) and recently in terms of functions of $q$-variables (on ${\mathbb
K}_{q}$). We formulate the Gel'fand-Dikii (GD) formalism on time scales by
using the delta differentiation operator and find more general integrable
nonlinear evolutionary equations. In particular they yield integrable equations
over integers (difference equations) and over $q$-numbers ($q$-difference
equations). We formulate the GD formalism also in terms of shift operators for
all regular-discrete time scales. We give a method to construct the recursion
operators for integrable systems on time scales. Finally, we give a trace
formula on time...
161.
