arXiv
(422,153 recursos)
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Mostrando recursos 101 - 120 de 13,166
101.
Finite geometries and diffractive orbits in isospectral billiards - Giraud, Olivier
Several examples of pairs of isospectral planar domains have been produced in
the two-dimensional Euclidean space by various methods. We show that all these
examples rely on the symmetry between points and blocks in finite projective
spaces; from the properties of these spaces, one can derive a relation between
Green functions as well as a relation between diffractive orbits in isospectral
billiards.
102.
On Deviations from Gaussian Statistics for Surface Gravity Waves - Onorato, M.; Osborne, A. R.; Serio, M.
Here we discuss some issues concerning the statistical properties of ocean
surface waves. We show that, using the approach of weak turbulence theory,
deviations from Gaussian statistics can be naturally included. In particular we
discuss the role of bound and free modes for the determination of the
statistical properties of the surface elevation. General formulas for skewness
and kurtosis as a function of the spectral wave action density are here
derived.
103.
Doubling the Intensity of an ERL Based Light Source - Hutton, Andrew
A light source based on an Energy Recovered Linac (ERL) [1] consist of a
superconducting linac and a transfer line that includes wigglers and undulators
to produce the synchrotron light. The transfer line brings the electrons
bunches back to the beginning of the linac so that their energy can be
recovered when they traverse the linac a second time, lambda/2 out of phase.
There is another interesting condition when the length of the transfer line is
(n+/- 1/4) lambda. In this case, the electrons drift through on the zero RF
crossing, and make a further pass around the transfer line, effectively
doubling the circulating current in the wigglers...
104.
Synchronization in driven versus autonomous coupled chaotic maps - Pineda, M.; Cosenza, M. G.
The phenomenon of synchronization occurring in a locally coupled map lattice
subject to an external drive is compared to the synchronization process in an
autonomous coupled map system with similar local couplings plus a global
interaction. It is shown that chaotic synchronized states in both systems are
equivalent, but the collective states arising after the chaotic synchronized
state becomes unstable can be different in these two systems. It is found that
the external drive induces chaotic synchronization as well as synchronization
of unstable periodic orbits of the local dynamics in the driven lattice. On the
other hand, the addition of a global interaction in the autonomous system
allows for...
105.
Kovalevskaya Top and Generalizations of Integrable Systems - Borisov, A. V.; Mamaev, I. S.; Kholmskaya, A. G.
Generalizations of the Kovalevskaya, Chaplygin, Goryachev-Chaplygin and
Bogoyavlensky systems on a bundle are considered in this paper. Moreover, a
method of introduction of separating variables and action-angle variables is
described. Another integration method for the Kovalevskaya top on the bundle is
found. This method uses a coordinate transformation that reduces the
Kovalevskaya system to the Neumann system. The Kolosov analogy is considered. A
generalization of a recent Gaffet system to the bundle of Poisson brackets is
obtained at the end of the paper.
106.
On Justification of Gibbs Distribution - Kozlov, V. V.
The paper develop a new approach to the justification of Gibbs canonical
distribution for Hamiltonian systems with finite number of degrees of freedom.
It uses the condition of nonintegrability of the ensemble of weak interacting
Hamiltonian systems.
107.
Two-dimensional solitons on the surface of magnetic fluids - Richter, Reinhard; Barashenkov, I. V.
We report an observation of a stable soliton-like structure on the surface of
a ferrofluid, generated by a local perturbation in the hysteretic regime of the
Rosensweig instability. Unlike other pattern-forming systems with localized 2D
structures, magnetic fluids are characterized by energy conservation; hence
their mechanism of soliton stabilization is different from the previously
discussed gain/loss balance mechanism. The radioscopic measurements of the
soliton's surface profile suggest that locking on the underlying periodic
structure is instrumental in its stabilization.
108.
Anomalous synchronization threshold in coupled logistic maps - Anteneodo, C.; Batista, A. M.; Viana, R. L.
We consider regular lattices of coupled chaotic maps. Depending on lattice
size, there may exist a window in parameter space where complete
synchronization is eventually attained after a transient regime. Close outside
this window, an intermittent transition to synchronization occurs. While
asymptotic transversal Lyapunov exponents allow to determine the
synchronization threshold, the distribution of finite-time Lyapunov exponents,
in the vicinity of the critical frontier, is expected to provide relevant
information on phenomena such as intermittency. In this work we scrutinize the
distribution of finite-time exponents when the local dynamics is ruled by the
logistic map $x \mapsto 4x(1-x)$. We obtain a theoretical estimate for the
distribution of finite-time exponents, that...
109.
Counting function for a sphere of anisotropic quartz - Sondergaard, N.; Guhr, T.; Oxborrow, M.; Schaadt, K.; Ellegaard, C.
We calculate the leading Weyl term of the counting function for a
mono-crystalline quartz sphere. In contrast to other studies of counting
functions, the anisotropy of quartz is a crucial element in our investigation.
Hence, we do not obtain a simple analytical form, but we carry out a numerical
evaluation. To this end we employ the Radon transform representation of the
Green's function. We compare our result to a previously measured unique data
set of several tens of thousands of resonances.
110.
Superintegrable systems on sphere - Borisov, A. V.; Mamaev, I. S.
We consider various generalizations of the Kepler problem to
three-dimensional sphere $S^3$, a compact space of constant curvature. These
generalizations include, among other things, addition of a spherical analog of
the magnetic monopole (the Poincar\'e--Appell system) and addition of a more
complicated field, which itself is a generalization of the MICZ-system. The
mentioned systems are integrable -- in fact, superintegrable. The latter is due
to the vector integral, which is analogous to the Laplace--Runge--Lenz vector.
We offer a classification of the motions and consider a trajectory isomorphism
between planar and spatial motions. The presented results can be easily
extended to Lobachevsky space $L^3$.
111.
Chaotic Turing Patterns displaying the beauty of chaos - Xiao, Jinghua; Yang, Junzhong; Hu, Gang
The problem of Turing pattern formation has attracted much attention in
nonlinear science as well as physics, chemistry and biology. So far all Turing
patterns have been observed in stationary and oscillatory media only. In this
letter we find for the first time that ordered Turing patterns exist in chaotic
extended systems. And chaotic Turing patterns are strikingly rich and
surprisingly beautiful with their space structures. These findings are in sharp
contrast with the intuition of pseudo-randomness of chaos. The richness and
beauty of the chaotic Turing patterns are attributed to a large variety of
symmetry properties realized by various types of self-organizations of partial
chaos synchronizations. Some statistical...
112.
Diophantine Integrability - Halburd, R. G.
The heights of iterates of the discrete Painleve equations over number fields
appear to grow no faster than polynomials while the heights of generic
solutions of non-integrable discrete equations grow exponentially. This gives
rise to a simple and effective numerical test for the integrability of discrete
equations. Numerical evidence and theoretical results are presented.
Connections with other tests for integrability and Vojta's dictionary are
discussed.
113.
Bifurcation scenario to Nikolaevskii turbulence in small systems - Tanaka, Dan
We show that the chaos in Kuramoto-Sivashinsky equation occurs through
period-doubling cascade (Feigenbaum scenario), in contrast, the chaos in
Nikolaevskii equation occurs through torus-doubling bifurcation
(Ruelle-Takens-Newhouse scenario).
114.
Dynamic scaling in stick-slip friction - Feder, J.; Nordhagen, H.; Watters, W. A.
We introduce a generalized homogeneous function to describe the joint
probability density for magnitude and duration of events in self-organized
critical systems (SOC). It follows that the cumulative distributions of
magnitude and of duration are power-laws with exponents $\alpha$ and $\tau$
respectively. A power-law relates duration and magnitude (exponent $\gamma$) on
the average. The exponents satisfy the dynamic scaling relation
$\alpha=\gamma\tau$. The exponents classify SOC systems into universality
classes that do not depend on microscopic details provided that both $\alpha<1$
and $\tau<1$. We also present new experimental results on the stick-slip motion
of a sandpaper slowly pulled across a carpet that are consistent with our
criteria for SOC systems. Our...
115.
Energy diffusion in strongly driven quantum chaotic systems - Elyutin, P. V.
The energy evolution of a quantum chaotic system under the perturbation that
harmonically depends on time is studied for the case of large perturbation, in
which the rate of transition calculated from the Fermi golden rule exceeds the
frequency of perturbation. It is shown that the energy evolution retains its
diffusive character, with the diffusion coefficient that is asymptotically
proportional to the magnitude of perturbation and to the square root of the
density of states. The results are supported by numerical calculation. They
imply the absence of the quantum-classical correspondence for the energy
diffusion and the energy absorption in the classical limit $\hbar \to 0$.
116.
q-Breathers and the Fermi-Pasta-Ulam Problem - Flach, S.; Ivanchenko, M. V.; Kanakov, O. I.
The Fermi-Pasta-Ulam (FPU) paradox consists of the nonequipartition of energy
among normal modes of a weakly anharmonic atomic chain model. In the harmonic
limit each normal mode corresponds to a periodic orbit in phase space and is
characterized by its wave number $q$. We continue normal modes from the
harmonic limit into the FPU parameter regime and obtain persistence of these
periodic orbits, termed here $q$-Breathers (QB). They are characterized by time
periodicity, exponential localization in the $q$-space of normal modes and
linear stability up to a size-dependent threshold amplitude. Trajectories
computed in the original FPU setting are perturbations around these exact QB
solutions. The QB concept is applicable...
117.
Leray and LANS-$\alpha$ modeling of turbulent mixing - Geurts, Bernard J.; Holm, Darryl D.
Mathematical regularisation of the nonlinear terms in the Navier-Stokes
equations provides a systematic approach to deriving subgrid closures for
numerical simulations of turbulent flow. By construction, these subgrid
closures imply existence and uniqueness of strong solutions to the
corresponding modelled system of equations. We will consider the large eddy
interpretation of two such mathematical regularisation principles, i.e., Leray
and LANS$-\alpha$ regularisation. The Leray principle introduces a {\bfi
smoothed transport velocity} as part of the regularised convective
nonlinearity. The LANS$-\alpha$ principle extends the Leray formulation in a
natural way in which a {\bfi filtered Kelvin circulation theorem},
incorporating the smoothed transport velocity, is explicitly satisfied. These
regularisation principles give rise to implied...
118.
Integrable Systems and Discrete Geometry - Doliwa, A.; Santini, P. M.
This is an expository article for Elsevier's Encyclopedia of Mathematical
Physics on the subject in the title. Comments/corrections welcome.
119.
Fidelity amplitude of the scattering matrix in microwave cavities - Schaefer, R.; Gorin, T.; Seligman, T. H.; Stoeckmann, H. -J.
The concept of fidelity decay is discussed from the point of view of the
scattering matrix, and the scattering fidelity is introduced as the parametric
cross-correlation of a given S-matrix element, taken in the time domain,
normalized by the corresponding autocorrelation function. We show that for
chaotic systems, this quantity represents the usual fidelity amplitude, if
appropriate ensemble and/or energy averages are taken. We present a microwave
experiment where the scattering fidelity is measured for an ensemble of chaotic
systems. The results are in excellent agreement with random matrix theory for
the standard fidelity amplitude. The only parameter, namely the perturbation
strength could be determined independently from level dynamics...
120.
An approach to chaotic synchronization - Hramov, Alexander E.; Koronovskii, Alexey A.
This paper deals with the chaotic oscillator synchronization. A new approach
to the synchronization of chaotic oscillators has been proposed. This approach
is based on the analysis of different time scales in the time series generated
by the coupled chaotic oscillators. It has been shown that complete
synchronization, phase synchronization, lag synchronization and generalized
synchronization are the particular cases of the synchronized behavior called as
"time-scale synchronization". The quantitative measure of chaotic oscillator
synchronous behavior has been proposed. This approach has been applied for the
coupled R\"ossler systems and two coupled Chua's circuits.
101.
