arXiv
(422,153 recursos)
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Mostrando recursos 141 - 160 de 13,166
141.
Lattice system of interacting spins in the thermodynamical limit - Sergeev, S.
In this paper we investigate some particular spin lattice (a higher
dimensional generalization of a spin chain) related to Zamolodchikov model, in
the limit when both sizes of the lattice tend to infinity. An infinite set of
bilinear equations, describing a distribution of eigenvalues of infinite set of
mutually commuting operators, is derived. The distribution for the maximal
eigenvalues is obtained explicitly. The way to obtain the excitations is
discussed.
142.
Proof of Nishida's conjecture on anharmonic lattices - Rink, Bob
We prove Nishida's 1971 conjecture stating that almost all low-energetic
motions of the anharmonic Fermi-Pasta-Ulam lattice with fixed endpoints are
quasi-periodic. The proof is based on the formal computations of Nishida, the
KAM theorem, discrete symmetry considerations and an algebraic trick that
considerably simplifies earlier results.
143.
sl_2 Gaudin model with Jordanian twist - Cirilo-Antonio, N.; Manojlovic, N.
sl_2 Gaudin model with Jordanian twist is studied. This system can be
obtained as the semiclassical limit of the XXX spin chain deformed by the
Jordanian twist. The appropriate creation operators that yield the Bethe states
of the Gaudin model and consequently its spectrum are defined. Their
commutation relations with the generators of the corresponding loop algebra as
well as with the generating function of integrals of motion are given. The
inner products and norms of Bethe states and the relation to the solutions of
the Knizhnik-Zamolodchikov equations are discussed.
144.
Statistics of quantum recurrences in the Hilbert space - Iomin, A.; Zaslavsky, G. M.
Statistics of Poincar\'e recurrences in the Hilbert space for a quantum
kicked rotor is studied. A strong correlation between classical accelerator
mode dynamics in the phase space and statistics of the quantum recurrences (QR)
in the Hilbert space is found. It is shown numerically that the appearance of
accelerator mode islands (AMI) by bifurcation leads to power law distribution
of the QR in the Hilbert space. Conversely, for chaotic dynamics, when the AMI
are absent or their influence is negligible, the QR have an exponential
distribution.
145.
Multiple permanent-wave trains in nonlinear systems - Yang, Jianke
Multiple permanent-wave trains in nonlinear systems are constructed by the
asymptotic tail-matching method. Under some general assumptions, simple
criteria for the construction are presented. Applications to fourth-order
systems and coupled nonlinear Schr\"odinger equations are discussed.
146.
Stochastic Resonance in Underdamped, Bistable Systems - Ray, Rajarshi; Sengupta, Supratim
We carry out a detailed numerical investigation of stochastic resonance in
underdamped systems in the non-perturbative regime. We point out that an
important distinction between stochastic resonance in overdamped and
underdamped systems lies in the lack of dependence of the amplitude of the
noise-averaged trajectory on the noise strength, in the latter case. We provide
qualitative explanations for the observed behavior and show that signatures
such as the initial decay and long-time oscillatory behaviour of the temporal
correlation function and peaks in the noise and phase averaged power spectral
density, clearly indicate the manifestation of resonant behaviour in noisy,
underdamped bistable systems in the weak to moderate noise regime.
147.
On the mobility and efficiency of mechanical systems - Wolansky, G.
The definition of a mobilized system and its efficiency are introduced. The
existence of an optimal (maximally efficient) system is proved by an
application of Young measures and compensated compactness.
148.
Enstrophy dissipation in freely evolving two-dimensional turbulence - Tran, Chuong V.
Freely decaying two-dimensional Navier--Stokes turbulence is studied. The
conservation of vorticity by advective nonlinearities renders a class of
Casimirs that decays under viscous effects. A rigorous constraint on the
palinstrophy production by nonlinear transfer is derived, and an upper bound
for the enstrophy dissipation is obtained. This bound depends only on the
decaying Casimirs, thus allowing the enstrophy dissipation to be bounded from
above in terms of initial data of the flows. An upper bound for the enstrophy
dissipation wavenumber is derived and the new result is compared with the
classical dissipation wavenumber.
149.
Fokker - Planck equation in curvilinear coordinates - Tanski, Igor A.
The aim of this paper is to rewrite the Fokker - Planck equation according to
transformation of space coordinates. This is nontrivial problem, because
transformation of space coordinates induces transformation of velocities. We
can use covariant, contravariant or physical velocity components as independent
variables in curvilinear coordinate system. These 3 possibilities are
considered in this paper and 3 kinds of Fokker - Planck equation in curvilinear
coordinates are formulated.
150.
An Overview of Complex Adaptive Systems - Ahmed, E.; Elgazzar, A. S.; Hegazi, A. S.
Almost every biological, economic and social system is a complex adaptive
system (CAS). Mathematical and computer models are relevant to CAS. Some
approaches to modeling CAS are given. Applications in vaccination and the
immune system are studied. Mathematical topics motivated by CAS are discussed.
151.
Trigonometric Lax matrix for the Kowalevski gyrostat on so(4) - Komarov, I. V.; Tsiganov, A. V.
We present trigonometric Lax matrix and classical $r$-matrix for the
Kowalevski gyrostat on $so(4)$ algebra by using auxiliary matrix algebras
$so(3,2)$ or $sp(4)$.
152.
Completeness of the cubic and quartic H\'enon-Heiles Hamiltonians - Conte, Robert; Musette, Micheline; Verhoeven, Caroline
The quartic H\'enon-Heiles Hamiltonian $H = (P_1^2+P_2^2)/2+(\Omega_1
Q_1^2+\Omega_2 Q_2^2)/2
+C Q_1^4+ B Q_1^2 Q_2^2 + A Q_2^4
+(1/2)(\alpha/Q_1^2+\beta/Q_2^2) - \gamma Q_1$ passes the Painlev\'e test for
only four sets of values of the constants. Only one of these, identical to the
traveling wave reduction of the Manakov system, has been explicitly integrated
(Wojciechowski, 1985), while the three others are not yet integrated in the
generic case $(\alpha,\beta,\gamma)\not=(0,0,0)$. We integrate them by building
a birational transformation to two fourth order first degree equations in the
classification (Cosgrove, 2000) of such polynomial equations which possess the
Painlev\'e property. This transformation involves the stationary reduction of
various partial differential equations (PDEs). The...
153.
Darboux Transformation for the Non-stationary Shr\"odinger Equation - Gutshabash, E. Sh.
The Lax representation for the nonstationary Schr\"odinger equation with
rather arbitrary potential is proposed. Some examples of the construction of
exact solutions are given by means of Darboux Transformation method.
154.
Synchronization of coupled chaotic oscillators as a phase transition - Arecchi, F. T.; Ciszak, M.
We characterize the synchronization of an array of coupled chaotic elements
as a phase transition where order parameters related to the joint probability
at two sites obey power laws versus the mutual coupling strength; the phase
transition corresponds to a change in the exponent of the power law. Since
these studies are motivated by the behaviour of the cortical neurons in
cognitive tasks, we account for the short time available to any brain decision
by studying how the mutual coupling affects the transient behaviour of a
synchronization transition over a fixed time interval. We present a novel
feature, namely, the absence of decay of the initial defect density...
155.
Aerodynamics at the Particle Level - Crummer, Charles A.
All aerodynamic forces on a surface are caused by collisions of fluid
particles with the surface. While the standard approach to fluid dynamics,
which is founded on the fluid approximation, is effective in providing a means
of calculating various behavior and properties, it begs the question of
causality. This is because it cannot account for the interaction of the fluid
either with itself, other fluids, or with solid bodies. The fluid approximation
and assumptions required for the application of Bernoulli's equation amount to
denying any interaction of the fluid either with a solid object or with itself.
It is these very interactions, however, which are the causes of...
156.
Finite-size effects on open chaotic advection - Vilela, Rafael Dias; de Moura, Alessandro P. S.; Grebogi, Celso
We study the effects of finite-sizeness on small, neutrally buoyant,
spherical particles advected by open chaotic flows. We show that, when
projected onto configuration space, the advected finite-size particles disperse
about the unstable manifold of the chaotic saddle that governs the passive
advection. Using a discrete-time system for the dynamics, we obtain an
expression predicting the dispersion of the finite-size particles in terms of
their Stokes parameter at the onset of the finite-sizeness induced dispersion.
We test our theory in a system derived from a flow and find remarkable
agreement between our expression and the numerically measured dispersion.
157.
BLP dissipative structures in plane - Yurov, A. V.
We study the Darboux and Laplace transformations for the
Boiti-Leon-Pempinelli equations (BLP). These equations are the (1+2)
generalization of the sinh-Gordon equation. In addition, the BLP equations
reduced to the Burgers (and anti-Burgers) equation in a one-dimensional limit.
Localized nonsingular solutions in both spatial dimensions and (anti) "blow-up"
solutions are constructed. The Burgers equation's "dressing" procedure is
suggested. This procedure allows us to construct such solutions of the BLP
equations which are reduced to the solutions of the dissipative Burgers
equations when $t\to \infty$. These solutions we call the BLP dissipative
structures.
158.
An ant-based algorithm for annular sorting - Don, Oliver; Amos, Martyn
In this paper we describe a minimal model for annular sorting by Leptothorax
ants. Simulation results are consistent with the structures observed in actual
ant colonies.
159.
Wave turbulence and vortices in Bose-Einstein condensation - Nazarenko, Sergey; Onorato, Miguel
We report a numerical study of turbulence and Bose-Einstein condensation
within the two-dimmensional Gross-Pitaevski model with repulsive interaction.
In presence of weak forcing localized around some wave number in the Fourier
space, we observe three qualitatively different evolution stages. At the
initial stage a thermodynamic energy equipartition spectrum forms at both
smaller and larger scales with respect to the forcing scale. This agrees with
predictions of the the four-wave kinetic equation of the Wave Turbulence (WT)
theory. At the second stage, WT breaks down at large scales and the
interactions become strongly nonlinear. Here, we observe formation of a gas of
quantum vortices whose number decreases due to an...
160.
Large-scale effects on meso-scale modeling for scalar transport - Cencini, M.; Mazzino, A.; Musacchio, S.; Vulpiani, A.
The transport of scalar quantities passively advected by velocity fields with
a small-scale component can be modeled at meso-scale level by means of an
effective drift and an effective diffusivity, which can be determined by means
of multiple-scale techniques. We show that the presence of a weak large-scale
flow induces interesting effects on the meso-scale scalar transport. In
particular, it gives rise to non-isotropic and non-homogeneous corrections to
the meso-scale drift and diffusivity. We discuss an approximation that allows
us to retain the second-order effects caused by the large-scale flow. This
provides a rather accurate meso-scale modeling for both asymptotic and
pre-asymptotic scalar transport properties. Numerical simulations in model
flows...
141.
