arXiv
(422,153 recursos)
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Mostrando recursos 81 - 100 de 13,166
81.
Flow distributed oscillation, flow velocity modulation and resonance - McGraw, Patrick N.; Menzinger, Michael
We examine the effects of a periodically varying flow velocity on the
standing and travelling wave patterns formed by the flow-distributed
oscillation (FDO) mechanism. In the kinematic (or diffusionless) limit, the
phase fronts undergo a simple, spatiotemporally periodic longitudinal
displacement. On the other hand, when the diffusion is significant, periodic
modulation of the velocity can disrupt the wave pattern, giving rise in the
downstream region to travelling waves whose frequency is a rational multiple of
the velocity perturbation frequency. We observe frequency locking at ratios of
1:1, 2:1 and 3:1, depending on the amplitude and frequency of the velocity
modulation. This phenomenon can be viewed as a novel, rather...
82.
Notes on diffusion in collisionless medium - Kozlov, V. V.
A collisionless continuous medium in Euclidean space is discussed, i.e. a
continuum of free particles moving inertially, without interacting with each
other. It is shown that the distribution density of such medium is weakly
converging to zero as time increases indefinitely. In the case of Maxwell's
velocity distribution of particles, this density satisfies the well-known
diffusion equation, the diffusion coefficient increasing linearly with time.
83.
Perturbative analysis of wave interactions in nonlinear systems - Veksler, Alex; Zarmi, Yair
This work proposes a new way for handling obstacles to asymptotic
integrability in perturbed nonlinear PDEs within the method of Normal Forms -
NF - for the case of multi-wave solutions. Instead of including the whole
obstacle in the NF, only its resonant part is included, and the remainder is
assigned to the homological equation. This leaves the NF intergable and its
solutons retain the character of the solutions of the unperturbed equation. We
exploit the freedom in the expansion to construct canonical obstacles which are
confined to te interaction region of the waves. Fo soliton solutions, e.g., in
the KdV equation, the interaction region is a finite...
84.
Wave interactions and the analysis of the perturbed Burgers equation - Veksler, Alex; Zarmi, Yair
In multiple-front solutions of the Burgers equation, all the fronts, except
for two, are generated through the inelastic interaction of exponential wave
solutions of the Lax pair associated with the equation. The inelastically
generated fronts are the source of two difficulties encountered in the standard
Normal Form expansion of the approximate solution of the perturbed Burgers
equation, when the zero-order term is a multiple-front solution: (i) The
higher-order terms in the expansion are not bounded; (ii) The Normal Form
(equation obeyed by the zero-order approximation) is not asymptotically
integrable; its solutions lose the simple wave structure of the solutions of
the un-perturbed equation. The freedom inherent in the Normal...
85.
Kinetics of Collisionless Continuous Medium - Kozlov, V. V.
In this article we develop Poincar\'e ideas about a heat balance of ideal gas
considered as a collisionless continuous medium. We obtain the theorems on
diffusion in nondegenerate completely integrable systems. As a corollary we
show that for any initial distribution the gas will be eventually irreversibly
and uniformly distributed over all volume, although every particle during this
process approaches arbitrarily close to the initial position indefinitely many
times. However, such individual returnability is not uniform, which results in
diffusion in a reversible and conservative system. Balancing of pressure and
internal energy of ideal gas is proved, the formulas for limit values of these
quantities are given and the...
86.
On the Integration Theory of Equations of Nonholonomic Mechanics - Kozlov, V. V.
The paper deals with the problem of integration of equations of motion in
nonholonomic systems. By means of well-known theory of the differential
equations with an invariant measure the new integrable systems are discovered.
Among them there are the generalization of Chaplygin's problem of rolling
nonsymmetric ball in the plane and the Suslov problem of rotation of rigid body
with a fixed point. The structure of dynamics of systems on the invariant
manifold in the integrable problems is shown. Some new ideas in the theory of
integration of the equations in nonholonomic mechanics are suggested. The first
of them consists in using known integrals as the constraints. The...
87.
Statistics of tumbling of a single polymer molecule in shear flow - Gerashchenko, Sergiy; Steinberg, Victor
We present experimental results on statistics of polymer orientation angles
relatively to shear plane and tumbling times in shear flow with thermal noise.
Strong deviation of probability distribution functions (PDF) of these
parameters from Gaussian was observed and a good accord with theory was found.
The scaling relations of PDF widths for both angles as a function of the
control parameter $Wi$ are verified and compared with numerics. An universal
exponential PDF tail for the tumbling times and its predicted scaling with $Wi$
are also tested experimentally against numerics.
88.
Multi-peakon solutions of the Degasperis-Procesi equation - Lundmark, Hans; Szmigielski, Jacek
We present an inverse scattering approach for computing n-peakon solutions of
the Degasperis-Procesi equation (a modification of the Camassa-Holm (CH)
shallow water equation). The associated non-self-adjoint spectral problem is
shown to be amenable to analysis using the isospectral deformations induced
from the n-peakon solution, and the inverse problem is solved by a method
generalizing the continued fraction solution of the peakon sector of the CH
equation.
89.
Pattern dynamics in a two-dimensional gas discharge system - Sugawara, Takeshi; Kaneko, Kunihiko
Reaction-diffusion equation model for a 2-dimensional gas discharge system is
introduced in close relationship with the recent experiment by Nasuno. The
model shows formation of spots, molecule-like organization of a cluster of
spots, moving of spots, and intermittent collapse and recreation of spots, in
agreement with experiments. The pattern dynamics are classified into
distributed, localized, and moving spots, and periodic wave pattern. The phase
diagram displayed against the current and pressure has some agreement with that
observed in the experiment. Dynamic change of spot numbers as well as the
structure of the spot cluster is studied in terms of the collective flow of
charge, and discussed as chaotic itinerancy.
90.
Boundary effects on localized structures in spatially extended systems - Yadav, A.; Browne, D. A.
We present a general method of analyzing the influence of finite size and
boundary effects on the dynamics of localized solutions of non-linear spatially
extended systems. The dynamics of localized structures in infinite systems
involve solvability conditions that require projection onto a Goldstone mode.
Our method works by extending the solvability conditions to finite sized
systems, by incorporating the finite sized modifications of the Goldstone mode
and associated nonzero eigenvalue. We apply this method to the special case of
non-equilibrium domain walls under the influence of Dirichlet boundary
conditions in a parametrically forced complex Ginzburg Landau equation, where
we examine exotic nonuniform domain wall motion due to the influence...
91.
Dynamics and statics of vortices on a plane and a sphere - I - Borisov, A. V.; Pavlov, A. E.
In the present paper a description of a problem of point vortices on a plane
and a sphere in the "internal" variables is discussed. The hamiltonian
equations of motion of vortices on a plane are built on the Lie-Poisson
algebras, and in the case of vortices on a sphere on the quadratic Jacobi
algebras. The last ones are obtained by deformation of the corresponding linear
algebras. Some partial solutions of the systems of three and four vortices are
considered. Stationary and static vortex configurations are found.
92.
Resemblances and differences in mechanisms of noise-induced resonance - Centurelli, R.; Musacchio, S.; Pasmanter, R. A.; Vulpiani, A.
Systems showing stochastic resonance (SR) or coherent resonance (CR) share
some features, in particular the nearby periodic character of the signal. We
show that in spite of this resemblance the different underlying dynamics can be
detected in experimental data by studying the histogram of inter-spikes times
and some statistical properties like two-times correlation functions. We
discuss the possible relevance for climate modeling.
93.
Discrete Toda field equations - Habibullin, Ismagil
Discrete analogs of the finite and affine Toda field equations are found
corresponding to the Lie algebras of series $C_N$ and $\tilde{C_N}$. Their Lax
pairs are represented.
94.
On the motion of a heavy rigid body in an ideal fluid with circulation - Borisov, A. V.; Mamaev, I. S.
Chaplygin's equations describing the planar motion of a rigid body in an
unbounded volume of an ideal fluid involved in a circular flow around the body
are considered. Hamiltonian structures, new integrable cases, and partial
solutions are revealed, and their stability is examined. The problems of
non-integrability of the equations of motion because of a chaotic behavior of
the system are discussed.
95.
Correlation Function Bootstrapping in Quantum Chaotic Systems - Kaplan, L.
We discuss a general and efficient approach for "bootstrapping" short-time
correlation data in chaotic or complex quantum systems to obtain information
about long-time dynamics and stationary properties, such as the local density
of states. When the short-time data is sufficient to identify an individual
quantum system, we obtain a systematic approximation for the spectrum and wave
functions. Otherwise, we obtain statistical properties, including wave function
intensity distributions, for an ensemble of all quantum systems sharing the
given short-time correlations. The results are valid for open or closed
systems, and are stable under perturbation of the short-time input data.
Numerical examples include quantum maps and two-dimensional anharmonic
oscillators.
96.
Kovalevskaya Exponents and Poisson Structures - Borisov, A. V.; Dudoladov, S. L.
We consider generalizations of pairing relations for Kovalevskaya exponents
in quasihomogeneous systems with quasihomogeneous tensor invariants. The case
of presence of a Poisson structure in the system is investigated in more
detail. We give some examples which illustrate general theorems.
97.
Convection-induced nonlinear-symmetry-breaking in wave mixing - Zambrini, Roberta; Miguel, Maxi San; Durniak, Celine; Taki, Majid
We show that the combined action of diffraction and convection (walk-off) in
wave mixing processes leads to a nonlinear-symmetry-breaking in the generated
traveling waves. The dynamics near to threshold is reduced to a Ginzburg-Landau
model, showing an original dependence of the nonlinear self-coupling term on
the convection. Analytical expressions of the intensity and the velocity of
traveling waves emphasize the utmost importance of convection in this
phenomenon. These predictions are in excellent agreement with the numerical
solutions of the full dynamical model.
98.
Lie algebras in vortex dynamics and celestial mechanics - IV - Bolsinov, A. V.; Borisov, A. V.; Mamaev, I. S.
The work of A.V. Borisov, A.E. Pavlov, Dynamics and Statics of Vortices on a
Plane and a Sphere - I (Reg. & Ch. Dynamics, 1998, Vol. 3, No 1, p.28-39)
introduces a naive description of dynamics of point vortices on a plane in
terms of variables of distances and areas which generate Lie-Poisson structure.
Using this approach a qualitative description of dynamics of point vortices on
a plane and a sphere is obtained in the works Dynamics of Three Vortices on a
Plane and a Sphere - II. General compact case by A.V. Borisov, V.G. Lebedev
(Reg. & Ch. Dynamics, 1998, Vol. 3, No 2, p.99-114), Dynamics...
99.
Periodic orbits and semiclassical form factor in barrier billiards - Giraud, Olivier
Using heuristic arguments based on the trace formulas, we analytically
calculate the semiclassical two-point correlation form factor for a family of
rectangular billiards with a barrier of height irrational with respect to the
side of the billiard and located at any rational position p/q from the side. To
do this, we first obtain the asymptotic density of lengths for each family of
periodic orbits by a Siegel-Veech formula. The result K(0)=1/2+1/q obtained for
these pseudo-integrable, non-Veech billiards is different but not far from the
value of 1/2 expected for semi-Poisson statistics and from values of K(0)
obtained previously in the case of Veech billiards.
100.
Stability of Thomson's Configurations of Vortices on a Sphere - Borisov, A. V.; Kilin, A. A.
In this work stability of polygonal configurations on a plane and sphere is
investigated. The conditions of linear stability are obtained. A nonlinear
analysis of the problem is made with the help of Birkhoff normalization. Some
problems are also formulated.
81.
