arXiv
(422,153 recursos)
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Mostrando recursos 61 - 80 de 13,166
61.
Elementary Darboux transformations and factorization - Musso, F.; Shabat, A.
A general theorem on factorization of matrices with polynomial entries is
proven and it is used to reduce polynomial Darboux matrices to linear ones.
Some new examples of linear Darboux matrices are discussed.
62.
Painleve tests, singularity structure and integrability - Hone, Andrew N. W.
After a brief introduction to the Painlev\'{e} property for ordinary
differential equations, we present a concise review of the various methods of
singularity analysis which are commonly referred to as Painlev\'{e} tests. The
tests are applied to several different examples, and we discuss the connection
between singularity structure and integrability for ordinary and partial
differential equations.
63.
Tsunami wave runup on coasts of narrow bays - Zahibo, Narcisse; Pelinovsky, Efim; Golinko, Vladimir; Osipenko, Nataly
The runup of tsunami waves on the coasts of the barrow bays, channels and
straits is studied in the framework of the nonlinear shallow water theory.
Using the narrowness of the water channel, the one-dimensional equations are
applied; they include the variable cross-section of channel. It is shown that
the analytical solutions can be obtained with use of the hodograph (Legendre)
transformation similar to the wave runup on the plane beach. As a result, the
linear wave equation is derived and all physical variables (water displacement,
fluid velocity, coordinate and time) can be determined. The dynamics of the
moving shoreline (boundary of the flooding zone) is investigated in...
64.
Experimental Synchronization of Spatiotemporal Chaos in Nonlinear Optics - Ramazza, P. L.; Bortolozzo, U.; Boccaletti, S.
We demonstrate that a unidirectional coupling between a pattern forming
system and its replica induces complete synchronization of the slave to the
master system onto a spatiotemporal chaotic state.
65.
Motion of a circular cylinder and n point vortices in a perfect fluid - Borisov, A. V.; Mamaev, I. S.; Ramodanov, S. M.
The paper studies the system of a rigid body interacting dynamically with
point vortices in a perfect fluid. For arbitrary value of vortex strengths and
circulation around the cylinder the system is shown to be Hamiltonian (the
corresponding Poisson bracket structure is rather complicated). We also reduced
the number of degrees of freedom of the system by two using the reduction by
symmetry technique and performed a thorough qualitative analysis of the
integrable system of a cylinder interacting with one vortex.
66.
Euler-Poisson Equations and Integrable Cases - Borisov, A. V.; Mamaev, I. S.
In this paper we propose a new approach to the study of integrable cases
based on intensive computer methods' application. We make a new investigation
of Kovalevskaya and Goryachev-Chaplygin cases of Euler-Poisson equations and
obtain many new results in rigid body dynamics in absolute space. Also we
present the visualization of some special particular solutions.
67.
Second order additive invariants in elementary cellular automata - Fuk?, Henryk
We investigate second order additive invariants in elementary cellular
automata rules. Fundamental diagrams of rules which possess additive invariants
are either linear or exhibit singularities similar to singularities of rules
with first-order invariant. Only rules which have exactly one invariants
exhibit singularities. At the singularity, the current decays to its
equilibrium value as a power law $t^{\alpha}$, and the value of the exponent
$\alpha$ obtained from numerical simulations is very close to -1/2. This is in
agreements with values previously reported for number-conserving rules, and
leads to a conjecture that regardless of the order of the invariant, exponent
$\alpha$ seems to have a universal value of 1/2.
68.
Dynamics of rolling disk - Borisov, A. V.; Mamaev, I. S.; Kilin, A. A.
In the paper we present the qualitative analysis of rolling motion without
slipping of a homogeneous round disk on a horisontal plane. The problem was
studied by S.A. Chaplygin, P. Appel and D. Korteweg who showed its
integrability. The behavior of the point of contact on a plane is investigated
and conditions under which its trajectory is finit are obtained. The
bifurcation diagrams are constructed.
69.
On the History of the Development of the Nonholonomic Dynamics - Borisov, A. V.; Mamaev, I. S.
The main directions in the development of the nonholonomic dynamics are
briefly considered in this paper. The first direction is connected with the
general formalizm of the equations of dynamics that differs from the Lagrangian
and Hamiltonian methods of the equations of motion's construction. The second
direction, substantially more important for dynamics, includes investigations
concerning the analysis of the specific nonholonomic problems. We also point
out rather promising direction in development of nonholonomic systems that is
connected with intensive use of the modern computer-aided methods.
70.
Localized patterns and hole solutions in one-dimension extended sytem - Clerc, M. G.; Falcon, C.
The existence, stability properties, and bifurcation diagrams of localized
patterns and hole solutions in one-dimensional extended systems is studied from
the point of view of front interactions. An adequate envelope equation is
derived from a prototype model that exhibits these particle-type solutions.
This equation allow us to obtain an analytical expression for the front
interaction, which is in good agreement with numerical simulations.
71.
Nonlinear dynamics and chaos in parametric sound generation - Sanchez-Morcillo, Victor J.; Espinosa, Victor; Redondo, Javier; Alba, Jesus
A theoretical analysis of the subharmonic generation process in an acoustical
resonator (interferometer) with plane walls is performed. It is shown that,
when both the pumping wave and the generated subharmonic are detuned with
respect to the resonator modes, the fields can display complex temporal
behaviour such as self-pulsing and chaos. A discussion about the acoustical
parameters required for the experimental observation of the phenomenon is
given.
72.
Gap Solitons in Periodic Discrete Nonlinear Schroedinger Equations - Pankov, A.
It is shown that the periodic DNLS, with cubic nonlinearity, possesses gap
solutions, i. e. standing waves, with the frequency in a spectral gap, that are
exponentially localized in spatial variable. The proof is based on the linking
theorem in combination with periodic approximations.
73.
Filling Gaps in Chaotic Time Series - Paparella, Francesco
We propose a method for filling arbitrarily wide gaps in deterministic time
series. Crucial to the method is the ability to apply Takens' theorem in order
to reconstruct the dynamics underlying the time series. We introduce a
functional to evaluate how compatible is a filling sequence of data with the
reconstructed dynamics. An algorithm for minimizing the functional with a
reasonable computational effort is then discussed.
74.
"Locally homogeneous turbulence" Is it an inconsistent framework? - Frisch, Uriel; Bec, Jeremie; Aurell, Erik
In his first 1941 paper Kolmogorov assumed that the velocity has increments
which are homogeneous and independent of the velocity at a suitable reference
point. This assumption of local homogeneity is consistent with the nonlinear
dynamics only in an asymptotic sense when the reference point is far away. The
inconsistency is illustrated numerically using the Burgers equation.
Kolmogorov's derivation of the four-fifths law for the third-order structure
function and its anisotropic generalization are actually valid only for
homogeneous turbulence, but a local version due to Duchon and Robert still
holds. A Kolomogorov--Landau approach is proposed to handle the effect of
fluctuations in the large-scale velocity on small-scale statistical properties;
it...
75.
Integrable Quasiclassical Deformations of Cubic Curves - Kodama, Y.; Konopelchenko, B.; Alonso, L. Martinez; Medina, E.
A general scheme for determining and studying hydrodynamic type systems
describing integrable deformations of algebraic curves is applied to cubic
curves. Lagrange resolvents of the theory of cubic equations are used to derive
and characterize these deformations.
76.
Scaling properties in the production range of shear dominated flows - Casciola, C. M.; Gualtieri, P.; Jacob, B.; Piva, R.
Recent developments in turbulence are focused on the effect of large scale
anisotropy on the small scale statistics of velocity increments. According to
Kolmogorov, isotropy is recovered in the large Reynolds number limit as the
scale is reduced and, in the so-called inertial range, universal features
-namely the scaling exponents of structure functions - emerge clearly. However
this picture is violated in a number of cases, typically in the high shear
region of wall bounded flows. The common opinion ascribes this effect to the
contamination of the inertial range by the larger anisotropic scales, i.e. the
residual anisotropy is assumed as a weak perturbation of an otherwise isotropic
dynamics....
77.
Two Cellular Automata for the 3x+1 Map - Bruschi, M.
Two simple Cellular Automata, which mimic the Collatz-Ulam iterated map (3x+1
map), are introduced. These Cellular Automata allow to test efficiently the
Collatz conjecture for very large numbers.
78.
Hydrodynamic Reductions of Dispersionless Harry Dym Hierarchy - Chang, Jen-Hsu
We investigate the reductions of dispersionless Harry Dym hierarchy to
systems of finitely many partial differential equations. These equations must
satisfy the compatibility condition and they are diagonalizable and
semi-Hamiltonian. By imposing a further constraint, the compatibility is
reduced to a system of algebraic equations, whose solutions are described.
79.
Generalized problem of two and four Newtonian centers - Borisov, A.; Mamaev, I.
We consider integrable spherical analogue of the Darboux potential, which
appear in the problem (and its generalizations) of the planar motion of a
particle in the field of two and four fixed Newtonian centers. The obtained
results can be useful when constructing a theory of motion of satellites in the
field of an oblate spheroid in constant curvature spaces.
80.
How much information can one store in a non-equilibrium medium? - Coullet, P.; Toniolo, C.; Tresser, C.
It has recently been emphasized again that the very existence of stationary
stable localized structures with short range interactions might allow to store
information in non-equilibrium media, opening new perspectives on information
storage. We show how to use generalized topological entropies to measure
aspects of the quantities of storable and non-storable information. This leads
us to introduce a measure of the long term stably storable information. As a
first example to illustrate these concepts, we revisit a mechanism for the
appearance of stationary stable localized structures that is related to the
stabilization of fronts between structured and unstructured states (or between
differently structured states).
61.
