title:
Two-loop calculation of the scaling behavior of two-dimensional forced
  Navier-Stokes equation

abstract:
  Asymptotic properties of the solution of two-dimensional randomly forced
Navier-Stokes equation with long-range correlations of the driving force are
analyzed in the two-loop order of perturbation theory with the use of
renormalization group. Kolmogorov constant of the energy spectrum is calculated
for both the inverse energy cascade and the direct enstrophy cascade in the
second order of the $\epsilon$ expansion.


title: The N=2 supersymmetric unconstrained matrix GNLS hierarchies

abstract:
  The generalization of the N=2 supersymmetric chiral matrix (k|n,m)--GNLS
hierarchy (Lett. Math. Phys. 45 (1998) 63, solv-int/9711009) to the case when
matrix entries are bosonic and fermionic unconstrained N=2 superfields is
proposed. This is done by exhibiting the corresponding matrix Lax--pair
representation in terms of N=2 unconstrained superfields. It is demonstrated
that when matrix entries are chiral and antichiral N=2 superfields, it
reproduces the N=2 chiral matrix (k|n,m)-GNLS hierarchy, while in the scalar
case, k=1, it is equivalent to the N=2 supersymmetric multicomponent hierarchy
(J. Phys. A29 (1996) 1281, hep-th/9510185). The simplest example --the N=2
unconstrained (1|1,0)--GNLS hierarchy-- and its reduction to the N=2
supersymmetric {\alpha}=1 KdV hierarchy are discussed in more detail, and its
rich symmetry structure is uncovered.


title: Hierarchical Markovian modeling of multi-time scale systems

abstract:
  We present a systematic way to analyze and model systems having many
characteristic time-scales. The method we propose is employed for a test-case
of a meandering jet model manifesting chaotic tracer dispersion with long
time-correlations. We first choose a suitable state space partition and analyze
the symbolic dynamics associated to the fluid particle position. In a second
step we construct a stochastic process in terms of a multi-time Markovian
model. This corresponds to a hierarchy of random travelers on a graph where
each traveler moves at his own time scale. The results are compared on the
basis of statistical measures such as entropies and correlation functions.


title: The quasi-bi-Hamiltonian formulation of the Lagrange top

abstract:
  Starting from the tri-Hamiltonian formulation of the Lagrange top in a
six-dimensional phase space, we discuss the possible reductions of the Poisson
tensors, the vector field and its Hamiltonian functions on a four-dimensional
space. We show that the vector field of the Lagrange top possesses, on the
reduced phase space, a quasi-bi-Hamiltonian formulation, which provides a set
of separation variables for the corresponding Hamilton-Jacobi equation.


title: Stable spinning optical solitons in three dimensions

abstract:
  We introduce spatiotemporal spinning solitons (vortex tori) of the
three-dimensional nonlinear Schrodinger equation with focusing cubic and
defocusing quintic nonlinearities. The first ever found completely stable
spatiotemporal vortex solitons are demonstrated. A general conclusion is that
stable spinning solitons are possible as a result of competition between
focusing and defocusing nonlinearities.


title: Electromigration-Induced Propagation of Nonlinear Surface Waves

abstract:
  Due to the effects of surface electromigration, waves can propagate over the
free surface of a current-carrying metallic or semiconducting film of thickness
h_0. In this paper, waves of finite amplitude, and slow modulations of these
waves, are studied. Periodic wave trains of finite amplitude are found, as well
as their dispersion relation. If the film material is isotropic, a wave train
with wavelength lambda is unstable if lambda/h_0 < 3.9027..., and is otherwise
marginally stable. The equation of motion for slow modulations of a finite
amplitude, periodic wave train is shown to be the nonlinear Schrodinger
equation. As a result, envelope solitons can travel over the film's surface.


title: Symbolic Dynamics of Homoclinic Orbits in a Symmetric Map

abstract:
  Symbolic dynamics for homoclinic orbits in the two-dimensional symmetric map,
$x_{n+1}+cx_{n}+x_{n-1}=3x_{n}^3$, is discussed. Above a critical $c^{\ast}$,
the system exhibits a fully-developed horse-shoe so that its global behavior is
described by a complete ternary symbolic dynamics. The relative location of
homoclinic orbits is determined by their sequences according to a simple rule,
which can be used to numerically locate orbits in phase space. With the
decrease of $c$, more and more pairs of homoclinic orbits collide and
disappear. Forbidden zone in the symbolic space induced by the collision is
discussed.


title:
Lag time and parameter mismatches in synchronization of unidirectionally
  coupled chaotic external cavity semiconductor lasers

abstract:
  We report an analysis of synchronization between two unidirectionally coupled
chaotic external cavity master/slave semiconductor lasers with two
characteristic delay times, where the delay time in the coupling is different
from the delay time in the coupled systems themselves. We demonstrate for the
first time that parameter mismatches in photon decay rates for the master and
slave lasers can explain the experimental observation that the lag time is
equal to the coupling delay time.


title:
An exact derivation of the dissipation rate correlation exponent \mu in
  fully-developed turbulence

abstract:
  We derive for the Navier-Stokes equation an exact equation satisfied by the
dissipation rate correlation function. In the equal time limit, in the inertial
range, for the homogeneous, isotropic state of fully-developed turbulence, we
show that the correlation is characterized by two exponents, one of which
depends on the sixth-order static structure function exponent and the other
involves the behavior of the fourth-order dynamical structure function. This
provides a direct derivation of the intermittency exponent of the
dissipation-rate correlation.


title: Modeling Vocal Fold Motion with a New Hydrodynamic Semi-Continuum Model

abstract:
  Vocal fold (VF) motion is a fundamental process in voice production, and is
also a challenging problem for direct numerical computation because the VF
dynamics depend on nonlinear coupling of air flow with the response of elastic
channels (VF), which undergo opening and closing, and induce internal flow
separation. A traditional modeling approach makes use of steady flow
approximation or Bernoulli's law which is known to be invalid during VF
opening. We present a new hydrodynamic semi-continuum system for VF motion. The
airflow is modeled by a quasi-one dimensional continuum aerodynamic system, and
the VF by a classical lumped two mass system. The reduced flow system contains
the Bernoulli's law as a special case, and is derivable from the two
dimensional compressible Navier-Stokes equations. Since we do not make steady
flow approximation, we are able to capture transients and rapid changes of
solutions, e.g. the double pressure peaks at opening and closing stages of VF
motion consistent with experimental data. We demonstrate numerically that our
system is robust, and models in-vivo VF oscillation more physically. It is also
much simpler than a full two-dimensional Navier-Stokes system.


title: Stretching of polymers in a turbulent environment

abstract:
  The interaction of polymers with small-scale velocity gradients can trigger a
coil-stretch transition in the polymers. We analyze this transition within a
direct numerical simulation of shear turbulence with an Oldroyd-B model for the
polymer. In the coiled state the lengths of polymers are distributed
algebraically with an exponent alpha=2 gamma-1/De, where gamma is a
characteristic stretching rate of the flow and De the Deborah number. In the
stretched state we demonstrate that the length distribution of the polymers is
limited by the feedback to the flow.


title: Collapse arrest and soliton stabilization in nonlocal nonlinear media

abstract:
  We investigate the properties of localized waves in systems governed by
nonlocal nonlinear Schrodinger type equations. We prove rigorously by bounding
the Hamiltonian that nonlocality of the nonlinearity prevents collapse in,
e.g., Bose-Einstein condensates and optical Kerr media in all physical
dimensions. The nonlocal nonlinear response must be symmetric, but can be of
completely arbitrary shape. We use variational techniques to find the soliton
solutions and illustrate the stabilizing effect of nonlocality.


title: Stability of Synchronized Chaos in Coupled Dynamical Systems

abstract:
  We consider the stability of synchronized chaos in coupled map lattices and
in coupled ordinary differential equations. Applying the theory of Hermitian
and positive semidefinite matrices we prove two results that give simple bounds
on coupling strengths which ensure the stability of synchronized chaos.
Previous results in this area involving particular coupling schemes (e.g.
global coupling and nearest neighbor diffusive coupling) are included as
special cases of the present work.


title: Decoherence of spin echoes

abstract:
  We define a quantity, the so-called purity fidelity, which measures the rate
of dynamical irreversibility due to decoherence, observed e.g in echo
experiments, in the presence of an arbitrary small perturbation of the total
(system + environment) Hamiltonian. We derive a linear response formula for the
purity fidelity in terms of integrated time correlation functions of the
perturbation. Our relation predicts, similarly to the case of fidelity decay,
faster decay of purity fidelity the slower decay of time correlations is. In
particular, we find exponential decay in quantum mixing regime and faster,
initially quadratic and later typically gaussian decay in the regime of
non-ergodic, e.g. integrable quantum dynamics. We illustrate our approach by an
analytical calculation and numerical experiments in the Ising spin 1/2 chain
kicked with tilted homogeneous magnetic field where part of the chain is
interpreted as a system under observation and part as an environment.


title:
Nonlinear Dynamics on the Plane and Integrable Hierarchies of
  Infinitesimal Deformations

abstract:
  A class of nonlinear problems on the plane, described by nonlinear
inhomogeneous $\bar{\partial}$-equations, is considered. It is shown that the
corresponding dynamics, generated by deformations of inhomogeneous terms
(sources) is described by Hamilton-Jacobi type equations associated with
hierarchies of dispersionless integrable systems. These hierarchies are
constructed by applying the quasiclassical $\bar{\partial}$-dressing method.


title:
A tree of linearisable second-order evolution equations by generalised
  hodograph transformations

abstract:
  We present a list of (1+1)-dimensional second-order evolution equations all
connected via a proposed generalised hodograph transformation, resulting in a
tree of equations transformable to the linear second-order autonomous evolution
equation. The list includes autonomous and nonautonomous equations.


title: Efficiency of a stirred chemical reaction in a closed vessel

abstract:
  We perform a numerical study of the reaction efficiency in a closed vessel.
Starting with a little spot of product, we compute the time needed to complete
the reaction in the container following an advection-reaction-diffusion
process. Inside the vessel it is present a cellular velocity field that
transports the reactants. If the size of the container is not very large
compared with the typical length of the velocity field one has a plateau of the
reaction time as a function of the strength of the velocity field, $U$. This
plateau appears both in the stationary and in the time-dependent flow. A
comparison of the results for the finite system with the infinite case (for
which the front speed, $v_f$, gives a simple estimate of the reacting time)
shows the dramatic effect of the finite size.


title: Coupled Map Networks as Communication Schemes

abstract:
  Networks of chaotic coupled maps are considered as string and language
generators. It is shown that such networks can be used as encrypting systems
where the ciphertext contains information about the evolution of the network
and also about the way to select the plaintext symbols from the string
associated to the network evolution. The secret key provides the network
parameters, such as the coupling strengths.


title: Athermodynamic Alignment in the Two-Dimensional Enstrophy Cascade

abstract:
  We study inertial-range statistics in the direct enstrophy cascade of
two-dimensional turbulence via a numerical simulation of the forced
Navier-Stokes equation. In particular, we obtain the distribution of the
enstrophy flux and of the angle of alignment of the large-scale vorticity
gradient with the small-scale vorticity transport vector. These distributions
are surprisingly symmetrical and ``athermodynamic'', not explainable by a local
eddy-viscosity approximation with coefficient of either positive or negative
sign. By a systematic evaluation of the role of various triadic interactions,
we can trace the origin of the strong symmetry to the dominance of infrared
non-local triads in the enstrophy cascade.


title:
Front propagation techniques to calculate the largest Lyapunov exponent
  of dilute hard disk gases

abstract:
  A kinetic approach is adopted to describe the exponential growth of a small
deviation of the initial phase space point, measured by the largest Lyapunov
exponent, for a dilute system of hard disks, both in equilibrium and in a
uniform shear flow. We derive a generalized Boltzmann equation for an extended
one-particle distribution that includes deviations from the reference phase
space point. The equation is valid for very low densities n, and requires an
unusual expansion in powers of 1/|ln n|. It reproduces and extends results from
the earlier, more heuristic clock model and may be interpreted as describing a
front propagating into an unstable state. The asymptotic speed of propagation
of the front is proportional to the largest Lyapunov exponent of the system.
Its value may be found by applying the standard front speed selection mechanism
for pulled fronts to the case at hand. For the equilibrium case, an explicit
expression for the largest Lyapunov exponent is given and for sheared systems
we give explicit expressions that may be evaluated numerically to obtain the
shear rate dependence of the largest Lyapunov exponent.


title: Lyapunov spectra of periodic orbits for a many-particle system

abstract:
  The Lyapunov spectrum corresponding to a periodic orbit for a two dimensional
many particle system with hard core interactions is discussed. Noting that the
matrix to describe the tangent space dynamics has the block cyclic structure,
the calculation of the Lyapunov spectrum is attributed to the eigenvalue
problem of a 16x16 reduced matrices regardless of the number of particles. We
show that there is the thermodynamic limit of the Lyapunov spectrum in this
periodic orbit. The Lyapunov spectrum has a step structure, which is explained
by using symmetries of the reduced matrices.


title: Intelligent systems in the context of surrounding environment

abstract:
  We investigate the behavioral patterns of a population of agents, each
controlled by a simple biologically motivated neural network model, when they
are set in competition against each other in the Minority Model of Challet and
Zhang. We explore the effects of changing agent characteristics, demonstrating
that crowding behavior takes place among agents of similar memory, and show how
this allows unique `rogue' agents with higher memory values to take advantage
of a majority population. We also show that agents' analytic capability is
largely determined by the size of the intermediary layer of neurons.
  In the context of these results, we discuss the general nature of natural and
artificial intelligence systems, and suggest intelligence only exists in the
context of the surrounding environment (embodiment).
  Source code for the programs used can be found at http://neuro.webdrake.net .


title: Unstable manifolds and Schroedinger dynamics of Ginzburg-Landau vortices

abstract:
  The time evolution of several interacting Ginzburg-Landau vortices according
to an equation of Schroedinger type is approximated by motion on a
finite-dimensional manifold. That manifold is defined as an unstable manifold
of an auxiliary dynamical system, namely the gradient flow of the
Ginzburg-Landau energy functional. For two vortices the relevant unstable
manifold is constructed numerically and the induced dynamics is computed. The
resulting model provides a complete picture of the vortex motion for arbitrary
vortex separation, including well-separated and nearly coincident vortices.


title: Modulation of Localized States in Electroconvection

abstract:
  We report on the effects of temporal modulation of the driving force on a
particular class of localized states, known as worms, that have been observed
in electroconvection in nematic liquid crystals. The worms consist of the
superposition of traveling waves and have been observed to have unique, small
widths, but to vary in length. The transition from the pure conduction state to
worms occurs via a backward bifurcation. A possible explanation of the
formation of the worms has been given in terms of coupled amplitude equations.
Because the worms consist of the superposition of traveling waves, temporal
modulation of the control parameter is a useful probe of the dynamics of the
system. We observe that temporal modulation increases the average length of the
worms and stabilizes worms below the transition point in the absence of
modulation.


title: A nonlinear component of the analytical error

abstract:
  In clinical chemistry, a number of studies shows that the probability of very
large errors is much greater than expected from the Gaussian distribution. In
addition, it has been empirically found that the behavior of nonlinear complex
systems is often asymptotically exponential. Consequently, we may assume that
the error of some analytical systems may be approximated by the sum of a linear
component of error with Gaussian distribution and a nonlinear component with
Laplacian. Then, the probability density function (pdf) of the total error is
approximated by the convolution integral of the Gaussian and the Laplacian pdf.
To explore the hypothesis of a nonlinear component of the analytical error I
have evaluated this distribution and calculated various quality control related
statistics with numerical methods. Large errors are much more probable with the
proposed distribution than with the Gaussian. Simulated series of measurements
with the proposed distribution often meet the criteria for normality. The
critical errors and the probabilities for critical error detection are less
than the respective ones of the Gaussian distribution. The probabilities for
false rejection are greater. Therefore, to optimize the quality control
planning process, we should explore the possibility that there exists a
nonlinear component of the analytical error.


title: Bushes of vibrational modes for Fermi-Pasta-Ulam chains

abstract:
  Some exact solutions and multi-mode invariant submanifolds were found for the
Fermi-Pasta-Ulam (FPU) beta-model by Poggi and Ruffo in Phys. D 103 (1997) 251.
In the present paper we demonstrate how results of such a type can be obtained
for an arbitrary N-particle chain with periodic boundary conditions with the
aid of our group-theoretical approach [Phys. D 117 (1998) 43] based on the
concept of bushes of normal modes for mechanical systems with discrete
symmetry. The integro-differential equation describing the FPU-alfa dynamics in
the modal space is derived. The loss of stability of the bushes of modes for
the FPU-alfa model, in particular, for the limiting case N >> 1 for the
dynamical regime with displacement pattern having period twice the lattice
spacing (Pi-mode) is studied. Our results for the FPU-alfa chain are compared
with those by Poggi and Ruffo for the FPU-beta chain.


title:
Self-organized and driven phase synchronization in coupled map scale
  free networks

abstract:
  As a model of evolving networks, we study coupled logistic maps on scale free
networks. For small coupling strengths nodes show turbulent behavior but form
phase synchronized clusters as coupling increases. We identify two different
ways of cluster formation. For small coupling strengths we get {\it
self-organized clusters} which have mostly intra-cluster couplings and for
large coupling strengths there is a crossover and reorganization to {\it driven
clusters} which have mostly inter-cluster couplings. In the novel driven
synchronization the nodes of one cluster are driven by those of the others.


title: More ergodic billiards with an infinite cusp

abstract:
  In a previous paper (nlin.CD/0107041) the following class of billiards was
studied: For $f: [0, +\infty) \longrightarrow (0, +\infty)$ convex,
sufficiently smooth, and vanishing at infinity, let the billiard table be
defined by $Q$, the planar domain delimited by the positive $x$-semiaxis, the
positive $y$-semiaxis, and the graph of $f$.
  For a large class of $f$ we proved that the billiard map was hyperbolic.
Furthermore we gave an example of a family of $f$ that makes this map ergodic.
Here we extend the latter result to a much wider class of functions.


title: Quantum Dynamics and Random Matrix Theory

abstract:
  We compute the survival probability of an initial state, with an energy in a
certain window, by means of random matrix theory. We determine its probability
distribution and show that is is universal, i.e. caracterised only by the
symmetry class of the hamiltonian and independent of the initial state.


title: Multicomponent dipole-mode spatial solitons

abstract:
  We study (2+1)-dimensional multicomponent spatial vector solitons with a
nontrivial topological structure of their constituents, and demonstrate that
these solitary waves exhibit a symmetry-breaking instability provided their
total topological charge is nonzero. We describe a novel type of stable
multicomponent dipole-mode solitons with intriguing swinging dynamics.


abstract:
  We define the notion of C^{(2)}_{N+1} Ruijsenaars-Schneider models and
construct their Lax formulation. They are obtained by a particular folding of
the A_{2N+1} systems. Their commuting Hamiltonians are linear combinations of
Koornwinder-van Diejen ``external fields'' Ruijsenaars-Schneider models, for
specific values of the exponential one-body couplings but with the most general
2 double-poles structure as opposed to the formerly studied BC_N case.
Extensions to the elliptic potentials are briefly discussed.


title: Non-autonomous Degenerate KdV Systems

abstract:
  Non-autonomous degenerate KdV systems in (1+1) dimensions are considered for
integrability classification. Integrability of the systems is associated with
the existence of a recursion operator. Some new non-autonomous degenerate
two-component KdV systems are found.


title: Isolated resonances in conductance fluctuations and hierarchical states

abstract:
  We study the isolated resonances occurring in conductance fluctuations of
quantum systems with a classically mixed phase space. We demonstrate that the
isolated resonances and their scattering states can be associated to
eigenstates of the closed system. They can all be categorized as hierarchical
or regular, depending on where the corresponding eigenstates live in the
classical phase space.


title: Separation of variables in quasi-potential systems of bi-cofactor form

abstract:
  We perform variable separation in the quasi-potential systems of equations of
the form $\ddot{q}=-A^{-1}\nabla k=-\tilde{A}^{-1}\nabla\tilde{k}${}, where $A$
and $\tilde{A}$ are Killing tensors, by embedding these systems into a
bi-Hamiltonian chain and by calculating the corresponding Darboux-Nijenhuis
coordinates on the symplectic leaves of one of the Hamiltonian structures of
the system. We also present examples of the corresponding separation
coordinates in two and three dimensions.


title:
Microscopic chaos from Brownian motion in a one-dimensional anharmonic
  oscillator chain

abstract:
  The problem of relating microscopic chaos to macroscopic behavior in a
many-degrees-of-freedom system is numerically investigated by analyzing
statistical properties associated to the position and momentum of a heavy
impurity embedded in a chain of nearest-neighbor anharmonic Fermi-Pasta-Ulam
oscillators. For this model we have found that the behavior of the relaxation
time of the momentum autocorrelation function of the impurity is different
depending on the dynamical regime (either regular or chaotic) of the lattice.


title:
The Lyapunov stability of first order dynamic equations with respect to
  time-dependent Riemannian metrics

abstract:
  Solutions of a smooth first order dynamic equation can be made Lyapunov
stable at will by the choice of an appropriate time-dependent Riemannian
metric.


title:
Bi-Hamiltonian structure of the N=2 supersymmetric {\alpha}=1 KdV
  hierarchy

abstract:
  The N=2 supersymmetric {\alpha}=1 KdV hierarchy in N=2 superspace is
considered and its rich symmetry structure is uncovered. New nonpolynomial and
nonlocal, bosonic and fermionic symmetries and Hamiltonians, bi-Hamiltonian
structure as well as a recursion operator connecting all symmetries and
Hamiltonian structures of the N=2 {\alpha}=1 KdV hierarchy are constructed in
explicit form. It is observed that the algebra of symmetries of the N=2
supersymmetric {\alpha}=1 KdV hierarchy possesses two different subalgebras of
N=2 supersymmetry.


title: A Micro-Thermodynamic Formalism

abstract:
  We consider the micro-canonical ensemble of a classical Hamiltonian dynamical
system, the Hamiltonian being parameter dependent and in the possible presence
of other first integrals. We describe a thermodynamic formalism in which a 1st
law of thermodynamics, or fundamental relation, is based upon the bulk-entropy,
S. Under an ergodic hypothesis, S is shown to be an adiabatic invariant.
Expressions for derivatives and thermodynamic relations are derived within the
micro-canonical ensemble itself.


title: Symmetry classification of KdV-type nonlinear evolution equations

abstract:
  Group classification of a class of third-order nonlinear evolution equations
generalizing KdV and mKdV equations is performed. It is shown that there are
two equations admitting simple Lie algebras of dimension three. Next, we prove
that there exist only four equations invariant with respect to Lie algebras
having nontrivial Levi factors of dimension four and six. Our analysis shows
that there are no equations invariant under algebras which are semi-direct sums
of Levi factor and radical. Making use of these results we prove that there are
three, nine, thirty-eight, fifty-two inequivalent KdV-type nonlinear evolution
equations admitting one-, two-, three-, and four-dimensional solvable Lie
algebras, respectively. Finally, we perform a complete group classification of
the most general linear third-order evolution equation.


title:
Finite-size scaling in the steady state of the fully asymmetric
  exclusion process

abstract:
  Finite-size scaling expressions for the current near the continuous phase
transition, and for the local density near the first-order transition, are
found in the steady state of the one-dimensional fully asymmetric
simple-exclusion process (FASEP) with open boundaries and discrete-time
dynamics. The corresponding finite-size scaling variables are identified as the
ratio of the chain length to the localization length of the relevant domain
wall.


title: Negative order MKdV hierarchy and a new integrable Neumann-like system

abstract:
  The purpose of this paper is to develop the negative order MKdV hierarchy and
to present a new related integrable Neumann-like Hamiltonian flow from the view
point of inverse recursion operator and constraint method. The whole MKdV
hierarchy both positive and negative is generated by the kernel elements of
Lenard's operators pair and recursion operator. Through solving a key operator
equation, the whole MKdV hierarchy is shown to have the Lax representation. In
particular, some new integrable equation together with the Liouville equations,
the sine-Gordon equation, and the sinh-Gordon equation are derived from the
negative order MKdV hierarchy. It is very interesting that the restricted flow,
corresponding to the negative order MKdV hierarchy, is just a new kind of
Neumann-like system. This new Neumann-like system is obtained through
restricting the MKdV spectral problem onto a symplectic submanifold and is
proven to be completely integrable under the Dirac-Poisson bracket, which we
define on the symplectic submanifold. Finally, with the help of the constraint
between the Neumann-like system and the negative order MKdV hierarchy, all
equations in the hierarchy are proven to have the parametric representations of
solutions. In particular, we obtain the parametric solutions of the sine-Gordon
equation and the sinh-Gordon equation.


title:
Category of nonlinear evolution equations, algebraic structure, and
  r-matrix

abstract:
  This paper deals with the category of nonlinear evolution equations (NLEEs)
associated with the spectral problem and provides an approach for constructing
their algebraic structure and $r$-matrix. First we introduce the category of
NLEEs, which composes of various positive order and negative order hierarchies
of NLEEs both integrable and non-integrable. The whole category of NLEEs
possesses a generalized Lax representation. Next, we present two different Lie
algebraic structures of the Lax operator, one of them is universal in the
category,i.e. independent of the hierarchy, while the other one is nonuniversal
in the hierarchy, i.e. dependent on the underlying hierarchy. Moreover, we find
that two kinds of adjoint maps are $r$-matrices under the algebraic structures.
In particular, the Virasoro algebraic structures without central extension of
isospectral and non-isospectral Lax operators can be viewed as reductions of
our algebraic structure. Finally, we give several concrete examples to
illustrate our methods. Particularly, the Burgers category is linearized when
the generator, which generates the category, is chosen to be independent of the
potential function. Furthermore, an isospectral negative order hierarchy in the
Burger's category is solved with its general solution. Additionally, in the KdV
category we find an interesting fact: the Harry-Dym hierarchy is contained in
this category as well as the well-known Harry-Dym equation is included in a
positive order KdV hierarchy.


title:
From bi-Hamiltonian geometry to separation of variables: stationary
  Harry-Dym and the KdV dressing chain

abstract:
  Separability theory of one-Casimir Poisson pencils, written down in arbitrary
coordinates, is presented. Separation of variables for stationary Harry-Dym and
the KdV dressing chain illustrates the theory.


title: Geometry and dynamics of billiards in symmetric phase space

abstract:
  The billiard problem of statistical physics is considered in a new geometric
approach with a symmetric phase space. The structure and topological features
of typical billiard phase portrait are defined. The connection between
geometric, dynamic and statistic properties of smooth billiard is established.
Other directions of the theory on development are pointed out.


title:
Linear and nonlinear marginal stability for fronts of hyperbolic
  reaction diffusion equations

abstract:
  We study travelling fronts of equations of the form $u_{tt} + \phi(u) u_x =
u_{xx} + f(u)$. A criterion for the transition from linear to nonlinear
marginal stability is established for positive functions $\phi(u)$ and for any
reaction term $f(u)$ for which the usual parabolic reaction diffusion equation
$u_t = u_{xx} + f(u)$ admits a front. As an application, we treat reaction
diffusion systems with transport memory.


title:
Time Domain Computation of a Nonlinear Nonlocal Cochlear Model with
  Applications to Multitone Interaction in Hearing

abstract:
  A nonlinear nonlocal cochlear model of the transmission line type is studied
in order to capture the multitone interactions and resulting tonal suppression
effects. The model can serve as a module for voice signal processing, it is a
one dimensional (in space) damped dispersive nonlinear PDE based on mechanics
and phenomenology of hearing. It describes the motion of basilar membrane (BM)
in the cochlea driven by input pressure waves. Both elastic damping and
selective longitudinal fluid damping are present. The former is nonlinear and
nonlocal in BM displacement, and plays a key role in capturing tonal
interactions. The latter is active only near the exit boundary (helicotrema),
and is built in to damp out the remaining long waves. The initial boundary
value problem is numerically solved with a semi-implicit second order finite
difference method. Solutions reach a multi-frequency quasi-steady state.
Numerical results are shown on two tone suppression from both high-frequency
and low-frequency sides, consistent with known behavior of two tone
suppression. Suppression effects among three tones are demonstrated by showing
how the response magnitudes of the fixed two tones are reduced as we vary the
third tone in frequency and amplitude. We observe qualitative agreement of our
model solutions with existing cat auditory neural data. The model is thus
simple and efficient as a processing tool for voice signals.


title:
Analyzing intramolecular vibrational energy redistribution via the
  overlap intensity-level velocity correlator

abstract:
  Numerous experimental and theoretical studies have established that
intramolecular vibrational energy redistribution (IVR) in isolated molecules
has a heirarchical tier structure. The tier structure implies strong
correlations between the energy level motions of a quantum system and its
intensity-weighted spectrum. A measure, which explicitly accounts for this
correaltion, was first introduced by one of us as a sensitive probe of phase
space localization. It correlates eigenlevel velocities with the overlap
intensities between the eigenstates and some localized state of interest. A
semiclassical theory for the correlation is developed for systems that are
classically integrable and complements earlier work focusing exclusively on the
chaotic case. Application to a model two dimensional effective spectroscopic
Hamiltonian shows that the correlation measure can provide information about
the terms in the molecular Hamiltonian which play an important role in an
energy range of interest and the character of the dynamics. Moreover, the
correlation function is capable of highlighting relevant phase space structures
including the local resonance features associated with a specific bright state.
In addition to being ideally suited for multidimensional systems with a large
density of states, the measure can also be used to gain insights into the phase
space transport and localization. It is argued that the overlap intensity-level
velocity correlation function provides a novel way of studying vibrational
energy redistribution in isolated molecules. The correlation function is
ideally suited to analyzing the parametric spectra of molecules in external
fields.


title:
Dark breathers in Klein-Gordon lattices. Band analysis of their
  stability properties

abstract:
  Discrete bright breathers are well known phenomena. They are localized
excitations that consist of a few excited oscillators in a lattice and the rest
of them having very small amplitude or none. In this paper we are interested in
the opposite kind of localization, or discrete dark breathers, where most of
the oscillators are excited and one or a few units of them have very small
amplitude. We investigate using band analysis, Klein--Gordon lattices at
frequencies not close to the linear ones. Dark breathers at low coupling are
shown to be stable for Klein--Gordon chains with soft on--site potentials and
repulsive dispersive interaction, and with hard on--site potentials and
attractive dispersive interactions. At higher coupling dark breathers lose
their stability via subharmonic, harmonic or oscillatory bifurcations,
depending on the model. However, most of these bifurcations are harmless in the
sense that they preserve dark localization. None of these bifurcations
disappear when the system is infinite. Dark breathers in dissipative systems
are found to be stable for both kinds of dispersive interaction.


title: Moving breathers in a bent DNA-related model

abstract:
  We study the properties of moving breathers in a bent DNA-related model with
short range interaction, due to the stacking of the base pairs, and long range
interaction, due to the finite dipole moment of the bonds within each base
pair. We show that the movement of a breather is hindered by the bending of the
chain as a particle in a potential barrier. We have also found that the
behaviour of moving breathers in an homogeneous bent chain and in a straight
chain with a small impurity is qualitatively equivalent.


title:
Energy-dependent potentials revisited: A universal hierarchy of
  hydrodynamic type

abstract:
  A hierarchy of infinite-dimensional systems of hydrodynamic type is
considered and a general scheme for classifying its reductions is provided.
Wide families of integrable systems including, in particular, those associated
with energy-dependent spectral problems of Schr\" odinger type, are
characterized as reductions of this hierarchy. $N$-phase type reductions and
their corresponding Dubrovin equations are analyzed. A symmetry transformation
connecting different classes of reductions is formulated.


title:
The Camassa-Holm hierarchy, related N-dimensional integrable systems,
  and algebro-geometric solution on a symplectic submanifold

abstract:
  This paper shows that the Camassa-Holm (CH) spectral problem yields two
different integrable hierarchies of nonlinear evolution equations (NLEEs), one
is of negative order CH hierachy while the other one is of positive order CH
hierarchy. The two CH hierarchies possess the zero curvature representations
through solving a key matrix equation. We find that the well-known CH equation
is included in the negative order CH hierarchy while a Dym type equation is
included in the positive order CH hierarchy. Furthermore, under two constraint
conditions between the eigenfunctions and the potentials, the CH spectral
problem is cast in: (enumerate) a new Neumann-like N-dimensional system when it
is restricted into a symplectic submanifold of $\R^{2N}$ which is proven to be
integrable by using the Dirac-Poisson bracket and the r-matrix process; and a
new Bargmann-like N-dimensional system when it is considered in the whole
$\R^{2N}$ which is proven to be integrable by using the standard Poisson
bracket and the r-matrix process. (enumerate) In the paper, we present two
$4\times4$ instead of $N\times N$ r-matrix structures. One is for the
Neumann-like CH system (not the peaked CH system), while the other one is for
the Bargmann-like CH system. The whole CH hierarchy (both positive and negative
order) is shown to have the parametric solution which obey the constraint
relation. In particular, the CH equation constrained to some symplectic
submanifold, and the Dym type equation have the parametric solutions. Moreover,
we see that the kind of parametric solution of the CH equation is not gauge
equivalent to the peakons. Solving the parametric representation of solution on
the symplectic submanifold gives a class of new algebro-geometric solution of
the CH equation.


title:
Information transfer and nontrivial collective behavior in chaotic
  coupled map networks

abstract:
  The emergence of nontrivial collective behavior in networks of coupled
chaotic maps is investigated by means of a nonlinear mutual prediction method.
The resulting prediction error is used to measure the amount of information
that a local unit possesses about the collective dynamics. Applications to
locally and globally coupled map systems are considered. The prediction error
exhibits phase transitions at critical values of the coupling for the onset of
ordered collective behavior in these networks. This information measure may be
used as an order parameter for the characterization of complex behavior in
extended chaotic systems.


title:
Polynomial \tau-functions of the NLS-Toda hierarchy and the Virasoro
  singular vectors

abstract:
  A family of polynomial \tau-functions for the NLS-Toda hierarchy is
constructed. The hierarchy is associated with the homogeneous vertex operator
representation of the affine algebra \g of type A_1^{(1)}. These \tau-functions
are given explicitly in terms of Schur functions that correspond to rectangular
Young diagrams. It is shown that an arbitrary polynomial \tau-function which is
an eigenvector of d, the degree operator of \g, is contained in the family. By
the construction, any \tau-function in the family becomes a Virasoro singular
vector. This consideration gives rise to a simple proof of known results on the
Fock representation of the Virasoro algebra with c=1.


title: Alpha-modeling strategy for LES of turbulent mixing

abstract:
  The $\alpha$-modeling strategy is followed to derive a new subgrid
parameterization of the turbulent stress tensor in large-eddy simulation (LES).
The LES-$\alpha$ modeling yields an explicitly filtered subgrid
parameterization which contains the filtered nonlinear gradient model as well
as a model which represents `Leray-regularization'. The LES-$\alpha$ model is
compared with similarity and eddy-viscosity models that also use the dynamic
procedure. Numerical simulations of a turbulent mixing layer are performed
using both a second order, and a fourth order accurate finite volume
discretization. The Leray model emerges as the most accurate, robust and
computationally efficient among the three LES-$\alpha$ subgrid
parameterizations for the turbulent mixing layer. The evolution of the resolved
kinetic energy is analyzed and the various subgrid-model contributions to it
are identified. By comparing LES-$\alpha$ at different subgrid resolutions, an
impression of finite volume discretization error dynamics is obtained.


title: Quasiconformal Mappings and Solutions of the Dispersionless KP hierarchy

abstract:
  A $\bar{\partial}$-formalism for studying dispersionless integrable
hierarchies is applied to the dKP hierarchy. Connections with the theory of
quasiconformal mappings on the plane are described and some clases of explicit
solutions of the dKP hierarchy are presented.


title: Trouble of Non-Linearity

abstract:
  All complex fluid motions, such as transition and turbulence, obeying the
Navier-Stokes equations are non-linear phenomena. Some aspects of the
non-linear terms of these equations are not well understood and are, in fact,
misunderstood. The one-dimensional Kuramoto-Sivashinsky (KS) equation is used
as a simple model non-linear partial differential equation to show some
essential functions of its non-linear term and its consequences, which, we
believe, are shared with other non-linear partial differential equations. We
show that solutions of nonlinear partial differential equations above their
critical parameters may be linearly stable, but are nonlinearly unstable. No
stable solution exists above the critical parameter, contrary to the prediction
of the linear-stability analysis. This is because a linearly stable disturbance
can transfer energy simultaneously, not necessarily in cascade from small wave
numbers to large wave numbers. An initial disturbance can breed its entire
harmonics simultaneously. Second, I show that a long-time numerical chaotic
solution cannot be achieved by a discrete numerical method.


title:
Pairing of Lyapunov Exponents for a Hard-Sphere Gas under Shear in the
  Thermodynamic Limit

abstract:
  We consider a dilute gas of hard spheres under shear. We use one of the
predominant models to study this system, namely the SLLOD equations of motion,
with an iso-kinetic Gaussian thermostat in between collisions, to get a
stationary total peculiar kinetic energy. Based on the previously obtained
result that in the non-equilibrium steady state and in case the number of
particles $N$ becomes large, the coefficient of dynamical friction representing
the iso-kinetic Gaussian thermostat for the SLLOD dynamics fluctuates with
$1/\sqrt{N}$ fluctuations around a fixed value, we show on analytical grounds
that for a hard sphere gas at small shear rate and with a large number of
spheres, the conjugate pairing of the Lyapunov exponents is expected to be
violated at the fourth power of the constant shear rate in the bulk.


title:
Lyapunov Exponent Pairing for a Thermostatted Hard-Sphere Gas under
  Shear in the Thermodynamic Limit

abstract:
  We demonstrate why for a sheared gas of hard spheres, described by the SLLOD
equations with an iso-kinetic Gaussian thermostat in between collisions,
deviations of the conjugate pairing rule for the Lyapunov spectrum are to be
expected, employing a previous result that for a large number of particles $N$,
the iso-kinetic Gaussian thermostat is equivalent to a constant friction
thermostat, up to $1/\sqrt{N}$ fluctuations. We also show that these deviations
are at most of the order of the fourth power in the shear rate.


title:
Fractal Diffusion in Smooth Dynamical Systems with Virtual Invariant
  Curves

abstract:
  Preliminary results of extensive numerical experiments on a simple model
specified by the smooth canonical strongly chaotic 2D-map with global virtual
invariant curves (VICs) are presented and discussed. We focus on the statistics
of the diffusion rate of individual trajectories in dependence on the model
parameters. Our previous conjecture about the fractal statistics determined by
the critical structure of both the phase space and the motion is confirmed and
studied in some detail. Particularly, we have found specific characteristics of
what we termed the VIC diffusion suppression which is related to a new type of
the critical structure. An example of ergodic motion with a surprising "hidden"
critical structure strongly affecting the diffusion rate was also encountered
and discussed.


title: Noncoaxial multivortices in the complex sine-Gordon theory on the plane

abstract:
  We construct explicit multivortex solutions for the complex sine-Gordon
equation (the Lund-Regge model) in two Euclidean dimensions. Unlike the
previously found (coaxial) multivortices, the new solutions comprise $n$ single
vortices placed at arbitrary positions (but confined within a finite part of
the plane.) All multivortices, including the single vortex, have an infinite
number of parameters. We also show that, in contrast to the coaxial complex
sine-Gordon multivortices, the axially-symmetric solutions of the
Ginzburg-Landau model (the stationary Gross-Pitaevskii equation) {\it do not}
belong to a broader family of noncoaxial multivortex configurations.

categories: nlin.SI cond-mat.supr-con hep-th math-ph math.AP math.MP nlin.AO nlin.PS physics.flu-dyn physics.optics


title: On the dual cascade in two-dimensional turbulence

abstract:
  We study the dual cascade scenario for two-dimensional turbulence driven by a
spectrally localized forcing applied over a finite wavenumber range
$[k_\min,k_\max]$ (with $k_\min > 0$) such that the respective energy and
enstrophy injection rates $\epsilon$ and $\eta$ satisfy
$k_\min^2\epsilon\le\eta\le k_\max^2\epsilon$. The classical
Kraichnan--Leith--Batchelor paradigm, based on the simultaneous conservation of
energy and enstrophy and the scale-selectivity of the molecular viscosity,
requires that the domain be unbounded in both directions. For two-dimensional
turbulence either in a doubly periodic domain or in an unbounded channel with a
periodic boundary condition in the across-channel direction, a direct enstrophy
cascade is not possible. In the usual case where the forcing wavenumber is no
greater than the geometric mean of the integral and dissipation wavenumbers,
constant spectral slopes must satisfy $\beta>5$ and $\alpha+\beta\ge8$, where
$-\alpha$ ($-\beta$) is the asymptotic slope of the range of wavenumbers lower
(higher) than the forcing wavenumber. The influence of a large-scale
dissipation on the realizability of a dual cascade is analyzed. We discuss the
consequences for numerical simulations attempting to mimic the classical
unbounded picture in a bounded domain.


title:
Quasi-stationary Stefan problem and computer simulation of interface
  dynamics

abstract:
  The computer simulation of quasistationary Stefan problem has been realized.
Different representations of the Laplacian growth model are considered. The
main attention has been paid for the interface dynamics represented by integro
differential equations. Numerical approach has been realized by use of
interpolating polynomials and exact quadrature formulae. As a result system of
ordinary differential equations has been simulated.


title:
R-matrix for a geodesic flow associated with a new integrable peakon
  equation

abstract:
  We use the r-matrix formulation to show the integrability of geodesic flow on
an $N$-dimensional space with coordinates $q_k$, with $k=1,...,N$, equipped
with the co-metric $g^{ij}=e^{-|q_i-q_j|}\big(2-e^{-|q_i-q_j|}\big)$. This flow
is generated by a symmetry of the integrable partial differential equation
(pde) $m_t+um_x+3mu_x=0, m=u-\alpha^2u_{xx}$ ($\al $ is a constant). This
equation -- called the Degasperis-Procesi (DP) equation -- was recently proven
to be completely integrable and possess peakon solutions by Degasperis, Holm
and Hone (DHH[2002]). The isospectral eigenvalue problem associated with the
integrable DP equation is used to find a new $L$-matrix, called the Lax matrix,
for the geodesic dynamical flow. By employing this Lax matrix we obtain the
$r$-matrix for the integrable geodesic flow.


title: A mechanism for randomness

abstract:
  We investigate explicit functions that can produce truly random numbers. We
use the analytical properties of the explicit functions to show that certain
class of autonomous dynamical systems can generate random dynamics. This
dynamics presents fundamental differences with the known chaotic systems. We
present realphysical systems that can produce this kind of random time-series.
We report theresults of real experiments with nonlinear circuits containing
direct evidence for this new phenomenon. In particular, we show that a
Josephson junction coupled to a chaotic circuit can generate unpredictable
dynamics. Some applications are discussed.


title: Bi-Hamiltonian aspects of the separability of the Neumann system

abstract:
  The Neumann system on the 2-dimensional sphere is used as a tool to convey
some ideas on the bi-Hamiltonian point of view on separation of variables. It
is shown that, from this standpoint, its separation coordinates and its
integrals of motion can be found in a systematic way.


title:
Classification of integrable equations on quad-graphs. The consistency
  approach

abstract:
  A classification of discrete integrable systems on quad-graphs, i.e. on
surface cell decompositions with quadrilateral faces, is given. The notion of
integrability laid in the basis of the classification is the three-dimensional
consistency. This property yields, among other features, the existence of the
discrete zero curvature with a spectral parameter. For all integrable systems
of the obtained exhaustive list, the so called three-leg forms are found. This
establishes Lagrangian and symplectic structures for these systems, and the
connection to discrete systems of the Toda type on arbitrary graphs.
Generalizations of these ideas to the three-dimensional integrable systems and
to the quantum context are also discussed.


title: Two-time synchronism and induced synchronization

abstract:
  A pair (A,B) of interacting oscillators treated as a master system sending
signals to its slave copy (a,b) through two communication channels A-->a and
B-->b is considered. The effect of non-simultaneous (two-time) synchronization
of the pairs (a,A) and (b,B) is demonstrated with the help of coupled Kerr
oscillators producing hyperchaos. An individual pair, for example, (b,B) can
also be synchronized when its communication channel B-->b is turned off,
provided that the second channel for the pair (a,A) is turned on. The resulted
synchronization is termed induced. The efficiencies of the presented
synchronization precesses are studied.


title:
Landau Damping and Coherent Structures in Narrow-Banded 1+1 Deep Water
  Gravity Waves

abstract:
  We study the nonlinear energy transfer around the peak of the spectrum of
surface gravity waves by taking into account nonhomogeneous effects. In the
narrow-banded approximation the kinetic equation resulting from a
nonhomogeneous wave field is a Vlasov-Poisson type equation which includes at
the same time the random version of the Benjamin-Feir instability and the
Landau damping phenomenon. We analytically derive the values of the Phillips'
constant $\alpha$ and the enhancement factor $\gamma$ for which the
narrow-banded approximation of the JONSWAP spectrum is unstable. By performing
numerical simulations of the nonlinear Schr\"{o}dinger equation we check the
validity of the prediction of the related kinetic equation. We find that the
effect of Landau damping is to suppress the formation of coherent structures.
The problem of predicting freak waves is briefly discussed.


title: A class of steady solutions to two-dimensional free convection

abstract:
  We obtained steady solutions to the two-dimensional Boussinesq approximation
equations without mean temperature gradient. This system is referred to as free
convection in this paper. Under an external flow described by the stream
function $\mPsi = - Ayf(x)$, two types of steady solutions are found depending
on the boundary conditions. One is kept steady by the balance between the
strain of $\mPsi$ and the diffusion. The solution is similar to the Burgers
vortex layer solution. The other is done by the balance between vorticity
induced by the buoyancy and vorticity flux caused by the external flow.
Detailed argument on these two balances is presented for $f(x) = x$. Then two
examples other than $f(x) = x$ are shown to have either of the two balancing
mechanism. We discuss the relation between these solutions and long-lived fine
scale coherent structures observed in direct numerical simulations of
two-dimensional free convection turbulence.


title:
Semiclassical trace formulae for systems with spin-orbit interactions:
  successes and limitations of present approaches

abstract:
  We discuss the semiclassical approaches for describing systems with
spin-orbit interactions by Littlejohn and Flynn (1991, 1992), Frisk and Guhr
(1993), and by Bolte and Keppeler (1998, 1999). We use these methods to derive
trace formulae for several two- and three-dimensional model systems, and
exhibit their successes and limitations. We discuss, in particular, also the
mode conversion problem that arises in the strong-coupling limit.

categories: nlin.CD cond-mat.mes-hall math-ph math.MP nlin.SI nucl-th


title: A mechanical model of normal and anomalous diffusion

abstract:
  The overdamped dynamics of a charged particle driven by an uniform electric
field through a random sequence of scatterers in one dimension is investigated.
Analytic expressions of the mean velocity and of the velocity power spectrum
are presented. These show that above a threshold value of the field normal
diffusion is superimposed to ballistic motion. The diffusion constant can be
given explicitly. At the threshold field the transition between conduction and
localization is accompanied by an anomalous diffusion. Our results exemplify
that, even in the absence of time-dependent stochastic forces, a purely
mechanical model equipped with a quenched disorder can exhibit normal as well
as anomalous diffusion, the latter emerging as a critical property.


title:
Properties of Stationary Nonequilibrium States in the Thermostatted
  Periodic Lorentz Gas II: The many point particles system

abstract:
  We study the stationary nonequilibrium states of N point particles moving
under the influence of an electric field E among fixed obstacles (discs) in a
two dimensional torus. The total kinetic energy of the system is kept constant
through a Gaussian thermostat which produces a velocity dependent mean field
interaction between the particles. The current and the particle distribution
functions are obtained numerically and compared for small E with analytic
solutions of a Boltzmann type equation obtained by treating the collisions with
the obstacles as random independent scatterings. The agreement is surprisingly
good for both small and large N. The latter system in turn agrees with a self
consistent one particle evolution expected to hold in the limit of N going to
infinity.


title: Bilinearization of N=1 Supersymmetric Modified KdV Equations

abstract:
  Two different types of N=1 modified KdV equations are shown to possess $N$
soliton solutions. The soliton solutions of these equations are obtained by
casting the equations in the bilinear forms using the supersymmetric extension
of the Hirota method. The distinguishing features of the soliton solutions of
N=1 mKdV and N=1 mKdV B equations are discussed.


title: Solitons Solutions for the N=2 Supersymmetric KdV Equation

abstract:
  The N=2 supersymmetric KdV equation of Inami and Kanno is bilinearized
employing the Hirota method and the existence of $N$ soliton solutions is
demonstrated. The exact form of the solutions are explicitly obtained and an
interesting symmetry of the equations of motion is observed.


title: Dynamical Networks in Function Dynamics

abstract:
  As a first step toward realizing a dynamical system that evolves while
spontaneously determining its own rule for time evolution, function dynamics
(FD) is analyzed. FD consists of a functional equation with a self-referential
term, given as a dynamical system of a 1-dimensional map. Through the time
evolution of this system, a dynamical graph (a network) emerges. This graph has
three interesting properties: i) vertices appear as stable elements, ii) the
terminals of directed edges change in time, and iii) some vertices determine
the dynamics of edges, and edges determine the stability of the vertices,
complementarily. Two aspects of FD are studied, the generation of a graph
(network) structure and the dynamics of this graph (network) in the system.


title: Modelling Food Webs

abstract:
  We review theoretical approaches to the understanding of food webs. After an
overview of the available food web data, we discuss three different classes of
models. The first class comprise static models, which assign links between
species according to some simple rule. The second class are dynamical models,
which include the population dynamics of several interacting species. We focus
on the question of the stability of such webs. The third class are species
assembly models and evolutionary models, which build webs starting from a few
species by adding new species through a process of "invasion" (assembly models)
or "speciation" (evolutionary models). Evolutionary models are found to be
capable of building large stable webs.


title: Relations of al Functions over Subvarieties in a Hyperelliptic Jacobian

abstract:
  The sine-Gordon equation has hyperelliptic al function solutions over a
hyperelliptic Jacobian for $y^2 = f(x)$ of arbitrary genus $g$. This article
gives an extension of the sine-Gordon equation to that over subvarieties of the
hyperelliptic Jacobian.
  We also obtain the condition that the sine-Gordon equation in a proper
subvariety of the Jacobian is defined.


title: Polymer transport by laminar flows

abstract:
  Polymer transport is investigated for two paradigmatic laminar flows having
open and closed streamlines, respectively. For both types of flows we find
transport depletion owing to the action of the polymers elastic degree of
freedom. For flows with closed streamlines the leading mechanism for the
observed transport reduction is the (dynamical) formation of barriers. For
flows with open streamlines the reduction of transport is induced by the
renormalization of the bare diffusion coefficient. Results have been obtained
by means of Lagrangian simulations.


title: Rational solutions to the Pfaff lattice and Jack polynomials

abstract:
  The finite Pfaff lattice is given by commuting Lax pairs involving a finite
matrix L (zero above the first subdiagonal) and a projection onto Sp(N). The
lattice admits solutions such that the entries of the matrix L are rational in
the time parameters t_1,t_2,..., after conjugation by a diagonal matrix. The
sequence of polynomial tau-functions, solving the problem, belongs to an
intriguing chain of subspaces of Schur polynomials, associated to Young
diagrams, dual with respect to a finite chain of rectangles. Also, this
sequence of tau-functions is given inductively by the action of a fixed vertex
operator.
  As examples, one such sequence is given by Jack polynomials for rectangular
Young diagrams, while another chain starts with any two-column Jack polynomial.

categories: nlin.SI hep-th math-ph math.CA math.CO math.MP math.QA


title:
On model selection and the disability of neural networks to decompose
  tasks

abstract:
  A neural network with fixed topology can be regarded as a parametrization of
functions, which decides on the correlations between functional variations when
parameters are adapted. We propose an analysis, based on a differential
geometry point of view, that allows to calculate these correlations. In
practise, this describes how one response is unlearned while another is
trained. Concerning conventional feed-forward neural networks we find that they
generically introduce strong correlations, are predisposed to forgetting, and
inappropriate for task decomposition. Perspectives to solve these problems are
discussed.


title: A neural model for multi-expert architectures

abstract:
  We present a generalization of conventional artificial neural networks that
allows for a functional equivalence to multi-expert systems. The new model
provides an architectural freedom going beyond existing multi-expert models and
an integrative formalism to compare and combine various techniques of learning.
(We consider gradient, EM, reinforcement, and unsupervised learning.) Its
uniform representation aims at a simple genetic encoding and evolutionary
structure optimization of multi-expert systems. This paper contains a detailed
description of the model and learning rules, empirically validates its
functionality, and discusses future perspectives.


title: Understanding deterministic diffusion by correlated random walks

abstract:
  Low-dimensional periodic arrays of scatterers with a moving point particle
are ideal models for studying deterministic diffusion. For such systems the
diffusion coefficient is typically an irregular function under variation of a
control parameter. Here we propose a systematic scheme of how to approximate
deterministic diffusion coefficients of this kind in terms of correlated random
walks. We apply this approach to two simple examples which are a
one-dimensional map on the line and the periodic Lorentz gas. Starting from
suitable Green-Kubo formulas we evaluate hierarchies of approximations for
their parameter-dependent diffusion coefficients. These approximations converge
exactly yielding a straightforward interpretation of the structure of these
irregular diffusion coeficients in terms of dynamical correlations.


title:
Exact form factors for the Josephson tunneling current and relative
  particle number fluctuations in a model of two coupled Bose-Einstein
  condensates

abstract:
  Form factors are derived for a model describing the coherent Josephson
tunneling between two coupled Bose-Einstein condensates. This is achieved by
studying the exact solution of the model in the framework of the algebraic
Bethe ansatz. In this approach the form factors are expressed through
determinant representations which are functions of the roots of the Bethe
ansatz equations.


title:
An integrable system on the moduli space of rational functions and its
  variants

abstract:
  We study several integrable Hamiltonian systems on the moduli spaces of
meromorphic functions on Riemann surfaces (the Riemann sphere, a cylinder and a
torus). The action-angle variables and the separated variables (in Sklyanin's
sense) are related via a canonical transformation, the generating function of
which is the Abel-Jacobi type integral of the Seiberg-Witten differential over
the spectral curve.


title: Hierarchy of quantum explicitly solvable and integrable models

abstract:
  Realizing bosonic field v(x) as current of massless (chiral) fermions we
derive hierarchy of quantum polynomial interactions of the field v(x) that are
completely integrable and lead to linear evolutions for the fermionic field. It
is proved that in the classical limit this hierarchy reduces to the
dispersionless KdV hierarchy. Application of our construction to quantization
of generic completely integrable interaction is demonstrated by example of the
mKdV equation.


title:
On a class of algebraic solutions to Painlev\'e VI equation, its
  determinant formula and coalescence cascade

abstract:
  A determinant formula for a class of algebraic solutions to Painlev\'e VI
equation (P$_{\rm VI}$) is presented. This expression is regarded as a special
case of the universal characters. The entries of the determinant are given by
the Jacobi polynomials. Degeneration to the rational solutions of P$_{\rm V}$
and P$_{\rm III}$ is discussed by applying the coalescence procedure.
Relationship between Umemura polynomials associated with P$_{\rm VI}$ and our
formula is also discussed.


title: Controlling strong scarring for quantized ergodic toral automorphisms

abstract:
  We show that in the semi-classical limit the eigenfunctions of quantized
ergodic symplectic toral automorphisms can not concentrate in measure on a
finite number of closed orbits of the dynamics. More generally, we show that,
if the pure point component of the limit measure has support on a finite number
of such orbits, then the mass of this component must be smaller than two thirds
of the total mass. The proofs use only the algebraic (i.e. not the number
theoretic) properties of the toral automorphisms together with the exponential
instability of the dynamics and therefore work in all dimensions.


title: Supersymmetric t-J Gaudin Models and KZ Equations

abstract:
  Supersymmetric t-J Gaudin models with both periodic and open boundary
conditions are constructed and diagonalized by means of the algebraic Bethe
ansatz method. Off-shell Bethe ansatz equations of the Gaudin systems are
derived, and used to construct and solve the KZ equations associated with
$sl(2|1)^{(1)}$ superalgebra.


title: A Theory for Quantum Accelerator Modes in Atom Optics

abstract:
  Unexpected accelerator modes were recently observed experimentally for cold
cesium atoms when driven in the presence of gravity. A detailed theoretical
explanation of this quantum effect is presented here. The theory makes use of
invariance properties of the system, that are similar to the ones of solids,
leading to a separation into independent kicked rotor problems. The analytical
solution makes use of a limit that is very similar to the semiclassical limit,
but with a small parameter that is not Planck's constant, but rather the
detuning from the frequency that is resonant in absence of gravity.


title: Strong and weak clustering of inertial particles in turbulent flows

abstract:
  We suggested a theory of clustering of inertial particles advected by a
turbulent velocity field caused by an instability of their spatial
distribution. The reason of the {\em clustering instability} is a combined
effect of the particle inertia and finite correlation time of the velocity
field. The crucial parameter for the instability is a size of the particles.
The critical size is estimated for a {\em strong clustering} (with a finite
fraction of particles in clusters) associated with the growth of the mean
absolute value of the particles number density and for a {\em weak clustering}
associated with the growth of the second and higher moments. A nonlinear
mechanism for a saturation of the clustering instability (particles collisions
in the clusters) is suggested. Applications of the analyzed effects to the
dynamics of aerosols and droplets in the turbulent atmosphere are discussed.
The critical size of atmospheric aerosols and droplets in clustering is of the
order of $(20 - 30)\mu$m, and a lower estimate of the number of particles in a
cluster is about hundreds.


title:
Quasi-Gaussian Statistics of Hydrodynamic Turbulence in 3/4+\epsilon
  dimensions

abstract:
  The statistics of 2-dimensional turbulence exhibit a riddle: the scaling
exponents in the regime of inverse energy cascade agree with the K41 theory of
turbulence far from equilibrium, but the probability distribution functions are
close to Gaussian like in equilibrium. The skewness $\C S \equiv
S_3(R)/S^{3/2}_2(R)$ was measured as $\C S_{\text{exp}}\approx 0.03$. This
contradiction is lifted by understanding that 2-dimensional turbulence is not
far from a situation with equi-partition of enstrophy, which exist as true
thermodynamic equilibrium with K41 exponents in space dimension of $d=4/3$. We
evaluate theoretically the skewness $\C S(d)$ in dimensions ${4/3}\le d\le 2$,
show that $\C S(d)=0$ at $d=4/3$, and that it remains as small as $\C
S_{\text{exp}}$ in 2-dimensions.


title:
Fully parallel algorithm for simulating dispersion-managed
  wavelength-division-multiplexed optical fiber systems

abstract:
  An efficient numerical algorithm is presented for massively parallel
simulations of dispersion-managed wavelength-division-multiplexed optical fiber
systems. The algorithm is based on a weak nonlinearity approximation and
independent parallel calculations of fast Fourier transforms on multiple CPUs.
The algorithm allows one to implement numerical simulations M/2 times faster
than a direct numerical simulation by a split-step method, where M is a number
of CPUs in parallel network.


title:
Geometrical Obstruction to the Integrability of Geodesic Flows: an
  Application to the Anisotropic Kepler Problem

abstract:
  Resorting to classical techniques of Riemannian geometry we develop a
geometrical method suitable to investigate the nonintegrability of geodesic
flows and of natural Hamiltonian systems. Then we apply such method to the
Anisotropic Kepler Problem (AKP) and we prove that it is not analytically
integrable.


title: Transitions to equilibrium state in classical \phi ^{4} lattice

abstract:
  Statistical behavior of a classical $\phi ^{4}$ Hamiltonian lattice is
investigated from microscopic dynamics. The largest Lyapunov exponent and
entropies are considered for manifesting chaos and equipartition behaviors of
the system. It is found, for the first time, that for any large while finite
system size there exist two critical couplings for the transitions to
equipartitions, and the scaling behaviors of these lower and upper critical
couplings vs the system size is numerically obtained.


title:
Generalization of Sato equation and systems of multidimensional
  nonlinear Partial Differential Equations

abstract:
  This paper develops one of the methods for study of nonlinear Partial
Differential equations. We generalize Sato equation and represent the algorithm
for construction of some classes of nonlinear Partial Differential Equations
(PDE) together with solutions parameterized by the set of arbitrary functions.


title: Retracting fronts induce spatio-temporal intermittency

abstract:
  The intermittent route to spatio-temporal complexity is analyzed in a simple
model which displays a subcritical bifurcation without hysteresis. A new type
of spatio-temporal complexity is found, induced by fronts which "convectively
clean" the perturbations around an unstable state. The mechanism which leads to
the existence of these "retracting fronts" is analyzed in the frame of simple
models.


title: Chaotic mixing induced transitions in reaction-diffusion systems

abstract:
  We study the evolution of a localized perturbation in a chemical system with
multiple homogeneous steady states, in the presence of stirring by a fluid
flow. Two distinct regimes are found as the rate of stirring is varied relative
to the rate of the chemical reaction. When the stirring is fast localized
perturbations decay towards a spatially homogeneous state. When the stirring is
slow (or fast reaction) localized perturbations propagate by advection in form
of a filament with a roughly constant width and exponentially increasing
length. The width of the filament depends on the stirring rate and reaction
rate but is independent of the initial perturbation. We investigate this
problem numerically in both closed and open flow systems and explain the
results using a one-dimensional "mean-strain" model for the transverse profile
of the filament that captures the interplay between the propagation of the
reaction-diffusion front and the stretching due to chaotic advection.


title: Sampling Chaotic Trajectories Quickly in Parallel

abstract:
  The parallel computational complexity of the quadratic map is studied. A
parallel algorithm is described that generates typical pseudotrajectories of
length t in a time that scales as log t and increases slowly in the accuracy
demanded of the pseudotrajectory. Long pseudotrajectories are created in
parallel by putting together many short pseudotrajectories; Monte Carlo
procedures are used to eliminate the discontinuities between these short
pseudotrajectories and then suitably randomize the resulting long
pseudotrajectory. Numerical simulations are presented that show the scaling
properties of the parallel algorithm. The existence of the fast parallel
algorithm provides a way to formalize the intuitive notion that chaotic systems
do not generate complex histories.


title: Adaptive Detection of Instabilities: An Experimental Feasibility Study

abstract:
  We present an example of the practical implementation of a protocol for
experimental bifurcation detection based on on-line identification and feedback
control ideas. The idea is to couple the experiment with an on-line
computer-assisted identification/feedback protocol so that the closed-loop
system will converge to the open-loop bifurcation points. We demonstrate the
applicability of this instability detection method by real-time,
computer-assisted detection of period doubling bifurcations of an electronic
circuit; the circuit implements an analog realization of the Roessler system.
The method succeeds in locating the bifurcation points even in the presence of
modest experimental uncertainties, noise and limited resolution. The results
presented here include bifurcation detection experiments that rely on
measurements of a single state variable and delay-based phase space
reconstruction, as well as an example of tracing entire segments of a
codimension-1 bifurcation boundary in two parameter space.


title: Nonparametric modeling and spatiotemporal dynamical systems

abstract:
  In this article, it is described how to use statistical data analysis to
obtain models directly from data. The focus is put on finding nonlinearities
within a generalized additive model. These models are found by the means of
backfitting algorithms or more general versions, like the alternating
conditional expectation value method. The method is illustrated by numerically
generated data. As an application the example of vortex ripple dynamics, a
highly complex fluid-granular system is treated.


title:
Wave Structures and Nonlinear Balances in a Family of 1+1 Evolutionary
  PDEs

abstract:
  We study the following family of evolutionary 1+1 PDEs that describe the
balance between convection and stretching for small viscosity in the dynamics
of 1D nonlinear waves in fluids: \[ m_t + \underbrace{um_x \}
_{(-2mm)\hbox{convection}(-2mm)} + \underbrace{b u_xm \}
_{(-2mm)\hbox{stretching}(-2mm)} = \underbrace{\nu m_{xx}\
}_{(-2mm)\hbox{viscosity}}, \quad\hbox{with}\quad u=g*m . \] Here $u=g*m$
denotes $ u(x)=\int_{-\infty}^\infty g(x-y)m(y) dy . $ We study exchanges of
stability in the dynamics of solitons, peakons, ramps/cliffs, leftons,
stationary solutions and other solitary wave solutions associated with this
equation under changes in the nonlinear balance parameter $b$.


title: Mel'nikov method revisited

abstract:
  We illustrate a completely analytic approach to Mel'nikov theory, which is
based on a suitable extension of a classical method, and which is parallel and
-- at least in part -- complementary to the standard procedure. This approach
can be also applied to some ``degenerate'' situations, as to the case of
nonhyperbolic unstable points, or of critical points located at the infinity
(thus giving rise to unbounded orbits, e.g. the Keplerian parabolic orbits),
and it is naturally ``compatible'' with the presence of general symmetry
properties of the problem.


title:
Universal behaviour of entrainment due to coherent structures in
  turbulent shear flow

abstract:
  I suggest a solution to a persistent mystery in the physics of turbulent
shear flows: cumulus clouds rise to towering heights, practically without
entraining the ambient medium, while apparently similar turbulent jets in
general lose their identity within a small distance through entrainment and
mixing. From dynamical systems computations on a model chaotic vortical flow, I
show that entrainment and mixing due to coherent structures depend sensitively
on the relative speeds of different portions of the flow. A small change in
these speeds, effected for example by heating, drastically alters the sizes of
the KAM tori and the chaotic mixing region. The entrainment rate and, hence,
the lifetime of a turbulent shear flow, shows a universal, non-monotone
dependence on the heating.


title: Leray simulation of turbulent shear layers

abstract:
  We consider so-called Leray regularization of the convective contributions.
This gives rise to a subgrid parameterization which involves both explicit
filtering and (approximate) inversion. The Leray model also arises from the
alpha-modeling strategy derived via Kelvin's circulation theorem. We study the
dynamics associated with the Leray model in a turbulent mixing layer and
compare predictions with filtered DNS results and findings due to dynamic
(mixed) models. In particular, the kinetic energy, momentum thickness and
energy-spectra are analyzed, establishing favorable performance of the Leray
model and robustness at arbitrarily high Reynolds number. This is unique for a
similarity-type model that does not contain an explicit eddy-viscosity term.


title: Limiter Control of a Chaotic RF Transistor Oscillator

abstract:
  We report experimental control of chaos in an electronic circuit at 43.9 MHz,
which is the fastest chaos control reported in the literature to date. Limiter
control is used to stabilize a periodic orbit in a tuned collector transistor
oscillator modified to exhibit simply folded band chaos. The limiter is
implemented using a transistor to enable monitoring the relative magnitude of
the control perturbation. A plot of the relative control magnitude vs. limiter
level shows a local minimum at period-1 control, thereby providing strong
evidence that the controlled state is an unstable periodic orbit (UPO) of the
uncontrolled system.


title: Buoyant turbulent mixing in shear layers

abstract:
  Buoyancy effects in unstably stratified mixing layers express themselves
through gravity currents of heavy fluid which propagate in an ambient lighter
fluid. These currents are encountered in numerous geophysical flows, industrial
safety and environmental protection issues. During transition to turbulence a
strong distortion of the separating interface between regions containing
`heavy' or `light' fluid arises. The complexity of this interface will be used
to monitor the progress of the mixing. We concentrate on the enhancement of
surface-area and `surface-wrinkling' of the separating interface as a result of
gravity-effects. We also show that this process can be simulated quite
accurately using large-eddy simulation with dynamic subgrid modeling. However,
the subgrid resolution, defined as the ratio between filter-width Delta and
grid-spacing h, should be sufficiently high to avoid contamination due to
spatial discretization error effects.


title:
Event synchronization: a simple and fast method to measure synchronicity
  and time delay patterns

abstract:
  We propose a simple method to measure synchronization and time delay patterns
between signals. It is based on the relative timings of events in the time
series, defined e.g. as local maxima. The degree of synchronization is obtained
from the number of quasi-simultaneous appearances of events, and the delay is
calculated from the precedence of events in one signal with respect to the
other. Moreover, we can easily visualize the time evolution of the delay and
synchronization level with an excellent resolution.
  We apply the algorithm to short rat EEG signals, some of them containing
spikes. We also apply it to an intracranial human EEG recording containing an
epileptic seizure, and we propose that the method might be useful for the
detection of foci and for seizure prediction. It can be easily extended to
other types of data and it is very simple and fast, thus being suitable for
on-line implementations.


title:
Interaction of Coupled Higher Order Nonlinear SCHR\"Odinger Equation
  Solitons

abstract:
  The novel inelastic collision properties of two-soliton interaction for an
$n$-component coupled higher order nonlinear Schr\"odinger equation are
studied. Some interesting features of three soliton interactions, related to
the integrability of the $n$-component coupled higher order nonlinear
Schr\"odinger equation are also discussed.


title: Excitation of travelling multibreathers in anharmonic chains

abstract:
  We study the dynamics of the "externally" forced and damped Fermi-Pasta-Ulam
(FPU) 1D lattice. The forcing has the spatial symmetry of the Fourier mode with
wavenumber p and oscillates sinusoidally in time with the frequency omega. When
omega is in the phonon band, the p-mode becomes modulationally unstable above a
critical forcing, which we determine analytically in terms of the parameters of
the system. For omega above the phonon band, the instability of the p-mode
leads to the formation of a travelling multibreather, that, in the
low-amplitude limit could be described in terms of soliton solutions of a
suitable driven-damped nonlinear Schroedinger (NLS) equation. Similar
mechanisms of instability could show up in easy-axis magnetic structures, that
are governed by such NLS equations.


title: Integrable tops and non-commutative torus

abstract:
  We consider the hydrodynamics of the ideal fluid on a 2-torus and its Moyal
deformations. The both type of equations have the form of the Euler-Arnold
tops. The Laplace operator plays the role of the inertia-tensor. It is known
that 2-d hydrodynamics is non-integrable. After replacing of the Laplace
operator by a distinguish pseudo-differential operator the deformed system
becomes integrable. It is an infinite rank Hitchin system over an elliptic
curve with transition functions from the group of the non-commutative torus. In
the classical limit we obtain an integrable analog of the hydrodynamics on a
torus with the inertia-tensor operator $\bar\partial^2$ instead of the
conventional Laplace operator $\partial\bar\partial$.


title:
Broken symmetries and pattern formation in two-frequency forced Faraday
  waves

abstract:
  We exploit the presence of approximate (broken) symmetries to obtain general
scaling laws governing the process of pattern formation in weakly damped
Faraday waves. Specifically, we consider a two-frequency forcing function and
trace the effects of time translation, time reversal and Hamiltonian structure
for three illustrative examples: hexagons, two-mode superlattices, and two-mode
rhomboids. By means of explicit parameter symmetries, we show how the size of
various three-wave resonant interactions depends on the frequency ratio m:n and
on the relative temporal phase of the two driving terms. These symmetry-based
predictions are verified for numerically calculated coefficients, and help
explain the results of recent experiments.


title:
Synergetic System Analysis for the Delay-Induced Hopf Bifurcation in the
  Wright Equation

abstract:
  We apply the synergetic elimination procedure for the stable modes in
nonlinear delay systems close to a dynamical instability and derive the normal
form for the delay-induced Hopf bifurcation in the Wright equation. The
resulting periodic orbit is confirmed by numerical simulations.


title:
Lax pair formulation of the N=4 Toda chain (KdV) hierarchy in N=4
  superspace

abstract:
  Lax pair and Hamiltonian formulations of the N=4 supersymmetric Toda chain
(KdV) hierarchy in N=4 superspace are proposed. The general formulae for the
infinite tower of its bosonic flows in terms of the Lax operator in N=4
superspace are derived. A new N=4 superfield basis in which the flows are local
is constructed and its embedding in the N=4 O(4) superconformal supercurrent is
established. A proof that the flows possess five complex conjugations and
aninfinite-dimensional group of discrete symmetries in N=4 superspace is
presented. A relation between the two descriptions of the hierarchy in N=4
superspace used in the literature is established. All known N=2 superfield
representations of the N=4 KdV hierarchy are shown to derive from our N=4
superspace Lax representation.


title:
Nonlinear balance and exchange of stability in dynamics of solitons,
  peakons, ramps/cliffs and leftons in a 1+1 nonlinear evolutionary pde

abstract:
  We study exchange of stability in the dynamics of solitary wave solutions
under changes in the nonlinear balance in a 1+1 evolutionary partial
differential equation related both to shallow water waves and to turbulence. We
find that solutions of the equation $ m_t + um_x +b u_xm = \nu m_{xx} $ with $m
= u - \alpha^2 u_{xx}$ for fluid velocity $u(x,t)$ change their behavior at the
special values $b=0,\pm1,\pm2,\pm3$.


title: Large Deviations and a Fluctuation Symmetry for Chaotic Homeomorphisms

abstract:
  We consider expansive homeomorphisms with the specification property. We give
a new simple proof of a large deviation principle for Gibbs measures
corresponding to a regular potential and we establish a general symmetry of the
rate function for the large deviations of the antisymmetric part, under
time-reversal, of the potential. This generalizes the Gallavotti-Cohen
fluctuation theorem to a larger class of chaotic systems.


title:
Higher-order hbar corrections in the semiclassical quantization of
  chaotic billiards

abstract:
  In the periodic orbit quantization of physical systems, usually only the
leading-order hbar contribution to the density of states is considered.
Therefore, by construction, the eigenvalues following from semiclassical trace
formulae generally agree with the exact quantum ones only to lowest order of
hbar. In different theoretical work the trace formulae have been extended to
higher orders of hbar. The problem remains, however, how to actually calculate
eigenvalues from the extended trace formulae since, even with hbar corrections
included, the periodic orbit sums still do not converge in the physical domain.
For lowest-order semiclassical trace formulae the convergence problem can be
elegantly, and universally, circumvented by application of the technique of
harmonic inversion. In this paper we show how, for general scaling chaotic
systems, also higher-order hbar corrections to the Gutzwiller formula can be
included in the harmonic inversion scheme, and demonstrate that corrected
semiclassical eigenvalues can be calculated despite the convergence problem.
The method is applied to the open three-disk scattering system, as a prototype
of a chaotic system.


title:
Possibilities of the Discrete Fourier Transform for Determining the
  Order-Chaos Transition in a Dynamical System

abstract:
  This paper is devoted to a discussion of the Discrete Fourier Transform (DFT)
representation of a chaotic finite-duration sequence. This representation has
the advantage that is itself a finite-duration sequence corresponding to
samples equally spaced in the frequency domain. The Fast Fourier Transform
(FFT) algoritm allows us an effective computation, and it can be applied to a
relatively short time series. DFT representation requirements were analized and
applied for determining the order-chaos transition in a nonlinear system
described by the equation $x[n+1]=rx[n](1-x[n])$. Its effectiveness was
demonstrated by comparing the results with those obtained by calculating the
largest Lyapounov exponent for the time series set, obtained from the logistic
equation.


title: Geometric discretization of the Koenigs nets

abstract:
  We introduce the Koenigs lattice, which is a new integrable reduction of the
quadrilateral lattice (discrete conjugate net) and provides natural integrable
discrete analogue of the Koenigs net. We construct the Darboux-type
transformations of the Koenigs lattice and we show permutability of
superpositions of such transformations, thus proving integrability of the
Koenigs lattice. We also investigate the geometry of the discrete Koenigs
transformation. In particular we characterize the Koenigs transformation in
terms of an involution determined by a congruence conjugate to the lattice.


title: Decentralization as Organizing Principle of Emergent Urban Structures

abstract:
  With a view to the ongoing Bologna project
(www.arXiv.org/pdf/nlin.AO/0109025) general organizing principles of emergent
structures in social systems are being discussed with a view to the meaning of
decentralization. It is proposed to introduce decentralization as a principle
for organizing emergent structures in a generic way utilizing aspects of the
insight gained by the Santa Fe school dealing with self-organized criticality.
The techniques utilized come from graph theory, category theory, and in
particular quantum gravity, which bear a strong potential for a multitude of
applications in research fields with a significant interdisciplinary scope.
This is especially important for applications in the organization of social
systems which usually call for an interaction of logic and hermeneutic.


title: Anomalous and dimensional scaling in anisotropic turbulence

abstract:
  We present a numerical study of anisotropic statistical fluctuations in
homogeneous turbulent flows. We give an argument to predict the dimensional
scaling exponents, (p+j)/3, for the projections of p-th order structure
function in the j-th sector of the rotational group. We show that measured
exponents are anomalous, showing a clear deviation from the dimensional
prediction. Dimensional scaling is subleading and it is recovered only after a
random reshuffling of all velocity phases, in the stationary ensemble. This
supports the idea that anomalous scaling is the result of a genuine inertial
evolution, independent of large-scale behavior.


title: A Laplace ladder of discrete Laplace equations

abstract:
  The notion of a Laplace ladder for a discrete analogue of the
  Laplace equation is presented. The adjoint of the discrete Moutard equation
and a discrete counterpart of the nonlinear form of Goursat equation are
introduced.


title:
Semiclassical theory of spin-orbit interactions using spin coherent
  states

abstract:
  We formulate a semiclassical theory for systems with spin-orbit interactions.
Using spin coherent states, we start from the path integral in an extended
phase space, formulate the classical dynamics of the coupled orbital and spin
degrees of freedom, and calculate the ingredients of Gutzwiller's trace formula
for the density of states. For a two-dimensional quantum dot with a spin-orbit
interaction of Rashba type, we obtain satisfactory agreement with fully
quantum-mechanical calculations. The mode-conversion problem, which arose in an
earlier semiclassical approach, has hereby been overcome.

categories: nlin.CD cond-mat.mes-hall math-ph math.MP


title: One-fluid description of turbulently flowing suspension

abstract:
  We suggested a one-fluid model of a turbulent dilute suspension which
accounts for the ``two-way'' fluid-particle interactions by $k$-dependent
effective density of suspension and additional damping term in the
Navier-Stokes equation. We presented analytical description of the particle
modification of turbulence including scale invariant suppression of a small $k$
part of turbulent spectrum (independent of the particle response time) and
possible enhancemenent of large $k$ region [up to the factor $(1+\phi)^{2/3}$].
Our results are in agreement with qualitative picture of isotropic homogeneous
turbulence of dilute suspensions previously observed in laboratory and
numerical experiments.


title: Different regimes of synchronization in nonidentical time-delayed maps

abstract:
  We study the synchronization of time-delayed nonidentical maps subject to
unidirectional (master-slave) coupling. The individual dynamics of the maps
have a delay n1, and the coupling acts with a delay n2. We show analytically
that, suitably tuning the slave map parameters, two distinct synchronization
regimes can occur. In one regime the lag time between the slave and the master
maps is given by the delay of the coupling, n2, while in the other regime is
given by the difference between the delays, n1-n2. We analyze the effect of the
coupling strength on the different synchronization regimes in logistic and
H\'enon maps.


title:
Periodic Solutions of Nonlinear Equations Obtained by Linear
  Superposition

abstract:
  We show that a type of linear superposition principle works for several
nonlinear differential equations. Using this approach, we find periodic
solutions of the Kadomtsev-Petviashvili (KP) equation, the nonlinear
Schrodinger (NLS) equation, the $\lambda \phi^4$ model, the sine-Gordon
equation and the Boussinesq equation by making appropriate linear
superpositions of known periodic solutions. This unusual procedure for
generating solutions is successful as a consequence of some powerful, recently
discovered, cyclic identities satisfied by the Jacobi elliptic functions.


title:
Heat Conduction and Entropy Production in a One-Dimensional
  Hard-Particle Gas

abstract:
  We present large scale simulations for a one-dimensional chain of hard-point
particles with alternating masses. We correct several claims in the recent
literature based on much smaller simulations. Both for boundary conditions with
two heat baths at different temperatures at both ends and from heat current
autocorrelations in equilibrium we find heat conductivities kappa to diverge
with the number N of particles. These depended very strongly on the mass
ratios, and extrapolation to N -> infty resp. t -> infty is difficult due to
very large finite-size and finite-time corrections. Nevertheless, our data seem
compatible with a universal power law kappa ~ N^alpha with alpha approx 0.33.
This suggests a relation to the Kardar-Parisi-Zhang model. We finally show that
the hard-point gas with periodic boundary conditions is not chaotic in the
usual sense and discuss why the system, when kept out of equilibrium, leads
nevertheless to energy dissipation and entropy production.


title: Nonlinearity effects in the kicked oscillator

abstract:
  The quantum kicked oscillator is known to display a remarkable richness of
dynamical behaviour, from ballistic spreading to dynamical localization. Here
we investigate the effects of a Gross Pitaevskii nonlinearity on quantum
motion, and provide evidence that the qualitative features depend strongly on
the parameters of the system.


title:
Construction of particular solutions to nonlinear equations of
  Mathematical Physics by using matrix algebraic equation

abstract:
  The paper develops the method for construction of the families of particular
solutions to the nonlinear Partial Differential Equations (PDE) without
relation to the complete integrability. Method is based on the specific link
between algebraic matrix equations and PDE. Example of (2+2)-dimensional
generalization of Burgers equation is given.


title:
Parry measure and the topological entropy of chaotic repellers embedded
  within chaotic attractors

abstract:
  We study the topological entropy of chaotic repellers formed by those points
in a given chaotic attractor that never visit some small forbidden hole-region
in the phase space. The hole is a set of points in the phase space that have a
sequence $\alpha=(\alpha_0\alpha_1...\alpha_{l-1})$ as the first $l$ letters in
their itineraries. We point out that the difference between the topological
entropies of the attractor and the embedded repeller is for most choices of
$\alpha$ approximately equal to the Parry measure corresponding to $\alpha$,
$\mu_P(\alpha)$. When the hole encompasses a point of a short periodic orbit,
the entropy difference is significantly smaller than $\mu_P(\alpha)$. This
discrepancy is described by the formula which relates the length of the short
periodic orbit, the Parry measure $\mu_P(\alpha)$, and the topological
entropies of the two chaotic sets.


title: Periodic orbit quantization of chaotic systems with strong pruning

abstract:
  The three-disk system, which for many years has served as a paradigm for the
usefulness of cycle expansion methods, represents an extremely hard problem to
semiclassical quantization when the disks are moved closer and closer together,
since (1) pruning of orbits sets in, rendering the symbolic code incomplete,
and (2) the number of orbits necessary to obtain accurate semiclassical
eigenvalues proliferates exponentially. In this note we show that an
alternative method, viz. harmonic inversion, which does not rely on the
existence of complete symbolic dynamics or other specific properties of
systems, provides a key to solving the problem of semiclassical quantization of
systems with strong pruning. For the closed three-disk system we demonstrate
how harmonic inversion, augmented by a signal cross-correlation technique,
allows one to semiclassically calculate the energies up to the 28th excited
state with high accuracy.