title:
A New Parameter $F$ to Classify Cellular Automata Rule Table Space and a
  Phase Diagram in $\lambda-F$ Plane

abstract:
  It is shown that for the N-neighbor and K-state cellular automata, the class
II, class III and class IV patterns coexist at least in the range $\frac{1}{K}
\le \lambda \le 1-\frac{1}{K} $. The mechanism which determines the difference
between the pattern classes at a fixed $\lambda$ is found, and it is studied
quantitatively by introducing a new parameter $F$. Using the parameter F and
$\lambda$, the phase diagram of cellular automata is obtained for 5-neighbor
and 4-state cellular automata. PACS: 89.75.-k Complex Systems


title: Anderson Localization in Atoms

abstract:
  A statistical analysis of the ionization yield of one-dimensional,
periodically driven hydrogen Rydberg states is provided. We find excellent
agreement with predictions for the conductance across an Anderson-localized,
quasi one-dimensional, disordered wire, in the semiclassical limit of highly
excited atomic initial states.


title:
Signatures of Anderson localization in the ionization rates of
  periodically driven Rydberg states

abstract:
  We provide a statistical characterization of the ionization yield of
one-dimensional, periodically driven Rydberg states of atomic hydrogen, in the
spirit of Anderson localization theory. We find excellent agreement with
predictions for the conductance across an Anderson localized, quasi
one-dimensional, disordered wire, in the semiclassical limit of highly excited
atomic initial states. For the moderate atomic excitations typically
encountered in state of the art laboratory experiments, finite-size effects
induce significant deviations from the solid-state picture. However, large
scale fluctuations of the atomic conductance prevail and are robust when
averaged over a finite interval of driving field amplitudes, as inevitably done
in the experiment.


title:
Classical R-matrix theory of dispersionless systems: II. (2+1)-dimension
  theory

abstract:
  A systematic way of construction of (2+1)-dimensional dispersionless
integrable Hamiltonian systems is presented. The method is based on the
so-called central extension procedure and classical R-matrix applied to the
Poisson algebras of formal Laurent series. Results are illustrated with the
known and new (2+1)-dimensional dispersionless systems.


title: Chaotic Free-Space Laser Communication over Turbulent Channel

abstract:
  The dynamics of errors caused by atmospheric turbulence in a
self-synchronizing chaos based communication system that stably transmits
information over a $\sim$5 km free-space laser link is studied experimentally.
Binary information is transmitted using a chaotic sequence of short-term pulses
as carrier. The information signal slightly shifts the chaotic time position of
each pulse depending on the information bit. We report the results of an
experimental analysis of the atmospheric turbulence in the channel and the
impact of turbulence on the Bit-Error-Rate (BER) performance of this chaos
based communication system.


title: On Twistor Solutions of the dKP Equation

abstract:
  The factorization problem for the group of canonical transformations close to
the identity and the corresponding twistor equations for an ample family of
canonical variables are considered. A method to deal with these reductions is
developed for the construction classes of nontrivial solutions of the dKP
equation.


title: Integrable systems whose spectral curve is the graph of a function

abstract:
  For some integrable systems, such as the open Toda molecule, the spectral
curve of the Lax representation becomes the graph $C = \{(\lambda,z) \mid z =
A(\lambda)\}$ of a function $A(\lambda)$. Those integrable systems provide an
interesting ``toy model'' of separation of variables. Examples of this type of
integrable systems are presented along with generalizations for which
$A(\lambda)$ lives on a cylinder, a torus or a Riemann surface of higher genus.


title: Monodromy approach to the scaling limits in the isomonodromy systems

abstract:
  The isomonodromy deformation method is applied to the scaling limits in the
linear NxN matrix equations with rational coefficients to obtain the
deformation equations for the algebraic curves which describe the local
behavior of the reduced versions for the relevant isomonodromy deformation
equations. The approach is illustrated by the study of the algebraic curve
associated to the n-large asymptotics in the sequence of the bi-orthogonal
polynomials with cubic potentials.


title: Irregular diffusion in the bouncing ball billiard

abstract:
  We call a system bouncing ball billiard if it consists of a particle that is
subjected to a constant vertical force and bounces inelastically on a
one-dimendional vibrating periodically corrugated floor. Here we choose
circular scatterers that are very shallow, hence this billiard is a
deterministic diffusive version of the well-known bouncing ball problem on a
flat vibrating plate. Computer simulations show that the diffusion coefficient
of this system is a highly irregular function of the vibration frequency
exhibiting pronounced maxima whenever there are resonances between the
vibration frequency and the average time of flight of a particle. In addition
there exist irregularities on finer scales that are due to higher-order
dynamical correlations pointing towards a fractal structure of this curve. We
analyze the diffusive dynamics by classifying the attracting sets and by
working out a simple random walk approximation for diffusion, which is
systematically refined by using a Green-Kubo formula.


title:
Exploring the cooperative regimes in a model of agents without memory or
  "tags": indirect reciprocity vs. selfish incentives

abstract:
  The self-organization in cooperative regimes in a simple mean-field version
of a model based on "selfish" agents which play the Prisoner's Dilemma (PD)
game is studied. The agents have no memory and use strategies not based on
direct reciprocity nor 'tags'. Two variables are assigned to each agent $i$ at
time $t$, measuring its capital $C(i;t)$ and its probability of cooperation
$p(i;t)$. At each time step $t$ a pair of agents interact by playing the PD
game. These 2 agents update their probability of cooperation $p(i)$ as follows:
they compare the profits they made in this interaction $\delta C(i;t)$ with an
estimator $\epsilon(i;t)$ and, if $\delta C(i;t) \ge \epsilon(i;t)$, agent $i$
increases its $p(i;t)$ while if $\delta C(i;t) < \epsilon(i;t)$ the agent
decreases $p(i;t)$. The 4!=24 different cases produced by permuting the four
Prisoner's Dilemma canonical payoffs 3, 0, 1, and 5 -
corresponding,respectively, to $R$ (reward), $S$ (sucker's payoff), $T$
(temptation to defect) and $P$ (punishment) - are analyzed. It turns out that
for all these 24 possibilities, after a transient,the system self-organizes
into a stationary state with average equilibrium probability of cooperation
$\bar{p}_\infty$ = constant $ > 0$.Depending on the payoff matrix, there are
different equilibrium states characterized by their average probability of
cooperation and average equilibrium per-capita-income
($\bar{p}_\infty,\bar{\delta C}_\infty$).

categories: nlin.AO cond-mat cs.CE hep-lat nlin.CG physics.soc-ph


title:
Exact Localized Solutions of Quintic Discrete Nonlinear Schr\"odinger
  Equation

abstract:
  We study a new quintic discrete nonlinear Schr\"odinger (QDNLS) equation
which reduces naturally to an interesting symmetric difference equation of the
form $\phi_{n+1}+\phi_{n-1}=F(\phi_n)$. Integrability of the symmetric mapping
is checked by singularity confinement criteria and growth properties. Some new
exact localized solutions for integrable cases are presented for certain sets
of parameters. Although these exact localized solutions represent only a small
subset of the large variety of possible solutions admitted by the QDNLS
equation, those solutions presented here are the first example of exact
localized solutions of the QDNLS equation. We also find chaotic behavior for
certain parameters of nonintegrable case.

categories: nlin.PS math-ph math.MP nlin.SI physics.optics


title:
Charge transport in a nonlinear, three--dimensional DNA model with
  disorder

abstract:
  We study the transport of charge due to polarons in a model of DNA which
takes in account its 3D structure and the coupling of the electron wave
function with the H--bond distortions and the twist motions of the base pairs.
Perturbations of the ground states lead to moving polarons which travel long
distances. The influence of parametric and structural disorder, due to the
impact of the ambient, is considered, showing that the moving polarons survive
to a certain degree of disorder. Comparison of the linear and tail analysis and
the numerical results makes possible to obtain further information on the
moving polaron properties.


title:
Heteroclinic intersections between Invariant Circles of
  Volume-Preserving Maps

abstract:
  We develop a Melnikov method for volume-preserving maps with codimension one
invariant manifolds. The Melnikov function is shown to be related to the flux
of the perturbation through the unperturbed invariant surface. As an example,
we compute the Melnikov function for a perturbation of a three-dimensional map
that has a heteroclinic connection between a pair of invariant circles. The
intersection curves of the manifolds are shown to undergo bifurcations in
homology


title: On complete integrability of the generalized Weierstrass system

abstract:
  In this paper we study certain aspects of the complete integrability of the
Generalized Weierstrass system in the context of the Sinh-Gordon type equation.
Using the conditional symmetry approach, we construct the B\"{a}cklund
transformation for the Generalized Weierstrass system which is determined by
coupled Riccati equations. Next a linear spectral problem is found which is
determined by nonsingular $2 \times 2$ matrices based on an $sl (2, \mathbb C)$
representation. We derive the explicit form of the Darboux transformation for
the Weierstrass system. New classes of multisoliton solutions of the
Generalized Weierstrass system are obtained through the use of the B\"{a}cklund
transformation and some physical applications of these results in the area of
classical string theory are presented.


title: Amplification by stochastic interference

abstract:
  A new method is introduced to obtain a strong signal by the interference of
weak signals in noisy channels. The method is based on the interference of 1/f
noise from parallel channels. One realization of stochastic interference is the
auditory nervous system. Stochastic interference may have broad potential
applications in the information transmission by parallel noisy channels.


title: Reflectionless analytic difference operators III. Hilbert space aspects

abstract:
  In the previous two parts of this series of papers, we introduced and studied
a large class of analytic difference operators admitting reflectionless
eigenfunctions, focusing on algebraic and function-theoretic features in the
first part, and on connections with solitons in the second one. In this third
part we study our difference operators from a quantum mechanical viewpoint. We
show in particular that for an arbitrary difference operator $A$ from a certain
subclass, the reflectionless $A$-eigenfunctions can be used to construct an
unbounded self-adjoint reflectionless operator $\hat{A}$ on $L^2({\mathbb
R},dx$ whose action on a suitable core coincides with that of $A$.


title:
Solitary wave solutions and their velocity selections and prohibitions
  for a general Boussinesq type fluid model

abstract:
  The possible solitary wave solutions for a general Boussinesq (GBQ) type
fluid model are studied analytically. After proving the non-Painlev\'e
integrability of the model, the first type of exact explicit travelling
solitary wave with a special velocity selection is found by the truncated
Painlev\'e expansion. The general solitary waves with different travelling
velocities can be studied by casting the problems to the Newtonian
quasi-particles moving in some proper one dimensional potential fields. For
some special velocity selections, the solitary waves possess different shapes,
say, the left moving solitary waves may possess different shapes and/or
amplitudes with those of the right moving solitons. For some other velocities,
the solitary waves are completely prohibited. There are three types of GBQ
systems (GBQSs) according to the different selections of the model parameters.
For the first type of GBQS, both the faster moving and lower moving solitary
waves allowed but the solitary waves with"middle" velocities are prohibit. For
the second type of GBQS all the slower moving solitary waves are completely
prohibit while for the third type of GBQS only the slower moving solitary waves
are allowed.


title: Rational Approximate Symmetries of KdV Equation

abstract:
  We construct one-parameter deformation of the Dorfman Hamiltonian operator
for the Riemann hierarchy using the quasi-Miura transformation from topological
field theory. In this way, one can get the approximately rational symmetries of
KdV equation and then investigate its bi-Hamiltonian structure.


title:
Phase shift experiments identifying Kramers doublets in a chaotic
  superconducting microwave billiard of threefold symmetry

abstract:
  The spectral properties of a two-dimensional microwave billiard showing
threefold symmetry have been studied with a new experimental technique. This
method is based on the behavior of the eigenmodes under variation of a phase
shift between two input channels, which strongly depends on the symmetries of
the eigenfunctions. Thereby a complete set of 108 Kramers doublets has been
identified by a simple and purely experimental method. This set clearly shows
Gaussian unitary ensemble statistics, although the system is time-reversal
invariant.


title:
Invariant Sets and Explicit Solutions to a Third-Order Model for the
  Shearless Stratified Turbulent Flow

abstract:
  We study dynamics of the shearless stratified turbulent flows. Using the
method of differential constraints we find a class of explicit solutions to the
problem under consideration and establish that the differential constraint
obtained coincides with the well-known Zeman--Lumley model for stratified
flows.


title: Breathers in FPU systems, near and far from the phonon band

abstract:
  There exists a recent mathematical proof on the existence of small amplitude
breathers in FPU systems near the phonon band, which includes a prediction of
their amplitude and width. In this work we obtain numerically these breathers,
and calculate the range of validity of the predictions, which extends
relatively far from the phonon band. There exist also large amplitude breathers
with the same frequency, with the consequence that there is an energy gap for
breather creation in these systems.


title: Chaotic Mixing in a Torus Map

abstract:
  The advection and diffusion of a passive scalar is investigated for a map of
the 2-torus. The map is chaotic, and the limit of almost-uniform stretching is
considered. This allows an analytic understanding of the transition from a
phase of constant scalar variance (for short times) to exponential decay (for
long times). This transition is embodied in a short superexponential phase of
decay. The asymptotic state in the exponential phase is an eigenfunction of the
advection-diffusion operator, in which most of the scalar variance is
concentrated at small scales, even though a large-scale mode sets the decay
rate. The duration of the superexponential phase is proportional to the
logarithm of the exponential decay rate; if the decay is slow enough then there
is no superexponential phase at all.


title: The Onset of Chaos in Spinning Particle Models

abstract:
  The onset of chaos in one-dimensional spinning particle models derived from
pseudoclassical mechanical hamiltonians with a bosonic Duffing potential is
examined. Using the Melnikov method, we indicate the presence of homoclinic
entanglements in models with general potentials for the spins, and thus show
that chaotic motions occur in these models.


title: How to excite the internal modes of sine-Gordon solitons

abstract:
  We investigate the dynamics of the sine-Gordon solitons perturbed by
spatiotemporal external forces. We prove the existence of internal (shape)
modes of sine-Gordon solitons when they are in the presence of inhomogeneous
space-dependent external forces, provided some conditions (for these forces)
hold. Additional periodic time-dependent forces can sustain oscillations of the
soliton width. We show that, in some cases, the internal mode even can become
unstable, causing the soliton to decay in an antisoliton and two solitons. In
general, in the presence of spatiotemporal forces the soliton behaves as a
deformable (non-rigid) object. A soliton moving in an array of inhomogeneities
can also present sustained oscillations of its width. There are very important
phenomena (like the soliton-antisoliton collisions) where the existence of
internal modes plays a crucial role. We show that, under some conditions, the
dynamics of the soliton shape modes can be chaotic. A short report of some of
our results has been published in [J. A. Gonzalez et al., Phys. Rev. E, 65
(2002) 065601(R)].


title: New Scenario to Chaos Transition in the Mappings with Discontinuities

abstract:
  We consider a many-parametric piecewise mapping with discontinuity. That is a
one dimensional model of singular dynamic system. The stability boundary are
calculated analytically and numerically. New typical features of stable cycle
structures and scenario to chaos transition provoked by discontinuity are
found.


title:
Projective differential geometry of higher reductions of the
  two-dimensional Dirac equation

abstract:
  We investigate reductions of the two-dimensional Dirac equation imposed by
the requirement of the existence of a differential operator $D_n$ of order $n$
mapping its eigenfunctions to adjoint eigenfunctions. For first order operators
these reductions (and multi-component analogs thereof) lead to the Lame
equations descriptive of orthogonal coordinate systems. Our main observation is
that $n$-th order reductions coincide with the projective-geometric
`Gauss-Codazzi' equations governing special classes of line congruences in the
projective space $P^{2n-1}$, which is the projectivised kernel of $D_n$. In the
second order case this leads to the theory of $W$-congruences in $P^3$ which
belong to a linear complex, while the third order case corresponds to isotropic
congruences in $P^5$. Higher reductions are compatible with odd-order flows of
the Davey-Stewartson hierarchy. All these flows preserve the kernel $D_n$, thus
defining nontrivial geometric evolutions of line congruences. Multi-component
generalizations are also discussed. The correspondence between geometric
picture and the theory of integrable systems is established; the definition of
the class of reductions and all geometric objects in terms of the
multicomponent KP hierarchy is presented. Generating forms for reductions of
arbitrary order are constructed.


title: Emergence of patterns in driven and in autonomous spatiotemporal systems

abstract:
  The relationship between a driven extended system and an autonomous
spatiotemporal system is investigated in the context of coupled map lattice
models. Specifically, a locally coupled map lattice subjected to an external
drive is compared to a coupled map system with similar local couplings plus a
global interaction. It is shown that, under some conditions, the emergent
patterns in both systems are analogous. Based on the knowledge of the dynamical
responses of the driven lattice, we present a method that allows the prediction
of parameter values for the emergence of ordered spatiotemporal patterns in a
class of coupled map systems having local coupling and general forms of global
interactions.


title: Fronts in reactive convection: bounds, stability and instability

abstract:
  We consider front propagation in a reactive Boussinesq system in an infinite
vertical strip. We establish nonlinear stability of planar fronts for narrow
domains when the Rayleigh number is not too large. Planar fronts are shown to
be linearly unstable with respect to long wavelength perturbations if the
Rayleigh number is sufficiently large. We also prove uniform bounds on the bulk
burning rate and the Nusselt number in the KPP reaction case.


title:
The Hirota equation over finite fields. Algebro-geometric approach and
  multisoliton solutions

abstract:
  We consider the Hirota equation (the discrete analog of the generalized Toda
system) over a finite field. We present the general algebro-geometric method of
construction of solutions of the equation. As an example we construct analogs
of the multisoliton solutions for which the wave functions and the
$\tau$-function can be found using rational functions. Within the class of
multisoliton solutions we isolate generalized breather-type solutions which
have no direct counterparts in the complex field case.


title: Locating periodic orbits by Topological Degree theory

abstract:
  We consider methods based on the topological degree theory to compute
periodic orbits of area preserving maps. Numerical approximations of the
Kronecker integral and the application of Stenger's method allows us to compute
the value of the topological degree in a bounded region of the phase space. If
the topological degree of an appropriate set of equations has a non--zero
value, we know that there exists at least one periodic orbit of a given period
in the given region. We discuss in detail the problems that these methods face,
due to the existence of periodic orbits near the domain's boundary and due to
the discontinuity curves that appear in maps defined on the torus. We use the
characteristic bisection method for actually locating periodic orbits. We apply
this method successfully, both to the standard map, which is a map defined on
the torus, and to the beam--beam map which is a continuous map on the plane.
Specifically we find a large number of periodic orbits of periods up to 40,
which give us a clear picture of the dynamics of both maps.


title:
A Gibbs-like measure for single-time, multi-scale energy transfer in
  stochastic signals and Shell Model of turbulence

abstract:
  A Gibbs-like approach for simultaneous multi-scale correlation functions in
random, time-dependent, multiplicative processes for the turbulent energy
cascade is investigated. We study the optimal log-normal Gibbs-like
distribution able to describe the subtle effects induced by non-trivial time
dependency on both single-scale (structure functions) and multi-scale
correlation functions. We provide analytical expression for the general
multi-scale correlation functions in terms of the two-point correlations
between multipliers and we show that the log-normal distribution is already
accurate enough to reproduce quantitatively many of the observed behavior. The
main result is that non-trivial time effects renormalize the Gibbs-like
effective potential necessary to describe single-time statistics. We also
present a generalization of this approach to more general, non log-normal,
potential. In the latter case one obtains a formal expansion of both structure
functions and multi-scale correlations in terms of cumulants of all orders.


title: Is there chaos in the electron microscope?

abstract:
  High-temperature superconductor $Bi_{2}Sr_{2}CaCu_{2}O_{8}+x$ has been
investigated by the high-resolution electron microscope (HREM) and the
photodensitometric technique in order to resolve the sub-atomic shifts in the
modulated structure. This investigation has shown that the background noise is
pronounced, indicating some kind of ordering in certain crystallographic
directions. We have found that the "mapping" of the charge densities by the
inverse Fourier transform of the diffracted electron image and the connections
to the crystal structure can be easily established in the case of elastically,
as well as the inelastically scattered electrons. The order of the details in
so obtained "inelastic" electron "micrographs", as well as the dependence of
the structure of the EM image on the initial conditions of the inverse Fourier
transform, leads to the conclusion that there is an order emerging from the
diffuse scattered electron diffraction patterns. Data sets from digitalized
densitograms are analysed by the Rescaled range (R/S) method in order to study
fractal and long-range correlation properties of the inelastic scattered
electrons in the "noise" region between Bragg reflections. The results of the
R/S analysis showed that the value of the Hurst exponent was H$\neq$ 0.5,
indicating that the "ordering" of the noise in the Inverse (Fourier) space was
much more pronounced at longer distances (about 440 atom spacings), then for
shorter distances of about 55 atom spacings.


title: Perturbed phase-space dynamics of hard-disk fluids

abstract:
  The Lyapunov spectrum describes the exponential growth, or decay, of
infinitesimal phase-space perturbations. The perturbation associated with the
maximum Lyapunov exponent is strongly localized in space, and only a small
fraction of all particles contributes to the perturbation growth at any instant
of time. This fraction converges to zero in the thermodynamic
large-particle-number limit. For hard-disk and hard-sphere systems the
perturbations belonging to the small positive and large negative exponents are
coherently spread out and form orthogonal periodic structures in space, the
``Lyapunov modes''. There are two types of mode polarizations, transverse and
longitudinal. The transverse modes do not propagate, but the longitudinal modes
do with a speed about one third of the sound speed. We characterize the
symmetry and the degeneracy of the modes. In the thermodynamic limit the
Lyapunov spectrum has a diverging slope near the intersection with the
abscissa. No positive lower bound exists for the positive exponents. The mode
amplitude scales with the inverse square root of the particle number as
expected from the normalization of the perturbation vectors.


title: The Painlev\'e methods

abstract:
  This short review is an introduction to a great variety of methods, the
collection of which is called the Painlev\'e analysis, intended at producing
all kinds of exact (as opposed to perturbative) results on nonlinear equations,
whether ordinary, partial, or discrete.


title: The Discrete Nonlinear Schr\"odinger equation - 20 Years on

abstract:
  We review work on the Discrete Nonlinear Schr\"odinger (DNLS) equation over
the last two decades.


title:
Applications of recurrence quantified analysis to study the dynamics of
  chaotic chemical reaction

abstract:
  Recurrence plot is a quite easy tool to be used in time series analysis,in
particular for measuring unstable periodic orbits embedded in a chaotic
dynamical system. Recurrence quantified analysis (RQA) is an advance tool that
allows the study of intrinsic complexity of dynamical system with a set of few
parameters. We use RQA for measuring chaotic transitions of NADH chemical
reaction and determine numerically its characteristic parameters such as:
Correlation integral, information entropy, Maximal Lyapunov's exponent, etc.
For this work we have developed command sets with performance better than
TISEAN package


title: Scalar products of symmetric functions and matrix integrals

abstract:
  We present relations between Hirota-type bilinear operators, scalar products
on spaces of symmetric functions and integrals defining matrix model partition
functions. Using the fermionic Fock space representation, a proof of the
expansion of an associated class of KP and 2-Toda tau functions $\tau_{r,n}$ in
a series of Schur functions generalizing the hypergeometric series is given and
related to the scalar product formulae. It is shown how special cases of such
$\tau$-functions may be identified as formal series expansions of partition
functions. A closed form exapnsion of $\log \tau_{r,n}$ in terms of Schur
functions is derived.


title:
A Generalization of Chaitin's Halting Probability \Omega and Halting
  Self-Similar Sets

abstract:
  We generalize the concept of randomness in an infinite binary sequence in
order to characterize the degree of randomness by a real number D>0. Chaitin's
halting probability \Omega is generalized to \Omega^D whose degree of
randomness is precisely D. On the basis of this generalization, we consider the
degree of randomness of each point in Euclidean space through its base-two
expansion. It is then shown that the maximum value of such a degree of
randomness provides the Hausdorff dimension of a self-similar set that is
computable in a certain sense. The class of such self-similar sets includes
familiar fractal sets such as the Cantor set, von Koch curve, and Sierpinski
gasket. Knowledge of the property of \Omega^D allows us to show that the
self-similar subset of [0,1] defined by the halting set of a universal
algorithm has a Hausdorff dimension of one.


title: Nonlinear superposition formula for N=1 supersymmetric KdV Equation

abstract:
  In this paper, we derive a B\"{a}cklund transformation for the supersymmetric
Kortweg-de Vries equation. We also construct a nonlinear superposition formula,
which allows us to rebuild systematically for the supersymmetric KdV equation
the soliton solutions of Carstea, Ramani and Grammaticos.


title: Accelerator modes of square well system

abstract:
  We study accelerator modes of a particle, confined in an one-dimensional
infinite square well potential, subjected to a time-periodic pulsed field.
Dynamics of such a particle can be described by one generalization of the
kicked rotor. In comparison with the kicked rotor, this generalization is shown
to have a much larger parametric space for existence of the modes. Using this
freedom we provide evidence that accelerator mode assisted anomalous transport
is greatly enhanced when low order resonances are exposed at the border of
chaos. We also present signature of the enhanced transport in the quantum
domain.


title:
Unifying scheme for generating discrete integrable systems including
  inhomogeneous and hybrid models

abstract:
  A unifying scheme based on an ancestor model is proposed for generating a
wide range of integrable discrete and continuum as well as inhomogeneous and
hybrid models. They include in particular discrete versions of sine-Gordon,
Landau-Lifshitz, nonlinear Schr\"odinger (NLS), derivative NLS equations,
Liouville model, (non-)relativistic Toda chain, Ablowitz-Ladik model etc. Our
scheme introduces the possibility of building a novel class of integrable
hybrid systems including multi-component models like massive Thirring, discrete
self trapping, two-mode derivative NLS by combining different descendant
models. We also construct inhomogeneous systems like Gaudin model including new
ones like variable mass sine-Gordon, variable coefficient NLS, Ablowitz-Ladik,
Toda chains etc. keeping their flows isospectral, as opposed to the standard
approach. All our models are generated from the same ancestor Lax operator (or
its q -> 1 limit) and satisfy the classical Yang-Baxter equation sharing the
same r-matrix. This reveals an inherent universality in these diverse systems,
which become explicit at their action-angle level.


title: Semiclassical quantization of maps with a variable time scale

abstract:
  Quantization of energy balance equations, which describe a separatrix -- like
motion is presented. The method is based on an exact canonical transformation
of the energy--time pair to the action-angle canonical pair, $ (E,t)\to
(I,\theta) $. Quantum mechanical dynamics can be studied in the framework of
the new Hamiltonian. This transformation also establishes a relation between a
wide class of the energy balance equations and dynamical localization of
classical diffusion by quantum interference, that was studied in the field of
quantum chaos. An exact solution for a simple system is presented as well.


title: Avoided intersections of nodal lines

abstract:
  We consider real eigen-functions of the Schr\"odinger operator in 2-d. The
nodal lines of separable systems form a regular grid, and the number of nodal
crossings equals the number of nodal domains. In contrast, for wave functions
of non integrable systems nodal intersections are rare, and for random waves,
the expected number of intersections in any finite area vanishes. However,
nodal lines display characteristic avoided crossings which we study in the
present work. We define a measure for the avoidance range and compute its
distribution for the random waves ensemble. We show that the avoidance range
distribution of wave functions of chaotic systems follow the expected random
wave distributions, whereas for wave functions of classically integrable but
quantum non-separable wave functions, the distribution is quite different.
Thus, the study of the avoidance distribution provides more support to the
conjecture that nodal structures of chaotic systems are reproduced by the
predictions of the random waves ensemble.


title:
New Integrable Family in the n-Dimensional Homogeneous Lotka-Volterra
  Systems with Abelian Lie Algebra

abstract:
  We present an n-dimensional integrable homogeneous Lotka--Volterra system,
which has $(n^2-1)$-dimensional Lie symmetry algebra. Moreover a wider
integrable family is derived from the structure of the Lie algebra.


title: Nodal domain distributions for quantum maps

abstract:
  The statistics of the nodal lines and nodal domains of the eigenfunctions of
quantum billiards have recently been observed to be fingerprints of the
chaoticity of the underlying classical motion by Blum et al. (Phys. Rev. Lett.,
Vol. 88 (2002), 114101) and by Bogomolny and Schmit (Phys. Rev. Lett., Vol. 88
(2002), 114102). These statistics were shown to be computable from the random
wave model of the eigenfunctions. We here study the analogous problem for
chaotic maps whose phase space is the two-torus. We show that the distributions
of the numbers of nodal points and nodal domains of the eigenvectors of the
corresponding quantum maps can be computed straightforwardly and exactly using
random matrix theory. We compare the predictions with the results of numerical
computations involving quantum perturbed cat maps.


title: Interaction of a soliton with a localized gain in a fiber Bragg grating

abstract:
  A model of a lossy nonlinear fiber grating with a "hot spot", which combines
a local gain and an attractive perturbation of the refractive index, is
introduced. A family of exact solutions for pinned solitons is found in the
absence of loss and gain. In the presence of the loss and localized gain, an
instability threshold of the zero solution is found. If the loss and gain are
small, it is predicted what soliton is selected by the energy-balance
condition. Direct simulations demonstrate that only one pinned soliton is
stable in the conservative model: solitons with a larger energy relax to it via
emission of radiation, while those with a smaller energy decay. In the model
with the loss and gain, stable pinned pulses demonstrate persistent internal
vibrations and emission of radiation. If these solitons are nearly stationary,
the prediction based on the energy balance underestimates the necessary gain by
10% to 15% (due to radiation loss). If the loss and gain are larger, the
intrinsic vibrations of the pinned soliton become chaotic. The local gain
alone, without the attractive perturbation of the local refractive index,
cannot maintain a stable pinned soliton. For collisions of moving solitons with
the "hot spot", passage and capture regimes are identified, the capture
actually implying splitting of the soliton.


title: HebbNets: Dynamic network with Hebbian learning rule

abstract:
  It has been demonstrated that one of the most striking features of the
nervous system, the so called 'plasticity' (i.e high adaptability at different
structural levels) is primarily based on Hebbian learning which is a collection
of slightly different mechanisms that modify the synaptic connections between
neurons. The changes depend on neural activity and assign a special dynamic
behavior to the neural networks. From a structural point of view, it is an open
question what network structures may emerge in such dynamic structures under
'sustained' conditions when input to the system is only noise. In this paper we
present and study the `HebbNets', networks with random noise input, in which
structural changes are exclusively governed by neurobiologically inspired
Hebbian learning rules. We show that Hebbian learning is able to develop a
broad range of network structures, including scale-free small-world networks.


title:
Evanescent wave approach to diffractive phenomena in convex billiards
  with corners

abstract:
  What we are going to call in this paper "diffractive phenomena" in billiards
is far from being deeply understood. These are sorts of singularities that, for
example, some kind of corners introduce in the energy eigenfunctions. In this
paper we use the well-known scaling quantization procedure to study them. We
show how the scaling method can be applied to convex billiards with corners,
taking into account the strong diffraction at them and the techniques needed to
solve their Helmholtz equation. As an example we study a classically
pseudointegrable billiard, the truncated triangle. Then we focus our attention
on the spectral behavior. A numerical study of the statistical properties of
high-lying energy levels is carried out. It is found that all computed
statistical quantities are roughly described by the so-called semi-Poisson
statistics, but it is not clear whether the semi-Poisson statistics is the
correct one in the semiclassical limit.


title: On geometry effects in Rayleigh-Benard convection

abstract:
  Various recent experiments hint at a geometry dependence of scaling relations
in Rayleigh-B\'enard convection. Aspect ratio and shape dependences have been
found. In this paper a mechanism is offered which can account for such
dependences. It is based on Prandtl's theory for laminar boundary layers and on
the conservation of volume flux of the large scale wind. The mechanism implies
the possibility of different thicknesses of the kinetic boundary layers at the
sidewalls and the top/bottom plates, just as experimentally found by Qiu and
Xia (Phys. Rev. E58, 486 (1998)), and also different $Ra$-scaling of the wind
measured over the plates and at the sidewalls. In the second part of the paper
a scaling argument for the velocity and temperature fluctuations in the bulk is
developeVarious recent experiments hint at a geometry dependence of scaling
relations in Rayleigh-Benard convection. Aspect ratio and shape dependences
have been found. In this paper a mechanism is offered which can account for
such dependences. It is based on Prandtl's theory for laminar boundary layers
and on the conservation of volume flux of the large scale wind. The mechanism
implies the possibility of different thicknesses of the kinetic boundary layers
at the sidewalls and the top/bottom plates, just as experimentally found by Qiu
and Xia (Phys. Rev. E58, 486 (1998)), and also different $Ra$-scaling of the
wind measured over the plates and at the sidewalls. In the second part of the
paper a scaling argument for the velocity and temperature fluctuations in the
bulk is develope


title: The ultimate state of thermal convection

abstract:
  The ultimate regime of thermal convection, the so called Kraichnan regime (R.
H. Kraichnan, Phys. Fluids 5, 1374 (1962)), hitherto has been elusive. Here,
numerical evidence for that regime is presented by performing simulations of
the bulk of turbulence only, eliminating the thermal and kinetic boundary
layers and replacing them by periodic boundary conditions.


title: The Baecklund transformation equations for the ultradiscrete KP equation

abstract:
  The Baecklund transformation for the ultradiscrete KP equation is proposed.
An algorithm to eliminate variables from the ultradiscrete linear equations is
proposed. The consistency condition for the Baecklund transformation equations
is obtained via the algorithm.


title:
Local dimension and finite time prediction in spatiotemporal chaotic
  systems

abstract:
  We show how a recently introduced statistics [Patil et al, Phys. Rev. Lett.
81 5878 (2001)] provides a direct relationship between dimension and
predictability in spatiotemporal chaotic systems. Regions of low dimension are
identified as having high predictability and vice-versa. This conclusion is
reached by using methods from dynamical systems theory and Bayesian modelling.
We emphasize in this work the consequences for short time forecasting and
examine the relevance for factor analysis. Although we concentrate on coupled
map lattices and coupled nonlinear oscillators for convenience, any other
spatially distributed system could be used instead, such as turbulent fluid
flows.


title: Closed orbits and their bifurcations in the crossed-fields hydrogen atom

abstract:
  A systematic study of closed classical orbits of the hydrogen atom in crossed
electric and magnetic fields is presented. We develop a local bifurcation
theory for closed orbits which is analogous to the well-known bifurcation
theory for periodic orbits and allows identifying the generic closed-orbit
bifurcations of codimension one. Several bifurcation scenarios are described in
detail. They are shown to have as their constituents the generic
codimension-one bifurcations, which combine into a rich variety of complicated
scenarios. We propose heuristic criteria for a classification of closed orbits
that can serve to systematize the complex set of orbits.


title:
Semiclassical quantization of the hydrogen atom in crossed electric and
  magnetic fields

abstract:
  The S-matrix theory formulation of closed-orbit theory recently proposed by
Granger and Greene is extended to atoms in crossed electric and magnetic
fields. We then present a semiclassical quantization of the hydrogen atom in
crossed fields, which succeeds in resolving individual lines in the spectrum,
but is restricted to the strongest lines of each n-manifold. By means of a
detailed semiclassical analysis of the quantum spectrum, we demonstrate that it
is the abundance of bifurcations of closed orbits that precludes the resolution
of finer details. They necessitate the inclusion of uniform semiclassical
approximations into the quantization process. Uniform approximations for the
generic types of closed-orbit bifurcation are derived, and a general method for
including them in a high-resolution semiclassical quantization is devised.


title: Mean flow and spiral defect chaos in Rayleigh-Benard convection

abstract:
  We describe a numerical procedure to construct a modified velocity field that
does not have any mean flow. Using this procedure, we present two results.
Firstly, we show that, in the absence of mean flow, spiral defect chaos
collapses to a stationary pattern comprising textures of stripes with angular
bends. The quenched patterns are characterized by mean wavenumbers that
approach those uniquely selected by focus-type singularities, which, in the
absence of mean flow, lie at the zig-zag instability boundary. The quenched
patterns also have larger correlation lengths and are comprised of rolls with
less curvature. Secondly, we describe how mean flow can contribute to the
commonly observed phenomenon of rolls terminating perpendicularly into lateral
walls. We show that, in the absence of mean flow, rolls begin to terminate into
lateral walls at an oblique angle. This obliqueness increases with Rayleigh
number.


title:
Cyclic bases of zero-curvature representations: five illustrations to
  one concept

abstract:
  The paper contains five examples of using cyclic bases of zero-curvature
representations in studies of weak and strong Lax pairs, hierarchies of
evolution systems, and recursion operators.


title: Multiplicity of Limit Cycle Attractors in Coupled Heteroclinic Cycles

abstract:
  A square lattice distribution of coupled oscillators that have heteroclinic
cycle attractors is studied. In this system, we find a novel type of patterns
that is spatially disordered and periodic in time. These patterns are limit
cycle attractors in the ambient phase space (i.e. not chaotic) and many limit
cycles exist dividing the phase space as their basins. The patterns are
constructed with a local law of difference of phases between the oscillators.
The number of patterns grows exponentially with increasing of the number of
oscillators.


title:
Correlation functions of scattering matrix elements in microwave
  cavities with strong absorption

abstract:
  The scattering matrix was measured for microwave cavities with two antennas.
It was analyzed in the regime of overlapping resonances. The theoretical
description in terms of a statistical scattering matrix and the rescaled
Breit-Wigner approximation has been applied to this regime. The experimental
results for the auto-correlation function show that the absorption in the
cavity walls yields an exponential decay. This behavior can only be modeled
using a large number of weakly coupled channels. In comparison to the
auto-correlation functions, the cross-correlation functions of the diagonal
S-matrix elements display a more pronounced difference between regular and
chaotic systems.


title: Decay Rates and Survival Probabilities in Open Quantum Systems

abstract:
  We provide the first statistical analysis of the decay rates of strongly
driven 3D atomic Rydberg states. The distribution of the rates exhibits
universal features due to Anderson localization, while universality of the time
dependent decay requires particular initial conditions.


title: Observation of a Chiral State in a Microwave Cavity

abstract:
  A microwave experiment has been realized to measure the phase difference of
the oscillating electric field at two points inside the cavity. The technique
has been applied to a dissipative resonator which exhibits a singularity --
called exceptional point -- in its eigenvalue and eigenvector spectrum. At the
singularity, two modes coalesce with a phase difference of $\pi/2 .$ We
conclude that the state excited at the singularity has a definitiv chirality.


title: Some Applications of Fractional Equations

abstract:
  We present two observations related to theapplication of linear (LFE) and
nonlinear fractional equations (NFE). First, we give the comparison and
estimates of the role of the fractional derivative term to the normal diffusion
term in a LFE. The transition of the solution from normal to anomalous
transport is demonstrated and the dominant role of the power tails in the long
time asymptotics is shown. Second, wave propagation or kinetics in a nonlinear
media with fractal properties is considered. A corresponding fractional
generalization of the Ginzburg-Landau and nonlinear Schrodinger equations is
proposed.


title:
A model of cardiac tissue as a conductive system with interacting
  pacemakers and refractory time

abstract:
  A model of the heart tissue as a conductive system with two interacting
pacemakers and a refractory time, is proposed. In the parametric space of the
model the phase locking areas are investigated in detail. Obtained results
allow us to predict the behaviour of excitable systems with two pacemakers
depending on the type and intensity of their interaction and the initial phase.
Comparison of the described phenomena with intrinsic pathologies of cardiac
rhythms is presented.


title:
Reciprocal transformations of Hamiltonian operators of hydrodynamic
  type: nonlocal Hamiltonian formalism for linearly degenerate systems

abstract:
  Reciprocal transformations of Hamiltonian operators of hydrodynamic type are
investigated. The transformed operators are generally nonlocal, possessing a
number of remarkable algebraic and differential-geometric properties. We apply
our results to linearly degenerate semi-Hamiltonian systems in Riemann
invariants. Since all such systems are linearizable by appropriate
(generalized) reciprocal transformations, our formulae provide an infinity of
mutually compatible nonlocal Hamiltonian structures, explicitly parametrized by
arbitrary functions of one variable.


title:
Strong Evidence of Normal Heat Conduction in a one-Dimensional Quantum
  System

abstract:
  We investigate how the normal energy transport is realized in one-dimensional
quantum systems using a quantum spin system. The direct investigation of local
energy distribution under thermal gradient is made using the quantum master
equation, and the mixing properties and the convergence of the Green-Kubo
formula are investigated when the number of spin increases. We find that the
autocorrelation function in the Green-Kubo formula decays as $\sim t^{-1.5}$ to
a finite value which vanishes rapidly with the increase of the system size. As
a result, the Green-Kubo formula converges to a finite value in the
thermodynamic limit. These facts strongly support the realization of Fourier
heat law in a quantum system.


title: Modulated structures in electroconvection in nematic liquid crystals

abstract:
  Motivated by experiments in electroconvection in nematic liquid crystals with
homeotropic alignment we study the coupled amplitude equations describing the
formation of a stationary roll pattern in the presence of a weakly-damped mode
that breaks isotropy. The equations can be generalized to describe the planarly
aligned case if the orienting effect of the boundaries is small, which can be
achieved by a destabilizing magnetic field. The slow mode represents the
in-plane director at the center of the cell. The simplest uniform states are
normal rolls which may undergo a pitchfork bifurcation to abnormal rolls with a
misaligned in-plane director.We present a new class of defect-free solutions
with spatial modulations perpendicular to the rolls. In a parameter range where
the zig-zag instability is not relevant these solutions are stable attractors,
as observed in experiments. We also present two-dimensionally modulated states
with and without defects which result from the destabilization of the
one-dimensionally modulated structures. Finally, for no (or very small)
damping, and away from the rotationally symmetric case, we find static chevrons
made up of a periodic arrangement of defect chains (or bands of defects)
separating homogeneous regions of oblique rolls with very small amplitude.
These states may provide a model for a class of poorly understood stationary
structures observed in various highly-conducting materials ("prechevrons" or
"broad domains").


title:
Nonlinear optics and optical limiting properties of multifunctional
  fullerenol/polymer composite

abstract:
  The nonlinear optics and optical limiting properties of materials based on
multifunctional fullerenol and poly(styrene-co-4-vinylpyridine) matrix were
studied using 7 ns pulses of nanosecond laser operating at 532 nm wavelength.
The observed imaginary and real parts of third order susceptibility of the
fullerenol/polymer composite are found to be lower than that of its parent C60.
The optical limiting performances of fullerenol and fullerenol incorporated
with poly(styrene-co-4-vinylpyridine) have been proved to be poorer than that
of C60 due to their higher limiting thresholds. Concentration dependence of
poly(styrene-co-4-vinylpyridine) containing 32 mol% has been mainly contributed
to the optical limiting performance of fullerenol.

categories: nlin.SI cond-mat.mtrl-sci physics.chem-ph physics.optics


title:
The structure of evolutionary exploration: On crossover, buildings
  blocks and Estimation-Of-Distribution Algorithms

abstract:
  The notion of building blocks can be related to the structure of the
offspring probability distribution: loci of which variability is strongly
correlated constitute a building block. We call this correlated exploration.
With this background we analyze the structure of the offspring probability
distribution, or exploration distribution, for a GA with mutation only, a
crossover GA, and an Estimation-Of-Distribution Algorithm (EDA). The results
allow a precise characterization of the structure of the crossover exploration
distribution. Essentially, the crossover operator destroys mutual information
between loci by transforming it into entropy; it does the inverse of correlated
exploration. In contrast, the objective of EDAs is to model the mutual
information between loci in the fitness distribution and thereby they induce
correlated exploration.


title: Interaction of a soliton with a local defect in a fiber Bragg grating

abstract:
  We study the interactions of a Bragg-grating soliton with a localized
attractive defect which is a combined perturbation of the grating and
refractive index. A family of exact analytical solutions for solitons trapped
by the delta-like defect is found. Direct simulations demonstrate that, up to
the numerical accuracy available, the trapped soliton is stable at a single
value of its intrinsic parameter ("mass"). Trapped solitons with larger mass
relax to the stable one through the emission of radiation, while the solitons
with smaller mass decay. Depending on values of parameters, simulations of
collisions between moving solitons and the defect show that the soliton can get
captured, pass through, or even bounce from the defect. If the defect is strong
and the soliton is heavy enough, it may split, as a result of the collision,
into three fragments: trapped, transmitted, and reflected ones.


title: Signatures of chaotic tunnelling

abstract:
  Recent experiments with cold atoms provide a significant step toward a better
understanding of tunnelling when irregular dynamics is present at the classical
level. In this paper, we lay out numerical studies which shed light on the
previous experiments, help to clarify the underlying physics and have the
ambition to be guidelines for future experiments.


title: Quantum resonances and decoherence for delta-kicked atoms

abstract:
  The quantum resonances occurring with delta-kicked atoms when the kicking
period is an integer multiple of the half-Talbot time are analyzed in detail.
Exact results about the momentum distribution at exact resonance are
established, both in the case of totally coherent dynamics and in the case when
decoherence is induced by Spontaneous Emission. A description of the dynamics
when the kicking period is close to, but not exactly at resonance, is derived
by means of a quasi-classical approximation where the detuning from exact
resonance plays the role of the Planck constant. In this way scaling laws
describing the shape of the resonant peaks are obtained. Such analytical
results are supported by extensive numerical simulations, and explain some
recent surprising experimental observations.


title: Stable vortex and dipole vector solitons in a saturable nonlinear medium

abstract:
  We study both analytically and numerically the existence, uniqueness, and
stability of vortex and dipole vector solitons in a saturable nonlinear medium
in (2+1) dimensions. We construct perturbation series expansions for the vortex
and dipole vector solitons near the bifurcation point where the vortex and
dipole components are small. We show that both solutions uniquely bifurcate
from the same bifurcation point. We also prove that both vortex and dipole
vector solitons are linearly stable in the neighborhood of the bifurcation
point. Far from the bifurcation point, the family of vortex solitons becomes
linearly unstable via oscillatory instabilities, while the family of dipole
solitons remains stable in the entire domain of existence. In addition, we show
that an unstable vortex soliton breaks up either into a rotating dipole soliton
or into two rotating fundamental solitons.


title:
Using the Continuous Spectrum to "Feel" Integrability: the Effect of
  Boundary Conditions

abstract:
  The scope of this work is to propose a method for testing the integrability
of a model partial differential (PDE) and/or differential difference equation
(DDE). For monoparametric families of PDE/DDE's, that are known to possess
isolated integrable points, we find that very special features occur in the
continuous (``phonon'') spectrum at these ``singular'' points. We identify
these features in the case example of a PDE and a DDE (that sustain front and
pulse-like solutions respectively) for different types of boundary conditions.
The key finding of the work is that such spectral features are generic near the
singular, integrable points and hence we propose to explore a given PDE/DDE for
such traits, as a means of assessing its potential integrability.


title: Crossover from Diffusive to Ballistic Transport in Periodic Quantum Maps

abstract:
  We derive an expression for the mean square displacement of a particle whose
motion is governed by a uniform, periodic, quantum multi-baker map. The
expression is a function of both time, $t$, and Planck's constant, $\hbar$, and
allows a study of both the long time, $t\to\infty$, and semi-classical,
$\hbar\to 0$, limits taken in either order. We evaluate the expression using
random matrix theory as well as numerically, and observe good agreement between
both sets of results. The long time limit shows that particle transport is
generically ballistic, for any fixed value of Planck's constant. However, for
fixed times, the semi-classical limit leads to diffusion. The mean square
displacement for non-zero Planck's constant, and finite time, exhibits a
crossover from diffusive to ballistic motion, with crossover time on the order
of the inverse of Planck's constant. We argue, that these results are generic
for a large class of 1D quantum random walks, similar to the quantum
multi-baker, and that a sufficient condition for diffusion in the
semi-classical limit is classically chaotic dynamics in each cell. Some
connections between our work and the other literature on quantum random walks
are discussed. These walks are of some interest in the theory of quantum
computation.


title:
Delay-induced Synchronization Phenomena in an Array of Globally Coupled
  Logistic Maps

abstract:
  We study the synchronization of a linear array of globally coupled identical
logistic maps. We consider a time-delayed coupling that takes into account the
finite velocity of propagation of the interactions. We find globally
synchronized states in which the elements of the array evolve along a periodic
orbit of the uncoupled map, while the spatial correlation along the array is
such that an individual map sees all other maps in his present, current, state.
For values of the nonlinear parameter such that the uncoupled maps are chaotic,
time-delayed mutual coupling suppress the chaotic behavior by stabilizing a
periodic orbit which is unstable for the uncoupled maps. The stability analysis
of the synchronized state allows us to calculate the range of the coupling
strength in which global synchronization can be obtained.


title:
Fast Monte Carlo simulations and singularities in the probability
  distributions of non-equilibrium systems

abstract:
  A numerical technique is introduced that reduces exponentially the time
required for Monte Carlo simulations of non-equilibrium systems. Results for
the quasi-stationary probability distribution in two model systems are compared
with the asymptotically exact theory in the limit of extremely small noise
intensity. Singularities of the non-equilibrium distributions are revealed by
the simulations.


title:
Front dynamics in reaction-diffusion systems with Levy flights: a
  fractional diffusion approach

abstract:
  The use of reaction-diffusion models rests on the key assumption that the
underlying diffusive process is Gaussian. However, a growing number of studies
have pointed out the prevalence of anomalous diffusion, and there is a need to
understand the dynamics of reactive systems in the presence of this type of
non-Gaussian diffusion. Here we present a study of front dynamics in
reaction-diffusion systems where anomalous diffusion is due to the presence of
asymmetric Levy flights. Our approach consists of replacing the Laplacian
diffusion operator by a fractional diffusion operator, whose fundamental
solutions are Levy $\alpha$-stable distributions. Numerical simulation of the
fractional Fisher-Kolmogorov equation, and analytical arguments show that
anomalous diffusion leads to the exponential acceleration of fronts and a
universal power law decay, $x^{-\alpha}$, of the tail, where $\alpha$, the
index of the Levy distribution, is the order of the fractional derivative.


title: Tip Oscillation of Dendritic Patterns in a Phase Field Model

abstract:
  We study dendritic growth numerically with a phase field model. Tip
oscillation and regular side-branching are observed in a parameter region where
the anisotropies of the surface tension and the kinetic effect compete. The
transition from a needle pattern to a dendritic pattern is conjectured to be a
supercritical Hopf bifurcation.


title:
On a two-parameter extension of the lattice KdV system associated with
  an elliptic curve

abstract:
  A general structure is developed from which a system of integrable partial
difference equations is derived generalising the lattice KdV equation. The
construction is based on an infinite matrix scheme with as key ingredient a
(formal) elliptic Cauchy kernel. The consistency and integrability of the
lattice system is discussed as well as special solutions and associated
continuum equations.


title: Zeta Function Zeros, Powers of Primes, and Quantum Chaos

abstract:
  We present a numerical study of Riemann's formula for the oscillating part of
the density of the primes and their powers. The formula is comprised of an
infinite series of oscillatory terms, one for each zero of the zeta function on
the critical line and was derived by Riemann in his paper on primes assuming
the Riemann hypothesis. We show that high resolution spectral lines can be
generated by the truncated series at all powers of primes and demonstrate
explicitly that the relative line intensities are correct. We then derive a
Gaussian sum rule for Riemann's formula. This is used to analyze the numerical
convergence of the truncated series. The connections to quantum chaos and
semiclassical physics are discussed.


title:
Statistical approach of the modulational instability of the discrete
  self-trapping equation

abstract:
  The discrete self-trapping equation (DST) represents an useful model for
several properties of one-dimensional nonlinear molecular crystals. The
modulational instability of DST equation is discussed from a statistical point
of view, considering the oscillator amplitude as a random variable. A kinetic
equation for the two-point correlation function is written down, and its linear
stability is studied. Both a Gaussian and a Lorentzian form for the initial
unperturbed wave spectrum are discussed. Comparison with the continuum limit
(NLS equation) is done.


title:
Correspondence theorems for hierarchies of equations of pseudo-spherical
  type

abstract:
  Hierarchies of evolution equations of pseudo-spherical type are introduced,
generalizing the notion of a single equation describing pseudo-spherical
surfaces due to S.S. Chern and K. Tenenblat, and providing a connection between
differential geometry and the study of hierarchies of equations which are the
integrability condition of $sl(2,{\bf R})$--valued linear problems. As an
application, it is shown that there exists a local correspondence between any
two (suitably generic) solutions of arbitrary hierarchies of equations of
pseudo-spherical type.


title:
Pseudo-potentials, nonlocal symmetries and integrability of some shallow
  water equations

abstract:
  Zero curvature formulations, pseudo-potentials, modified versions, ``Miura
transformations'', and nonlocal symmetries of the Korteweg--de Vries, Camassa--
Holm and Hunter--Saxton equations are investigated from an unified point of
view: these three equations belong to a two--parameters family of equations
``describing pseudo-spherical surfaces'', and therefore their basic
integrability properties can be studied by geometrical means.


title:
The hydrogen atom in an electric field: Closed-orbit theory with
  bifurcating orbits

abstract:
  Closed-orbit theory provides a general approach to the semiclassical
description of photo-absorption spectra of arbitrary atoms in external fields,
the simplest of which is the hydrogen atom in an electric field. Yet, despite
its apparent simplicity, a semiclassical quantization of this system by means
of closed-orbit theory has not been achieved so far. It is the aim of this
paper to close that gap. We first present a detailed analytic study of the
closed classical orbits and their bifurcations. We then derive a simple form of
the uniform semiclassical approximation for the bifurcations that is suitable
for an inclusion into a closed-orbit summation. By means of a generalized
version of the semiclassical quantization by harmonic inversion, we succeed in
calculating high-quality semiclassical spectra for the hydrogen atom in an
electric field.


title: Wave Propagation in Nonlocally Coupled Oscillators With Noise

abstract:
  The onset of undamped wave propagation in noisy self-oscillatory media is
identified with a Hopf bifurcation of the corresponding effective dynamical
system obtained by properly renormalizing the effects of noise. We illustrate
this fact on a dense array of nonlocally coupled phase oscillators for which a
mean-field idea works exactly in deriving such effective dynamical equations.


title: Monodromy in the resonant swing spring

abstract:
  This paper shows that an integrable approximation of the spring pendulum,
when tuned to be in $1:1:2$ resonance, has monodromy. The stepwise precession
angle of the swing plane of the resonant spring pendulum is shown to be a
rotation number of the integrable approximation. Due to the monodromy, this
rotation number is not a globally defined function of the integrals. In fact at
lowest order it is given by $\arg(a+ib)$ where $a$ and $b$ are functions of the
integrals. The resonant swing spring is therefore a system where monodromy has
easily observed physical consequences.


title:
Inverse Modeling of Complex Networks Using Embedded Complex Logistic
  Maps

abstract:
  An inverse modeling technique is introduced that combines elements of coupled
logistic map models and wavelet analysis for the purpose of analyzing partial
synchronization states in high-dimensional systems. Using Embedded Complex
Logistic Maps (ECLM), time series data derived from individual system
components is directly mapped to a wavelet-like space generated from iterations
of specific complex logistic maps. These maps are selected from the complex
plane according to "best fit" scoring criteria with the data. The embedding
topology within and near the familiar Mandelbrot Set provides metrics which are
used to aid in clustering similarities (synchronization) between these selected
point models. The dynamics within the individual models and the correlation
between (synchronized) models is analyzed to reconstruct a unified picture of
the underlying dynamics of local system components within the global system
network topology. In this paper, ECLM is used to extract system parameters,
network graphs, and wavelet-like analytics from two real-world systems, a gene
expression network and a financial market network. Preliminary results appear
to validate the assumptions and methods used in ECLM through agreement with
current theory and recent findings. Some potentially new findings regarding
synchronization, scale-free networks, on-off intermittency, and energy
dissipation within the examples studied will also be discussed.


title: Chaotic Combustion in Spark Ignition Engines

abstract:
  We analyse the combustion process in a spark ignition engine using the
experimental data of an internal pressure during the combustion process and
show that the system can be driven to chaotic behaviour. Our conclusion is
based on the observation of unperiodicity in the time series, suitable
stroboscopic maps and a complex structure of a reconstructed strange attractor.
This analysis can explain that in some circumstances the level of noise in
spark ignition engines increases considerably due to nonlinear dynamics of a
combustion process.


title: General Stability Analysis of Synchronized Dynamics in Coupled Systems

abstract:
  We consider the stability of synchronized states (including equilibrium
point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical
systems (maps or ordinary differential equations). We develop a general
approach, based on the master stability function and Gershgorin disc theory, to
yield constraints on the coupling strengths to ensure the stability of
synchronized dynamics. Systems with specific coupling schemes are used as
examples to illustrate our general method.


title: Parametrically Driven Dark Solitons

abstract:
  We show that unlike the bright solitons, the parametrically driven kinks are
immune from instabilities for all dampings and forcing amplitudes; they can
also form stable bound states. In the undamped case, the two types of stable
kinks and their complexes can travel with nonzero velocities.

categories: nlin.PS cond-mat.stat-mech cond-mat.str-el nlin.SI physics.flu-dyn physics.optics


title: A new class of linearizable equations

abstract:
  Using the symmetry approach, we find a class of integrable nonlinear PDEs
with dispersion law $\omega(k)=k^{\frac32}$. All these equations turn out to be
linearizable by means of a differential parametrization.


title: Hierarchy of random deterministic chaotic maps with an invariant measure

abstract:
  Hierarchy of one and many-parameter families of random trigonometric chaotic
maps and one-parameter random elliptic chaotic maps of $\bf{cn}$ type with an
invariant measure have been introduced. Using the invariant measure
(Sinai-Ruelle-Bowen measure), the Kolmogrov-Sinai entropy of the random chaotic
maps have been calculated analytically, where the numerical simulations support
the results


title:
An open-system approach for the characterization of spatio-temporal
  chaos

abstract:
  We investigate the structure of the invariant measure of space-time chaos by
adopting an "open-system" point of view. We consider large but finite windows
of formally infinite one-dimensional lattices and quantify the effect of the
interaction with the outer region by mapping the problem on the dynamical
characterization of localized perturbations. This latter task is performed by
suitably generalizing the concept of Lyapunov spectrum to cope with
perturbations that propagate outside the region under investigation. As a
result, we are able to introduce a "volume"-propagation velocity, i.e. the
velocity with which ensembles of localized perturbations tend to fill volumes
in the neighbouring regions.


title: Semiclassical Study on Tunneling Processes via Complex-Domain Chaos

abstract:
  We investigate the semiclassical mechanism of tunneling process in
non-integrable systems. The significant role of complex-phase-space chaos in
the description of the tunneling process is elucidated by studying a simple
scattering map model. Behaviors of tunneling orbits are encoded into symbolic
sequences based on the structure of complex homoclinic tanglement. By means of
the symbolic coding, the phase space itineraries of tunneling orbits are
related with the amounts of imaginary parts of actions gained by the orbits, so
that the systematic search of significant tunneling orbits becomes possible.


title: Meta-mimetism in Spatial Games

abstract:
  The aim of this article is to address the question of the endogenization of
mimetic processes in formal models of social systems. Starting from some
studies about cognitive differences between humans and animals, we propose a
formal framework which has the advantage to endogenise mimetic rules and give a
comprehensive description of a heterogeneous population structure at the
behavioural level as well as at the level of the choices of mimetic laws. In
order to illustrate this point, we apply this formalism to a spatial
evolutionary game.


title: Frequency spanning homoclinic families

abstract:
  A family of maps or flows depending on a parameter $\nu$ which varies in an
interval, spans a certain property if along the interval this property depends
continuously on the parameter and achieves some asymptotic values along it. We
consider families of periodically forced Hamiltonian systems for which the
appropriately scaled frequency $\bar{\omega}(\nu)$ is spanned, namely it covers
the semi-infinite line $[0,\infty).$ Under some natural assumptions on the
family of flows and its adiabatic limit, we construct a convenient labelling
scheme for the primary homoclinic orbits which may undergo a countable number
of bifurcations along this interval. Using this scheme we prove that a properly
defined flux function is $C^{1}$ in $\nu.$ Combining this proof with previous
results of RK and Poje, immediately establishes that the flux function and the
size of the chaotic zone depend on the frequency in a non-monotone fashion for
a large class of Hamiltonian flows.


title: Defect-mediated turbulence in systems with local deterministic chaos

abstract:
  We show that defect-mediated turbulence can exist in media where the
underlying local dynamics is deterministically chaotic. While many of the
characteristics of defect-mediated turbulence, such as the exponential decay of
correlations and a squared Poissonian distribution for the number of defects,
are identical to those seen in oscillatory media, the fluctuations in the
number of defects differ significantly. The power spectra suggest the existence
of underlying correlations that lead to a different and non-universal scaling
structure in chaotic media.


title:
Fractional Kinetic Description of Chaotic Transport in Complex Dynamical
  Systems

abstract: See hep-ph/0304045


title:
Unified Model, and Novel Reverse Recovery Nonlinearities, of the Driven
  Diode Resonator

abstract:
  We study the origins of period doubling and chaos in the driven series
resistor-inductor-varactor diode (RLD) nonlinear resonant circuit. We find that
resonators driven at frequencies much higher than the diode reverse recovery
rate do not show period doubling, and that models of chaos based on the
nonlinear capacitance of the varactor diode display a reverse-recovery-like
effect, and this effect strongly resembles reverse recovery of real diodes. We
find for the first time that in addition to the known dependence of the reverse
recovery time on past current maxima, there are also important nonlinear
dependencies on pulse frequency, duty-cycle, and DC voltage bias. Similar
nonlinearities are present in the nonlinear capacitance models of these diodes.
We conclude that a history-dependent and nonlinear reverse recovery time is an
essential ingredient for chaotic behavior of this circuit, and demonstrate for
the first time that all major competing models have this effect, either
explicitly or implicitly. Besides unifying the two major models of RLD chaos,
our work reveals that the nonlinearities of the reverse recovery time must be
included for a complete understanding of period doubling and chaos in this
circuit.


title: Integrable hydrodynamic chains

abstract:
  A new approach for derivation of Benney-like momentum chains and integrable
hydrodynamic type systems is presented. New integrable hydrodynamic chains are
constructed, all their reductions are described and integrated. New (2+1)
integrable hydrodynamic type systems are found.


title:
General solution for Hamiltonians with extended cubic and quartic
  potentials

abstract:
  We integrate with hyperelliptic functions a two-particle Hamiltonian with
quartic potential and additionnal linear and nonpolynomial terms in the
Liouville integrable cases 1:6:1 and 1:6:8.


title: Quantum Manifestations of Classical Stochasticity in the Mixed State

abstract:
  We investigate the QMCS in structure of the eigenfunctions, corresponding to
mixed type classical dynamics in smooth potential of the surface quadrupole
oscillations of a charged liquid drop. Regions of different regimes of
classical motion are strictly separated in the configuration space, allowing
direct observation of the correlations between the wave function structure and
type of the classical motion by comparison of the parts of the eigenfunction,
corresponding to different local minima.


title: Spontaneous pattern formation in an acoustical resonator

abstract:
  A dynamical system of equations describing parametric sound generation (PSG)
in a dispersive large aspect ratio resonator is derived. The model generalizes
previously proposed descriptions of PSG by including diffraction effects, and
is analogous to the model used in theoretical studies of optical parametric
oscillation. A linear stability analysis of the solution below the threshold of
subharmonic generation reveals the existence of a pattern forming instability,
which is confirmed by numerical integration. The conditions of emergence of
periodic patterns in transverse space are discussed in the acoustical context.


title: Spectral properties of noisy classical and quantum propagators

abstract:
  We study classical and quantum maps on the torus phase space, in the presence
of noise. We focus on the spectral properties of the noisy evolution operator,
and prove that for any amount of noise, the quantum spectrum converges to the
classical one in the semiclassical limit. The small-noise behaviour of the
classical spectrum highly depends on the dynamics generated by the map. For a
chaotic dynamics, the outer spectrum consists in isolated eigenvalues
(``resonances'') inside the unit circle, leading to an exponential damping of
correlations. On the opposite, in the case of a regular map, part of the
spectrum accumulates along a one-dimensional ``string'' connecting the origin
with unity, yielding a diffusive behaviour. We finally study the
non-commutativity between the semiclassical and small-noise limits, and
illustrate this phenomenon by computing (analytically and numerically) the
classical and quantum spectra for some maps.


title:
Resonant triad dynamics in weakly damped Faraday waves with
  two-frequency forcing

abstract:
  Many of the interesting patterns seen in recent multi-frequency Faraday
experiments can be understood on the basis of three-wave interactions (resonant
triads). In this paper we consider two-frequency forcing and focus on a
resonant triad that occurs near the bicritical point where two pattern-forming
modes with distinct wavenumbers emerge simultaneously. This triad has been
observed directly (in the form of rhomboids) and has also been implicated in
the formation of quasipatterns and superlattices. We show how the symmetries of
the undamped unforced problem (time translation, time reversal, and Hamiltonian
structure) can be used, when the damping is weak, to obtain general scaling
laws and additional qualitative properties of the normal form coefficients
governing the pattern selection process near onset; such features help to
explain why this particular triad is seen only for certain "low" forcing
ratios, and predict the existence of drifting solutions and heteroclinic
cycles. We confirm the anticipated parameter dependence of the coefficients and
investigate its dynamical consequences using coefficients derived numerically
from a quasipotential formulation of the Faraday problem due to Zhang and
Vinals.


title:
Cascades of subharmonic stationary states in strongly non-linear driven
  planar systems

abstract:
  The dynamics of a one-degree of freedom oscillator with arbitrary polynomial
non-linearity subjected to an external periodic excitation is studied. The
sequences (cascades) of harmonic and subharmonic stationary solutions to the
equation of motion are obtained by using the harmonic balance approximation
adapted for arbitrary truncation numbers, powers of non-linearity, and orders
of subharmonics. A scheme for investigating the stability of the harmonic
balance stationary solutions of such a general form is developed on the basis
of the Floquet theorem. Besides establishing the stable/unstable nature of a
stationary solution, its stability analysis allows obtaining the regions of
parameters, where symmetry-breaking and period-doubling bifurcations occur.
Thus, for period-doubling cascades, each unstable stationary solution is used
as a base solution for finding a subsequent stationary state in a cascade. The
procedure is repeated until this stationary state becomes stable provided that
a stable solution can finally be achieved. The proposed technique is applied to
calculate the sequences of subharmonic stationary states in driven hardening
Duffing's oscillator. The existence of stable subharmonic motions found is
confirmed by solving the differential equation of motion numerically by means
of a time-difference method, with initial conditions being supplied by the
harmonic balance approximation.


title:
On integration of some classes of $(n+1)$ dimensional nonlinear Partial
  Differential Equations

abstract:
  The paper represents the method for construction of the families of
particular solutions to some new classes of $(n+1)$ dimensional nonlinear
Partial Differential Equations (PDE). Method is based on the specific link
between algebraic matrix equations and PDE. Admittable solutions depend on
arbitrary functions of $n$ variables.


title:
Schmidt number dependence of derivative moments for quasistatic
  straining motion

abstract:
  Bounds on high-order derivative moments of a passive scalar are obtained for
large values of the Schmidt number, $Sc$. The procedure is based on the
approach pioneered by Batchelor for the viscous-convective range. The upper
bounds for derivative moments of order $n$ are shown to grow as $Sc^{n/2}$ for
very large Schmidt numbers. The results are consistent with direct numerical
simulations of a passive scalar, whose $Sc$ varies between 1/4 and 64, mixed by
homogeneous isotropic turbulence. Although the analysis does not provide proper
bounds for normalized moments, the combination of analysis and numerical data
suggests that they decay with $Sc$, at least for odd orders.
  This paper has been withdrawn by the authors due to copyright. It appears in
Journal of Fluid Mechanics (2003). http://jfm-www.damtp.cam.ac.uk/


title:
Persistent global power fluctuations near a dynamic transition in
  electroconvection

abstract:
  This is a study of the global fluctuations in power dissipation and light
transmission through a liquid crystal just above the onset of
electroconvection.
  The source of the fluctuations is found to be the creation and annihilation
of defects. They are spatially uncorrelated and yet temporally correlated. The
temporal correlation is seen to persist for extremely long times. There seems
to be an especially close relation between defect creation/annihilat ion in
electroconvection and thermal plumes in Rayleigh-B\'enard convection.


title:
Separability preserving Dirac reductions of Poisson pencils on
  Riemannian manifolds

abstract:
  Dirac deformation of Poisson operators of arbitrary rank is considered. The
question when Dirac reduction does not destroy linear Poisson pencils is
studied. A class of separability preserving Dirac reductions in the
corresponding quasi-bi-Hamiltonian systems of Benenti type is discussed. Two
examples of such reductions are given.


title: Statistical properties of resonance widths for open Quantum Graphs

abstract:
  We connect quantum compact graphs with infinite leads, and turn them into
scattering systems. We derive an exact expression for the scattering matrix,
and explain how it is related to the spectrum of the corresponding closed
graph. The resulting expressions allow us to get a clear understanding of the
phenomenon of resonance trapping due to over-critical coupling with the leads.
Finally, we analyze the statistical properties of the resonance widths and
compare our results with the predictions of Random Matrix Theory. Deviations
appearing due to the dynamical nature of the system are pointed out and
explained.


title: New Characterization of Disorder Taming Spatiotemporal Chaos

abstract:
  In the present letter, we introduce a new method to quantify the effect of
disorder on spatiotemporal chaos [Y. Braiman, etc. Nature, 378, p465 (1995)].
Base on the autocorrelation function, we define a parameter to measure the
effect of disorder. The results are intriguing and similar to the results
obtained by J. Lindner etc. [J. Lindner, etc. Physics Letters A, 231, p164
(1997)]. Using this order parameter, the effect of disorder on spatiotemporal
chaos in different conditions has also been discussed.


title: Spatial Solitons in Optically-Induced Gratings

abstract:
  We study experimentally nonlinear localization effects in optically-induced
gratings created by interfering plane waves in a photorefractive crystal. We
demonstrate the generation of spatial bright solitons similar to those observed
in arrays of coupled optical waveguides. We also create pairs of out-of-phase
solitons which resemble ``twisted'' localized states in nonlinear lattices.


title: Manipulation and removal of defects in spontaneous optical patterns

abstract:
  Defects play an important role in a number of fields dealing with ordered
structures. They are often described in terms of their topology, mutual
interaction and their statistical characteristics. We demonstrate theoretically
and experimentally the possibility of an active manipulation and removal of
defects. We focus on the spontaneous formation of two-dimensional spatial
structures in a nonlinear optical system, a liquid crystal light valve under
single optical feedback. With increasing distance from threshold, the
spontaneously formed hexagonal pattern becomes disordered and contains several
defects. A scheme based on Fourier filtering allows us to remove defects and to
restore spatial order. Starting without control, the controlled area is
progressively expanded, such that defects are swept out of the active area.


title: Classical decays in decoherent quantum maps

abstract:
  We study the asymptotic long-time behavior of open quantum maps and relate
the decays to the eigenvalues of a coarse-grained superoperator. In specific
ranges of coarse graining, and for chaotic maps, these decay rates are given by
the Ruelle-Pollicott resonances of the classical map.


title: Ray dynamics in a long-range acoustic propagation experiment

abstract:
  A ray-based wavefield description is employed in the interpretation of
measurements made during the November 1994 Acoustic Engineering Test (the AET
experiment). In this experiment phase-coded pulse-like signals with 75 Hz
center frequency and 37.5 Hz bandwidth were transmitted near the sound channel
axis in the eastern North Pacific Ocean. The resulting acoustic signals were
recorded on a moored vertical receiving array at a range of 3252 km. In our
analysis both mesoscale and internal-wave-induced sound speed perturbations are
taken into account. Much of this analysis exploits results that relate to the
subject of ray chaos; these results follow from the Hamiltonian structure of
the ray equations. We present evidence that all of the important features of
the measured AET wavefields, including their stability, are consistent with a
ray-based wavefield description in which ray trajectories are predominantly
chaotic.


title:
Analytical description of Recurrence Plots of white noise and chaotic
  processes

abstract:
  We present an analytical description of the distribution of diagonal lines in
Recurrence Plots (RPs) for white noise and chaotic systems, and find that the
latter one is linked to the correlation entropy. Further we identify two
scaling regions in the distribution of diagonals for oscillatory chaotic
systems that are hinged to two prediction horizons and to the geometry of the
attractor. These scaling regions cannot be observed with the
Grassberger-Procaccia algorithm. Finally, we propose methods to estimate
dynamical invariants from RPs.


title: Classical Resonances and Quantum Scarring

abstract:
  We study the correspondence between phase-space localization of quantum
(quasi-)energy eigenstates and classical correlation decay, given by
Ruelle-Pollicott resonances of the Frobenius-Perron operator. It will be shown
that scarred (quasi-)energy eigenstates are correlated: Pairs of eigenstates
strongly overlap in phase space (scar in same phase-space regions) if the
difference of their eigenenergies is close to the phase of a leading classical
resonance. Phase-space localization of quantum states will be measured by $L^2$
norms of their Husimi functions.


title: Soliton "molecules": robust clusters of light bullets

abstract:
  We show how to generate robust self-sustained clusters of soliton
bullets-spatiotemporal (optical or matter-wave) solitons. The clusters carry an
orbital angular momentum being supported by competing nonlinearities. The
"atoms" forming the "molecule" are fully three-dimensional solitons linked via
a staircase-like macroscopic phase. Recent progress in generating
atomic-molecular coherent mixing in Bose-Einstein condensates might open
potential scenarios for the experimental generation of these soliton molecules
with matter-waves.


title:
Power market dynamics: the statistical mechanics of transaction-based
  control

abstract:
  Statistical mechanics provides a useful analog for understanding the behavior
of complex adaptive systems, including power markets and the power systems they
intend to govern. Transaction-based control is founded on the conjecture that
the regulation of complex systems based on price-mediated strategies (e.g.,
auctions, markets) results in an optimal allocation of resources and an
emergent optimal control. We outline a model based on strict analogies to
thermodynamic quantities. The model accurately describes power market data
collected from three North American independent system operators (ISO) in
recent years. The ISO data is analyzed, comparing the behavioral similarities
and differences that are observed.


title:
Can billiard eigenstates be approximated by superpositions of plane
  waves?

abstract:
  The plane wave decomposition method (PWDM) is one of the most popular
strategies for numerical solution of the quantum billiard problem. The method
is based on the assumption that each eigenstate in a billiard can be
approximated by a superposition of plane waves at a given energy. By the
classical results on the theory of differential operators this can indeed be
justified for billiards in convex domains. On the contrary, in the present work
we demonstrate that eigenstates of non-convex billiards, in general, cannot be
approximated by any solution of the Helmholtz equation regular everywhere in
$\R^2$ (in particular, by linear combinations of a finite number of plane waves
having the same energy). From this we infer that PWDM cannot be applied to
billiards in non-convex domains. Furthermore, it follows from our results that
unlike the properties of integrable billiards, where each eigenstate can be
extended into the billiard exterior as a regular solution of the Helmholtz
equation, the eigenstates of non-convex billiards, in general, do not admit
such an extension.


title: Applications of CRACK in the Classification of Integrable Systems

abstract:
  Work on different classification problems is described as: the classification
of integrable vector evolution equations, NLS systems with two vector unknowns,
systems with one scalar and one vector unknown, classification of integrable
Hamiltonians and non-local 2+1 dimensional equations. All these problems lead
to large bi-linear algebraic systems to be solved. In an extended appendix an
overview of the computer algebra package is given that was used to solve these
systems.


title: Effective Hamiltonians for periodically driven systems

abstract:
  The dynamics of classical and quantum systems which are driven by a high
frequency ($\omega$) field is investigated. For classical systems the motion is
separated into a slow part and a fast part. The motion for the slow part is
computed perturbatively in powers of $\omega^{-1}$ to order $\omega^{-4}$ and
the corresponding time independent Hamiltonian is calculated. Such an effective
Hamiltonian for the corresponding quantum problem is computed to order
$\omega^{-4}$ in a high frequency expansion. Its spectrum is the quasienergy
spectrum of the time dependent quantum system. The classical limit of this
effective Hamiltonian is the classical effective time independent Hamiltonian.
It is demonstrated that this effective Hamiltonian gives the exact
quasienergies and quasienergy states of some simple examples as well as the
lowest resonance of a non trivial model for an atom trap. The theory that is
developed in the paper is useful for the analysis of atomic motion in atom
traps of various shapes.


title: Domain Walls in Two-Component Dynamical Lattices

abstract:
  We introduce domain-wall (DW) states in the bimodal discrete nonlinear
Schr{\"{o}}dinger equation, in which the modes are coupled by cross phase
modulation (XPM). By means of continuation from various initial patterns taken
in the anti-continuum (AC) limit, we find a number of different solutions of
the DW type, for which different stability scenarios are identified. In the
case of strong XPM coupling, DW configurations contain a single mode at each
end of the chain. The most fundamental solution of this type is found to be
always stable. Another solution, which is generated by a different AC pattern,
demonstrates behavior which is unusual for nonlinear dynamical lattices: it is
unstable for small values of the coupling constant $C$ (which measures the
ratio of the nonlinearity and coupling lengths), and becomes stable at larger
$C$. Stable bound states of DWs are also found. DW configurations generated by
more sophisticated AC patterns are identified as well, but they are either
completely unstable, or are stable only at small values of $C$. In the case of
weak XPM, a natural DW solution is the one which contains a combination of both
polarizations, with the phase difference between them 0 and $\pi $ at the
opposite ends of the lattice. This solution is unstable at all values of $C$,
but the instability is very weak for large $C$, indicating stabilization as the
continuum limit is approached. The stability of DWs is also verified by direct
simulations, and the evolution of unstable DWs is simulated too; in particular,
it is found that, in the weak-XPM system, the instability may give rise to a
moving DW.


title:
How does the Smaller Alignment Index (SALI) distinguish order from
  chaos?

abstract:
  The ability of the Smaller Alignment Index (SALI) to distinguish chaotic from
ordered motion, has been demonstrated recently in several
publications.\cite{Sk01,GRACM} Basically it is observed that in chaotic regions
the SALI goes to zero very rapidly, while it fluctuates around a nonzero value
in ordered regions. In this paper, we make a first step forward explaining
these results by studying in detail the evolution of small deviations from
regular orbits lying on the invariant tori of an {\bf integrable} 2D
Hamiltonian system. We show that, in general, any two initial deviation vectors
will eventually fall on the ``tangent space'' of the torus, pointing in
different directions due to the different dynamics of the 2 integrals of
motion, which means that the SALI (or the smaller angle between these vectors)
will oscillate away from zero for all time.


title: Nonlinear charge transport in DNA mediated by twist modes

abstract:
  Recent works on localized charge transport along DNA, based on a
three--dimensional, tight--binding model (Eur. Phys. J. B 30:211, 2002; Phys. D
180:256, 2003), suggest that charge transport is mediated by the coupling of
the radial and electron variables. However, these works are based on a linear
approximation of the distances among nucleotides, which forces for consistency
the assumption that the parameter $\alpha$, that describes the coupling between
the transfer integral and the distance between nucleotides is fairly small. In
the present letter we perform an improvement of the model which allows larger
values of $\alpha$, showing that there exist two very different regimes.
Particulary, for large $\alpha$, the conclusions of the previous works are
reversed and charge transport can be produced only by the coupling with the
twisting modes.


title: Acceleration of chemical reaction by chaotic mixing

abstract:
  Theory of fast binary chemical reaction, ${\cal A}+{\cal B}\to{\cal C}$, in a
statistically stationary chaotic flow at large Schmidt number ${Sc}$ and large
Damk\"ohler number ${Da}$ is developed. For stoichiometric condition we
identify subsequent stages of the chemical reaction. The first stage
corresponds to the exponential decay, $\propto\exp(-\lambda t)$ (where
$\lambda$ is the Lyapunov exponent of the flow), of the chemicals in the bulk
part of the flow. The second and the third stages are related to the chemicals
remaining in the boundary region. During the second stage the amounts of ${\cal
A}$ and ${\cal B}$ decay $\propto 1/\sqrt{t}$, whereas the decay law during the
third stage is exponential, $\propto\exp(-\gamma t)$, where
$\gamma\sim\lambda/\sqrt{Sc}$.


title: Fractal fractal dimensions of deterministic transport coefficients

abstract:
  If a point particle moves chaotically through a periodic array of scatterers
the associated transport coefficients are typically irregular functions under
variation of control parameters. For a piecewise linear two-parameter map we
analyze the structure of the associated irregular diffusion coefficient and
current by numerically computing dimensions from box-counting and from the
autocorrelation function of these graphs. We find that both dimensions are
fractal for large parameter intervals and that both quantities are themselves
fractal functions if computed locally on a uniform grid of small but finite
subintervals. We furthermore show that there is a simple functional
relationship between the structure of fractal fractal dimensions and the
difference quotient defined on these subintervals.