title: Nonlinear charge transport mechanism in periodic and disordered DNA

abstract:
  We study a model for polaron-like charge transport mechanism along DNA
molecules with emphasis on the impact of parametrical and structural disorder.
Our model Hamiltonian takes into account the coupling of the charge carrier to
two different kind of modes representing fluctuating twist motions of the base
pairs and H-bond distortions within the double helix structure of
$\lambda-$DNA. Localized stationary states are constructed with the help of a
nonlinear map approach for a periodic double helix and in the presence of
intrinsic static parametrical and/or structural disorder reflecting the impact
of ambient solvent coordinates. It is demonstrated that charge transport is
mediated by moving polarons respectively breather compounds carrying not only
the charge but causing also local temporal deformations of the helix structure
through the traveling torsion and bond breather components illustrating the
interplay of structure and function in biomolecules.


title: The decay of homogeneous anisotropic turbulence

abstract:
  We present the results of a numerical investigation of three-dimensional
decaying turbulence with statistically homogeneous and anisotropic initial
conditions. We show that at large times, in the inertial range of scales: (i)
isotropic velocity fluctuations decay self-similarly at an algebraic rate which
can be obtained by dimensional arguments; (ii) the ratio of anisotropic to
isotropic fluctuations of a given intensity falls off in time as a power law,
with an exponent approximately independent of the strength of the fluctuation;
(iii) the decay of anisotropic fluctuations is not self-similar, their
statistics becoming more and more intermittent as time elapses. We also
investigate the early stages of the decay. The different short-time behavior
observed in two experiments differing by the phase organization of their
initial conditions gives a new hunch on the degree of universality of
small-scale turbulence statistics, i.e. its independence of the conditions at
large scales.


title: Quantization of Classical Maps with tunable Ruelle-Pollicott Resonances

abstract:
  We investigate the correspondence between the decay of correlation in
classical system, governed by Ruelle--Pollicott resonances, and the properties
of the corresponding quantum system. For this purpose we construct classical
systems with controllable resonances together with their quantum counterpart.
As an application of such tailormade resonances we reveal the role of
Ruelle--Pollicott resonances for the localization properties of quantum energy
eigenstates.


title: Coverings and fundamental algebras for partial differential equations

abstract:
  Following I. S. Krasilshchik and A. M. Vinogradov, we regard PDEs as
infinite-dimensional manifolds with involutive distributions and consider their
special morphisms called differential coverings, which include constructions
like Lax pairs and Backlund transformations. We show that, similarly to usual
coverings in topology, at least for some PDEs differential coverings are
determined by actions of a sort of fundamental group. This is not a group, but
a certain system of Lie algebras, which generalize Wahlquist-Estabrook
algebras. From this we deduce an algebraic necessary condition for two PDEs to
be connected by a Backlund transformation. We compute these
infinite-dimensional Lie algebras for several KdV type equations and prove
non-existence of Backlund transformations.
  As a by-product, for some class of Lie algebras g we prove that any
subalgebra of g of finite codimension contains an ideal of g of finite
codimension.


title: Painleve test and higher order differential equations

abstract:
  Starting from the second Painlev\'{e} equation, we obtain Painlev\'{e} type
equations of higher order by using the singular point analysis.


title: Spectral properties of distance matrices

abstract:
  Distance matrices are matrices whose elements are the relative distances
between points located on a certain manifold. In all cases considered here all
their eigenvalues except one are non-positive. When the points are uncorrelated
and randomly distributed we investigate the average density of their
eigenvalues and the structure of their eigenfunctions. The spectrum exhibits
delocalized and strongly localized states which possess different power-law
average behaviour. The exponents depend only on the dimensionality of the
manifold.


title: Space-Time Complexity in Hamiltonian Dynamics

abstract:
  New notions of the complexity function C(epsilon;t,s) and entropy function
S(epsilon;t,s) are introduced to describe systems with nonzero or zero Lyapunov
exponents or systems that exhibit strong intermittent behavior with
``flights'', trappings, weak mixing, etc. The important part of the new notions
is the first appearance of epsilon-separation of initially close trajectories.
The complexity function is similar to the propagator p(t0,x0;t,x) with a
replacement of x by the natural lengths s of trajectories, and its introduction
does not assume of the space-time independence in the process of evolution of
the system. A special stress is done on the choice of variables and the
replacement t by eta=ln(t), s by xi=ln(s) makes it possible to consider
time-algebraic and space-algebraic complexity and some mixed cases. It is shown
that for typical cases the entropy function S(epsilon;xi,eta) possesses
invariants (alpha,beta) that describe the fractal dimensions of the space-time
structures of trajectories. The invariants (alpha,beta) can be linked to the
transport properties of the system, from one side, and to the Riemann
invariants for simple waves, from the other side. This analog provides a new
meaning for the transport exponent mu that can be considered as the speed of a
Riemann wave in the log-phase space of the log-space-time variables. Some other
applications of new notions are considered and numerical examples are
presented.


title: Local amplitude equation from non-local dynamics

abstract:
  We derive a closed equation for the shape of the free surface of a magnetic
fluid subject to an external magnetic field. The equation is strongly non-local
due to the long range character of the magnetic interaction. We develop a
systematic multiple scale perturbation expansion in which the non-locality is
reduced to the occurrence of the Hilbert transform of the surface profile. The
resulting third order amplitude equation describing the slow modulation of the
basic pattern is shown to be purely local.


title: Multi-site H-bridge breathers in a DNA--shaped double strand

abstract:
  We investigate the formation process of nonlinear vibrational modes
representing broad H-bridge multi--site breathers in a DNA--shaped double
strand.
  Within a network model of the double helix we take individual motions of the
bases within the base pair plane into account. The resulting H-bridge
deformations may be asymmetric with respect to the helix axis. Furthermore the
covalent bonds may be deformed distinctly in the two backbone strands.
  Unlike other authors that add different extra terms we limit the interaction
to the hydrogen bonds within each base pair and the covalent bonds along each
strand. In this way we intend to make apparent the effect of the characteristic
helicoidal structure of DNA. We study the energy exchange processes related
with the relaxation dynamics from a non-equilibrium conformation. It is
demonstrated that the twist-opening relaxation dynamics of a radially distorted
double helix attains an equilibrium regime characterized by a multi-site
H-bridge breather.


title: Hydrodynamic reductions of the heavenly equation

abstract:
  We demonstrate that Pleba\'nski's first heavenly equation decouples in
infinitely many ways into a triple of commuting (1+1)-dimensional systems of
hydrodynamic type which satisfy the Egorov property. Solving these systems by
the generalized hodograph method, one can construct exact solutions of the
heavenly equation parametrized by arbitrary functions of a single variable. We
discuss explicit examples of hydrodynamic reductions associated with the
equations of one-dimensional nonlinear elasticity, linearly degenerate systems
and the equations of associativity.


title: Classification of integrable quadratic Hamiltonians on e(3)

abstract:
  Linear Poisson brackets on e(3) typical of rigid body dynamics are
considered. All quadratic Hamiltonians of Kowalevski type having additional
first integral of fourth degree are found. Quantum analogs of these
Hamiltonians are listed.


title: Some notes on Ishimori's magnet model

abstract:
  Gauge transformation properties for an associated linear system of model
Ishimori's magnet model have been discussed. Explicit formulas for the gauge
transformation matrix have been obtained. Darboux Transformation has been
suggested and appropriate dressing relations have been found.


title:
The Zero-Dispersion Limit for the Odd Flows in the Focusing
  Zakharov-Shabat Hierarchy

abstract:
  We present a numerical and theoretical study of the zero-dispersion limit of
the focusing Zakharov-Shabat hierarchy, which includes NLS and mKdV flows as
its second and third members. All the odd flows in the hierachy are shown to
preserve real-valued data. We establish the zero-dispersion limit of all the
nontrivial conserved densities and associated fluxes for these odd flows for a
large class of real-valued initial data which includes all ``single hump''
initial data. In particular, it is done for the ``focusing'' mKdV flow. The
method is based on the Lax-Levermore KdV strategy, but here it is carried out
in the context of a nonselfadjoint spectral problem. We find that after an
algebraic transformation the limiting dynamics of the mKdV equation is
identical to that of the KdV equation.


title: The CKP hierarchy and the WDVV prepotential

abstract:
  Using a multicomponent version of the CKP hierarchy we construct the
prepotential of the WDVV equations.


title:
Coarse Bifurcation Diagrams via Microscopic Simulators: A State-Feedback
  Control-Based Approach

abstract:
  The arc-length continuation framework is used for the design of state
feedback control laws that enable a microscopic simulator trace its own
open-loop coarse bifurcation diagram. The steering of the system along solution
branches is achieved through the manipulation of the bifurcation parameter,
which becomes our actuator. The design approach is based on the assumption that
the eigenvalues of the linearized system can be decomposed into two well
separated clusters: one containing eigenvalues with large negative real parts
and one containing (possibly unstable) eigenvalues close to the origin.


title: Higher order terms in multiscale expansions: a linearized KdV hierarchy

abstract:
  We consider a wide class of model equations, able to describe wave
propagation in dispersive nonlinear media. The Korteweg-de Vries (KdV) equation
is derived in this general frame under some conditions, the physical meanings
of which are clarified. It is obtained as usual at leading order in some
multiscale expansion. The higher order terms in this expansion are studied
making use of a multi-time formalism and imposing the condition that the main
term satisfies the whole KdV hierarchy. The evolution of the higher order terms
with respect to the higher order time variables can be described through the
introduction of a linearized KdV hierarchy. This allows one to give an
expression of the higher order time derivatives that appear in the right hand
member of the perturbative expansion equations, to show that overall the higher
order terms do not produce any secularity and to prove that the formal
expansion contains only bounded terms.


title:
Solutions of the generalized Weierstrass representation in
  four-dimensional Euclidean space

abstract:
  Several classes of solutions of the generalized Weierstrass system, which
induces constant mean curvature surfaces into four-dimensional Euclidean space
are constructed. A gauge transformation allows us to simplify the system
considered and derive factorized classes of solutions. A reduction of the
generalized Weierstrass system to decoupled CP^1 sigma models is also
considered. A new procedure for constructing certain classes of solutions,
including elementary solutions (kinks and bumps) and multisoliton solutions is
described in detail. The constant mean curvature surfaces associated with
different types of solutions are presented. Some physical interpretations of
the results obtained in the area of string theory are given.


title:
Competition of synchronization domains in arrays of chaotic homoclinic
  systems

abstract:
  We investigate the response of an open chain of bidirectionally coupled
chaotic homoclinic systems to external periodic stimuli. When one end of the
chain is driven by a periodic signal, the system propagates a phase
synchronization state in a certain range of coupling strengths and external
frequencies. When two simultaneous forcings are applied at different points of
the array, a rich phenomenology of stable competitive states is observed,
including temporal alternation and spatial coexistence synchronization domains.


title: Additional symmetries and solutions of the dispersionless KP hierarchy

abstract:
  The dispersionless KP hierarchy is considered from the point of view of the
twistor formalism. A set of explicit additional symmetries is characterized and
its action on the solutions of the twistor equations is studied. A method for
dealing with the twistor equations by taking advantage of hodograph type
equations is proposed. This method is applied for determining the orbits of
solutions satisfying reduction constraints of Gelfand--Dikii type under the
action of additional symmetries.


title: Instabilities and Bifurcations of Nonlinear Impurity Modes

abstract:
  We study the structure and stability of nonlinear impurity modes in the
discrete nonlinear Schr{\"o}dinger equation with a single on-site nonlinear
impurity emphasizing the effects of interplay between discreteness,
nonlinearity and disorder. We show how the interaction of a nonlinear localized
mode (a discrete soliton or discrete breather) with a repulsive impurity
generates a family of stationary states near the impurity site, as well as
examine both theoretical and numerical criteria for the transition between
different localized states via a cascade of bifurcations.


title:
Semiclassical theory of spin-orbit interaction in the extended phase
  space

abstract:
  We consider the semiclassical theory in a joint phase space of spin and
orbital degrees of freedom. The method is developed from the path integrals
using the spin-coherent-state representation, and yields the trace formula for
the density of states. We discuss special cases, such as weak and strong
spin-orbit coupling, and relate the present theory to the earlier approaches.


title: Painleve equations from Darboux chains - Part 1: P3-P5

abstract:
  We show that the Painleve equations P3-P5 can be derived (in a unified way)
from a periodic sequence of Darboux transformations for a Schrodinger problem
with quadratic eigenvalue dependency. The general problem naturally divides
into three different branches, each described by an infinite chain of
equations. The Painleve equations are obtained by closing the chain
periodically at the lowest nontrivial level(s). The chains provide ``symmetric
forms'' for the Painleve equations, from which Hirota bilinear forms and Lax
pairs are derived. In this paper (Part 1) we analyze in detail the cases P3-P5,
while P6 will be studied in Part 2.


title: Anomalous transport: a deterministic approach

abstract:
  We introduce a cycle-expansion (fully deterministic) technique to compute the
asymptotic behavior of arbitrary order transport moments. The theory is applied
to different kinds of one-dimensional intermittent maps, and Lorentz gas with
infinite horizon, confirming the typical appearance of phase transitions in the
transport spectrum.


title: Fluctuational transitions through a fractal basin boundary

abstract:
  Fluctuational transitions between two co-existing chaotic attractors,
separated by a fractal basin boundary, are studied in a discrete dynamical
system. It is shown that the mechanism for such transitions is determined by a
hierarchy of homoclinic points. The most probable escape path from the chaotic
attractor to the fractal boundary is found using both statistical analyses of
fluctuational trajectories and the Hamiltonian theory of fluctuations.


title:
Non-deterministic density classification with diffusive probabilistic
  cellular automata

abstract:
  We present a probabilistic cellular automaton (CA) with two absorbing states
which performs classification of binary strings in a non-deterministic sense.
In a system evolving under this CA rule, empty sites become occupied with a
probability proportional to the number of occupied sites in the neighborhood,
while occupied sites become empty with a probability proportional to the number
of empty sites in the neighborhood. The probability that all sites become
eventually occupied is equal to the density of occupied sites in the initial
string.


title: Markovian solutions of inviscid Burgers equation

abstract:
  For solutions of (inviscid, forceless, one dimensional) Burgers equation with
random initial condition, it is heuristically shown that a stationary
Feller-Markov property (with respect to the space variable) at some time is
conserved at later times, and an evolution equation is derived for the
infinitesimal generator. Previously known explicit solutions such as
Frachebourg-Martin's (white noise initial velocity) and Carraro-Duchon's L\'evy
process intrinsic-statistical solutions (including Brownian initial velocity)
are recovered as special cases.


title:
Flame Front Propagation and Finger Competition and Formation of a Single
  Saffman-Taylor Finger without Surface Tension - PhD Thesis

abstract:
  Problems of interface growth have received much attention recently Such are,
for example, the duffusion limited aggregation (DLA), random sequential
adsorption (RSA), Laplacian growth or flame front propagation. We will mainly
pay attention in this Thesis to the numerical and analytical investigation of
the last two problems. In addition to the fact that flame front propagation is
an interesting physical problem we feel that we can also explain experimental
results on the basis of theoretical investigations. There exists possibility to
use methods found for the flame front propagation, in different fields where
similar problems appear such as the important model of Laplacian growth .


title: A classical scaling theory of quantum resonances

abstract:
  The quantum resonances occurring with delta-kicked particles are studied with
the help of a fictitious classical limit, establishing a direct correspondence
between the nearly resonant quantum motion and the classical resonances of a
related system. A scaling law which characterizes the structure of the resonant
peaks is derived and numerically demonstrated.


title:
Flame front propagation I: The Geometry of Developing Flame Fronts:
  Analysis with Pole Decomposition

abstract:
  The roughening of expanding flame fronts by the accretion of cusp-like
singularities is a fascinating example of the interplay between instability,
noise and nonlinear dynamics that is reminiscent of self-fractalization in
Laplacian growth patterns. The nonlinear integro-differential equation that
describes the dynamics of expanding flame fronts is amenable to analytic
investigations using pole decomposition. This powerful technique allows the
development of a satisfactory understanding of the qualitative and some
quantitative aspects of the complex geometry that develops in expanding flame
fronts.


title:
Flame front propagation V: Stability Analysis of Flame Fronts: Dynamical
  Systems Approach in the Complex Plane

abstract:
  We consider flame front propagation in channel geometries. The steady state
solution in this problem is space dependent, and therefore the linear stability
analysis is described by a partial integro-differential equation with a space
dependent coefficient. Accordingly it involves complicated eigenfunctions. We
show that the analysis can be performed to required detail using a finite order
dynamical system in terms of the dynamics of singularities in the complex
plane, yielding detailed understanding of the physics of the eigenfunctions and
eigenvalues.


title:
Flame front propagation III: Random Noise and Pole-Dynamics in Unstable
  Front Propagation (new version)

abstract:
  The problem of flame propagation is studied as an example of unstable fronts
that wrinkle on many scales. The analytic tool of pole expansion in the complex
plane is employed to address the interaction of the unstable growth process
with random initial conditions and perturbations. We argue that the effect of
random noise is immense and that it can never be neglected in sufficiently
large systems. We present simulations that lead to scaling laws for the
velocity and acceleration of the front as a function of the system size and the
level of noise, and analytic arguments that explain these results in terms of
the noisy pole dynamics.terms of the dynamics of singularities in the complex
plane, yielding detailed understanding of the physics of the eigenfunctions and
eigenvalues.


title:
Flame front propagation VI: Dynamics and Wrinkling of Radially
  Propagating Fronts Inferred from Scaling Laws in Channel Geometries

abstract:
  Flame Propagation is used as a prototypical example of expanding fronts that
wrinkle without limit in radial geometries but reach a simple shape in channel
geometry. We show that the relevant scaling laws that govern the radial growth
can be inferred once the simpler channel geometry is understood in detail. In
radial geometries (in contrast to channel geometries) the effect of external
noise is crucial in accelerating and wrinkling the fronts. Nevertheless, once
the interrelations between system size, velocity of propagation and noise level
are understood in channel geometry, the scaling laws for radial growth follow.


title: Time independent description of rapidly oscillating potentials

abstract:
  The classical and quantum dynamics in a high frequency field are found to be
described by an effective time independent Hamiltonian. It is calculated in a
systematic expansion in the inverse of the frequency ($\omega$) to order
$\omega^{-4}$. The work is an extension of the classical result for the Kapitza
pendulum, which was calculated in the past to order $\omega^{-2}$. The analysis
makes use of an implementation of the method of separation of time scales and
of a quantum gauge transformation in the framework of Floquet theory. The
effective time independent Hamiltonian enables one to explore the dynamics in
presence of rapidly oscillating fields, in the framework of theories that were
developed for systems with time independent Hamiltonians. The results are
relevant, in particular, for exploration of the dynamics of cold atoms.


title:
Feedback Loops Between Fields and Underlying Space Curvature: an
  Augmented Lagrangian Approach

abstract:
  We demonstrate a systematic implementation of coupling between a scalar field
and the geometry of the space (curve, surface, etc.) which carries the field.
This naturally gives rise to a feedback mechanism between the field and the
geometry. We develop a systematic model for the feedback in a general form,
inspired by a specific implementation in the context of molecular dynamics (the
so-called Rahman-Parrinello molecular dynamics, or RP-MD). We use a generalized
Lagrangian that allows for the coupling of the space's metric tensor (the first
fundamental form) to the scalar field, and add terms motivated by RP-MD. We
present two implementations of the scheme: one in which the metric is only
time-dependent [which gives rise to ordinary differential equation (ODE) for
its temporal evolution], and one with spatio-temporal dependence [wherein the
metric's evolution is governed by a partial differential equation (PDE)].
Numerical results are reported for the (1+1)-dimensional model with a
nonlinearity of the sine-Gordon type.


title: Discrete gap solitons in a diffraction-managed waveguide array

abstract:
  A model including two nonlinear chains with linear and nonlinear couplings
between them, and opposite signs of the discrete diffraction inside the chains,
is introduced. For [$\chi ^{(3)}$] nonlinearity, the model finds two different
interpretations in terms of optical waveguide arrays, based on the
diffraction-management concept. A straightforward discrete [$\chi ^{(2)}$]
model, with opposite signs of the diffraction at the fundamental and second
harmonics, is introduced also. Starting from the anti-continuum (AC) limit,
soliton solutions in the $\chi ^{(3)}$ model are found, both above the phonon
band and inside the gap. Solitons above the gap may be stable as long as they
exist, but in the transition to the continuum limit they inevitably disappear.
On the contrary, solitons inside the gap persist all the way up to the
continuum limit. In the zero-mismatch case, they lose their stability long
before reaching the continuum limit, but finite mismatch can have a stabilizing
effect on them. A special procedure is developed to find discrete counterparts
of the Bragg-grating gap solitons. It is concluded that they exist all the
values of the coupling constant, but are stable only in the AC and continuum
limits. Solitons are also found in the $\chi ^{(2)}$ model. They start as
stable solutions, but then lose their stability. Direct numerical simulations
in the cases of instability reveal a variety of scenarios, including
spontaneous transformation of the solitons into breather-like states,
destruction of one of the components (in favor of the other), and
symmetry-breaking effects. Quasi-periodic, as well as more complex, time
dependences of the soliton amplitudes are also observed as a result of the
instability development.


title:
Classical transcendental solutions of the Painlev\'e equations and their
  degeneration

abstract:
  We present a determinant expression for a family of classical transcendental
solutions of the Painlev\'e V and the Painlev\'e VI equation. Degeneration of
these solutions along the process of coalescence for the Painlev\'e equations
is discussed.


title: On Whitham theory for perturbed integrable equations

abstract:
  Whitham theory of modulations is developed for periodic waves described by
nonlinear wave equations integrable by the inverse scattering transform method
associated with $2\times2$ matrix or second order scalar spectral problems. The
theory is illustrated by derivation of the Whitham equations for perturbed
Korteweg-de Vries equation and nonlinear Schr\"odinger equation with linear
damping.


title: Breathers in a model of a polymer with secondary structure

abstract:
  A simple model of a polymer is considered: a chain of (different) point
masses, connected by harmonic springs, embedded in two dimensional space. In
order to determine conditions for existence and stability of breather
excitations, the method of numerical continuation of a breather solution from
the anticontinuous limit is employed. Approaching the limit of equal masses,
stable breather solutions are found only within an extremely narrow band of
frequencies.


title:
Noise-induced failures of chaos stabilization: large fluctuations and
  their control

abstract:
  Noise-induced failures in the stabilization of an unstable orbit in the
one-dimensional logistic map are considered as large fluctuations from a stable
state. The properties of the large fluctuations are examined by determination
and analysis of the optimal path and the optimal fluctuational force
corresponding to the stabilization failure. The problem of controlling
noise-induced large fluctuations is discussed, and methods of control have been
developed.


title: Negative Volterra flows

abstract:
  Taking the standard zero curvature approach we derive an infinite set of
integrable equations, which taken together form the negative Volterra
hierarchy. The resulting equations turn out to be nonlocal, which is usual for
the negative flows. However, in some cases the nonlocality can be eliminated.
Studying the combined action of both positive (classical) and negative Volterra
flows, i.e. considering the differential consequences of equations of the
extended Volterra hierarchy, we deduce local equations which seem to be
promising from the viewpoint of applications. The presented results give
answers to some questions related to the classification of integrable
differential-difference equations. We also obtain dark solitons of the negative
Volterra hierarchy using an elementary approach.


title:
Renormalization Group Reduction of the Henon Map and Application to the
  Transverse Betatron Motion in Cyclic Accelerators

abstract:
  The renormalization group method is applied to the study of discrete
dynamical systems. As a particular example, the Henon map is considered as
applied to describe the transverse betatron oscillations in a cyclic
accelerator or storage ring possessing a FODO-cell structure with a single thin
sextupole. A powerful renormalization group method is developed that is valid
correct to fourth order in the perturbation amplitude, and a technique for
resolving the resonance structure of the Henon map is also presented. This
calculation represents the first successful application of a renormalization
group method to the study of discrete dynamical system in a unified manner
capable of reducing the dynamics of the system both far from and close to
resonances, thus preserving the symplectic symmetry of the original map.


title: Kinematic simulation of multi point turbulent dispersion

abstract:
  As three particles are advected by a turbulent flow, they separate from each
other and develop non trivial geometries, which effectively reflect the
structure of the turbulence. We investigate here the geometry, in a statistical
sense, of three Lagrangian particles advected, in 2-dimensions, by Kinematic
Simulation (KS). KS is a Lagrangian model of turbulent diffusion that makes no
use of any delta correlation in time at any level. With this approach,
situations with a very large range of inertial scales and varying persistence
of spatial flow structure can be studied.
  We first show numerically that the model flow reproduces recent experimental
results at low Reynolds numbers. The statistical properties of the shape
distribution at much higher Reynolds number is then considered. Even at the
highest available inertial range, of scale, corresponding to a ratio between
large and small scales of $L/\eta \approx 17,000$, we find that the radius of
gyration of the three points does not precisely follow Richardson's prediction.
The shapes of the triangles have a high probability to be elongated. The
corresponding shape distribution is not found to be perfectly self similar,
even for our highest ratio of inertial scales. We also discuss how the
parameters of the synthetic flow, such as the exponent of the spectrum and the
effect of the sweeping affect our results. Our results suggest that a non
trivial distribution of shapes will be observed at high Reynolds numbers,
although it may not be exactly self similar. Special attention is given to the
effects of persistence of spatial flow structure.


title: Stability domains for time-delay feedback control with latency

abstract:
  We generalize a known analytical method for determining the stability of
periodic orbits controlled by time-delay feedback methods when latencies
associated with the generation and injection of the feedback signal cannot be
ignored. We discuss the case of extended time-delay autosynchronization (ETDAS)
and show that nontrivial qualitative features of the domain of control observed
in experiments can be explained by taking into account the effects of both the
unstable eigenmode and a single stable eigenmode in the Floquet theory.


title: On Breaking Time Reversal in a Simple, Smooth, Chaotic System

abstract:
  Within random matrix theory, the statistics of the eigensolutions depend
fundamentally on the presence (or absence) of time reversal symmetry. Accepting
the Bohigas-Giannoni-Schmit conjecture, this statement extends to quantum
systems with chaotic classical analogs. For practical reasons, much of the
supporting numerical studies of symmetry breaking have been done with billiards
or maps, and little with simple, smooth systems. There are two main
difficulties in attempting to break time reversal invariance in a continuous
time system with a smooth potential. The first is avoiding false symmetry
breaking. The second is locating a parameter regime in which the symmetry
breaking is strong enough to transition the fluctuation properties fully toward
the broken symmetry case, and yet remain weak enough so as not to regularize
the dynamics sufficiently that the system is no longer chaotic. We give an
example of a system of two-coupled quartic oscillators whose energy level
statistics closely match those of the Gaussian unitary ensemble, and which
possesses only a minor proportion of regular motion in its phase space.


title:
Light bullets in quadratic media with normal dispersion at the second
  harmonic

abstract:
  Stable two- and three-dimensional spatiotemporal solitons (STSs) in
second-harmonic-generating media are found in the case of normal dispersion at
the second harmonic (SH). This result, surprising from the theoretical
viewpoint, opens a way for experimental realization of STSs. An analytical
estimate for the existence of STSs is derived, and full results, including a
complete stability diagram, are obtained in a numerical form. STSs withstand
not only the normal SH dispersion, but also finite walk-off between the
harmonics, and readily self-trap from a Gaussian pulse launched at the
fundamental frequency.


title:
Universality of anisotropic fluctuations from numerical simulations of
  turbulent flows

abstract:
  We present new results from a direct numerical simulation of a three
dimensional homogeneous Rayleigh-Benard system (HRB), i.e. a convective cell
with an imposed linear mean temperature profile along the vertical direction.
We measure the SO(3)-decomposition of both velocity structure functions and
buoyancy terms. We give a dimensional prediction for the values of the
anisotropic scaling exponents in this Rayleigh-Benard systems. Measured scaling
does not follow dimensional estimate, while a better agreement can be found
with the anisotropic scaling of a different system, the random-Kolmogorov-flow
(RKF). Our findings support the conclusion that scaling properties of
anisotropic fluctuations are universal, i.e. independent of the forcing
mechanism sustaining the turbulent flow.


title:
Direct Scattering Processes and Signatures of Chaos in Quantum
  Waveguides

abstract:
  The effect of direct processes on the statistical properties of deterministic
scattering processes in a chaotic waveguide is examined. The single channel
Poisson kernel describes well the distribution of S-matrix eigenphases when
evaluated over an energy interval. When direct processes are transformed away,
the scattering processes exhibit universal random matrix behavior. The effect
of chaos on scattering wavefunctions,eigenphases, and time delays is discussed.


title:
Prevalence of Milnor Attractors and Chaotic Itinerancy in
  'High'-dimensional Dynamical Systems

abstract:
  Dominance of Milnor attractors in high-dimensional dynamical systems is
reviewed, with the use of globally coupled maps. From numerical simulations,
the threshold number of degrees of freedom for such prevalence of Milnor
attractors is suggested to be $5 \sim 10$, which is also estimated from an
argument of combinatorial explosion of basin boundaries. Chaotic itinerancy is
revisited from the viewpoint of Milnor attractors. Relevance to neural networks
is discussed.


title: Soliton generation by local resonance interaction

abstract:
  In this paper we show a mechanism of the soliton generation in nonlinear
Schrodinger equation due to a small fast oscillating driving force.


title:
Filament bifurcations in a one-dimensional model of reacting excitable
  fluid flow

abstract:
  Recently, it has been shown that properties of excitable media stirred by
two-dimensional chaotic flows can be properly studied in a one-dimensional
framework \cite{excitablePRL,excitablePRE}, describing the transverse profile
of the filament-like structures observed in the system. Here, we perform a
bifurcation analysis of this one-dimensional approximation as a function of the
{\it Damk{\"o}hler} number, the ratio between the chemical and the strain
rates. Different branches of stable solutions are calculated, and a Hopf
bifurcation, leading to an oscillating filament, identified.


title:
Instabilities in the two-dimensional cubic nonlinear Schrodinger
  equation

abstract:
  The two-dimensional cubic nonlinear Schrodinger equation (NLS) can be used as
a model of phenomena in physical systems ranging from waves on deep water to
pulses in optical fibers. In this paper, we establish that every
one-dimensional traveling wave solution of NLS with trivial phase is unstable
with respect to some infinitesimal perturbation with two-dimensional structure.
If the coefficients of the linear dispersion terms have the same sign then the
only unstable perturbations have transverse wavelength longer than a
well-defined cut-off. If the coefficients of the linear dispersion terms have
opposite signs, then there is no such cut-off and as the wavelength decreases,
the maximum growth rate approaches a well-defined limit.


title: Strong Universality in Forced and Decaying Turbulence

abstract:
  The weak version of universality in turbulence refers to the independence of
the scaling exponents of the $n$th order strcuture functions from the
statistics of the forcing. The strong version includes universality of the
coefficients of the structure functions in the isotropic sector, once
normalized by the mean energy flux. We demonstrate that shell models of
turbulence exhibit strong universality for both forced and decaying turbulence.
The exponents {\em and} the normalized coefficients are time independent in
decaying turbulence, forcing independent in forced turbulence, and equal for
decaying and forced turbulence. We conjecture that this is also the case for
Navier-Stokes turbulence.


title:
Non-local Interaction Effects on Pattern Formation in Population
  Dynamics

abstract:
  We consider a model for population dynamics such as for the evolution of
bacterial colonies which is of the Fisher type but where the competitive
interaction among individuals is non-local, and show that spatial structures
with interesting features emerge. These features depend on the nature of the
competitive interaction as well as on its range, specifically on the presence
or absence of tails in, and the central curvature of, the influence function of
the interaction.


title: Symmetry Induced Heteroclinic Cycles in a CO2 Laser

abstract:
  The conditions for the existence of heteroclinic connections between the
transverse modes of a CO2 laser whose setup has a perfect cylindrical symmetry
are discussed by symmetry arguments for the cases of three, four and five
interacting modes. Explicit conditions for the parameters are derived, which
can guide observation of such phenomena.


title:
Recovering Isotropic Statistics in Turbulence Simulations: The
  Kolmogorov 4/5th-Law

abstract:
  One of the main benchmarks in direct numerical simulations of
three-dimensional turbulence is the Kolmogorov 1941 prediction for third-order
structure functions with homogeneous and isotropic statistics in the
infinite-Reynolds number limit. Previous DNS techniques to obtain isotropic
statistics have relied on time-averaging structure functions in a few
directions over many eddy turnover times, using forcing schemes carefully
constructed to generate isotropic data. Motivated by recent theoretical work
which removes isotropy requirements by spherically averaging structure
functions over all directions, we will present results which supplement
long-time averaging by angle-averaging over up to 73 directions from a single
flow snapshot. The directions are among those natural to a square computational
grid, and are weighted to approximate the spherical average. The averaging
process is cheap, and for the
  Kolmogorov 1941 4/5ths law, reasonable results can be obtained from a single
snapshot of data. This procedure may be used to investigate the isotropic
statistics of any quantity of interest.


title: Nonperiodic Oscillations of Pressure in a Spark Ignition Engine

abstract:
  We report our results on non-periodic experimental time series of pressure in
a spark ignition engine. The experiments were performed for a low rotational
velocity of a crankshaft and a relatively large spark advance angle. We show
that the combustion process has many chaotic features. Surprisingly, the
reconstructed attractor has a characteristic butterfly shape similar to a
chaotic attractor of Lorentz type. The suitable recurrence plot shows that the
dynamics of the combustion is a nonlinear multidimensional process mediated by
stochastic noise.


title:
Uniform semiclassical approximations on a topologically non-trivial
  configuration space: The hydrogen atom in an electric field

abstract:
  Semiclassical periodic-orbit theory and closed-orbit theory represent a
quantum spectrum as a superposition of contributions from individual classical
orbits. Close to a bifurcation, these contributions diverge and have to be
replaced with a uniform approximation. Its construction requires a normal form
that provides a local description of the bifurcation scenario. Usually, the
normal form is constructed in flat space. We present an example taken from the
hydrogen atom in an electric field where the normal form must be chosen to be
defined on a sphere instead of a Euclidean plane. In the example, the necessity
to base the normal form on a topologically non-trivial configuration space
reveals a subtle interplay between local and global aspects of the phase space
structure. We show that a uniform approximation for a bifurcation scenario with
non-trivial topology can be constructed using the established uniformization
techniques. Semiclassical photo-absorption spectra of the hydrogen atom in an
electric field are significantly improved when based on the extended uniform
approximations.


title: Dynamics and computation in functional shifts

abstract:
  We introduce a new type of shift dynamics as an extended model of symbolic
dynamics, and investigate the characteristics of shift spaces from the
viewpoints of both dynamics and computation. This shift dynamics is called a
functional shift that is defined by a set of bi-infinite sequences of some
functions on a set of symbols. To analyze the complexity of functional shifts,
we measure them in terms of topological entropy, and locate their languages in
the Chomsky hierarchy. %Through this study, we argue that complexity of
dynamics does not correspond to that of computation. Through this study, we
argue that considering functional shifts from the viewpoints of both dynamics
and computation give us opposite results about the complexity of systems. We
also describe a new class of shift spaces whose languages are not recursively
enumerable.


title: Counting nodal domains

abstract:
  We consider the nodal domains of Gaussian random waves in two dimensions. We
present a method to calculate the distribution of the number of nodal domains
and the average connectivity with the help of auxiliary Potts-spins. An
analytical approach could be helpful to decide whether the pattern of nodal
domains belongs to the universality class of short-ranged percolation. This is
not completely evident since we find (weak) long-ranged correlations between
distant avoided nodal intersections.


title: Nonlinear Vibration in Gear Systems

abstract:
  Gear box dynamics is characterised by a periodically changing stiffness and a
backlash which can lead to a loss of the contact between the teeth. Due to
backlash, the gear system has piecewise linear stiffness characteristics and,
in consequence, can vibrate regularly or chaoticaly depending on the system
parameters and the initial conditions. We examine the possibility of a
nonfeedback system control by introducing a weak resonant excitation term and
through adding an additional degree of freedom to account for shaft flexibility
on one side of the gearbox. We shall show that by correctly choosing the
coupling values the system vibrations may be controlled.


title: Analytic solitary waves of nonintegrable equations

abstract:
  Even if it is nonintegrable, a differential equation may nevertheless admit
particular solutions which are globally analytic. On the example of the
dynamical system of Kuramoto and Sivashinsky, which is generically chaotic and
presents a high physical interest, we review various methods, all based on the
structure of singularities, allowing us to characterize the analytic solution
which depends on the largest possible number of constants of integration.


title: Wavefunction statistics in open chaotic billiards

abstract:
  We study the statistical properties of wavefunctions in a chaotic billiard
that is opened up to the outside world. Upon increasing the openings, the
billiard wavefunctions cross over from real to complex. Each wavefunction is
characterized by a phase rigidity, which is itself a fluctuating quantity. We
calculate the probability distribution of the phase rigidity and discuss how
phase rigidity fluctuations cause long-range correlations of intensity and
current density. We also find that phase rigidities for wavefunctions with
different incoming wave boundary conditions are statistically correlated.


title: Phase Structures of Resource Allocation Games

abstract:
  We consider a class of games that are generalizations of the minority game,
in that the demand and supply of the resource are specified independently. This
allows us to study systems in which agents compete for a resource under
different demand loads. Among other features, we find, using numerical
simulations the existence of a robust phase change with a coexistence region as
the demand load is varied, separating regions with nearly balanced supply and
demand from regions of scarce or abundant resources. The coexistence region
exists when the amount of information used by the agents to make their choices
is greater than a critical value, which is related to the point at which there
is a phase transition in the standard minority game.


title: Scars on quantum networks ignore the Lyapunov exponent

abstract:
  We show that enhanced wavefunction localization due to the presence of short
unstable orbits and strong scarring can rely on completely different
mechanisms. Specifically we find that in quantum networks the shortest and most
stable orbits do not support visible scars, although they are responsible for
enhanced localization in the majority of the eigenstates. Scarring orbits are
selected by a criterion which does not involve the classical Lyapunov exponent.
We obtain predictions for the energies of visible scars and the distributions
of scarring strengths and inverse participation ratios.


title:
Reverse Integration for Computing Stationary Points of Unstable Stiff
  Systems

abstract:
  Using existing, forward-in-time integration schemes, we demonstrate that it
is possible to compute unstable, saddle-type fixed points of stiff systems of
ODEs when the stable compenents are fast (i.e., rapidly damped) while the
unstable components are slow. The approach has implications for the reverse
(backward in time) integration of such stiff systems, and for the coarse
reverse integration of microscopic/stochastic simulations.


title:
Sur la "solution analytique ge'ne'rale" d'une e'quation diffe'rentielle
  chaotique du troisie`me ordre


title:
Efficient Algorithm on a Non-staggered Mesh for Simulating
  Rayleigh-Benard Convection in a Box

abstract:
  An efficient semi-implicit second-order-accurate finite-difference method is
described for studying incompressible Rayleigh-Benard convection in a box, with
sidewalls that are periodic, thermally insulated, or thermally conducting.
Operator-splitting and a projection method reduce the algorithm at each time
step to the solution of four Helmholtz equations and one Poisson equation, and
these are are solved by fast direct methods. The method is numerically stable
even though all field values are placed on a single non-staggered mesh
commensurate with the boundaries. The efficiency and accuracy of the method are
characterized for several representative convection problems.


title: Multi-gap discrete vector solitons

abstract:
  We analyze nonlinear collective effects in periodic systems with multi-gap
transmission spectra such as light in waveguide arrays or Bose-Einstein
condensates in optical lattices. We demonstrate that the inter-band
interactions in nonlinear periodic gratings can be efficiently managed by
controlling their geometry, and predict novel types of discrete vector solitons
supported by nonlinear coupling between different bandgaps and study their
stability.


title: N-soliton collision in the Manakov model

abstract:
  We investigate soliton collisions in the Manakov model, which is a system of
coupled nonlinear Schroedinger equations that is integrable via the inverse
scattering method. Computing the asymptotic forms of the general N-soliton
solution in the limits $t \to \mp \infty$, we elucidate a mechanism that
factorizes an N-soliton collision into a nonlinear superposition of $N \choose
2$ pair collisions with arbitrary order. This removes the misunderstanding that
multi-particle effects exist in the Manakov model and provides a new
``set-theoretical'' solution to the quantum Yang-Baxter equation. As a
by-product, we also obtain a new nontrivial relation among determinants and
extended determinants.

categories: nlin.SI hep-th math-ph math.MP math.QA physics.optics


title: Promiscuity and the Evolution of Sexual Transmitted Diseases

abstract:
  We study the relation between different social behaviors and the onset of
epidemics in a model for the dynamics of sexual transmitted diseases. The model
considers the society as a system of individual sexuated agents that can be
organized in couples and interact with each other. The different social
behaviors are incorporated assigning what we call a promiscuity value to each
individual agent. The individual promiscuity is taken from a distributions and
represents the daily probability of going out to look for a sexual partner,
abandoning its eventual mate. In terms of this parameter we find a threshold
for the epidemic which is much lower than the classical fully mixed model
prediction, i.e. $R_0$ (basic reproductive number) $= 1$. Different forms for
the distribution of the population promiscuity are considered showing that the
threshold is weakly sensitive to them. We study the homosexual and the
heterosexual case as well.


title:
The N=2 Supersymmetric Heavenly Equation and Its Super-Hydrodynamical
  Reduction

abstract:
  Manifest N=2 supersymmetric Toda systems are constructed from the $sl(n,n+1)$
superalgebras by taking into account their complex structure. In the $n\to
\infty$ continuum limit an N=2 extension of the $(2+1)$-dimensional heavenly
equation is obtained. The integrability is guaranteed by the existence of a
supersymmetric Lax pair. We further analyze the properties of the
$(1+1)$-dimensionally reduced system. Its bosonic sector is of hydrodynamical
type. This is not the case for the whole supersymmetric system which, however,
is super-hydrodynamical when properly expressed in terms of a supergeometry
involving superfields and fermionic derivatives.


title: Generalization of the Goryachev-Chaplygin Case

abstract:
  In this paper we present a generalization of the Goryachev-Chaplygin
integrable case on a bundle of Poisson brackets, and on Sokolov terms in his
new integrable case of Kirchhoff equations. We also present a new analogous
integrable case for the quaternion form of rigid body dynamics' equations. This
form of equations is recently developed and we can use it for the description
of rigid body motions in specific force fields, and for the study of different
problems of quantum mechanics. In addition we present new invariant relations
in the considered problems.


title:
An improved $\eps$ expansion for three-dimensional turbulence: summation
  of nearest dimensional singularities

abstract:
  An improved $\eps$ expansion in the $d$-dimensional ($d > 2$) stochastic
theory of turbulence is constructed by taking into account pole singularities
at $d \to 2$ in coefficients of the $\eps$ expansion of universal quantities.
Effectiveness of the method is illustrated by a two-loop calculation of the
Kolmogorov constant in three dimensions.


title: The discrete KP and KdV equations over finite fields

abstract:
  We propose the algebro-geometric mothod of construction of solutions of the
discrete KP equation over a finite field. We also perform the corresponding
reduction to the finite field version of the discrete KdV equation. We write
down formulas which allow to construct multisoliton solutions of the equations
starting from vacuum wave functions on arbitrary non-singular curve.


title: Homogeneous States of Finite Periodic CA with GKL Rules

abstract:
  For any finite lattice of size 2N, it is shown that the GKL automaton will
evolve into attractors if the initial configurations contains an homogeneous
block of size larger than N. The best time estimation for reaching these
attracting states is obtained. Our results also confirm to the case of infinite
lattice which has been obtained previously.


title: Liapunov Multipliers and Decay of Correlations in Dynamical Systems

abstract:
  The essential decorrelation rate of a hyperbolic dynamical system is the
decay rate of time-correlations one expects to see stably for typical
observables once resonances are projected out. We define and illustrate these
notions and study the conjecture that for observables in $C^1$, the essential
decorrelation rate is never faster than what is dictated by the {\em smallest}
unstable Liapunov multiplier.


title: Quadratic solitons as nonlocal solitons

abstract:
  We show that quadratic solitons are equivalent to solitons of a nonlocal Kerr
medium. This provides new physical insight into the properties of quadratic
solitons, often believed to be equivalent to solitons of an effective saturable
Kerr medium. The nonlocal analogy also allows for novel analytical solutions
and the prediction of novel bound states of quadratic solitons.


title: Passive fields and particles in chaotic flows

abstract:
  Two examples for the interplay between chaotic dynamics and stochastic forces
within hydrodynamical systems are considered. The first case concerns the
relaxation to equilibrium of a concentration field subject to both chaotic
advection and molecular diffusion. The concentration field develops filamentary
structures and the decay rate depends non-monotonically on the diffusion
strength. The second example concerns polymers, modelled as particles with an
internal degree of freedom, in a chaotic flow. The length distribution of the
polymers turns out to follow a power law with an exponent that depends on the
difference between Lyapunov exponent and internal relaxation rate.


title: Heun equation and Inozemtsev models

abstract:
  The BC_N elliptic Inozemtsev model is a quantum integrable systems with
N-particles whose potential is given by elliptic functions. Eigenstates and
eigenvalues of this model are investigated.


title: Eulerian Statistically Preserved Structures in Passive Scalar Advection

abstract:
  We analyze numerically the time-dependent linear operators that govern the
dynamics of Eulerian correlation functions of a decaying passive scalar
advected by a stationary, forced 2-dimensional Navier-Stokes turbulence. We
show how to naturally discuss the dynamics in terms of effective compact
operators that display Eulerian Statistically Preserved Structures which
determine the anomalous scaling of the correlation functions. In passing we
point out a bonus of the present approach, in providing analytic predictions
for the time-dependent correlation functions in decaying turbulent transport.


title:
Exact solution for a matrix dynamical system with usual and Hadamard
  inverses

abstract:
  Let A be an n*n matrix with entries a_ij in the field C. Consider the
following two involutive operations on such matrices: the matrix inversion I: A
-> A^-1 and the element-by-element (or Hadamard) inversion J: a_ij -> a_ij^-1.
We study the algebraic dynamical system generated by iterations of the product
JI. In the case n=3, we give the full explicit solution for this system in
terms of the initial matrix A. In the case n=4, we provide an explicit ansatz
in terms of theta-functions which is full in the sense that it works for a
Zariski open set of initial matrices. This ansatz also generalizes for higher n
where it gives partial solutions.


title: Two-dimensional turbulence of dilute polymer solutions

abstract:
  We investigate theoretically and numerically the effect of polymer additives
on two-dimensional turbulence by means of a viscoelastic model. We provide
compelling evidence that at vanishingly small concentrations, such that the
polymers are passively transported, the probability distribution of polymer
elongation has a power law tail: its slope is related to the statistics of
finite-time Lyapunov exponents of the flow, in quantitative agreement with
theoretical predictions. We show that at finite concentrations and sufficiently
large elasticity the polymers react on the flow with manifold consequences:
velocity fluctuations are drastically depleted, as observed in soap film
experiments; the velocity statistics becomes strongly intermittent; the
distribution of finite-time Lyapunov exponents shifts to lower values,
signalling the reduction of Lagrangian chaos.


title: Superintegrability, Lax matrices and separation of variables

abstract:
  We show how the superintegrability of certain systems can be deduced from the
presence of multiple parameters in the rational Lax matrix representation. This
is also related to the fact that such systems admit a separation of variables
in parametric families of coordinate systems.


title: Flicker Noise in a Model of Coevolving Biological Populations

abstract:
  We present long Monte Carlo simulations of a simple model of biological
macroevolution in which births, deaths, and mutational changes in the genome
take place at the level of individual organisms. The model displays punctuated
equilibria and flicker noise with a 1/f-like power spectrum, consistent with
some current theories of evolutionary dynamics.

categories: nlin.AO cond-mat.stat-mech physics.bio-ph q-bio.PE


title: Initialization and the quasi-geostrophic slow manifold

abstract:
  Atmospheric dynamics span a range of time-scales. The projection of measured
data to a slow manifold, ${\cal M}$, removes fast gravity waves from the
initial state for numerical simulations of the atmosphere. We explore further
the slow manifold for a simple atmospheric model introduced by Lorenz and
anticipate that our results will relevant to the vastly more detailed dynamics
of atmospheres and oceans. Within the dynamics of the Lorenz model, we make
clear the relation between a slow manifold $\cal M$ and the ``slowest invariant
manifold'' ({\SIM}), which was constructed by Lorenz in order to avoid the
divergence of approximation schemes for $\cal M$. These manifolds are shown to
be identical to within exponentially small terms, and so the {\SIM} in fact
shares the asymptotic nature of $\cal M$. We also investigate the issue of
balancing initial data in order to remove gravity waves. This is a question of
how to compute an ``initialized'' point on $\cal M$ whose subsequent evolution
matches that from the measured initial data that in general lie off $\cal M$.
We propose a choice based on the intuitive idea that the initialization
procedure should not significantly alter the forecast. Numerical results
demonstrate the utility of our initialization scheme. The normal form for
Lorenz' atmospheric model shows clearly how to separate the dynamics of the
different atmospheric waves. However, its construction demonstrates that {\em
any} initialization procedure must eventually alter the forecast--the
time-scale of the divergence between the initialized and the uninitialized
solutions is inevitable and is inversely proportional to the square of initial
level of gravity-wave activity.


title: Periodic waves in bimodal optical fibers

abstract:
  We consider coupled nonlinear Schrodinger equations (CNLSE) which govern the
propagation of nonlinear waves in bimodal optical fibers. The nonlinear
transform of a dual-frequency signal is used to generate an ultra-short-pulse
train. To predict the energy and width of pulses in the train, we derive three
new types of travelling periodic-wave solutions, using the Hirota bilinear
method. We also show that all the previously reported periodic wave solutions
of CNLSE can be derived in a systematic way, using the Hirota method.


title:
The Kolmogorov turbulence theory in the light of six-dimensional
  Navier-Stokes' equation

abstract:
  The classical turbulence theory by Kolmogorov is reconsidered using
Navier-Stokes' equation generalized to 6D physical-plus-eddy space. Strong
pseudo-singularity is shown to reveal itself along the boundary `ridge' line
separating the dissipation and inertial sub-ranges surrounding the origin of
the eddy space. A speculation is made that this singularity is generated by two
dipoles of opposite sign aligned on the common axis. It is supported by the
observation that the universal power spectrum calculated rediscovers the
Kolmogorov's -5/3 power law as independent of the dimensional approach.


title: Dirac reduction revisited

abstract:
  The procedure of Dirac reduction of Poisson operators on submanifolds is
discussed within a particularly useful special realization of the general
Marsden-Ratiu reduction procedure. The Dirac classification of constraints on
'first-class' constraints and 'second-class' constraints is reexamined.


title:
Self-trapped bidirectional waveguides in a saturable photorefractive
  medium

abstract:
  We introduce a time-dependent model for the generation of joint solitary
waveguides by counter-propagating light beams in a photorefractive crystal.
Depending on initial conditions, beams form stable steady-state structures or
display periodic and irregular temporal dynamics. The steady-state solutions
are non-uniform in the direction of propagation and represent a general class
of self-trapped waveguides, including counterpropagating spatial vector
solitons as a particular case.


title: Algorithmic Chaos

abstract:
  Many physical theories like chaos theory are fundamentally concerned with the
conceptual tension between determinism and randomness. Kolmogorov complexity
can express randomness in determinism and gives an approach to formulate
chaotic behavior.


title: Classical and semiclassical studies of the hydrogen molecule

abstract:
  The hydrogen molecule contains the basic ingredients to understand the
chemical bond, i.e, a pair of electrons. We show a step to understand The
Correspondence Principle for chaotic system in the Chemical World.
  The hydrogen molecule is studied classically as an extension of the helium
atom. Several types of orbits were found for two-fixed-centers system (hydrogen
molecule) starting from some known orbits for one-fixed center one (helium
atom), e.g., one dimension orbits as pendulum and axial and also Bohr and
Langmuir's orbits.
  The classical stability and the single quantization of some one-dimensional
periodic orbits are shown. These orbits are used to make a global quantization
of that molecular chaotic system. We discuss the importance of those periodic
orbits in the comprehension of the nature of chemical bond.


title: Chaotic Diffusion on Periodic Orbits: The Perturbed Arnol'd Cat Map

abstract:
  Chaotic diffusion on periodic orbits (POs) is studied for the perturbed
Arnol'd cat map on a cylinder, in a range of perturbation parameters
corresponding to an extended structural-stability regime of the system on the
torus. The diffusion coefficient is calculated using the following PO formulas:
(a) The curvature expansion of the Ruelle zeta function. (b) The average of the
PO winding-number squared, $w^{2}$, weighted by a stability factor. (c) The
uniform (nonweighted) average of $w^{2}$. The results from formulas (a) and (b)
agree very well with those obtained by standard methods, for all the
perturbation parameters considered. Formula (c) gives reasonably accurate
results for sufficiently small parameters corresponding also to cases of a
considerably nonuniform hyperbolicity. This is due to {\em uniformity sum
rules} satisfied by the PO Lyapunov eigenvalues at {\em fixed} $w$. These sum
rules follow from general arguments and are supported by much numerical
evidence.

categories: nlin.CD cond-mat.stat-mech math-ph math.MP physics.plasm-ph


title:
Discrete dynamical systems associated with the configuration space of 8
  points in P^3(C)

abstract:
  A 3 dimensional analogue of Sakai's theory concerning the relation between
rational surfaces and discrete Painlev\'e equations is studied. For a family of
rational varieties obtained by blow-ups at 8 points in general position in
${\mathbb P}^3$, we define its symmetry group using the inner product that is
associated with the intersection numbers and show that the group is isomorphic
to the Weyl group of type $E_7^{(1)}$. By normalizing the configuration space
by means of elliptic curves, the action of the Weyl group and the dynamical
system associated with a translation are explicitly described. As a result, it
is found that the action of the Weyl group on ${\mathbb P}^3$ preserves a one
parameter family of quadratic surfaces and that it can therefore be reduced to
the action on ${\mathbb P}^1\times {\mathbb P}^1$.


title: When Can we Call a System Self-organizing?

abstract:
  We do not attempt to provide yet another definition of selforganization, but
explore the conditions under which we can model a system as self-organizing.
These involve the dynamics of entropy, and the purpose, aspects, and
description level chosen by an observer. We show how, changing the level or
"graining" of description, the same system can appear selforganizing or
self-disorganizing. We discuss ontological issues we face when studying
self-organizing systems, and analyse when designing and controlling artificial
self-organizing systems is useful. We conclude that self-organization is a way
of observing systems, not an absolute class of systems.

categories: nlin.AO cond-mat.dis-nn cond-mat.stat-mech cs.CC


title: Contextual Random Boolean Networks

abstract:
  We propose the use of Deterministic Generalized Asynchronous Random Boolean
Networks [Gershenson, 2002] as models of contextual deterministic discrete
dynamical systems. We show that changes in the context have drastic effects on
the global properties of the same networks, namely the average number of
attractors and the average percentage of states in attractors. We introduce the
situation where we lack knowledge on the context as a more realistic model for
contextual dynamical systems. We notice that this makes the network
non-deterministic in a specific way, namely introducing a non-Kolmogorovian
quantum-like structure for the modelling of the network [Aerts, 1986]. In this
case, for example, a state of the network has the potentiality (probability) of
collapsing into different attractors, depending on the specific form of lack of
knowledge on the context.


title: Detectability of non-differentiable generalized synchrony

abstract:
  Generalized synchronization of chaos is a type of cooperative behavior in
directionally-coupled oscillators that is characterized by existence of stable
and persistent functional dependence of response trajectories from the chaotic
trajectory of driving oscillator. In many practical cases this function is
non-differentiable and has a very complex shape. The generalized synchrony in
such cases seems to be undetectable, and only the cases, in which a
differentiable synchronization function exists, are considered to make sense in
practice. We show that this viewpoint is not always correct and the
non-differentiable generalized synchrony can be revealed in many practical
cases. Conditions for detection of generalized synchrony are derived
analytically, and illustrated numerically with a simple example of
non-differentiable generalized synchronization.


title:
The Riemann Extensions in Theory of Ordinary Differential Equations and
  their Applications

abstract:
  Some properties of the 4-dim Riemannian spaces with the metrics $$
ds^2=2(za_3-ta_4)dx^2+4(za_2-ta_3)dxdy+2(za_1-ta_2)dy^2+2dxdz+2dydt $$
associated with the second order nonlinear differential equations $$
y''+a_{1}(x,y){y'}^3+3a_{2}(x,y){y'}^2+3a_{3}(x,y)y'+a_{4}(x,y)=0 $$ with
arbitrary coefficients $a_{i}(x,y)$ and 3-dim Einstein-Weyl spaces connected
with dual equations $b''=g(a,b,b')$ where the function $g(a,b,b')$ satisfied
the partial differential equation $$
g_{aacc}+2cg_{abcc}+2gg_{accc}+c^2g_{bbcc}+2cgg_{bccc}+
g^2g_{cccc}+(g_a+cg_b)g_{ccc}-4g_{abc}- $$ $$
  -4cg_{bbc} -cg_{c}g_{bcc}- 3gg_{bcc}-g_cg_{acc}+
4g_cg_{bc}-3g_bg_{cc}+6g_{bb} =0 $$ are considered. Some applications to the
studying of the nonlinear dynamical systems and the Riemann manifolds in
General Relativity are discussed.


title:
The Rolling Motion of a Ball on a Surface. New Integrals and Hierarchy
  of Dynamics

abstract:
  The paper is concerned with the problem on rolling of a homogeneous ball on
an arbitrary surface. New cases when the problem is solved by quadratures are
presented. The paper also indicates a special case when an additional integral
and invariant measure exist. Using this case, we obtain a nonholonomic
generalization of the Jacobi problem for the inertial motion of a point on an
ellipsoid. For a ball rolling, it is also shown that on an arbitrary cylinder
in the gravity field the ball's motion is bounded and, on the average, it does
not move downwards. All the results of the paper considerably expand the
results obtained by E. Routh in XIX century.


title:
Exact soliton solutions of coupled nonlinear Schr\"odinger equations:
  Shape changing collisions, logic gates and partially coherent solitons

abstract:
  The novel dynamical features underlying soliton interactions in coupled
nonlinear Schr{\"o}dinger equations, which model multimode wave propagation
under varied physical situations in nonlinear optics, are studied. In this
paper, by explicitly constructing multisoliton solutions (upto four-soliton
solutions) for two coupled and arbitrary $N$-coupled nonlinear Schr{\"o}dinger
equations using the Hirota bilinearization method, we bring out clearly the
various features underlying the fascinating shape changing (intensity
redistribution) collisions of solitons, including changes in amplitudes, phases
and relative separation distances, and the very many possibilities of energy
redistributions among the modes of solitons. However in this multisoliton
collision process the pair-wise collision nature is shown to be preserved in
spite of the changes in the amplitudes and phases of the solitons. Detailed
asymptotic analysis also shows that when solitons undergo multiple collisions,
there exists the exciting possibility of shape restoration of atleast one
soliton during interactions of more than two solitons represented by three and
higher order soliton solutions. From application point of view, we have shown
from the asymptotic expressions how the amplitude (intensity) redistribution
can be written as a generalized linear fractional transformation for the
$N$-component case. Also we indicate how the multisolitons can be reinterpreted
as various logic gates for suitable choices of the soliton parameters, leading
to possible multistate logic. In addition, we point out that the various
recently studied partially coherent solitons are just special cases of the
bright soliton solutions exhibiting shape changing collisions, thereby
explaining their variable profile and shape variation in collision process.


title:
A Spatiotemporal-chaos-based Encryption Having Overall Properties
  Considerably Better Than Advanced Encryption Standard

abstract:
  Spatiotemporal chaos of a two-dimensional one-way coupled map lattice is used
for chaotic cryptography. The chaotic outputs of many space units are used for
encryption simultaneously. This system shows satisfactory cryptographic
properties of high security; fast encryption (decryption) speed; and robustness
against noise disturbances in communication channel. The overall features of
this spatiotemporal-chaos-based cryptosystem are better than chaotic
cryptosystems known so far, and also than currently used conventional
cryptosystems, such as the Advanced Encryption Standard (AES).


title:
Characterization of Laser Propagation Through Turbulent Media by
  Quantifiers Based on the Wavelet Transform

abstract:
  The propagation of a laser beam through turbulent media is modeled as a
fractional Brownian motion (fBm). Time series corresponding to the center
position of the laser spot (coordinates x and y) after traveling across air in
turbulent motion, with different strength, are analyzed by the wavelet theory.
Two quantifiers are calculated, the Hurst exponent and the mean Normalized
Total Wavelet Entropy. It is verified that both quantifiers gives complementary
information about the turbulence state.


title: Interwoven basin structures of double logistic map at the edge of chaos

abstract:
  The carpeting regularity of basin structures for simply doubled logistic map
is studied. Examining the elementary structures of which global basin
structures are composed, we found them to have a impressive interrelation which
we call "all in one and one in all". Curves appearing in the basins and their
expressions are also discussed.


title:
Large-Eddy Simulations of Fluid and Magnetohydrodynamic Turbulence Using
  Renormalized Parameters

abstract:
  In this paper a procedure for large-eddy simulation (LES) has been devised
for fluid and magnetohydrodynamic turbulence in Fourier space using the
renormalized parameters. The parameters calculated using field theory have been
taken from recent papers by Verma [Phys. Rev. E, 2001; Phys. Plasmas, 2001]. We
have carried out LES on $64^3$ grid. These results match quite well with direct
numerical simulations of $128^3$. We show that proper choice of parameter is
necessary in LES.


title:
Generalized Turing Patterns and Their Selective Realization in
  Spatiotemporal Systems

abstract:
  We consider the pattern formation problem in coupled identical systems after
the global synchronized state becomes unstable. Based on analytical results
relating the coupling strengths and the instability of each spatial mode
(pattern) we show that these spatial patterns can be selectively realized by
varying the coupling strengths along different paths in the parameter space.
Furthermore, we discuss the important role of the synchronized state (fixed
point versus chaotic attractor) in modulating the temporal dynamics of the
spatial patterns.


title: Lagrangian dispersion in Gaussian self-similar ensembles

abstract:
  We analyze the Lagrangian flow in a family of simple Gaussian scale-invariant
velocity ensembles that exhibit both spatial roughness and temporal
correlations. We show that the behavior of the Lagrangian dispersion of pairs
of fluid particles in such models is determined by the scale dependence of the
ratio between the correlation time of velocity differences and the eddy
turnover time. For a non-trivial scale dependence, the asymptotic regimes of
the dispersion at small and large scales are described by the models with
either rapidly decorrelating or frozen velocities. In contrast to the
decorrelated case, known as the Kraichnan model and exhibiting Lagrangian flows
with deterministic or stochastic trajectories, fast separating or trapped
together, the frozen model is poorly understood. We examine the pair dispersion
behavior in its simplest, one-dimensional version, reinforcing analytic
arguments by numerical analysis. The collected information about the pair
dispersion statistics in the limiting models allows to partially predict the
extent of different phases and the scaling properties of the Lagrangian flow in
the model with time-correlated velocities.


title: _10E_9 solution to the elliptic Painlev'e equation

abstract:
  A $\tau$ function formalism for Sakai's elliptic Painlev'e equation is
presented. This establishes the equivalence between the two formulations by
Sakai and by Ohta-Ramani-Grammaticos. We also give a simple geometric
description of the elliptic Painlev'e equation as a non-autonomous deformation
of the addition formula on elliptic curves. By using these formulations, we
construct a particular solution of the elliptic Painlev'e equation expressed in
terms of the elliptic hypergeometric function_10E_9.


title:
Locality of symmetries generated by nonhereditary, inhomogeneous, and
  time-dependent recursion operators: a new application for formal symmetries

abstract:
  Using the methods of the theory of formal symmetries, we obtain new easily
verifiable sufficient conditions for a recursion operator to produce a
hierarchy of local generalized symmetries. An important advantage of our
approach is that under certain mild assumptions it allows to bypass the
cumbersome check of hereditariness of the recursion operator in question, what
is particularly useful for the study of symmetries of newly discovered
integrable systems. What is more, unlike the earlier work, the homogeneity of
recursion operators and symmetries under a scaling is not assumed as well. An
example of nonhereditary recursion operator generating a hierarchy of local
symmetries is presented.


title:
Low rank perturbations and the spectral statistics of pseudointegrable
  billiards

abstract:
  We present an efficient method to solve Schr\"odinger's equation for
perturbations of low rank. In particular, the method allows to calculate the
level counting function with very little numerical effort. To illustrate the
power of the method, we calculate the number variance for two pseudointegrable
quantum billiards: the barrier billiard and the right triangle billiard
(smallest angle $\pi/5$). In this way, we obtain precise estimates for the
level compressibility in the semiclassical (high energy) limit. In both cases,
our results confirm recent theoretical predictions, based on periodic orbit
summation.


title: R-matrix theory of driven electromagnetic cavities

abstract:
  Resonances of cylindrical symmetric microwave cavities are analyzed in
R-matrix theory which transforms the input channel conditions to the output
channels. Single and interfering double resonances are studied and compared
with experimental results, obtained with superconducting microwave cavities.
Because of the equivalence of the two-dimensional Helmholtz and the stationary
Schroedinger equations, the results present insight into the resonance
structure of regular and chaotic quantum billiards.


title: Yang-Baxter equation for the asymmetric eight-vertex model

abstract:
  In this note we study `a la Baxter [1] the possible integrable manifolds of
the asymmetric eight-vertex model. As expected they occur when the Boltzmann
weights are either symmetric or satisfy the free-fermion condition but our
analysis clarify the reason both manifolds need to share a universal invariant.
We also show that the free-fermion condition implies three distinct classes of
integrable models.


title:
Algebraic Bethe ansatz for a class of coupled asymmetric six-vertex
  free-fermion model

abstract:
  We present an algebraic Bethe ansatz for certain submanifolds of the bilayer
vertex models proposed by Shiroishi and Wadati as coupled asymmetric six-vertex
free-fermion models. A peculiar feature of our formulation is the presence of a
diagonal monodromy matrix element that does not generate unwanted terms. The
model contains two free-parameters entering into the Bethe ansatz equations as
a pure phase factor.


title: Pulsation and Precession of the Resonant Swinging Spring

abstract:
  When the frequencies of the elastic and pendular oscillations of an elastic
pendulum or swinging spring are in the ratio two-to-one, there is a regular
exchange of energy between the two modes of oscillation. We refer to this
phenomenon as pulsation. Between the horizontal excursions, or pulses, the
spring undergoes a change of azimuth which we call the precession angle. The
pulsation and stepwise precession are the characteristic features of the
dynamics of the swinging spring.
  The modulation equations for the small-amplitude resonant motion of the
system are the well-known three-wave equations. We use Hamiltonian reduction to
determine a complete analytical solution. The amplitudes and phases are
expressed in terms of both Weierstrass and Jacobi elliptic functions. The
strength of the pulsation may be computed from the invariants of the equations.
Several analytical formulas are found for the precession angle.
  We deduce simplified approximate expressions, in terms of elementary
functions, for the pulsation amplitude and precession angle and demonstrate
their high accuracy by numerical experiments. Thus, for given initial
conditions, we can describe the envelope dynamics without solving the
equations. Conversely, given the parameters which determine the envelope, we
can specify initial conditions which, to a high level of accuracy, yield this
envelope.


title: Fluctuations of energy injection rate in a shear flow

abstract:
  We study the instantaneous and local energy injection in a turbulent shear
flow driven by volume forces. The energy injection can be both positive and
negative. Extremal events are related to coherent streaks. The probability
distribution is asymmetric, deviates slightly from a Gaussian shape and depends
on the position in shear direction. The probabilities for positive and negative
injection are exponentially related, but the prefactor in the exponent varies
across the shear layer.


title: On integrability of one third-order nonlinear evolution equation

abstract:
  We study one third-order nonlinear evolution equation, recently introduced by
Chou and Qu in a problem of plane curve motions, and find its transformation to
the modified Korteweg - de Vries equation, its zero-curvature representation
with an essential parameter, and its second-order recursion operator.


title:
Spectral Characterization of Anomalous Diffusion of a Periodic Piecewise
  Linear Intermittent Map

abstract:
  For a piecewise linear version of the periodic map with anomalous diffusion,
the evolution of statistical averages of a class of observables with respect to
piecewise constant initial densities is investigated and generalized
eigenfunctions of the Frobenius-Perron operator are explicitly derived. The
evolution of the averages is controlled by real eigenvalues as well as
continuous spectra terminating at the unit circle. Appropriate scaling limits
are shown to give a normal diffusion if the reduced map is in the stationary
regime with normal fluctuations, a L\'evy flight if the reduced map is in the
stationary regime with L\'evy-type fluctuations and a transport of ballistic
type if the reduced map is in the non-stationary regime.


title:
Towards a theory of consciousness: Proposal for the resolution of the
  homunculus fallacy with predictions

abstract:
  In this paper we argue that no forms of Turing test are either necessary or
sufficient to establish if a machine is conscious or not. Furthermore, from a
modeling point of view, the problem is that the Turing test does not really
provide testable predictions. We believe that the model structure should
explain the function (of consciousness). We argue that the cornerstone of any
model on consciousness is to (partly) overcome the obstacle of the homunculus
fallacy about the use of representations. In this contribution a possible
solution is suggested, which makes use of reflexive architectures. The emerging
computational constraints on the proposed architecture have lead to testable
predictions on the dynamical behavior of the biological substrate.
Interestingly, these predictions are in good agreement with recent experimental
observations.


title: The modified tetrahedron equation and its solutions

abstract:
  A large class of 3-dimensional integrable lattice spin models is constructed.
The starting point is an invertible canonical mapping operator in the space of
a triple Weyl algebra. This operator is derived postulating a current branching
principle together with a Baxter Z-invariance. The tetrahedron equation for
this operator follows without further calculations. If the Weyl parameter is
taken to be a root of unity, the mapping operator decomposes into a matrix
conjugation and a C-number functional mapping. The operator of the matrix
conjugation satisfies a modified tetrahedron equation (MTE) in which the
"rapidities" are solutions of a classical integrable Hirota-type equation. The
matrix elements of this operator can be represented in terms of the
Bazhanov-Baxter Fermat curve cyclic functions, or alternatively in terms of
Gauss functions. The paper summarizes several recent publications on the
subject.


title:
Level spacing statistics of classically integrable systems
  -Investigation along the line of the Berry-Robnik approach-

abstract:
  By extending the approach of Berry and Robnik, the limiting level spacing
distribution of a system consisting of infinitely many independent components
is investigated. The limiting level spacing distribution is characterized by a
single monotonically increasing function $\bar{\mu}(S)$ of the level spacing
$S$. Three cases are distinguished: (i) Poissonian if $\bar{\mu}(+\infty)=0$,
(ii) Poissonian for large $S$, but possibly not for small $S$ if
$0<\bar{\mu}(+\infty)< 1$, and (iii) sub-Poissonian if $\bar{\mu}(+\infty)=1$.
This implies that, even when energy-level distributions of individual
components are statistically independent, non-Poissonian level spacing
distributions are possible.


title:
Non-Poissonian level spacing statistics of classically integrable
  quantum systems based on the Berry-Robnik approach

abstract:
  Along the line of thoughts of Berry and Robnik\cite{[1]}, we investigated the
gap distribution function of systems with infinitely many independent
components, and discussed the level-spacing distribution of classically
integrable quantum systems. The level spacing distribution is classified into
three cases: Case 1: Poissonian if $\bar{\mu}(+\infty)=0$, Case 2: Poissonian
for large $S$, but possibly not for small $S$ if $0<\bar{\mu}(+\infty)< 1$, and
Case 3: sub-Poissonian if $\bar{\mu}(+\infty)=1$. Thus, even when the energy
levels of individual components are statistically independent, non-Poisson
level spacing distributions are possible.


title:
Level statistics of systems with infinitely many independent components
  based on the Berry-Robnik approach

abstract:
  Along the line of thoughts of Berry and Robnik{\cite{Ber}}, the limiting gap
distribution function of classically integrable quantum systems is derived in
the limit of infinitely many independent components. The limiting gap
distribution function is characterized by a single monotonically increasing
function $\bar{\mu}(S)$ of the level spacing $S$, and the corresponding level
spacing distribution is classified into three cases: (i) Poissonian if
$\bar{\mu}(+\infty)=0$, (ii) Poissonian for large $S$, but possibly not for
small $S$ if $0<\bar{\mu}(+\infty)< 1$, and (iii) sub-Poissonian if
$\bar{\mu}(+\infty)=1$. This implies that even when the energy-level
distributions of individual components are statistically independent,
non-Poissonian level spacing distributions are possible.


title:
Bifurcations and Averages in the Homoclinic Chaos of a Laser with a
  Saturable Absorber

abstract:
  The dynamical bifurcations of a laser with a saturable absorber were
calculated, with the 3-2 level model, as function of the gain parameter. The
average power of the laser is shown to have specific behavior at bifurcations.
The succession of periodic-chaotic windows, known to occur in the homoclinic
chaos, was studied numerically. A critical exponent of 1/2 is found on the
tangent bifurcations from chaotic into periodic pulsations.


title:
Global well-posedness and multi-tone solutions of a class of nonlinear
  nonlocal cochlear models in hearing

abstract:
  We study a class of nonlinear nonlocal cochlear models of the transmission
line type, describing the motion of basilar membrane (BM) in the cochlea. They
are damped dispersive partial differential equations (PDEs) driven by time
dependent boundary forcing due to the input sounds. The global well-posedness
in time follows from energy estimates. Uniform bounds of solutions hold in case
of bounded nonlinear damping. When the input sounds are multi-frequency tones,
and the nonlinearity in the PDEs is cubic, we construct smooth quasi-periodic
solutions (multi-tone solutions) in the weakly nonlinear regime, where new
frequencies are generated due to nonlinear interaction. When the input is two
tones at frequencies $f_1$, $f_2$ ($f_1 < f_2$), and high enough intensities,
numerical results illustrate the formation of combination tones at $2 f_1 -f_2$
and $2f_2 -f_1$, in agreement with hearing experiments. We visualize the
frequency content of solutions through the FFT power spectral density of
displacement at selected spatial locations on BM.


title: Averages and Critical Exponents in Type-III Intermittent Chaos

abstract:
  The natural measure in a map with type-III intermittent chaos is used to
define critical exponents for the average of a variable from a dynamical system
near bifurcation. Numerical experiments were done with maps and verify the
analytical predictions. Physical experiments to test the usefulness of such
exponents to characterize the nonlinearity at bifurcations were done in a
driven electronic circuit with diode as nonlinear element. Two critical
exponents were measured: $\nu = 0.55$ for the critical exponent of the average
of the voltage across the diode and $\beta = 0.62$ for the exponent of the
average length of the laminar phases. Both values are consistent with the
predictions of a type-III intermittency of cubic nonlinearity. The averages of
variables in intermittent chaotic systems is a technique complementary to the
measurements of laminar phase histograms, to identify the nonlinear mechanisms.
The averages exponents may have a broad application in ultrafast chaotic
phenomena.


title: Classical basis for quantum spectral fluctuations in hyperbolic systems

abstract:
  We reason in support of the universality of quantum spectral fluctuations in
chaotic systems, starting from the pioneering work of Sieber and Richter who
expressed the spectral form factor in terms of pairs of periodic orbits with
self-crossings and avoided crossings. Dropping the restriction to uniformly
hyperbolic dynamics, we show that for general hyperbolic two-freedom systems
with time-reversal invariance the spectral form factor is faithful to
random-matrix theory, up to quadratic order in time. We relate the action
difference within the contributing pairs of orbits to properties of stable and
unstable manifolds. In studying the effects of conjugate points, we show that
almost self-retracing orbit loops do not contribute to the form factor. Our
findings are substantiated by numerical evidence for the concrete example of
two billiard systems.


title:
Spectral form factor of hyperbolic systems: leading off-diagonal
  approximation

abstract:
  The spectral fluctuations of a quantum Hamiltonian system with time-reversal
symmetry are studied in the semiclassical limit by using periodic-orbit theory.
It is found that, if long periodic orbits are hyperbolic and uniformly
distributed in phase space, the spectral form factor agrees with the GOE
prediction of random-matrix theory up to second order included in the time
measured in units of the Heisenberg time (leading off-diagonal approximation).
Our approach is based on the mechanism of periodic-orbit correlations
discovered recently by Sieber and Richter (Phys. Scr. T 90, 128, 2001). By
reformulating the theory of these authors in phase space, their result on the
free motion on a Riemann surface with constant negative curvature is extended
to general Hamiltonian hyperbolic systems with two degrees of freedom.


title: Isospectrality in Chaotic Billiards

abstract:
  We consider a modification of isospectral cavities whereby the classical
dynamics changes from pseudointegrable to chaotic. We construct an example
where we can prove that isospectrality is retained. We then demonstrate this
explicitly in microwave resonators.


title:
Leading off-diagonal contribution to the spectral form factor of chaotic
  quantum systems

abstract:
  We semiclassically derive the leading off-diagonal correction to the spectral
form factor of quantum systems with a chaotic classical counterpart. To this
end we present a phase space generalization of a recent approach for uniformly
hyperbolic systems (M. Sieber and K. Richter, Phys. Scr. T90, 128 (2001); M.
Sieber, J. Phys. A: Math. Gen. 35, L613 (2002)). Our results coincide with
corresponding random matrix predictions. Furthermore, we study the transition
from the Gaussian orthogonal to the Gaussian unitary ensemble.


title: Generation and stability of discrete gap solitons

abstract:
  We analyze stability and generation of discrete gap solitons in weakly
coupled optical waveguides. We demonstrate how both stable and unstable
solitons can be observed experimentally in the engineered binary waveguide
arrays, and also reveal a connection between the gap-soliton instabilities and
limitations on the mutual beam focusing in periodic photonic structures.


title: Spatial optical solitons supported by mutual focusing

abstract:
  We study composite spatial optical solitons supported by two-wave mutual
focusing induced by cross-phase modulation in Kerr-like nonlinear media. We
find the families of both single- and two-hump solitons and discuss their
properties and stability. We also reveal remarkable similarities between
recently predicted holographic solitons in photorefractive media and parametric
solitons in quadratic nonlinear crystals.


title:
Comparing modern and Pleistocene ENSO-like influences in NW Argentina
  using nonlinear time series analysis methods

abstract:
  Higher variability in rainfall and river discharge could be of major
importance in landslide generation in the north-western Argentine Andes. Annual
layered (varved) deposits of a landslide dammed lake in the Santa Maria Basin
(26 deg S, 66 deg W) with an age of 30,000 14C years provide an archive of
precipitation variability during this time. The comparison of these data with
present-day rainfall observations tests the hypothesis that increased rainfall
variability played a major role in landslide generation. A potential cause of
such variability is the El Nino/Southern Oscillation (ENSO). The causal link
between ENSO and local rainfall is quantified by using a new method of
nonlinear data analysis, the quantitative analysis of cross recurrence plots
(CRP). This method seeks similarities in the dynamics of two different
processes, such as an ocean-atmosphere oscillation and local rainfall. Our
analysis reveals significant similarities in the statistics of both modern and
palaeo-precipitation data. The similarities in the data suggest that an
ENSO-like influence on local rainfall was present at around 30,000 14C years
ago. Increased rainfall, which was inferred from a lake balance modeling in a
previous study, together with ENSO-like cyclicities could help to explain the
clustering of landslides at around 30,000 14C years ago.

categories: nlin.CD physics.ao-ph physics.data-an physics.geo-ph


title: Classical and Quantum Chaos in Fundamental Field Theories

abstract:
  An investigation of classical chaos and quantum chaos in gauge fields and
fermion fields, respectively, is presented for (quantum) electrodynamics. We
analyze the leading Lyapunov exponents of U(1) gauge field configurations on a
$12^3$ lattice which are initialized by Monte Carlo simulations. We find that
configurations in the strong coupling phase are substantially more chaotic than
in the deconfinement phase. Considering the quantum case, complete eigenvalue
spectra of the Dirac operator in quenched 4d compact QED are studied on $8^3
\times 4$ and $8^3 \times 6$ lattices. We investigate the behavior of the
nearest-neighbor spacing distribution $P(s)$ as a measure of the fluctuation
properties of the eigenvalues in the strong coupling and the Coulomb phase. In
both phases we find agreement with the Wigner surmise of the unitary ensemble
of random-matrix theory indicating quantum chaos.


title: Continuous families of embedded solitons in the third-order NLS equation

abstract:
  The nonlinear Schroedinger equation with a third-order dispersive term is
considered. Infinite families of embedded solitons, parameterized by the
propagation velocity, are found through a gauge transformation. By applying
this transformation, an embedded soliton can acquire any velocity above a
certain threshold value. It is also shown that all these families of embedded
solitons are linearly stable, but nonlinearly semi-stable.