title: Separating the influence of Brain Signals from the Dynamics of Heart

abstract:
  ECG signals appear to be quite complex. In this paper, we present results,
which show that a normal ECG signal, which is a function of time can be
transformed into a relatively simpler signal by stretching the time in a
predetermined way. Before such a transformation, if you were to analyze various
packets of the data for the Trans-Spectral Coherence (TSC) you could confirm
that the signal indeed is very complicated. This is because the TSC gives us an
idea of how various harmonics in a spectrum are related to one another. The
coherence dramatically improved once we found an intermediate variable..
However, there was one hurdle. To find this variable, we needed to postulate
that the complexified data lies on a 4-sheeted Riemann-Surface. With this
insight, we could identify a proper time transformation which led to extremely
high TSC.
  The transformed signal is quite simple. We can now rearrange the ECG data in
terms of a set of functions in an affine space, which we can explicitly
calculate from the data. This reveals that the dynamics of the heart, if freed
from the external influence is quite simple.


title: Computation of Spiral Spectra

abstract:
  A computational linear stability analysis of spiral waves in a
reaction-diffusion equation is performed on large disks. As the disk radius R
increases, eigenvalue spectra converge to the absolute spectrum predicted by
Sandstede and Scheel. The convergence rate is consistent with 1/R, except
possibly near the edge of the spectrum. Eigenfunctions computed on large disks
are compared with predicted exponential forms. Away from the edge of the
absolute spectrum the agreement is excellent, while near the edge computed
eigenfunctions deviate from predictions, probably due to finite-size effects.
In addition to eigenvalues associated with the absolute spectrum, computations
reveal point eigenvalues. The point eigenvalues and associated eigenfunctions
responsible for both core and far-field breakup of spiral waves are shown.


title: Chaotic advection and targeted mixing

abstract:
  The advection of passive tracers in an oscillating vortex chain is
investigated. It is shown that by adding a suitable perturbation to the ideal
flow, the induced chaotic advection exhibits two remarkable properties compared
with a generic perturbation : Particles remain trapped within a specific domain
bounded by two oscillating barriers (suppression of chaotic transport along the
channel), and the stochastic sea seems to cover the whole domain (enhancement
of mixing within the rolls).


title:
Coarse-graining of cellular automata, emergence, and the predictability
  of complex systems

abstract:
  We study the predictability of emergent phenomena in complex systems. Using
nearest neighbor, one-dimensional Cellular Automata (CA) as an example, we show
how to construct local coarse-grained descriptions of CA in all classes of
Wolfram's classification. The resulting coarse-grained CA that we construct are
capable of emulating the large-scale behavior of the original systems without
accounting for small-scale details. Several CA that can be coarse-grained by
this construction are known to be universal Turing machines; they can emulate
any CA or other computing devices and are therefore undecidable. We thus show
that because in practice one only seeks coarse-grained information, complex
physical systems can be predictable and even decidable at some level of
description. The renormalization group flows that we construct induce a
hierarchy of CA rules. This hierarchy agrees well with apparent rule complexity
and is therefore a good candidate for a complexity measure and a classification
method. Finally we argue that the large scale dynamics of CA can be very
simple, at least when measured by the Kolmogorov complexity of the large scale
update rule, and moreover exhibits a novel scaling law. We show that because of
this large-scale simplicity, the probability of finding a coarse-grained
description of CA approaches unity as one goes to increasingly coarser scales.
We interpret this large scale simplicity as a pattern formation mechanism in
which large scale patterns are forced upon the system by the simplicity of the
rules that govern the large scale dynamics.


title: Instability of solitary waves on Euler's elastica

abstract:
  Stability of solitary waves in a thin inextensible and unshearable rod of
infinite length is studied. Solitary-wave profile ofthe elastica of such a rod
without torsion has the form of a planar loop and its speed depends on a
tension in the rod. The linear instability of a solitary-wave profile subject
to perturbations escaping from the plane of the loop is established for a
certain range of solitary-wave speeds. It is done using the properties of the
Evans function, an analytic function on the right complex half-plane, that has
zeroes if and only if there exist the unstable modes of the linearization
around a solitary-wave solution. The result follows from comparison of the
behaviour of the Evans function in some neighbourhood of the origin with its
asymptotic at infinity. The explicit computation of the leading coefficient of
the Taylor series of the Evans function near the origin is performed by means
of the symbolic computer language.


title: Quantum spectrum as a time series : Fluctuation measures

abstract:
  The fluctuations in the quantum spectrum could be treated like a time series.
In this framework, we explore the statistical self-similarity in the quantum
spectrum using the detrended fluctuation analysis (DFA) and random matrix
theory (RMT). We calculate the Hausdorff measure for the spectra of atoms and
Gaussian ensembles and study their self-affine properties. We show that DFA is
equivalent to $\Delta_3$ statistics of RMT, unifying two different
approaches.We exploit this connection to obtain theoretical estimates for the
Hausdorff measure.


title:
On the Whitham equations for the defocusing nonlinear Schrodinger
  equation with step initial data

abstract:
  The behavior of solutions of the finite-genus Whitham equations for the weak
dispersion limit of the defocusing nonlinear Schrodinger equation is
investigated analytically and numerically for piecewise-constant initial data.
In particular, the dynamics of constant-amplitude initial conditions with one
or more frequency jumps (i.e., piecewise linear phase) are considered. It is
shown analytically and numerically that, for finite times, regions of
arbitrarily high genus can be produced; asymptotically with time, however, the
solution can be divided into expanding regions which are either of genus-zero,
genus-one or genus-two type, their precise arrangement depending on the
specifics of the initial datum given. This behavior should be compared to that
of the Korteweg-deVries equation, where the solution is devided into the
regions which are either genus-zero or genus-one asymptotically. Finally, the
potential application of these results to the generation of short optical
pulses is discussed: the method proposed takes advantage of nonlinear
compression via appropriate frequency modulation, and allows control of both
the pulse amplitude and its width, as well as the distance along the fiber at
which the pulse is produced.


title: One-Particle and Few-Particle Billiards

abstract:
  We study the dynamics of one-particle and few-particle billiard systems in
containers of various shapes. In few-particle systems, the particles collide
elastically both against the boundary and against each other. In the
one-particle case, we investigate the formation and destruction of resonance
islands in (generalized) mushroom billiards, which are a recently discovered
class of Hamiltonian systems with mixed regular-chaotic dynamics. In the
few-particle case, we compare the dynamics in container geometries whose
counterpart one-particle billiards are integrable, chaotic, and mixed. One of
our findings is that two-, three-, and four-particle billiards confined to
containers with integrable one-particle counterparts inherit some integrals of
motion and exhibit a regular partition of phase space into ergodic components
of positive measure. Therefore, the shape of a container matters not only for
noninteracting particles but also for interacting particles.


title: Uniaxial magnetocrystalline anisotropy in ${\rm CaRuO_3}$

abstract:
  ${\rm CaRuO_3}$ is a paramagnetic metal and since its low temperature
resistivity is described by $\rho=\rho_0+AT^\gamma $ with $\gamma \sim 1.5$, it
is also considered a non-Fermi liquid (NFL) metal. We have performed extensive
magnetoresistance and Hall effect measurements of untwinned epitaxial films of
${\rm CaRuO_3}$. These measurements reveal that ${\rm CaRuO_3}$ exhibits
uniaxial magnetocrystalline anisotropy. In addition, the low-temperature NFL
behavior is most effectively suppressed when a magnetic field is applied along
the easy axis, suggesting that critical spin fluctuations, possibly due to
proximity of a quantum critical phase transition, are related to the NFL
behavior.


title:
q-Breathers in Fermi-Pasta-Ulam chains: existence, localization and
  stability

abstract:
  The Fermi-Pasta-Ulam (FPU) problem consists of the nonequipartition of energy
among normal modes of a weakly anharmonic atomic chain model. In the harmonic
limit each normal mode corresponds to a periodic orbit in phase space and is
characterized by its wave number q. We continue normal modes from the harmonic
limit into the FPU parameter regime and obtain persistence of these periodic
orbits, termed here q-Breathers (QB). They are characterized by time
periodicity, exponential localization in the q-space of normal modes and linear
stability up to a size-dependent threshold amplitude. Trajectories computed in
the original FPU setting are perturbations around these exact QB solutions. The
QB concept is applicable to other nonlinear lattices as well.


title: Bethe ansatz at q=0 and periodic box-ball systems

abstract:
  A class of periodic soliton cellular automata is introduced associated with
crystals of non-exceptional quantum affine algebras. Based on the Bethe ansatz
at q=0, we propose explicit formulas for the dynamical period and the size of
certain orbits under the time evolution in A^{(1)}_n case.


title: Numerical study of polymer tumbling in linear shear flows

abstract:
  We investigate numerically the dynamics of a single polymer in a linear shear
flow. The effects of thermal fluctuations and randomly fluctuating velocity
gradients are both analyzed. Angular, elongation and tumbling time statistics
are measured numerically. We perform analytical calculations and numerical
simulations for a linear single-dumbbell polymer model comparing the results
with previous theoretical and experimental studies. For thermally driven
polymers the balance between relaxation and thermal fluctuations plays a
fundamental role, whereas for random velocity gradients the ratio between the
intensity of the random part and the mean shear is the most relevant quantity.
In the low-noise limit, many universal aspects of the motion of a polymer in a
shear flow can be understood in this simplified framework.


title: Directed chaos in a billiard chain with transversal magnetic field

abstract:
  In generic Hamiltonian systems with a mixed phase space chaotic transport may
be directed and ballistic rather than diffusive. We investigate one particular
model showing this behaviour, namely a spatially periodic billiard chain in
which electrons move under the influence of a perpendicular magnetic field. We
analyze the phase-space structure and derive an explicit expression for the
chaotic transport velocity. Unlike previous studies of directed chaos our model
has a parameter regime in which the dispersion of an ensemble of chaotic
trajectories around its moving center of mass is essentially diffusive. We
explain how in this limit the deterministic chaos reduces to a biased random
walk in a billiard with a rough surface. The diffusion constant for this
simplified model is calculated analytically.


title: Cultural propagation on social networks

abstract:
  In this work we present a model for the propagation of culture on networks of
different topology and by considering different underlying dynamics. We extend
a previous model proposed by Axelrod by letting a majority govern the dynamics
of changes. This in turn allows us to define a Lyapunov functional for the
system.


title:
Analytic doubly periodic wave patterns for the integrable discrete
  nonlinear Schroedinger (Ablowitz-Ladik) model

abstract:
  We derive two new solutions in terms of elliptic functions, one for the dark
and one for the bright soliton regime, for the semi-discrete cubic nonlinear
Schroedinger equation of Ablowitz and Ladik. When considered in the complex
plane, these two solutions are identical. In the continuum limit, they reduce
to known elliptic function solutions. In the long wave limit, the dark one
reduces to the collision of two discrete dark solitons, and the bright one to a
discrete breather.


title: A note on the forced Burgers equation

abstract:
  We obtain the exact solution for the Burgers equation with a time dependent
forcing, which depends linearly on the spatial coordinate. For the case of a
stochastic time dependence an exact expression for the joint probability
distribution for the velocity fields at multiple spatial points is obtained. A
connection with stretched vortices in hydrodynamic flows is discussed.


title:
Lattices for Dynamic, Hierarchic & Overlapping Categorization: the Case
  of Epistemic Communities

abstract:
  We present a method for hierarchic categorization and taxonomy evolution
description. We focus on the structure of epistemic communities (ECs), or
groups of agents sharing common knowledge concerns. Introducing a formal
framework based on Galois lattices, we categorize ECs in an automated and
hierarchically structured way and propose criteria for selecting the most
relevant epistemic communities - for instance, ECs gathering a certain
proportion of agents and thus prototypical of major fields. This process
produces a manageable, insightful taxonomy of the community. Then, the
longitudinal study of these static pictures makes possible an historical
description. In particular, we capture stylized facts such as field progress,
decline, specialization, interaction (merging or splitting), and paradigm
emergence. The detection of such patterns in social networks could fruitfully
be applied to other contexts.


title:
Description of Complex Systems in terms of Self-Organization Processes
  of Prime Integer Relations

abstract:
  In the paper we present a description of complex systems in terms of
self-organization processes of prime integer relations. A prime integer
relation is an indivisible element made up of integers as the basic
constituents following a single organizing principle. The prime integer
relations control correlation structures of complex systems and may describe
complex systems in a strong scale covariant form. It is possible to geometrize
the prime integer relations as two-dimensional patterns and isomorphically
express the self-organization processes through transformations of the
geometric patterns. As a result, prime integer relations can be measured by
corresponding geometric patterns specifying the dynamics of complex systems.
Determined by arithmetic only, the self-organization processes of prime integer
relations can describe complex systems by information not requiring further
explanations. This gives the possibility to develop an irreducible theory of
complex systems.


title: Entanglement measures in quantum and classical chaos

abstract:
  Entanglement is a Hilbert-space based measure of nonseparability of states
that leads to unique quantum possibilities such as teleportation. It has been
at the center of intense activity in the area of quantum information theory and
computation. In this paper we discuss the implications of quantum chaos on
entanglement, showing how chaos can lead to large entanglement that is
universal and describable using random matrix theory. We also indicate how this
measure can be used in the Hilbert space formulation of classical mechanics.
This leads us to consider purely Hilbert-space based measures of classical
chaos, rather than the usual phase-space based ones such as the Lyapunov
exponents, and can possibly lead to understanding of partial differential
equations and nonintegrable classical field theories.


title:
Guiding of dynamically modulated signals in arrays of photorefractive
  spatial solitons

abstract:
  As the formation of spatial optical solitons in photorefractive media is
governed by modification of the refractive index every single solitons in
complex configurations of solitons can act as a single waveguide for other
light beams. In this article we demonstrate guiding of amplitude modulated
beams in complex configurations of photorefractive solitons carrying
information and we analyze the received signal in the kHz frequency range. The
possibility of data transmission combined with waveguide couplers opens the
route to all-optical networks.


title:
Discrete light localization in one dimensional nonlinear lattices with
  arbitrary non locality

abstract:
  We model discrete spatial solitons in a periodic nonlinear medium
encompassing any degree of transverse non locality. Making a convenient
reference to a widely used material -nematic liquid crystals-, we derive a new
form of the discrete nonlinear Schrodinger equation and find a novel family of
discrete solitons. Such self-localized solutions in optical lattices can exist
with an arbitrary degree of imprinted chirp and a have breathing character. We
verify numerically that both local and non local discrete light propagation and
solitons can be observed in liquid crystalline arrays.


title:
On possibility of realization of the phenomena of complex analytic
  dynamics in physical systems. Novel mechanism of the synchronization loss in
  coupled period-doubling systems

abstract:
  The possibility of realization of the phenomena of complex analytic dynamics
for the realistic physical models are investigated. Observation of the
Mandelbrot and Julia sets in the parameter and phase spaces both for the
discrete maps and non-autonomous continuous systems is carried out. For these
purposes, the method, based on consideration of coupled systems, demonstrating
period-doubling cascade is suggested. Novel mechanism of synchronization loss
in coupled systems corresponded to the dynamical behavior intrinsic to the
complex analytic maps is offered.


title:
On possibility of realization of the Mandelbrot set in coupled
  continuous systems

abstract:
  According to the method, suggested in our previous work (nlin/0509012) and
based on the consideration of the specially coupled systems, the possibility of
physical realization of the phenomena of complex analytic dynamics (such as
Mandelbrot and Julia sets) is discussed. It is shown, that unlike the case of
discrete maps or differential systems with periodic driving, investigated in
mentioned work, there are some difficulties in attempts to obtain the
Mandelbrot set for the coupled autonomous continuous systems. A system of
coupled autonomous R\"{o}ssler oscillators is considered as an example.


title:
New R-matrices from Representations of Braid-Monoid Algebras based on
  Superalgebras

abstract:
  In this paper we discuss representations of the Birman-Wenzl-Murakami algebra
as well as of its dilute extension containing several free parameters. These
representations are based on superalgebras and their baxterizations permit us
to derive novel trigonometric solutions of the graded Yang-Baxter equation. In
this way we obtain the multiparametric $R$-matrices associated to the
$U_q[sl(r|2m)^{(2)}]$, $U_q[osp(r|2m)^{(1)}]$ and $U_q[osp(r=2n|2m)^{(2)}]$
quantum symmetries. Two other families of multiparametric $R$-matrices not
predicted before within the context of quantum superalgebras are also
presented. The latter systems are indeed non-trivial generalizations of the
$U_q[D^{(2)}_{n+1}]$ vertex model when both distinct edge variables statistics
and extra free-parameters are admissible.


title: Period tripling accumulation point for complexified Henon map

abstract:
  Accumulation point of period-tripling bifurcations for complexified Henon map
is found. Universal scaling properties of parameter space and Fourier spectrum
intrinsic to this critical point is demonstrated.


title: Stability of wave packet dynamics under perturbations

abstract:
  We introduce a novel method to investigate the stability of wave packet
dynamics under perturbations of the Hamiltonian. Our approach relies on
semiclassical approximations, but is non-perturbative. Two separate
contributions to the quantum fidelity are identified: one factor derives from
the dispersion of the wave packets, whereas the other factor is determined by
the separation of a trajectory of the perturbed classical system away from a
corresponding unperturbed trajectory. We furthermore estimate both
contributions in terms of classical Lyapunov exponents and find a decay of
fidelity that is, generically, at least exponential, but may also be doubly
exponential. The latter case is shown to be realised for inverted harmonic
oscillators.


title:
On the Whitham hierarchy: dressing scheme, string equations and
  additional symmetrie

abstract:
  A new description of the universal Whitham hierarchy in terms of a
factorization problem in the Lie group of canonical transformations is
provided. This scheme allows us to give a natural description of dressing
transformations, string equations and additional symmetries for the Whitham
hierarchy. We show how to dress any given solution and prove that any solution
of the hierarchy may be undressed, and therefore comes from a factorization of
a canonical transformation. A particulary important function, related to the
$\tau$-function, appears as a potential of the hierarchy. We introduce a class
of string equations which extends and contains previous classes of string
equations considered by Krichever and by Takasaki and Takebe. The scheme is
also applied for an convenient derivation of additional symmetries. Moreover,
new functional symmetries of the Zakharov extension of the Benney gas equations
are given and the action of additional symmetries over the potential in terms
of linear PDEs is characterized.


title: Nonsingular positon and complexiton solutions for the coupled KdV system

abstract:
  Taking the coupled KdV system as a simple example, analytical and nonsingular
complexiton solutions are firstly discovered in this letter for integrable
systems. Additionally, the analytical and nonsingular positon-negaton
interaction solutions are also firstly found for S-integrable model. The new
analytical positon, negaton and complexiton solutions of the coupled KdV system
are given out both analytically and graphically by means of the iterative
Darboux transformations.


title:
Generalised Perk--Schultz models: solutions of the Yang-Baxter equation
  associated with quantised orthosymplectic superalgebras

abstract:
  The Perk--Schultz model may be expressed in terms of the solution of the
Yang--Baxter equation associated with the fundamental representation of the
untwisted affine extension of the general linear quantum superalgebra
$U_q[sl(m|n)]$, with a multiparametric co-product action as given by
Reshetikhin. Here we present analogous explicit expressions for solutions of
the Yang-Baxter equation associated with the fundamental representations of the
twisted and untwisted affine extensions of the orthosymplectic quantum
superalgebras $U_q[osp(m|n)]$. In this manner we obtain generalisations of the
Perk--Schultz model.


title:
Thermodynamic limit of the first-order phase transition in the Kuramoto
  model

abstract:
  In the Kuramoto model, a uniform distribution of the natural frequencies
leads to a first-order (i.e., discontinuous) phase transition from incoherence
to synchronization, at the critical coupling parameter $K_c$. We obtain the
asymptotic dependence of the order parameter above criticality: $r-r_c \propto
(K-K_c)^{2/3}$. For a finite population, we demonstrate that the population
size $N$ may be included into a self-consistency equation relating $r$ and $K$
in the synchronized state. We analyze the convergence to the thermodynamic
limit of two alternative schemes to set the natural frequencies. Other
frequency distributions different from the uniform one are also considered.


title: Social network from communities of electronic mail

abstract:
  Social networks are analyzed as graphs under the scope of discrete
mathematics which have a great range of applications in different contexts such
as: technology, social phenomena and biological systems. At the present this
theory gives a set of tools for a phenomenological analysis that would be
difficult or almost impossible with a different approach. In this work social
networks for different technical communities from electronic mail and ``News''
in Spanish language are constructed. The algorithm was based on the use of
RFC2822 standards and RFC1036 to arm threads of messages. The results are quite
different from that obtained by another kind of community as the jazz musicians
community. Nevertheless they show an analogy to random graphs obtained by the
``Configuration Model'' method. This points the attention that some
generalization assumptions are not correct.


title: Coarse-graining the dynamics of coupled oscillators

abstract:
  We present an equation-free computational approach to the study of the
coarse-grained dynamics of {\it finite} assemblies of {\it non-identical}
coupled oscillators at and near full synchronization. We use coarse-grained
observables which account for the (rapidly developing) correlations between
phase angles and oscillator natural frequencies. Exploiting short bursts of
appropriately initialized detailed simulations, we circumvent the derivation of
closures for the long-term dynamics of the assembly statistics.


title: K"ahler Geometry and the Navier-Stokes Equations

abstract:
  We study the Navier-Stokes and Euler equations of incompressible
hydrodynamics in two and three spatial dimensions and show how the constraint
of incompressiblility leads to equations of Monge--Amp\`ere type for the stream
function, when the Laplacian of the pressure is known. In two dimensions a
K\"ahler geometry is described, which is associated with the Monge--Amp\`ere
problem. This K\"ahler structure is then generalised to `two-and-a-half
dimensional' flows, of which Burgers' vortex is one example. In three
dimensions, we show how a generalized Calabi--Yau structure emerges in a
special case.


title: Statistics of a noise-driven Manakov soliton

abstract:
  We investigate the statistics of a vector Manakov soliton in the presence of
additive Gaussian white noise. The adiabatic perturbation theory for Manakov
soliton yields a stochastic Langevin system which we analyze via the
corresponding Fokker-Planck equation for the probability density function (PDF)
for the soliton parameters. We obtain marginal PDFs for the soliton frequency
and amplitude as well as soliton amplitude and polarization angle. We also
derive formulae for the variances of all soliton parameters and analyze their
dependence on the initial values of polarization angle and phase.


title: Soliton mobility in nonlocal optical lattices

abstract:
  We address the impact of nonlocality in the physical features exhibited by
solitons supported by Kerr-type nonlinear media with an imprinted optical
lattice. We discover that nonlocality of nonlinear response can profoundly
affect the soliton mobility, hence all the related phenomena. Such behavior
manifests itself in significant reductions of the Peierls-Nabarro potential
with increase of the degree of nonlocality, a result that opens the rare
possibility in nature of almost radiationless propagation of highly localized
solitons across the lattice.


title:
Upper threshold for stability of multipole-mode solitons in nonlocal
  nonlinear media

abstract:
  We address the stability of multipole-mode solitons in nonlocal Kerr-type
nonlinear media. Such solitons comprise several out-of-phase peaks packed
together by the forces acting between them. We discover that dipole-, triple-,
and quadrupole-mode solitons can be made stable, whereas all higher-order
soliton bound states are unstable.


title: Lax Representation of WZNW-Like Systems

abstract:
  The Lax representation and Backlund transformations for the systems similar
to WZNW (Wess-Zumino-Novicov-Witten) systems and non-abelian affine Toda models
are obtained in present paper. One of these systems is a new integrable
extension of well known sine-Gordon equation.


title:
Smooth-Particle Phase Stability with density and density-gradient
  potentials

abstract:
  Stable fluid and solid particle phases are essential to the simulation of
continuum fluids and solids using Smooth Particle Applied Mechanics. We show
that density-dependent potentials, such as Phi=(1/2)Sum (rho-rho_0)^2, along
with their corresponding constitutive relations, provide a simple means for
characterizing fluids and that a special stabilization potential, Phi=(1/2)Sum
(delrho)^2, not only stabilizes crystalline solid phases (or meshes) but also
provides a surface tension which is missing in the usual
density-dependent-potential approach. We illustrate these ideas for
two-dimensional square, triangular, and hexagonal lattices.


title: Algebras of Charges

abstract:
  Two different algebras are applied to the system of charges. Such
generalizations of classical theory eliminate infinite seif-energy of
electrons. Paradoxical radiative self-acceleration of an electron is also
eliminated in this way. One of the algebras predicts some new effects of high
order.


title:
Convergence to the Critical Attractor at Infinite and Tangent
  Bifurcation Points

abstract:
  The dynamics of the convergence to the critical attractor for the logistic
map is investigated. At the border of chaos, when the Liapunov exponent is
zero, the use of the non-extensive statistical mechanics formalism allows to
define a weak sensitivity or insensitivity to initial conditions. Using this
formalism we analyse how a set of initial conditions spread all over the phase
space converges to the critical attractor in the case of infinite bifurcation
and tangent bifurcation points. We show that the phenomena is governed in both
cases by a power-law regime but the critical exponents depend on the type of
bifurcation and may also depend on the numerical experiment set-up. Differences
and similarities between the two cases are also discussed.


title: Stackel systems: bi-Hamiltonian property and systematic construction

abstract:
  It is shown that separation conditions (separation curves) are fundamental
objects of separability theory. They are used for the classification of certain
clases of separable systems, for the proof of bi-Hamiltonian property and
finally they allow to construct new separable systems from known ones.


title: Whitham systems and deformations

abstract:
  We consider the deformations of Whitham systems including the "dispersion
terms" and having the form of Dubrovin-Zhang deformations of Frobenius
manifolds. The procedure is connected with B.A. Dubrovin problem of
deformations of Frobenius manifolds corresponding to the Whitham systems of
integrable hierarchies. Under some non-degeneracy requirements we suggest a
general scheme of the deformation of the hyperbolic Whitham systems using the
initial non-linear system. The general form of the deformed Whitham system
coincides with the form of the "low-dispersion" asymptotic expansions used by
B.A. Dubrovin and Y. Zhang in the theory of deformations of Frobenius
manifolds.


title:
Gauge transformation and reciprocal link for (2+1)-dimensional
  integrable field systems

abstract:
  Appropriate restrictions of Lax operators which allows to construction of
(2+1)-dimensional integrable field systems, coming from centrally extended
algebra of pseudo-differential operators, are reviewed. The gauge
transformation and the reciprocal link between three classes of Lax hierarchies
are established.


title: General Quantum Resonances of the Kicked Particle

abstract:
  The quantum resonances (QRs) of the kicked particle are studied in a most
general framework by also considering {\em arbitrary} periodic kicking
potentials. It is shown that QR can arise, in general, for {\em any rational}
value of the Bloch quasimomentum. This is illustrated in the case of the main
QRs for arbitrary potentials. In this case, which is shown to be precisely
described by the linear kicked rotor, exact formulas are derived for the
diffusion coefficients determining the asymptotic evolution of the average
kinetic energy of either an incoherent mixture of plane waves or a general wave
packet. The momentum probability distribution is exactly calculated and studied
for a two-harmonic potential. It clearly exhibits new resonant values of the
quasimomentum and it is robust under small deviations from QR.

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


title: Hamiltonization of nonholonomic systems

abstract:
  We consider some issues of the representation in the Hamiltonian form of two
problems of nonholonomic mechanics, namely, the Chaplygin's ball problem and
the Veselova problem. We show that these systems can be written as generalized
Chaplygin systems and can be integrated by the method of reducing multiplier.
We also indicate the algebraic form of the Poisson brackets of these systems
(after the time substitution). Generalizations of the problems are considered
and new realizations of nonholonomic constraints are presented. Some
nonholonomic systems with an invariant measure and a sufficient number of first
integrals are indicated, for which the question of the representation in the
Hamiltonian form is still open, even after the time substitution.


title: Diagonal approximation of the form factor of the unitary group

abstract:
  The form factor of the unitary group U(N) endowed with the Haar measure
characterizes the correlations within the spectrum of a typical unitary matrix.
It can be decomposed into a sum over pairs of ``periodic orbits'', where by
periodic orbit we understand any sequence of matrix indices. From here the
diagonal approximation can be defined in the usual fashion as a sum only over
pairs of identical orbits. We prove that as we take the dimension $N$ to
infinity, the diagonal approximation becomes ``exact'', that is converges to
the full form factor.


title: Exact solutions of the 3-wave resonant interaction equation

abstract:
  The Darboux--Dressing Transformations are applied to the Lax pair associated
to the system of nonlinear equations describing the resonant interaction of
three waves in 1+1 dimensions. We display explicit solutions featuring
localized waves whose profile vanishes at the spacial boundary plus and minus
infinity, and which are not pure soliton solutions. These solutions depend on
an arbitrary function and allow to deal with collisions of waves with various
profiles.


title:
Vortices, circumfluence, symmetry groups and Darboux transformations of
  the Euler equations

abstract:
  The Euler equation (EE) is one of the basic equations in many physical fields
such as the fluids, plasmas, condense matters, astrophysics, oceanic and
atmospheric dynamics. A new symmetry group theorem of the two dimensional EE is
obtained via a simple direct method and the theorem is used to find \em exact
analytical \rm vortex and circumfluence solutions. Some types of Darboux
transformations (DTs) for the both two and three dimensional EEs are obtained
for \em arbitrary spectral parameters \rm which indicates that the EEs are
integrable and the Navier-Stockes (NS) equations with large Renoyed number are
nearly integrable, i.e, they are singular perturbations of the integrable EEs.
The possibility of the vortex and circumfluence solutions to approximately
explain the tropical cyclones (TCs), especially, the Hurricane Andrew 1992, is
discussed.


title: Turning light into a liquid via atomic coherence

abstract:
  We study a four level atomic system with electromagnetically induced
transparency with giant $\chi^{(3)}$ and $\chi^{(5)}$ susceptibilities of
opposite signs. This system would allow to obtain multidimensional solitons and
light condensates with surface tension properties analogous to those of usual
liquids.


title:
Instabilities of one-dimensional stationary solutions of the cubic
  nonlinear Schrodinger equation

abstract:
  The two-dimensional cubic nonlinear Schrodinger equation admits a large
family of one-dimensional bounded traveling-wave solutions. All such solutions
may be written in terms of an amplitude and a phase. Solutions with piecewise
constant phase have been well studied previously. Some of these solutions were
found to be stable with respect to one-dimensional perturbations. No such
solutions are stable with respect to two-dimensional perturbations. Here we
consider stability of the larger class of solutions whose phase is dependent on
the spatial dimension of the one-dimensional wave form. We study the spectral
stability of such nontrivial-phase solutions numerically, using Hill's method.
We present evidence which suggests that all such nontrivial-phase solutions are
unstable with respect to both one- and two-dimensional perturbations.
Instability occurs in all cases: for both the elliptic and hyperbolic nonlinear
Schrodinger equations, and in the focusing and defocusing case.


abstract:
  The Hamiltonian formalism of the Landau-Lifschitz equation for a spin chain
with full anisotropy is formulated completely, which constructs a stable base
for further investigations.


title: Integrability of $q$-oscillator lattice model

abstract:
  A simple formulation of an exactly integrable $q$-oscillator model on two
dimensional lattice (in 2+1 dimensional space-time) is given. Its
interpretation in the terms of 2d quantum inverse scattering method and nested
Bethe Ansatz equations is discussed.


title: Solitary Waves in Discrete Media with Four Wave Mixing

abstract:
  In this paper, we examine in detail the principal branches of solutions that
arise in vector discrete models with nonlinear inter-component coupling and
four wave mixing. The relevant four branches of solutions consist of two single
mode branches (transverse electric and transverse magnetic) and two mixed mode
branches, involving both components (linearly polarized and elliptically
polarized). These solutions are obtained explicitly and their stability is
analyzed completely in the anti-continuum limit (where the nodes of the lattice
are uncoupled), illustrating the supercritical pitchfork nature of the
bifurcations that give rise to the latter two, respectively, from the former
two. Then the branches are continued for finite coupling constructing a full
two-parameter numerical bifurcation diagram of their existence. Relevant
stability ranges and instability regimes are highlighted and, whenever
unstable, the solutions are dynamically evolved through direct computations to
monitor the development of the corresponding instabilities. Direct connections
to the earlier experimental work of Meier et al. [Phys. Rev. Lett. {\bf 91},
143907 (2003)] that motivated the present work are given.


title: On asymptotic properties of some complex Lorenz-like systems

abstract:
  The classical Lorenz lowest order system of three nonlinear ordinary
differential equations, capable of producing chaotic solutions, has been
generalized by various authors in two main directions: (i) for number of
equations larger than three (Curry1978) and (ii) for the case of complex
variables and parameters. Problems of laser physics and geophysical fluid
dynamics (baroclinic instability, geodynamic theory, etc. - see the references)
can be related to this second aspect of generalization. In this paper we study
the asymptotic properties of some complex Lorenz systems, keeping in the mind
the physical basis of the model mathematical equations.


title:
Lyapunov Modes and Time-Correlation Functions for Two-Dimensional
  Systems

abstract:
  The relation between the Lyapunov modes (delocalized Lyapunov vectors) and
the momentum autocorrelation function is discussed in two-dimensional hard-disk
systems. We show numerical evidence that the smallest time-oscillating period
of the Lyapunov modes is twice as long as the time-oscillating period of
momentum autocorrelation function for both square and rectangular
two-dimensional systems with hard-wall boundary conditions.


title: Kinks in dipole chains

abstract:
  It is shown that the topological discrete sine-Gordon system introduced by
Speight and Ward models the dynamics of an infinite uniform chain of electric
dipoles constrained to rotate in a plane containing the chain. Such a chain
admits a novel type of static kink solution which may occupy any position
relative to the spatial lattice and experiences no Peierls-Nabarro barrier.
Consequently the dynamics of a single kink is highly continuum like, despite
the strongly discrete nature of the model. Static multikinks and kink-antikink
pairs are constructed, and it is shown that all such static solutions are
unstable. Exact propagating kinks are sought numerically using the
pseudo-spectral method, but it is found that none exist, except, perhaps, at
very low speed.


title: Stability and Synchronism of certain coupled Dynamical Systems

abstract:
  We obtain sufficient conditions for the stability of the synchronized
solutions for a class of coupled dynamical systems. This is accomplished by
finding an analytical expression for the transverse Liapunov exponent through
spectral analysis. We then indicate some applications to population dynamics.


title: Ten Questions about Emergence

abstract:
  Self-Organization is of growing importance for large distributed computing
systems. In these systems, a central control and manual management is
exceedingly difficult or even impossible. Emergence is widely recognized as the
core principle behind self-organization. Therefore the idea to use both
principles to control and organize large-scale distributed systems is very
attractive and not so far off.
  Yet there are many open questions about emergence and self-organization,
ranging from a clear definition and scientific understanding to the possible
applications in engineering and technology, including the limitations of both
concepts. Self-organizing systems with emergent properties are highly
desirable, but also very challenging. We pose ten central questions about
emergence, give preliminary answers, and identify four basic limits of
self-organization: a size limit, a place limit, a complexity limit and finally
a combinatorial limit.


title: A 2 - Component or N=2 Supersymmetric Camassa - Holm Equation

abstract:
  The extended N=2 supersymmetric Camasa - Holm equation is presented. It is
accomplishe by formulation the supersymmeytric version of the Fuchssteiner
method. In this framework we use two supersymmetric recursion operators of the
N=2, $\alpha=-2,4$ Korteweg - de Vries equation and constructed two different
version of the supersymmetric Camassa - Holm equation. The bosonic sector of
N=2, $\alpha=4$ supersymmetric Camassa - Holm equation contains two component
generalization of this equation considered by Chen, Liu and Zhang and as a
special case two component generalized Hunter - Saxton equation considered by
Aratyn, Gomes and Zimerman, As a byproduct of our analysis we defined the N=2
supersymmetric Hunter - Saxton equation. The bihamiltonian structure is
constructed for the supersymmetric N=2, $\alpha=4$ Camassa - Holm equation.


title: Fractal diffusion coefficient from dynamical zeta functions

abstract:
  Dynamical zeta functions provide a powerful method to analyze low dimensional
dynamical systems when the underlying symbolic dynamics is under control. On
the other hand even simple one dimensional maps can show an intricate structure
of the grammar rules that may lead to a non smooth dependence of global
observable on parameters changes. A paradigmatic example is the fractal
diffusion coefficient arising in a simple piecewise linear one dimensional map
of the real line. Using the Baladi-Ruelle generalization of the
Milnor-Thurnston kneading determinant we provide the exact dynamical zeta
function for such a map and compute the diffusion coefficient from its smallest
zero.


title: Asymmetry of temporal cross-correlations in turbulent shear flows

abstract:
  We investigate spatial and temporal cross-correlations between streamwise and
normal velocity components in three shear flows: a low-dimensional model for
vortex-streak interactions, direct numerical simulations for a nearly
homogeneous shear flow and experimental data for a turbulent boundary layer. A
driving of streamwise streaks by streamwise vortices gives rise to a temporal
asymmetry in the short time correlation. Close to the wall or the bounding
surface in the free-slip situations, this asymmetry is identified. Further away
from the boundaries the asymmetry becomes weaker and changes character,
indicating the prevalence of other processes. The systematic variation of the
asymmetry measure may be used as a complementary indicator to separate
different layers in turbulent shear flows. The location of the extrema at
different streamwise displacements can be used to read off the mean advection
speed; it differs from the mean streamwise velocity because of asymmetries in
the normal extension of the structures.


title: Amplitude death in coupled chaotic oscillators

abstract:
  Amplitude death can occur in chaotic dynamical systems with time-delay
coupling, similar to the case of coupled limit cycles. The coupling leads to
stabilization of fixed points of the subsystems. This phenomenon is quite
general, and occurs for identical as well as nonidentical coupled chaotic
systems. Using the Lorenz and R\"ossler chaotic oscillators to construct
representative systems, various possible transitions from chaotic dynamics to
fixed points are discussed.


title: Distribution of the spacing between two adjacent avoided crossings

abstract:
  We consider the frequency at which avoided crossings appear in an energy
level structure when an external field is applied to a quantum chaotic system.
The distribution of the spacing in the parameter between two adjacent avoided
crossings is investigated. Using a random matrix model, we find that the
distribution of these spacings is well fitted by a power-law distribution for
small spacings. The powers are 2 and 3 for the Gaussian orthogonal ensemble and
Gaussian unitary ensemble, respectively. We also find that the distributions
decay exponentially for large spacings. The distributions in concrete quantum
chaotic systems agree with those of the random matrix model.


title: Noise Stabilized Random Attractor

abstract:
  A two dimensional flow model is introduced with deterministic behavior
consisting of bursts which become successively larger, with longer interburst
time intervals between them. The system is symmetric in one variable x and
there are bursts on either side of x = 0, separated by the presence of an
invariant manifold at x = 0. In the presence of arbitrarily small additive
noise in the x direction, the successive bursts have bounded amplitudes and
interburst intervals. This system with noise is proposed as a model for edge
localized modes in tokamaks. Further, the bursts can switch from positive to
negative x and vice-versa. The probability distribution of burst heights and
interburst periods is studied, as is the dependence of the statistics on the
noise variance. The modification of this behavior as the symmetry in x is
broken is studied, showing qualitatively similar behavior if the symmetry
breaking is small enough. Experimental observations of a nonlinear circuit
governed by the same equations are presented, showing good agreement.


title:
Bifurcations in nonlinear models of fluid-conveying pipes supported at
  both ends

abstract:
  Stationary bifurcations in several nonlinear models of fluid conveying pipes
fixed at both ends are analyzed with the use of Lyapunov-Schmidt reduction and
singularity theory. Influence of gravitational force, curvature and vertical
elastic support on various properties of bifurcating solutions are
investigated. In particular the conditions for occurrence of supercritical and
subcritical bifurcations are presented for the models of Holmes, Thurman and
Mote, and Paidoussis.


title:
String equations in Whitham hierarchies: tau-functions and Virasoro
  constraints

abstract:
  A scheme for solving Whitham hierarchies satisfying a special class of string
equations is presented. The tau-function of the corresponding solutions is
obtained and the differential expressions of the underlying Virasoro
constraints are characterized. Illustrative examples of exact solutions of
Whitham hierarchies are derived and applications to conformal maps dynamics are
indicated.


title: Synchronization by Reactive Coupling and Nonlinear Frequency Pulling

abstract:
  We present a detailed analysis of a model for the synchronization of
nonlinear oscillators due to reactive coupling and nonlinear frequency pulling.
We study the model for the mean field case of all-to-all coupling, deriving
results for the initial onset of synchronization as the coupling or
nonlinearity increase, and conditions for the existence of the completely
synchronized state when all the oscillators evolve with the same frequency.
Explicit results are derived for Lorentzian, triangular, and top-hat
distributions of oscillator frequencies. Numerical simulations are used to
construct complete phase diagrams for these distributions.


title:
Group classification of the general evolution equation: local and
  quasi-local symmetries

abstract:
  We expand our group classification of quasilinear evolution equations (Acta
Appl.Math., v.69, 2001) to the case of general evolution equation in one
spatial variable. This enables obtaining several new classes of evolution
equations with nontrivial Lie symmetry. As a by-product, we derive a number of
nonlinear evolution equations admitting quasilocal symmetries.


title: Survival probability time distribution in dielectric cavities

abstract:
  We study the survival probability time distribution (SPTD) in dielectric
cavities. In a circular dielectric cavity the SPTD has an algebraic long time
behavior, $\sim t^{-2}$ in both TM and TE cases, but shows different short time
behaviors due to the existence of the Brewster angle in TE case where the short
time behavior is exponential. The SPTD for a stadium-shaped cavity decays
exponentially, and the exponent shows a relation of $\gamma \sim n^{-2}$, $n$
is the refractive index, and the proportional coefficient is obtained from a
simple model of the steady probability distribution. We also discuss about the
SPTD for a quadrupolar deformed cavity and show that the long time behavior can
be algebraic or exponential depending on the location of islands.


title: Random matrix description of decaying quantum systems

abstract:
  This contribution describes a statistical model for decaying quantum systems
(e.g. photo-dissociation or -ionization). It takes the interference between
direct and indirect decay processes explicitely into account. The resulting
expressions for the partial decay amplitudes and the corresponding cross
sections may be considered a many-channel many-resonance generalization of
Fano's original work on resonance lineshapes [Phys. Rev 124, 1866 (1961)].
  A statistical (random matrix) model is then introduced. It allows to describe
chaotic scattering systems with tunable couplings to the decay channels. We
focus on the autocorrelation function of the total (photo) cross section, and
we find that it depends on the same combination of parameters, as the
Fano-parameter distribution. These combinations are statistical variants of the
one-channel Fano parameter. It is thus possible to study Fano interference
(i.e. the interference between direct and indirect decay paths) on the basis of
the autocorrelation function, and thereby in the regime of overlapping
resonances. It allows us, to study the Fano interference in the limit of
strongly overlapping resonances, where we find a persisting effect on the level
of the weak localization correction.


title:
Interaction between Kirchhoff vortices and point vortices in an ideal
  fluid

abstract:
  We consider the interaction of two vortex patches (elliptic Kirchhoff
vortices) which move in an unbounded volume of an ideal incompressible fluid. A
moment second-order model is used to describe the interaction. The case of
integrability of a Kirchhoff vortex and a point vortex by the variable
separation method is qualitatively analyzed. A new case of integrability of two
Kirchhoff vortices is found. A reduced form of equations for two Kirchhoff
vortices is proposed and used to analyze their regular and chaotic behavior.


title:
A Systems-Based Approach to Multiscale Computation: Equation-Free
  Detection of Coarse-Grained Bifurcations

abstract:
  We discuss certain basic features of the equation-free (EF) approach to
modeling and computation for complex/multiscale systems. We focus on links
between the equation-free approach and tools from systems and control theory
(design of experiments, data analysis, estimation, identification and
feedback). As our illustrative example, we choose a specific numerical task
(the detection of stability boundaries in parameter space) for stochastic
models of two simplified heterogeneous catalytic reaction mechanisms. In the
equation-free framework the stochastic simulator is treated as an experiment
(albeit a computational one). Short bursts of fine scale simulation (short
computational experiments) are designed, executed, and their results processed
and fed back to the process, in integrated protocols aimed at performing the
particular coarse-grained task (the detection of a macroscopic instability).
Two distinct approaches are presented; one is a direct translation of our
previous protocol for adaptive detection of instabilities in laboratory
experiments (Rico-Martinez et al., 2003); the second approach is motivated from
numerical bifurcation algorithms for critical point detection. A comparison of
the two approaches brings forth a key feature of equation-free computation:
computational experiments can be easily initialized at will, in contrast to
laboratory ones.


title: Synchronization of Coupled Chaotic Dynamics on Networks

abstract:
  We review some recent work on the synchronization of coupled dynamical
systems on a variety of networks. When nodes show synchronized behaviour, two
interesting phenomena can be observed. First, there are some nodes of the
floating type that show intermittent behaviour between getting attached to some
clusters and evolving independently. Secondly, two different ways of cluster
formation can be identified, namely self-organized clusters which have mostly
intra-cluster couplings and driven clusters which have mostly inter-cluster
couplings.


title:
The Fourier transform of the Hadamard transform: Multifractals,
  Sequences and Quantum Chaos

abstract:
  We introduce a class of functions that limit to multifractal measures and
which arise when one takes the Fourier transform of the Hadamard transform.
This introduces generalizations of the Fourier transform of the well-studied
and ubiquitous Thue-Morse sequence, and introduces also generalizations to
other intriguing sequences. We show their relevance to quantum chaos, by
displaying quantum eigenfunctions of the quantum bakers map that are
approximated well by such measures, thereby extending our recent work where we
pointed to the existence of ``Thue-Morse'' states.


title: Impact of noise on domain growth in electroconvection

abstract:
  The growth and ordering of striped domains has recently received renewed
attention due in part to experimental studies in diblock copolymers and
electroconvection. One surprising result has been the relative slow dynamics
associated with the growth of striped domains. One potential source of the slow
dynamics is the pinning of defects in the periodic potential of the stripes. Of
interest is whether or not external noise will have a significant impact on the
domain ordering, perhaps by reducing the pinning and increasing the rate of
ordering. In contrast, we present experiments using electroconvection in which
we show that a particular type of external noise decreases the rate of domain
ordering.


title: Isomonodromic deformation of resonant rational connections

abstract:
  We analyze isomonodromic deformations of rational connections on the Riemann
sphere with Fuchsian and irregular singularities. The Fuchsian singularities
are allowed to be of arbitrary resonant index; the irregular singularities are
also allowed to be resonant in the sense that the leading coefficient matrix at
each singularity may have arbitrary Jordan canonical form, with a genericity
condition on the Lidskii submatrix of the subleading term. We also give the
relevant notion of isomonodromic tau function extending the one of non-resonant
deformations introduced by Miwa-Jimbo-Ueno. The tau function is expressed
purely in terms of spectral invariants of the matrix of the connection.


title: A Collective Motion Algorithm for Tracking Time-Dependent Boundaries

abstract:
  We present a numerical method that allows a formation of communicating agents
to target the boundary of a time dependent concentration by following a time
dependent concentration gradient. The algorithm motivated by \cite{MB, BKM},
allows the agents to move in space in a non-stationary environment. Our method
is applicable to finding the boundary of any regular surface and may be of
interest for for studying motions of swarms in biology, as well as to
engineering applications where boundary detection is an issue.


title: The twistor theory of Whitham hierarchy

abstract:
  We have established a 1-1 correspondence between a solution of the universal
Whitham hierarchy and a twistor space. The twistor space consists of a complex
surface and a family of complex curves together with a meromorphic 2-form. The
solution of the Whitham hierarchy is given by deforming the curve in the
surface. By treating the family of algebraic curves in $CP^1 X CP^1$ as a
twistor space, we were able to express the deformations of the isomonodromic
spectral curve in terms of the deformations generated by the Whitham hierarchy.


title: On the Toda Lattice Equation with Self-Consistent Sources

abstract:
  The Toda lattice hierarchy with self-consistent sources and their Lax
representation are derived. We construct a forward Darboux transformation (FDT)
with arbitrary functions of time and a generalized forward Darboux
transformation (GFDT) for Toda lattice with self-consistent sources (TLSCS),
which can serve as a non-auto-Backlund transformation between TLSCS with
different degrees of sources. With the help of such DT, we can construct many
type of solutions to TLSCS, such as rational solution, solitons, positons,
negetons, and soliton-positons, soliton-negatons, positon-negatons etc., and
study properties and interactions of these solutions.


title: Synchronization of Limit Sets

abstract:
  In this Letter, we derive a sufficient condition of synchronizing limit sets
(attractors and repellers) by using the linear feedback control technique
proposed here. There examples are included. The numerical simulations and
computer graphics show that our method work well.


title: Irreversibility in a simple reversible model

abstract:
  This paper studies a parametrized family of familiar generalized baker maps,
viewed as simple models of time-reversible evolution. Mapping the unit square
onto itself, the maps are partly contracting and partly expanding, but they
preserve the global measure of the definition domain. They possess periodic
orbits of any period, and all maps of the set have attractors with well defined
structure. The explicit construction of the attractors is described and their
structure is studied in detail. There is a precise sense in which one can speak
about absolute age of a state, regardless of whether the latter is applied to a
single point, a set of points, or a distribution function. One can then view
the whole trajectory as a set of past, present and future states. This
viewpoint is then applied to show that it is impossible to define a priori
states with very large "negative age". Such states can be defined only a
posteriori. This gives precise sense to irreversibility -- or the "arrow of
time" -- in these time-reversible maps, and is suggested as an explanation of
the second law of thermodynamics also for some realistic physical systems.


title:
Comment on novel public key encryption technique based on multiple
  chaotic systems

abstract:
  Recently, a novel public key edcryption technique based on multiple chaotic
systems has been proposed. The scheme employs m-chaotic systmes and a set of
linear functions for key exchange over an insecure channel. The security of the
proposed algorithm grows as NPm, where M, P are the size of the key and the
computational commplexity fo the linear functions respectively. In this paper,
the fundamental weakness of the cryptosystme is pointed out and a successful
attack is described. Given the public keys and initial vector, one can
calculate the secret key based on Parsevala's theorem. Both theoretical and
experimental results show that the attacker can access to the secret key
without difficulty. The lack of security discourages the use of such algorithm
for practical application.


title: Hysteretic nonequilibrium Ising-Bloch transition

abstract:
  We show that a parametrically driven cubic-quintic complex Ginzburg-Landau
equation exhibits a hysteretic nonequilibrium Ising-Bloch transition for large
enough quintic nonlinearity. These results help to understand the recent
experimental observation of this pheomenon [A. Esteban-Martin et al., Phys.
Rev. Lett. 94, 223903 (2005)].


title:
On Quasitriviality and Integrability of a Class of Scalar Evolutionary
  PDEs

abstract:
  For certain class of perturbations of the equation $u_t=f(u) u_x$, we prove
the existence of change of coordinates, called quasi-Miura transformations,
that reduce these perturbed equations to the unperturbed ones. As an
application, we propose a criterion for the integrability of these equations.


title:
B\"{a}cklund transformations for the KP and mKP hierarchies with
  self-consistent sources

abstract:
  Using gauge transformations for the corresponding generating
pseudo-differential operators $L^n$ in terms of eigenfunctions and adjoint
eigenfunctions, we construct several types of auto-B\"{a}cklund transformations
for the KP hierarchy with self-consistent sources (KPHSCS) and mKP hierarchy
with self-consistent sources (mKPHSCS) respectively. The B\"{a}cklund
transformations from the KPHSCS to mKPHSCS are also constructed in this way.


title:
The quasiclassical limit of the symmetry constraint of the KP hierarchy
  and the dispersionless KP hierarchy with self-consistent sources

abstract:
  For the first time we show that the quasiclassical limit of the symmetry
constraint of the KP hierarchy leads to the generalized Zakharov reduction of
the dispersionless KP (dKP) hierarchy which has been proved to be result of
symmetry constraint of the dKP hierarchy recently. By either regarding the
constrained dKP hierarchy as its stationary case or taking the dispersionless
limit of the KP hierarchy with self-consistent sources directly, we construct a
new integrable dispersionless hierarchy, i.e., the dKP hierarchy with
self-consistent sources and find its associated conservation equations (or
equations of Hamilton-Jacobi type). Some solutions of the dKP equation with
self-consistent sources are also obtained by hodograph transformations.


title:
The constrained dispersionless mKP hierarchy and the dispersionless mKP
  hierarchy with self-consistent sources

abstract:
  We first show that the quasiclassical limit of the squared eigenfunction
symmetry constraint of the Sato operator for the mKP hierarchy leads to a
reduction of the Sato function for the dispersionless mKP hierarchy. The
constrained dispersionless mKP hierarchy (cdmKPH) is obtained and it is shown
that the (2+1)-dimensional dispersionless mKP hierarchy is decomposed to two
(1+1)-dimensional hierarchies of hydrodynamical type. The dispersionless mKP
hierarchy with self-consistent sources (dmKPHSCS) together with its associated
conservation equations are also constructed. Some solutions of dmKPESCS are
obtained by hodograph reduction method.


title:
Resonant light-light interaction in slab waveguides: angular filters and
  spectral hole burning

abstract:
  We consider the process of low-power light scattering by optical solitons in
a slab waveguide with homogeneous and inhomogeneous refractive index core. We
observe resonant reflection (Fano resonance) as well as resonant transmission
of light by optical solitons at certain incident angles. The resonance position
can be controlled experimentally by changing the soliton intensity and the
relative frequency detuning between the soliton and the probe light beams.


title:
Hamiltonian formulation and integrability of a complex symmetric
  nonlinear system

abstract:
  The integrability of a complex generalisation of the 'elegant' system,
proposed by D. Fairlie and its relation to the Nahm equation and the Manakov
top is discussed.


title: Higher-Order Nonlinear Contraction Analysis

abstract:
  Nonlinear contraction theory is a comparatively recent dynamic control system
design tool based on an exact differential analysis of convergence, in essence
converting a nonlinear stability problem into a linear time-varying stability
problem. Contraction analysis relies on finding a suitable metric to study a
generally nonlinear and time-varying system. This paper shows that the
computation of the metric may be largely simplified or indeed avoided
altogether by extending the exact differential analysis to the higher-order
dynamics of the nonlinear system. Simple applications in economics, classical
mechanics, and process control are described.


title: Energy Flux and Bottleneck Effect in Turbulence

abstract:
  Past numerical simulations and experiments of turbulence exhibit a hump in
the inertial range, called the bottleneck effect. In this paper we show that
sufficiently large inertial range (four decades) is required for an effective
energy cascade. We propose that the bottleneck effect is due to the
insufficient inertial range available in the reported simulations and
experiments. To facilitate the turbulent energy transfer, the spectrum near
Kolmogorov's dissipation wavenumber has a hump.


title:
Existence of anticipatory, complete and lag synchronizations in
  time-delay systems

abstract:
  Existence of different kinds of synchronizations, namely anticipatory,
complete and lag type synchronizations (both exact and approximate), are shown
to be possible in time-delay coupled piecewise linear systems. We deduce
stability condition for synchronization of such unidirectionally coupled
systems following Krasovskii-Lyapunov theory. Transition from anticipatory to
lag synchronization via complete synchronization as a function of coupling
delay is discussed. The existence of exact synchronization is preceded by a
region of approximate synchronization from desynchronized state as a function
of a system parameter, whose value determines the stability condition for
synchronization. The results are corroborated by the nature of similarity
functions. A new type of oscillating synchronization that oscillates between
anticipatory, complete and lag synchronization, is identified as a consequence
of delay time modulation with suitable stability condition.


title:
Delay time modulation induced oscillating synchronization and
  intermittent anticipatory/lag and complete synchronizations in time-delay
  nonlinear dynamical systems

abstract:
  Existence of a new type of oscillating synchronization that oscillates
between three different types of synchronizations (anticipatory, complete and
lag synchronizations) is identified in unidirectionally coupled nonlinear
time-delay systems having two different time-delays, that is feedback delay
with a periodic delay time modulation and a constant coupling delay.
Intermittent anticipatory, intermittent lag and complete synchronizations are
shown to exist in the same system with identical delay time modulations in both
the delays. The transition from anticipatory to complete synchronization and
from complete to lag synchronization as a function of coupling delay with
suitable stability condition is discussed. The intermittent anticipatory and
lag synchronizations are characterized by the minimum of similarity functions
and the intermittent behavior is characterized by a universal asymptotic
$-{3/2}$ power law distribution. It is also shown that the delay time carved
out of the trajectories of the time-delay system with periodic delay time
modulation cannot be estimated using conventional methods, thereby reducing the
possibility of decoding the message by phase space reconstruction.


title: Modulational instability in asymmetric coupled wave functions

abstract:
  The evolution of the amplitude of two nonlinearly interacting waves is
considered, via a set of coupled nonlinear Schroedinger-type equations. The
dynamical profile is determined by the wave dispersion laws (i.e. the group
velocities and the GVD terms) and the nonlinearity and coupling coefficients,
on which no assumption is made. A generalized dispersion relation is obtained,
relating the frequency and wave-number of a small perturbation around a coupled
monochromatic (Stokes') wave solution. Explicitly stability criteria are
obtained. The analysis reveals a number of possibilities. Two (individually)
stable systems may be destabilized due to coupling. Unstable systems may, when
coupled, present an enhanced instability growth rate, for an extended wave
number range of values. Distinct unstable wavenumber windows may arise
simultaneously.


title: Storage of localized structure matrixes in nematic liquid crystals

abstract:
  We show experimentally that large matrixes of localized structures can be
stored as elementary pixels in a nematic liquid crystal cell. Based on optical
feedback with phase modulated input beam, our system allows to store, erase and
actualize in parallel the localized structures in the matrix.


title:
On the attractors of two-dimensional Rayleigh oscillators including
  noise

abstract:
  We study sustained oscillations in two-dimensional oscillator systems driven
by Rayleigh-type negative friction. In particular we investigate the influence
of mismatch of the two frequencies. Further we study the influence of external
noise and nonlinearity of the conservative forces. Our consideration is
restricted to the case that the driving is rather weak and that the forces show
only weak deviations from radial symmetry. For this case we provide results for
the attractors and the bifurcations of the system. We show that for rational
relations of the frequencies the system develops several rotational excitations
with right/left symmetry, corresponding to limit cycles in the four-dimensional
phase space. The corresponding noisy distributions have the form of hoops or
tires in the four-dimensional space. For irrational frequency relations, as
well as for increasing strength of driving or noise the periodic excitations
are replaced by chaotic oscillations.

categories: nlin.AO cond-mat.stat-mech nlin.CD nlin.SI q-bio.PE


title: A fractal set from the binary reflected Gray code

abstract:
  The permutation associated with the decimal expression of the binary
reflected Gray code with $N$ bits is considered. Its cycle structure is
studied. Considered as a set of points, its self-similarity is pointed out. As
a fractal, it is shown to be the attractor of a IFS. For large values of $N$
the set is examined from the point of view of time series analysis


title:
The efficient computation of transition state resonances and reaction
  rates from a quantum normal form

abstract:
  A quantum version of a recent formulation of transition state theory in {\em
phase space} is presented. The theory developed provides an algorithm to
compute quantum reaction rates and the associated Gamov-Siegert resonances with
very high accuracy. The algorithm is especially efficient for
multi-degree-of-freedom systems where other approaches are no longer feasible.


title: Study of transport properties in rippled channels

abstract:
  We study dynamical properties of bouncing particles inside of channels with
sinusoidal walls. Taking as parameters the amplitude and the phases between the
walls we study the transmitivity and its dependence on these parameters. We
find an analytical approximation for transmitivity for small amplitudes, which
is corroborated by numerical calculation.


title: Supersymmetric Two-Boson Equation: Bilinearization and Solutions

abstract:
  A bilinear formulation for the supersymmetric two-boson equation is derived.
As applications, some solutions are calculated for it. We also construct a
bilinear Backlund transformation.


title:
On the complete integrability and linearization of nonlinear ordinary
  differential equations - Part II: Third order equations

abstract:
  We introduce a method for finding general solutions of third-order nonlinear
differential equations by extending the modified Prelle-Singer method. We
describe a procedure to deduce all the integrals of motion associated with the
given equation so that the general solution follows straightforwardly from
these integrals. The method is illustrated with several examples. Further, we
propose a powerful method of identifying linearizing transformations. The
proposed method not only unifies all the known linearizing transformations
systematically but also introduces a new and generalized linearizing
transformation (GLT). In addition to the above, we provide an algorithm to
invert the nonlocal linearizing transformation. Through this procedure the
general solution for the original nonlinear equation can be obtained from the
solution of the linear ordinary differential equation.


title: Effects of population mixing on the spread of SIR epidemics

abstract:
  We study dynamics of spread of epidemics of SIR type in a realistic
spatially-explicit geographical region, Southern and Central Ontario, using
census data obtained from Statistics Canada, and examine the role of population
mixing in epidemic processes. Our model incorporates the random nature of
disease transmission, the discreteness and heterogeneity of distribution of
host population. We find that introduction of a long-range interaction destroys
spatial correlations very easily if neighbourhood sizes are homogeneous. For
inhomogeneous neighbourhoods, very strong long-range coupling is required to
achieve a similar effect. Our work applies to the spread of in influenza during
a single season and our model is applicable to other geographic regions, if
suitable data is available.


title:
Links between dissipation, intermittency, and helicity in the GOY model
  revisited

abstract:
  High-resolution simulations within the GOY shell model are used to study
various scaling relations for turbulence. A power-law relation between the
second-order intermittency correction and the crossover from the inertial to
the dissipation range is confirmed. Evidence is found for the intermediate
viscous dissipation range proposed by Frisch and Vergassola. It is emphasized
that insufficient dissipation-range resolution systematically drives the energy
spectrum towards statistical-mechanical equipartition. In fully resolved
simulations the inertial-range scaling exponents depend on both model
parameters; in particular, there is no evidence that the conservation of a
helicity-like quantity leads to universal exponents.


title: Hierarchy of general invariants for bivariate LPDOs

abstract:
  We study invariants under gauge transformations of linear partial
differential operators on two variables. Using results of BK-factorization, we
construct hierarchy of general invariants for operators of an arbitrary order.
Properties of general invariants are studied and some examples are presented.
We also show that classical Laplace invariants correspond to some particular
cases of general invariants.


title: Scar Intensity Statistics in the Position Representation

abstract:
  We obtain general predictions for the distribution of wave function
intensities in position space on the periodic orbits of chaotic ballistic
systems. The expressions depend on effective system size N, instability
exponent lambda of the periodic orbit, and proximity to a focal point of the
orbit. Limiting expressions are obtained that include the asymptotic
probability distribution of rare high-intensity events and a perturbative
formula valid in the limit of weak scarring. For finite system sizes, a single
scaling variable lambda N describes deviations from the semiclassical N ->
infinity limit.


title: Dynamic coordinated control laws in multiple agent models

abstract:
  We present an active control scheme of a kinetic model of swarming. It has
been shown previously that the global control scheme for the model, presented
in \cite{JK04}, gives rise to spontaneous collective organization of agents
into a unified coherent swarm, via a long-range attractive and short-range
repulsive potential. We extend these results by presenting control laws whereby
a single swarm is broken into independently functioning subswarm clusters. The
transition between one coordinated swarm and multiple clustered subswarms is
managed simply with a homotopy parameter. Additionally, we present as an
alternate formulation, a local control law for the same model, which implements
dynamic barrier avoidance behavior, and in which swarm coherence emerges
spontaneously.


title: Dynamical epidemic suppression using stochastic prediction and control

abstract:
  We consider the effects of noise on a model of epidemic outbreaks, where the
outbreaks appear. randomly. Using a constructive transition approach that
predicts large outbreaks, prior to their occurrence, we derive an adaptive
control. scheme that prevents large outbreaks from occurring. The theory
inapplicable to a wide range of stochastic processes with underlying
deterministic structure.


title: Incompressible Turbulence as Nonlocal Field Theory

abstract:
  It is well known that incompressible turbulence is nonlocal in real space
because sound speed is infinite in incompressible fluids. The equation in
Fourier space indicates that it is nonlocal in Fourier space as well. Contrast
this with Burgers equation which is local in real space. Note that the sound
speed in Burgers equation is zero. In our presentation we will contrast these
two equations using nonlocal field theory. Energy spectrum and renormalized
parameters will be discussed.


title:
The method of moments for Nonlinear Schrodinger Equations: Theory and
  Applications

abstract:
  The method of moments in the context of Nonlinear Schrodinger Equations
relies on defining a set of integral quantities, which characterize the
solution of this partial differential equation and whose evolution can be
obtained from a set of ordinary differential equations. In this paper we find
all cases in which the method of moments leads to closed evolution equations,
thus extending and unifying previous works in the field of applications. For
some cases in which the method fails to provide rigorous information we also
develop approximate methods based on it, which allow to get some approximate
information on the dynamics of the solutions of the Nonlinear Schrodinger
equation.


title:
A unification in the theory of linearization of second order nonlinear
  ordinary differential equations

abstract:
  In this letter, we introduce a new generalized linearizing transformation
(GLT) for second order nonlinear ordinary differential equations (SNODEs). The
well known invertible point (IPT) and non-point transformations (NPT) can be
derived as sub-cases of the GLT. A wider class of nonlinear ODEs that cannot be
linearized through NPT and IPT can be linearized by this GLT. We also
illustrate how to construct GLTs and to identify the form of the linearizable
equations and propose a procedure to derive the general solution from this GLT
for the SNODEs. We demonstrate the theory with two examples which are of
contemporary interest.


title:
An exact solution to a kth order, nth degree nonlinear differential
  equation

abstract:
  An explicit analytic solution to the nonlinear differential equation d^k y
(--) ^n = y^l dx^kk is obtained for arbitrary integer values of k, l and n.


title: Weakly versus highly nonlinear dynamics in 1D systems

abstract:
  We analyze the morphological transition of a one-dimensional system described
by a scalar field, where a flat state looses its stability. This scalar field
may for example account for the position of a crystal growth front, an order
parameter, or a concentration profile. We show that two types of dynamics occur
around the transition: weakly nonlinear dynamics, or highly nonlinear dynamics.
The conditions under which highly nonlinear evolution equations appear are
determined, and their generic form is derived. Finally, examples are discussed.


title: Quantum curve in q-oscillator model

abstract:
  A lattice model of interacting q-oscillators, proposed in [V. Bazhanov, S.
Sergeev, arXiv:hep-th/0509181], is the quantum mechanical integrable model in
2+1 dimensional space-time. Its layer-to-layer transfer-matrix is a polynomial
of two spectral parameters, it may be regarded in the terms of quantum groups
both as a sum of sl(N) transfer matrices of a chain of length M and as a sum of
sl(M) transfer matrices of a chain of length N for reducible representations.
The aim of this paper is to derive the Bethe Ansatz equations for the
q-oscillator model entirely in the framework of 2+1 integrability providing the
evident rank-size duality.


title: Fjords in viscous fingering: Selection of width and opening angle

abstract:
  Our experiments on viscous fingering of air into oil contained between
closely spaced plates reveal two selection rules for the fjords of oil that
separate fingers of air. (Fjords are the building blocks of solutions of the
zero-surface-tension Laplacian growth equation.) Experiments in rectangular and
circular geometries yield fjords with base widths 1/2 lambda_c, where lambda_c
is the most unstable wavelength from a linear stability analysis. Further,
fjords open at an angle of 8.0 degrees plus or minus 1.0 degree. These
selection rules hold for a wide range of pumping rates and fjord lengths,
widths, and directions.


title: Mixing and reaction efficiency in closed domains

abstract:
  We present a numerical study of mixing and reaction efficiency in closed
domains. In particular we focus our attention on laminar flows. In the case of
inert transport the mixing properties of the flows strongly depend on the
details of the Lagrangian transport. We also study the reaction efficiency.
Starting with a little spot of product we compute the time needed to complete
the reaction in the container. We found that the reaction efficiency is not
strictly related to the mixing properties of the flow. In particular, reaction
acts as a "dynamical regulator".


title:
hbar expansions in semiclassical theories for systems with smooth
  potentials and discrete symmetries

abstract:
  We extend a theory of first order hbar corrections to Gutzwiller's trace
formula for systems with a smooth potential to systems with discrete symmetries
and, as an example, apply the method to the two-dimensional hydrogen atom in a
uniform magnetic field. We exploit the C_{4v}-symmetry of the system in the
calculation of the correction terms. The numerical results for the
semiclassical values will be compared with values extracted from exact quantum
mechanical calculations. The comparison shows an excellent agreement and
demonstrates the power of the hbar expansion method.


title: Statistics and geometry of passive scalars in turbulence

abstract:
  We present direct numerical simulations (DNS) of the mixing of the passive
scalar at modest Reynolds numbers (10 =< R_\lambda =< 42) and Schmidt numbers
larger than unity (2 =< Sc =< 32). The simulations resolve below the Batchelor
scale up to a factor of four. The advecting turbulence is homogeneous and
isotropic, and maintained stationary by stochastic forcing at low wavenumbers.
The passive scalar is rendered stationary by a mean scalar gradient in one
direction. The relation between geometrical and statistical properties of
scalar field and its gradients is examined. The Reynolds numbers and Schmidt
numbers are not large enough for either the Kolmogorov scaling or the Batchelor
scaling to develop and, not surprisingly, we find no fractal scaling of scalar
level sets, or isosurfaces, in the intermediate viscous range. The
area-to-volume ratio of isosurfaces reflects the nearly Gaussian statistics of
the scalar fluctuations. The scalar flux across the isosurfaces, which is
determined by the conditional probability density function (PDF) of the scalar
gradient magnitude, has a stretched exponential distribution towards the tails.
The PDF of the scalar dissipation departs distinctly, for both small and large
amplitudes, from the lognormal distribution for all cases considered. The joint
statistics of the scalar and its dissipation rate, and the mean conditional
moment of the scalar dissipation, are studied as well. We examine the effects
of coarse-graining on the probability density to simulate the effects of poor
probe-resolution in measurements.


title:
A new model of turbulent relative dispersion: a self-similar telegraph
  equation based on persistently separating motions

abstract:
  Turbulent relative dispersion is studied theoretically with a focus on the
evolution of probability distribution of the relative separation of two passive
particles. A finite separation speed and a finite correlation of relative
velocity, which are crucial for real turbulence, are implemented to a master
equation by multiple-scale consideration. A telegraph equation with
scale-dependent coefficients is derived in the continuous limit. Unlike the
conventional case, the telegraph equation has a similarity solution bounded by
the maximum separation. The evolution is characterized by two parameters: the
strength of persistency of separating motions and the coefficient of the drift
term. These parameters are connected to Richardson's constant and, thus,
expected to be universal. The relationship between the drift term and coherent
structures is discussed for two 2-D turbulences.


title: Sandpile behaviour in discrete water-wave turbulence

abstract:
  We construct a sandpile model for evolution of the energy spectrum of the
water surface waves in finite basins. This model take into account loss of
resonant wave interactions in discrete Fourier space and restoration of these
interactions at larger nonlinearity levels. For weak forcing, the waveaction
spectrum takes a critical $\omega^{-10}$ shape where the nonlinear resonance
broadening is equal to the Fourier grid spacing. The energy cascade in this
case takes form of rare weak avalanches on the critical slope background. For
larger forcing, this regime is replaced by a continuous cascade and
Zakharov-Filonenko $\omega^{-8}$ waveaction spectrum. For intermediate forcing
levels, both scalings will be seen: $\omega^{-10}$ at small and $\omega^{-8}$
at large frequencies. The interval between these two scaling regions is
characterised by strong avalanches.


title: Andrew Lenard: A Mystery Unraveled

abstract:
  The theory of bi-Hamiltonian systems has its roots in what is commonly
referred to as the "Lenard recursion formula". The story about the discovery of
the formula told by Andrew Lenard is the subject of this article.


title: Local Analysis of Dissipative Dynamical Systems

abstract:
  Linear transformation techniques such as singular value decomposition (SVD)
have been used widely to gain insight into the qualitative dynamics of data
generated by dynamical systems. There have been several reports in the past
that had pointed out the susceptibility of linear transformation approaches in
the presence of nonlinear correlations. In this tutorial review, local
dispersion along with the surrogate testing is proposed to discriminate
nonlinear correlations arising in deterministic and non-deterministic settings.


title:
Detection of synchronised chaos in coupled map networks using symbolic
  dynamics

abstract:
  We present a method based on symbolic dynamics for the detection of
synchronization in networks of coupled maps and distinguishing between chaotic
and random iterations. The symbolic dynamics are defined using special
partitions of the phase space which prevent the occurrence of certain symbol
sequences related to the characteristics of the dynamics. Synchrony in a large
network can be detected using measurements from only a single node by checking
for the presence of forbidden symbol transitions. The method utilises a
relatively short time series of measurements and hence is computationally very
fast. Furthermore, it is robust against parameter uncertainties, is independent
of the network size, and does not require knowledge of the connection
structure.


title: Recycling Parrondo games

abstract:
  We consider a deterministic realization of Parrondo games and use periodic
orbit theory to analyze their asymptotic behavior.


title: Nature of complex singularities for the 2D Euler equation

abstract:
  A detailed study of complex-space singularities of the two-dimensional
incompressible Euler equation is performed in the short-time asymptotic
r\'egime when such singularities are very far from the real domain; this allows
an exact recursive determination of arbitrarily many spatial Fourier
coefficients. Using high-precision arithmetic we find that the Fourier
coefficients of the stream function are given over more than two decades of
wavenumbers by $\hat F(\k) = C(\theta) k^{-\alpha} \ue ^ {-k \delta(\theta)}$,
where $\k = k(\cos \theta, \sin \theta)$. The prefactor exponent $\alpha$,
typically between 5/2 and 8/3, is determined with an accuracy better than 0.01.
It depends on the initial condition but not on $\theta$. The vorticity diverges
as $s^{-\beta}$, where $\alpha+\beta= 7/2$ and $s$ is the distance to the
(complex) singular manifold. This new type of non-universal singularity is
permitted by the strong reduction of nonlinearity (depletion) which is
associated to incompressibility. Spectral calculations show that the scaling
reported above persists well beyond the time of validity of the short-time
asymptotics. A simple model in which the vorticity is treated as a passive
scalar is shown analytically to have universal singularities with exponent
$\alpha =5/2$.

categories: nlin.CD math-ph math.CV math.DS math.MP physics.flu-dyn


title:
Probability of local bifurcation type from a fixed point: A random
  matrix perspective

abstract:
  Results regarding probable bifurcations from fixed points are presented in
the context of general dynamical systems (real, random matrices), time-delay
dynamical systems (companion matrices), and a set of mappings known for their
properties as universal approximators (neural networks). The eigenvalue spectra
is considered both numerically and analytically using previous work of Edelman
et. al. Based upon the numerical evidence, various conjectures are presented.
The conclusion is that in many circumstances, most bifurcations from fixed
points of large dynamical systems will be due to complex eigenvalues.
Nevertheless, surprising situations are presented for which the aforementioned
conclusion is not general, e.g. real random matrices with Gaussian elements
with a large positive mean and finite variance.


title:
Chaotic dynamics of three-dimensional H\'enon maps that originate from a
  homoclinic bifurcation

abstract:
  We study bifurcations of a three-dimensional diffeomorphism, $g_0$, that has
a quadratic homoclinic tangency to a saddle-focus fixed point with multipliers
$(\lambda e^{i\vphi}, \lambda e^{-i\vphi}, \gamma)$, where
$0<\lambda<1<|\gamma|$ and $|\lambda^2\gamma|=1$. We show that in a
three-parameter family, $g_{\eps}$, of diffeomorphisms close to $g_0$, there
exist infinitely many open regions near $\eps =0$ where the corresponding
normal form of the first return map to a neighborhood of a homoclinic point is
a three-dimensional H\'enon-like map. This map possesses, in some parameter
regions, a "wild-hyperbolic" Lorenz-type strange attractor. Thus, we show that
this homoclinic bifurcation leads to a strange attractor. We also discuss the
place that these three-dimensional H\'enon maps occupy in the class of
quadratic volume-preserving diffeomorphisms.


title: Multifractal clustering of passive tracers on a surface flow

abstract:
  We study the anomalous scaling of the mass density measure of Lagrangian
tracers in a compressible flow realized on the free surface on top of a three
dimensional flow. The full two dimensional probability distribution of local
stretching rates is measured. The intermittency exponents which quantify the
fluctuations of the mass measure of tracers at small scales are calculated from
the large deviation form of stretching rate fluctuations. The results indicate
the existence of a critical exponent $n_c \simeq 0.86$ above which exponents
saturate, in agreement with what has been predicted by an analytically solvable
model. Direct evaluation of the multi-fractal dimensions by reconstructing the
coarse-grained particle density supports the results for low order moments.


title: Stability of a nonlinear oscillator with random damping

abstract:
  A noisy damping parameter in the equation of motion of a nonlinear oscillator
renders the fixed point of the system unstable when the amplitude of the noise
is sufficiently large. However, the stability diagram of the system can not be
predicted from the analysis of the moments of the linearized equation. In the
case of a white noise, an exact formula for the Lyapunov exponent of the system
is derived. We then calculate the critical damping for which the {\em
nonlinear} system becomes unstable. We also characterize the intermittent
structure of the bifurcated state above threshold and address the effect of
temporal correlations of the noise by considering an Ornstein-Uhlenbeck noise.


title:
Continuous and Discrete Homotopy Operators: A Theoretical Approach made
  Concrete

abstract:
  Using standard calculus, explicit formulas for the one-dimensional continuous
and discrete homotopy operators are derived. It is shown that these formulas
are equivalent to those in terms of Euler operators obtained from the
variational complex.
  The continuous homotopy operator automates integration by parts on the jet
space. Its discrete analogue can be used in applications where summation by
parts is essential. Several examples illustrate the use of the homotopy
operators.
  The calculus-based formulas for the homotopy operators are easy to implement
in computer algebra systems such as Mathematica and Maple. The homotopy
operators can be readily applied to the symbolic computation of conservation
laws of nonlinear partial differential equations and differential-difference
equations.


title:
Equivalence transformations and differential invariants of a generalized
  nonlinear Schr\"{o}dinger equation

abstract:
  By using the Lie's invariance infinitesimal criterion we obtain the
continuous equivalence transformations of a class of nonlinear Schr\"{o}dinger
equations with variable coefficients. Starting from the equivalence generators
we construct the differential invariants of order one. We apply these latter
ones to find the most general subclass of variable coefficient nonlinear
Schr\"{o}dinger equations which can be mapped, by means of an equivalence
transformation, to the well known cubic Schr\"{o}dinger equation. We also
provide the explicit form of the transformation.


title: On-off intermittency in small-world networks of chaotic maps

abstract:
  Small-world networks are highly clustered networks with small average
distance among the nodes. There are many natural and technological networks
that present this kind of connections. The on-off intermittency is investigated
in small-world networks of chaotic maps in this paper. We show how the
small-world topology would affect the on-off intermittency behavior. The
distributions of the laminar phase are calculated numerically. The results show
that the laminar phases obey power-law distributions.


title: Rayleigh--Taylor turbulence in two dimensions

abstract:
  The first consistent phenomenological theory for two and three dimensional
Rayleigh--Taylor (RT) turbulence has recently been presented by Chertkov [Phys.
Rev. Lett. {\bf 91} 115001 (2003)]. By means of direct numerical simulations we
confirm the spatio/temporal prediction of the theory in two dimensions and
explore the breakdown of the phenomenological description due to intermittency
effects. We show that small-scale statistics of velocity and temperature follow
Bolgiano-Obukhov scaling. At the level of global observables we show that the
time-dependent Nusselt and Reynolds numbers scale as the square root of the
Rayleigh number. These results point to the conclusion that Rayleigh-Taylor
turbulence in two and three dimensions, thanks to the absence of boundaries,
provides a natural physical realization of the Kraichnan scaling regime
hitherto associated with the elusive ``ultimate state of thermal convection''.

categories: nlin.CD physics.flu-dyn physics.geo-ph physics.plasm-ph


title:
Meromorphic Lax representations of (1+1)-dimensional multi-Hamiltonian
  dispersionless systems

abstract:
  Rational Lax hierarchies introduced by Krichever are generalized. A
systematic construction of infinite multi-Hamiltonian hierarchies and related
conserved quantities is presented. The method is based on the classical
R-matrix approach applied to Poisson algebras. A proof, that Poisson operators
constructed near different points of Laurent expansion of Lax functions are
equal, is given. All results are illustrated by several examples.


title: Introduction to Statstical Theory of Fluid Turbulence

abstract:
  This is a brief introduction to the statistical theory of fluid turbulence,
with an emphasis on the field-theoretic treatment of renormalized viscosity and
energy fluxes.

categories: nlin.CD astro-ph cond-mat.stat-mech physics.flu-dyn