title: Coherence Resonance in an Autapse Neuron Model with Time Delay

abstract:
  We study the noise activated dynamics of a model {\it autapse} neuron system
that consists of a subcritical Hopf oscillator with a time delayed nonlinear
feedback. The coherence of the noise driven pulses of the neuron exhibits a
novel double peaked structure as a function of the noise amplitude. The two
peaks correspond to separate optimal noise levels for excitation of single
spikes and multiple spikes (bursts) respectively. The relative magnitudes of
these peaks are found to be a sensitive function of time delay. The physical
significance of our results and its practical implications in various real life
systems are discussed.


title:
Hexagonal, square and stripe patterns of the ion channel density in
  biomembranes

abstract:
  Transmembrane ion flow through channel proteins undergoing density
fluctuations may cause lateral gradients of the electrical potential across the
membrane giving rise to electrophoresis of charged channels. A model for the
dynamics of the channel density and the voltage drop across the membrane (cable
equation) coupled to a binding-release reaction with the cell skeleton (P.
  Fromherz and W. Zimmerman, Phys. Rev. E 51, R1659 (1995)) is analyzed in one
and two spatial dimensions. Due to the binding release reaction spatially
periodic modulations of the channel density with a finite wave number are
favored at the onset of pattern formation, whereby the wave number decreases
with the kinetic rate of the binding-release reaction. In a two-dimensional
extended membrane hexagonal modulations of the ion channel density are
preferred in a large range of parameters. The stability diagrams of the
periodic patterns near threshold are calculated and in addition the equations
of motion in the limit of a slow binding-release kinetics are derived.


title: Discrete surface solitons in semi-infinite binary waveguide arrays

abstract:
  We analyze discrete surface modes in semi-infinite binary waveguide arrays,
which can support simultaneously two types of discrete solitons. We demonstrate
that the analysis of linear surface states in such arrays provides important
information about the existence of nonlinear surface modes and their
properties. We find numerically the families of both discrete surface solitons
and nonlinear Tamm (gap) states and study their stability properties.


title: Natural coordinates for a class of Benenti systems

abstract:
  We present explicit formulas for the coordinates in which the Hamiltonians of
the Benenti systems with flat metrics take natural form and the metrics in
question are represented by constant diagonal matrices.


title:
The Cauchy Problem on the Plane for the Dispersionless Kadomtsev -
  Petviashvili Equation

abstract:
  We construct the formal solution of the Cauchy problem for the dispersionless
Kadomtsev - Petviashvili equation as application of the Inverse Scattering
Transform for the vector field corresponding to a Newtonian particle in a
time-dependent potential. This is in full analogy with the Cauchy problem for
the Kadomtsev - Petviashvili equation, associated with the Inverse Scattering
Transform of the time dependent Schroedinger operator for a quantum particle in
a time-dependent potential.


title:
Inverse Scattering Problem for Vector Fields and the Cauchy Problem for
  the Heavenly Equation

abstract:
  We solve the inverse scattering problem for multidimensional vector fields
and we use this result to construct the formal solution of the Cauchy problem
for the second heavenly equation of Plebanski, a scalar nonlinear partial
differential equation in four dimensions relevant in General Relativity, which
arises from the commutation of multidimensional Hamiltonian vector fields.


title: Form factor expansion for large graphs: a diagrammatic approach

abstract:
  The form factor of a quantum graph is a function measuring correlations
within the spectrum of the graph. It can be expressed as a double sum over the
periodic orbits on the graph. We propose a scheme which allows one to evaluate
the periodic orbit sum for a special family of graphs and thus to recover the
expression for the form factor predicted by the Random Matrix Theory. The
scheme, although producing the expected answer, undercounts orbits of a certain
structure, raising doubts about an analogous summation recently proposed for
quantum billiards.


title: The influence of parsimony and randomness on complexity growth in Tierra

abstract:
  The issue of how to create open-ended evolution in an artificial system is
one the open problems in artificial life. This paper examines two of the
factors that have some bearing on this issue, using the Tierra artificial life
system.
  {\em Parsimony pressure} is a tendency to penalise more complex organisms by
the extra cost needed to reproduce longer genotypes, encouraging simplification
to happen. In Tierra, parsimony is controlled by the \verb+SlicePow+ parameter.
When full parsimony is selected, evolution optimises the ancestral organism to
produce extremely simple organisms. With parsimony completely relaxed,
organisms grow larger, but not more complex. They fill up with ``junk''. This
paper looks at scanning a range of \verb+SlicePow+ from 0.9 to 1 to see if
there is an optimal value for generating complexity.
  Tierra (along with most ALife systems) use pseudo random number generators.
Algorithms can never create information, only destroy it. So the total
complexity of the Tierra system is bounded by the initial complexity, implying
that the individual organism complexity is bounded. Biological systems,
however, have plenty of sources of randomness, ultimately dependent on quantum
randomness, so do not have this complexity limit. Sources of real random
numbers exist for computers called {\em entropy gatherers} -- this paper
reports on the effect of changing Tierra's pseudo random number generator for
an entropy gatherer.


title: Exchange Bias and Vertical Shift in CoFe2O4 nanoparticles

abstract:
  Magnetic properties of core-shell cobalt ferrite nanoparticles 15 to 48nm
prepared by a sol-gel route have been studied. It is shown that the coercivity
follows non-monotonic size dependence varying as 1/d above the maximum (d is
the particle size). Field cooled magnetization exhibited both horizontal
(exchange bias) and vertical shifts. The exchange bias is understood as
originating at the interface between a surface region with structural and spin
disorder and a core ferrimagnetic region. The dependence of the exchange bias
and vertical shifts on the particle sizes and cooling fields are found to have
significant differences and the differences are explained in the light of
recent results which suggest that both weakly and strongly pinned spins are
present at the interface. It is suggested that the exchange bias is dominated
by the weakly pinned spins while the vertical shift is affected by the strongly
pinned ones.


title: Compressible advection of a passive scalar: Two-loop scaling regimes

abstract:
  The influence of compressibility on the stability of the scaling regimes of
the passive scalar advected by a Gaussian velocity field with finite
correlation time is investigated by the field theoretic renormalization group
within two-loop approximation. The influence of compressibility on the scaling
regimes is discussed as a function of the exponents $\epsilon$ and $\eta$,
where $\epsilon$ characterizes the energy spectrum of the velocity field in the
inertial range $E\propto k^{1-2\epsilon}$, and $\eta$ is related to the
correlation time at the wave number $k$ which is scaled as $k^{-2+\eta}$. The
restrictions given by nonzero compressibility on the regions with stable
infrared fixed points which correspond to the stable infrared scaling regimes
are discussed in detail. A special attention is paid to the case of so-called
frozen velocity field, when the velocity correlator is time independent. In
this case, explicit inequalities which must be fulfilled in the plane
$\epsilon-\eta$ are determined within two-loop approximation. The existence of
a "critical" value $\alpha_c$ of the parameter of compressibility $\alpha$ at
which one of the two-loop conditions is canceled as a result of the competition
between compressible and incompressible terms is discussed. Brief general
analysis of the stability of the scaling regime of the model with finite
correlations in time of the velocity field within two-loop approximation is
also given.


title:
Direct observation of a "devil's staircase'' in wave-particle
  interaction

abstract:
  We report the experimental observation of a "devil's staircase'' in a time
dependent system considered as a paradigm for the transition to large scale
chaos in the universality class of hamiltonian systems. A test electron beam is
used to observe its non-self-consistent interaction with externally excited
wave(s) in a Travelling Wave Tube (TWT). A trochoidal energy analyzer records
the beam energy distribution at the output of the interaction line. An
arbitrary waveform generator is used to launch a prescribed spectrum of waves
along the slow wave structure (a 4 m long helix) of the TWT. The resonant
velocity domain associated to a single wave is observed, as well as the
transition to large scale chaos when the resonant domains of two waves and
their secondary resonances overlap. This transition exhibits a "devil's
staircase'' behavior for increasing excitation amplitude, due to the nonlinear
forcing by the second wave on the pendulum-like motion of a charged particle in
one electrostatic wave.

categories: nlin.CD physics.acc-ph physics.class-ph physics.plasm-ph


title: Influence of helicity on scaling regimes in the extended Kraichnan model

abstract:
  We have investigated the advection of a passive scalar quantity by
incompressible helical turbulent flow in the frame of extended Kraichnan model.
Turbulent fluctuations of velocity field are assumed to have the Gaussian
statistics with zero mean and defined noise with finite time-correlation.
Actual calculations have been done up to two-loop approximation in the frame of
field-theoretic renormalization group approach. It turned out that space parity
violation (helicity) of turbulent environment does not affect anomalous scaling
which is peculiar attribute of corresponding model without helicity. However,
stability of asymptotic regimes, where anomalous scaling takes place, strongly
depends on the amount of helicity. Moreover, helicity gives rise to the
turbulent diffusivity, which has been calculated in one-loop approximation.


title: Nonlinearity Management in Optics: Experiment, Theory, and Simulation

abstract:
  We conduct an experimental investigation of nonlinearity management in optics
using femtosecond pulses and layered Kerr media consisting of glass and air. By
examining the propagation properties over several diffraction lengths, we show
that wave collapse can be prevented. We corroborate these experimental results
with numerical simulations of the (2 + 1)-dimensional focusing cubic nonlinear
Schr\"odinger equation with piecewise constant coefficients and a theoretical
analysis of this setting using a moment method.


title: Quasigraded Lie Algebras and Modified Toda Field Equations

abstract:
  We construct a family of quasigraded Lie algebras that coincide with the
deformations of the loop algebras in "principal" gradation and admit
Kostant-Adler-Symes scheme. Using them we obtain new Volterra coupled systems
and modified Toda field equations for all series of classical matrix Lie
algebras $\mathfrak{g}$.


title:
Interaction for Solitary Waves with a Phase Difference in a Nonlinear
  Dirac Model

abstract:
  This paper presents a further numerical study of the interaction dynamics for
solitary waves in a nonlinear Dirac field with scalar self-interaction by using
a fourth order accurate Runge-Kutta discontinuous Galerkin method. Our
experiments are conducted on the Dirac solitary waves with a phase difference.
Some interesting phenomena are observed: (a) full repulsion in binary and
ternary collisions and its dependence on the distance between initial waves;
(b) repulsing first, attracting afterwards, and then collapse in binary and
ternary collisions of initially resting two-humped waves; (c) one-overlap
interaction and two-overlap interaction in ternary collisions of initially
resting waves.


title: Integrable inhomogeneous Lakshmanan-Myrzakulov equation

abstract:
  The integrable inhomogeneous extension of the Lakshmanan-Myrzakulov equation
is constructed by using the prolongation structure theory. The corresponding
L-equivalent counterpart is also given, which is the (2+1)-dimensional
generalized NLSE.


title: Dynamic characterizers of spatiotemporal intermittency

abstract:
  Systems of coupled sine circle maps show regimes of spatiotemporally
intermittent behaviour with associated scaling exponents which belong to the DP
class, as well as regimes of spatially intermittent behaviour (with associated
regular dynamical behaviour) which do not belong to the DP class. Both types of
behaviour are seen along the bifurcation boundaries of the synchronized
solutions, and contribute distinct signatures to the dynamical characterizers
of the system, viz. the distribution of eigenvalues of the one step stability
matrix. Within the spatially intermittent (SI) class, the temporal behaviour of
the burst solutions can be quasi-periodic or travelling wave. The usual
characterizers of bifurcations, i.e. the eigenvalues of the stability matrix
crossing the unit circle, pick up the bifurcation from the synchronized
solution to SI with quasi-periodic bursts but are unable to pick up the
bifurcation of the synchronized solution to SI with TW bursts. Other
characterizers, such as the Shannon entropy of the eigenvalue distribution, and
the rate of change of the largest eigenvalue with parameter are required to
pick up this bifurcation. This feature has also been seen for other
bifurcations in this system, e.g. that from the synchronized solution to kink
solutions. We therefore conjecture that in the case of high dimensional
systems, entropic characterizers provide better signatures of bifurcations from
one ordered solution to another.


title: Macroscopic equations for the adiabatic piston

abstract:
  A simplified version of a classical problem in thermodynamics -- the
adiabatic piston -- is discussed in the framework of kinetic theory. We
consider the limit of gases whose relaxation time is extremely fast so that the
gases contained on the left and right chambers of the piston are always in
equilibrium (that is the molecules are uniformly distributed and their
velocities obey the Maxwell-Boltzmann distribution) after any collision with
the piston. Then by using kinetic theory we derive the collision statistics
from which we obtain a set of ordinary differential equations for the evolution
of the macroscopic observables (namely the piston average velocity and
position, the velocity variance and the temperatures of the two compartments).
The dynamics of these equations is compared with simulations of an ideal gas
and a microscopic model of gas settled to verify the assumptions used in the
derivation. We show that the equations predict an evolution for the macroscopic
variables which catches the basic features of the problem. The results here
presented recover those derived, using a different approach, by Gruber, Pache
and Lesne in J. Stat. Phys. 108, 669 (2002) and 112, 1177 (2003).


title:
Gap solitons supported by optical lattices in photorefractive crystals
  with asymmetric nonlocality

abstract:
  We address the impact of asymmetric nonlocal diffusion nonlinearity on the
properties of gap solitons supported by photorefractive crystal with an
imprinted optical lattice. We reveal how the asymmetric nonlocal response
alters the domains of existence and the stability of solitons originating from
different gaps. We find that in such media gap solitons cease to exist above a
threshold of the nonlocality degree. We discuss how the interplay between
nonlocality and lattice strength modifies the gap soliton mobility.


title: Differential invariants of generic hyperbolic Monge--Amp\`ere equations

abstract:
  In this paper basic differential invariants of generic hyperbolic
Monge--Amp\`ere equations with respect to contact transformations are
constructed and the equivalence problem for these equations is solved.


title:
Periodic and Localized Solutions of the Long Wave-Short Wave Resonance
  Interaction Equation

abstract:
  In this paper, we investigate the (2+1) dimensional long wave-short wave
resonance interaction (LSRI) equation and show that it possess the Painlev\'e
property. We then solve the LSRI equation using Painlev\'e truncation approach
through which we are able to construct solution in terms of three arbitrary
functions. Utilizing the arbitrary functions present in the solution, we have
generated a wide class of elliptic function periodic wave solutions and
exponentially localized solutions such as dromions, multidromions, instantons,
multi-instantons and bounded solitary wave solutions.


title: A 3-component extension of the Camassa-Holm hierarchy

abstract:
  We introduce a bi-Hamiltonian hierarchy on the loop-algebra of sl(2) endowed
with a suitable Poisson pair. It gives rise to the usual CH hierarchy by means
of a bi-Hamiltonian reduction, and its first nontrivial flow provides a
3-component extension of the CH equation.


title: Stabilization of vector soliton complexes in nonlocal nonlinear media

abstract:
  We introduce vector soliton complexes in nonlocal Kerr-type nonlinear media.
We discover that under proper conditions the combination of nonlocality and
vectorial coupling has a remarkable stabilizing action on multi-humped
solitons. In particular, we find that stable bound states featuring several
field oscillations in each soliton component do exist. This affords
stabilization of vector soliton trains incorporating large number of humps, a
class of structures known to self-destroy via strong instabilities in scalar
settings.


title: Universal Scaling Laws for Large Events in Driven Nonequilibrium Systems

abstract:
  For many driven-nonequilibrium systems, the probability distribution
functions of magnitude and recurrence-time of large events follow a powerlaw
indicating a strong temporal correlation. In this paper we argue why these
probability distribution functions are ubiquitous in driven nonequilibrium
systems, and we derive universal scaling laws connecting the magnitudes,
recurrence-time, and spatial intervals of large events. The relationships
between the scaling exponents have also been studied. We show that the
ion-channel current in Voltage-dependent Anion Channels obeys the universal
scaling law.


title:
Self-organised criticality and 1/f noise in single-channel current of
  voltage-dependent anion channel

abstract:
  Noise profile of Voltage Dependent Anion Channel (VDAC) is investigated in
open channel state. Single-channel currents through VDAC from mitochondria of
rat brain reconstituted into a planar lipid bilayer are recorded under
different voltage clamped conditions across the membrane. Power spectrum
analysis of current indicates powerlaw noise of 1/f nature. Moreover, this 1/f
nature of the open channel noise is seen throughout the range of applied
membrane potential -30 to +30 mV. It is being proposed that 1/f noise in open
ion channel arises out of obstruction in the passage of ions across the
membrane. The process is recognised as a phenomenon of
self-organized-criticality (SOC) like sandpile avalanche and other physical
systems. Based on SOC it has been theoretically established that the system of
ion channel follows powerlaw noise as observed in our experiments. We also show
that the first-time return probability of current fluctuations obeys a powerlaw
distribution.


title: Oblique dark solitons in supersonic flow of a Bose-Einstein condensate

abstract:
  In the framework of the Gross-Pitaevskii mean field approach it is shown that
the supersonic flow of a Bose-Einstein condensate can support a new type of
pattern--an oblique dark soliton. The corresponding exact solution of the
Gross-Pitaevskii equation is obtained. It is demonstrated by numerical
simulations that oblique solitons can be generated by an obstacle inserted into
the flow.


title:
Coexistence of Josephson oscillations and novel self-trapping regime in
  optical waveguide arrays

abstract:
  Considering the coherent nonlinear dynamics between two weakly linked optical
waveguide arrays, we find the first example of coexistence of Josephson
oscillations with a novel self-trapping regime. This macroscopic bistability is
explained by proving analytically the simultaneous existence of symmetric,
antisymmetric and asymmetric stationary solutions of the associated
Gross-Pitaevskii equation. The effect is, moreover, illustrated and confirmed
by numerical simulations. This property allows to conceive an optical switch
based on the variation of the refractive index of the linking central
waveguide.


title: Time-sliced path integrals with stationary states

abstract:
  The path integral approach to the quantization of one degree-of-freedom
Newtonian particles is considered within the discrete time-slicing approach, as
in Feynman's original development. In the time-slicing approximation the
quantum mechanical evolution will generally not have any stationary states. We
look for conditions on the potential energy term such that the quantum
mechanical evolution may possess stationary states without having to perform a
continuum limit. When the stationary states are postulated to be solutions of a
second-order ordinary differential equation (ODE) eigenvalue problem it is
found that the potential is required to be a solution of a particular
first-order ODE. Similarly, when the stationary states are postulated to be
solutions of a second-order ordinary difference equation (O$\Delta$E)
eigenvalue problem the potential is required to be a solution of a particular
first-order O$\Delta$E. The classical limits (which are at times very
nontrivial) are integrable maps.


title: On passage through resonances in volume-preserving systems

abstract:
  Resonance processes are common phenomena in multiscale (slow-fast) systems.
In the present paper we consider capture into resonance and scattering on
resonance in 3-D volume-preserving slow-fast systems. We propose a general
theory of those processes and apply it to a class of viscous Taylor-Couette
flows between two counter-rotating cylinders. We describe the phenomena during
a single passage through resonance and show that multiple passages lead to the
chaotic advection and mixing. We calculate the width of the mixing domain and
estimate a characteristic time of mixing. We show that the resulting mixing can
be described using a diffusion equation with a diffusion coefficient depending
on the averaged effect of the passages through resonances.


title:
A Classification of Integrable Quasiclassical Deformations of Algebraic
  Curves

abstract:
  A previously introduced scheme for describing integrable deformations of of
algebraic curves is completed. Lenard relations are used to characterize and
classify these deformations in terms of hydrodynamic type systems. A general
solution of the compatibility conditions for consistent deformations is given
and expressions for the solutions of the corresponding Lenard relations are
provided.


title: The Kupershmidt hydrodynamic chains and lattices

abstract:
  This paper is devoted to the very important class of hydrodynamic chains
first derived by B. Kupershmidt and later re-discovered by M. Blaszak. An
infinite set of local Hamiltonian structures, hydrodynamic reductions
parameterized by the hypergeometric function and reciprocal transformations for
the Kupershmidt hydrodynamic chains are described.


title:
Transformations of integrable hydrodynamic chains and their hydrodynamic
  reductions

abstract:
  Hydrodynamic reductions of the hydrodynamic chain associated with
dispersionless limit of 2+1 Harry Dym equation are found by the Miura type and
reciprocal transformations applied to the Benney hydrodynamic chain.


title:
Path Integral approach to kinematical browmian motion, due to random
  canonical transformation

abstract:
  The stochastization of the Jacobi second equality of classical mechanics, by
Gaussian white noises for the Lagrangian of a particle in an arbitrary field is
considered. The quantum mechanical Hamilton operator similar to that in
Euclidian quantum theory is obtained. The conditional transition probability
density of the presence of a Browmian particle is obtained with the help of the
functional integral. The technique of factorisation of the solution of the
Fokker-Planck equation is employed to evaluate the effective potential energy.


title: Denoising Deterministic Time Series

abstract:
  This paper is concerned with the problem of recovering a finite,
deterministic time series from observations that are corrupted by additive,
independent noise. A distinctive feature of this problem is that the available
data exhibit long-range dependence and, as a consequence, existing statistical
theory and methods are not readily applicable. This paper gives an analysis of
the denoising problem that extends recent work of Lalley, but begins from first
principles. Both positive and negative results are established. The positive
results show that denoising is possible under somewhat restrictive conditions
on the additive noise. The negative results show that, under more general
conditions on the noise, no procedure can recover the underlying deterministic
series.


title: Flat bidifferential ideals and semihamiltonian PDEs

abstract:
  In this paper we consider a class of semihamiltonian systems characterized by
the existence of a special conservation law.
  The density and the current of this conservation law satisfy a second order
system of PDEs which has a natural interpretation in the theory of flat
bifferential ideals. The class of systems we consider contains important
well-known examples of semihamiltonian systems. Other examples, like genus 1
  Whitham modulation equations for KdV, are related to this class by a
reciprocal trasformation.


title:
Bubble break-off in Hele-Shaw flows : Singularities and integrable
  structures

abstract:
  Bubbles of inviscid fluid surrounded by a viscous fluid in a Hele-Shaw cell
can merge and break-off. During the process of break-off, a thinning neck
pinches off to a universal self-similar singularity. We describe this process
and reveal its integrable structure: it is a solution of the dispersionless
limit of the AKNS hierarchy. The singular break-off patterns are universal, not
sensitive to details of the process and can be seen experimentally. We briefly
discuss the dispersive regularization of the Hele-Shaw problem and the
emergence of the Painlev\'e II equation at the break-off.


title:
Projective synchronization in fractional order chaotic systems and its
  control

abstract:
  The chaotic dynamics of fractional (non-integer) order systems have begun to
attract much attention in recent years. In this paper, we study the projective
synchronization in two coupled fractional order chaotic oscillators. It is
shown that projective synchronization can also exist in coupled fractional
order chaotic systems. A simple feedback control method for controlling the
scaling factor onto a desired value is also presented.


title:
Spatiotemporal intermittency and scaling laws in the coupled sine circle
  map lattice

abstract:
  We study spatio-temporal intermittency (STI) in a system of coupled sine
circle maps. The phase diagram of the system shows parameter regimes with STI
of both the directed percolation (DP) and non-DP class. STI with synchronized
laminar behaviour belongs to the DP class. The regimes of non-DP behaviour show
spatial intermittency (SI), where the temporal behaviour of both the laminar
and burst regions is regular, and the distribution of laminar lengths scales as
a power law. The regular temporal behaviour for the bursts seen in these
regimes of spatial intermittency can be periodic or quasi-periodic, but the
laminar length distributions scale with the same power-law, which is distinct
from the DP case. STI with traveling wave (TW) laminar states also appears in
the phase diagram. Soliton-like structures appear in this regime. These are
responsible for cross-overs with accompanying non-universal exponents. The
soliton lifetime distributions show power law scaling in regimes of long
average soliton life-times, but peak at characteristic scales with a power-law
tail in regimes of short average soliton life-times. The signatures of each
type of intermittent behaviour can be found in the dynamical characterisers of
the system viz. the eigenvalues of the stability matrix. We discuss the
implications of our results for behaviour seen in other systems which exhibit
spatio-temporal intermittency.


title:
Dynamics and Development of the International System: A Complexity
  Science Perspective

abstract:
  In this article I discuss the outcome of an exploratory research project
based on complexity science concepts and theories; this research is focused on
the Great Power war dynamics in the time period 1495 - 1945. According to this
research, the international system has self-organized critical (SOC)
characteristics. A critical point is the attractor of the international system.
The war dynamics of Great Powers can be illustrated by a power law. As a result
of a driving force, the international system is constantly being pushed toward
this critical point. The security dilemma is a booster of this driving force.
Tension and frustration build up in the international system as a result of
various system thresholds, and are periodically discharged through wars. The
SOC characteristics of the international system result in a punctuated
equilibrium dynamic. The punctuations produce new international systems, each
with its specific characteristics. A quantifiable development of the
international system toward a condition of increased stability and reduced
resilience can be observed. In addition to SOC characteristics, the
international system exhibits characteristics of a chaotic system. Chaos, order
and development are closely linked. The SOC dynamics generate a process of
social expansion. It is possible to explain the social integration of Europe
from this perspective.


title:
Criticality of a dissipative self-organizing process in a dynamic
  population

abstract:
  We derive a general formulation of the self-organized branching process by
considering sandpile dynamics in an evolving population characterized by
"birth" (excitation) and "death" (de-excitation) of active sites ($z=1$). New
active sites are born in empty sites ($z=0$) with a probability of $\eta$,
whereas active sites die, thus becoming empty, with a probability $\lambda$.
Subsequently, when an active site becomes unstable ($z=2$), it topples by
transferring two grains to two randomly chosen sites with probability $\alpha$
or, by transferring only one grain to a randomly selected site (while retaining
the other) with probability $\beta=1+\frac{\lambda}{\eta}-2\alpha$, thus
remaining active after toppling. We show that when sandpile dynamics occurs in
an evolving population, self-organized criticality, characterized by a
power-law avalanche size distribution with exponent $\tau_s=3/2$ and power-law
avalanche duration distribution with exponent $\tau_T=2$ at very high dimension
$n >> 1$, is achieved even in the presence of dissipation ($\epsilon = 1-\alpha
- \beta > 0$), contrary to previous claims.


title:
On the effects of vortex trapping on the velocity statistics of tracers
  and heavy particle in turbulent flows

abstract:
  The Lagrangian statistics of heavy particles and of fluid tracers transported
by a fully developed turbulent flow are investigated by means of high
resolution direct numerical simulations. The Lagrangian velocity structure
functions are measured in a time range spanning about three decades, from a
tenth of the Kolmogorov timescale up to a few large-scale eddy turnover time.
Strong evidence is obtained that fluid tracers statistics are contaminated in
the time span 1-10 times the dissipative time scale by a bottleneck effect due
to vortex trapping. This effect is found to be significantly reduced for heavy
particles which are expelled from vortices by inertia. These findings help in
clarifying the results of a recent study by H. Xu et al. Phys. Rev. Lett. 96,
024503 (2006), where differences between experimental and numerical results on
scaling properties of fluid tracers were reported.


title: Nonlinear surface impurity in a semi-infinite 2D square lattice

abstract:
  We examine the formation of localized states on a generalized nonlinear
impurity located at, or near the surface of a semi-infinite 2D square lattice.
Using the formalism of lattice Green functions, we obtain in closed form the
number of bound states as well as their energies and probability profiles, for
different nonlinearity parameter values and nonlinearity exponents, at
different distances from the surface. We specialize to two cases: impurity
close to an "edge" and impurity close to a "corner". We find that, unlike the
case of a 1D semi-infinite lattice, in 2D, the presence of the surface helps
the formation of a localized state.


title:
Profit Maximization, Industry Structure, and Competition: A critique of
  neoclassical theory

abstract:
  Neoclassical economics has two theories of competition between
profit-maximizing firms (Marshallian and Cournot-Nash) that start from
different premises about the degree of strategic interaction between firms, yet
reach the same result, that market price falls as the number of firms in an
industry increases. The Marshallian argument is strictly false. We integrate
the different premises, and establish that the optimal level of strategic
interaction between competing firms is zero. Simulations support our analysis
and reveal intriguing emergent behaviors.


title: Symmetry Breaking in Symmetric and Asymmetric Double-Well Potentials

abstract:
  Motivated by recent experimental studies of matter-waves and optical beams in
double well potentials, we study the solutions of the nonlinear Schr\"{o}dinger
equation in such a context. Using a Galerkin-type approach, we obtain a
detailed handle on the nonlinear solution branches of the problem, starting
from the corresponding linear ones and predict the relevant bifurcations of
solutions for both attractive and repulsive nonlinearities. The results
illustrate the nontrivial differences that arise between the steady
states/bifurcations emerging in symmetric and asymmetric double wells.


title: Integration of partially integrable equations

abstract:
  Most evolution equations %or wave equations are partially integrable and, in
order to explicitly integrate all possible cases, there exist several methods
of complex analysis, but none is optimal. The theory of Nevanlinna and
Wiman-Valiron on the growth of the meromorphic solutions gives predictions and
bounds, but it is not constructive and restricted to meromorphic solutions. The
Painleve' approach via the a priori singularities of the solutions gives no
bounds but it is often (not always) constructive. It seems that an adequate
combination of the two methods could yield much more output in terms of
explicit (i.e. closed form) analytic solutions. We review this question, mainly
taking as an example the chaotic equation of Kuramoto and Sivashinsky nu u''' +
b u'' + mu u' + u^2/2 +A=0, nu nonzero, with nu,b,mu,A constants.


title: Zero curvature representation for a new fifth-order integrable system

abstract:
  In this brief note we present a zero-curvature representation for one of the
new integrable system found by Mikhailov, Novikov and Wang in nlin.SI/0601046.


title: A bistable reaction--diffusion system in a stretching flow

abstract:
  We examine the evolution of a bistable reaction in a one-dimensional
stretching flow, as a model for chaotic advection. We derive two reduced
systems of ordinary differential equations (ODE's) for the dynamics of the
governing advection--reaction--diffusion partial differential equation (PDE),
for pulse-like and for plateau-like solutions, based on a non-perturbative
approach. This reduction allows us to study the dynamics in two cases: first,
close to a saddle--node bifurcation at which a pair of nontrivial steady states
are born as the dimensionless reaction rate (Damkohler number) is increased,
and, second, for large Damkohler number, far away from the bifurcation. The
main aim is to investigate the initial-value problem and to determine when an
initial condition subject to chaotic stirring will decay to zero and when it
will give rise to a nonzero final state. Comparisons with full PDE simulations
show that the reduced pulse model accurately predicts the threshold amplitude
for a pulse initial condition to give rise to a nontrivial final steady state,
and that the reduced plateau model gives an accurate picture of the dynamics of
the system at large Damkohler number.


title: On a discrete Davey-Stewartson system

abstract:
  We propose a differential difference equation in ${\mathcal R}^1\times
{\mathcal Z}^2$ and study it by
  Hirota's bilinear method. This equation has a singular continuum limit into a
system which admits the reduction to the Davey-Stewartson equation. The
solutions of this discrete DS system are characterized by Casorati and Grammian
determinants. Based on the bilinear form of this discrete DS system, we
construct the bilinear B\"{a}cklund transformation which enables us to obtain
its Lax pair.


title: A 2 - Component Generalization of the Degasperis - Procesi Equation

abstract:
  We present two different hamiltonian extensions of the Degasperis - Procesi
equation to the two component equations. The construction based on the
observation that the second Hamiltonian operator of the Degasperis - Procesi
equation could be considered as the Dirac reduced Poisson tensor of the second
Hamiltonian operator of the Boussinesq equation. The first extension is
generated by the Hamiltonian operator which is a Dirac reduced operator of the
generalized but degenerated second Hamiltonian operator of the Boussinesq
equation. The second one is obtained by the N=2 supersymmetric extension of the
mentioned method. As the byproduct of this procedure we obatined the
Hamiltonian system of interacting equations which contains the Camassa - Holm
and Degasperis - Procesi equation.


title:
Synchronization of Mutually Versus Unidirectionally Coupled Chaotic
  Semiconductor Lasers

abstract:
  Synchronization dynamics of mutually coupled chaotic semiconductor lasers are
investigated experimentally and compared to identical synchronization of
unidirectionally coupled lasers. Mutual coupling shows high quality
synchronization in a broad range of self-feedback and coupling strengths. It is
found to be tolerant to significant parameter mismatch which for unidirectional
coupling would result in loss of synchronization. The advantages of mutual
coupling are emphasized in light of its potential use in chaos communications.


title: Evolution of Complexity: Introduction to the Workshop

abstract:
  The evolution of complexity has been a central theme for Biology and
Artificial Life (Bonner, 1988; Bedau et al., 2000). Complexification has been
interpreted in different ways: as a process of diversification between evolving
units (Bonner, 1988) or as a scaling process that is related to the idea of
transitions between different levels of complexity (Smith and Szathmary, 1995).
There have been previous workshops on this topic, e.g. (Heylighen et al., 1999;
Lenaerts et al., 2002), but many open questions still remain. Trying to answer
these questions from a general perspective might not immediately produce
concrete answers for the different fields that are interested in this topic.
Consequently, this workshop is organised with a particular focus in mind: The
emergence of complexity through evolutionary mechanisms. Primarily we want to
have a discussion on evolutionary and related dynamics as mechanisms for
producing complexity. Furthermore, we want to bring together historical and
novel research in this context.


title:
Structure theorems for linear and non-linear differential operators
  admitting invariant polynomial subspaces

abstract:
  In this paper we derive structure theorems that characterize the spaces of
linear and non-linear differential operators that preserve finite dimensional
subspaces generated by polynomials in one or several variables. By means of the
useful concept of deficiency, we can write explicit basis for these spaces of
differential operators. In the case of linear operators, these results apply to
the theory of quasi-exact solvability in quantum mechanics, specially in the
multivariate case where the Lie algebraic approach is harder to apply. In the
case of non-linear operators, the structure theorems in this paper can be
applied to the method of finding special solutions of non-linear evolution
equations by nonlinear separation of variables.


title: Cellular Automata under the influence of noise

abstract:
  Noise in the local transition function is compared to fluctuations in the
updating times of the cells. Obtained results are shown to be quite different
in both cases. In this extended abstract we briefly explain the problem and
present results obtained and comment them.


title: Asymptotic Exponents from Low-Reynolds-Number Flows

abstract:
  The high-order statistics of fluctuations in velocity gradients in the
crossover range from the inertial to the Kolmogorov and sub-Kolmogorov scales
are studied by direct numerical simulations (DNS) of homogeneous isotropic
turbulence with vastly improved resolution. The derivative moments for orders 0
<= n <= 8 are represented well as powers of the Reynolds number, Re, in the
range 380 <= Re <= 5725, where Re is based on the periodic box length L_x.
These low-Reynolds-number flows give no hint of scaling in the inertial range
even when extended self-similarity is applied. Yet, the DNS scaling exponents
of velocity gradients agree well with those deduced, using a recent theory of
anomalous scaling, from the scaling exponents of the longitudinal structure
functions at infinitely high Reynolds numbers. This suggests that the
asymptotic state of turbulence is attained for the velocity gradients at far
lower Reynolds numbers than those required for the inertial range to appear. We
discuss these findings in the light of multifractal formalism. Our numerical
studies also resolve the crossover of the velocity gradient statistics from the
Gaussian to non-Gaussian behaviour that occurs as the Reynolds number is
increased.


title:
Exchange operator formalism for N-body spin models with near-neighbors
  interactions

abstract:
  We present a detailed analysis of the spin models with near-neighbors
interactions constructed in our previous paper [Phys. Lett. B 605 (2005) 214]
by a suitable generalization of the exchange operator formalism. We provide a
complete description of a certain flag of finite-dimensional spaces of spin
functions preserved by the Hamiltonian of each model. By explicitly
diagonalizing the Hamiltonian in the latter spaces, we compute several infinite
families of eigenfunctions of the above models in closed form in terms of
generalized Laguerre and Jacobi polynomials.


title:
Coexisting solutions and their neighbourhood in the dynamical system
  describing second-order optical processes

abstract:
  Coexisting periodic solutions of a dynamical system describing nonlinear
optical processes of the second-order are studied. The analytical results
concern both the simplified autonomous model and the extended nonautonomous
model, including the pump and damping mechanism. The nonlinearity in the
coexisting solutions of the autonomous system is in concealed frequencies
depending on the initial conditions. In the solutions of the nonautonomous
system the nonlinearity is convoluted in amplitudes. The neighbourhood of
periodic solutions is studied numerically, mainly in phase portraits. As a
result of disturbance, for example detuning, the periodic solutions are shown
to escape to other states, periodic, quasiperiodic (beats) or chaotic. The
chaotic behavior is indicated by the Lypunov exponents. We also investigate
selected aspects of synchronization (unidirectional or mutual) of two identical
systems being in two different coexisting states. The effects of quenching of
oscillations are shown. In the autonomous system the quenching is caused by a
change in frequency, whereas in the nonautonomous one by a change in amplitude.
The quenching seems very promising for design of some advanced signal
processing.


title:
q-breathers in finite two- and three-dimensional nonlinear acoustic
  lattices

abstract:
  Nonlinear interaction between normal modes dramatically affects energy
equipartition, heat conduction and other fundamental processes in extended
systems. In their celebrated experiment Fermi, Pasta and Ulam (FPU, 1955)
observed that in simple one-dimensional nonlinear atomic chains the energy must
not always be equally shared among the modes. Recently, it was shown that exact
and stable time-periodic orbits, coined $q$-breathers (QBs), localize the mode
energy in normal mode space in an exponential way, and account for many aspects
of the FPU problem. Here we take the problem into more physically important
cases of two- and three-dimensional acoustic lattices to find existence and
principally different features of QBs. By use of perturbation theory and
numerical calculations we obtain that the localization and stability of QBs is
enhanced with increasing system size in higher lattice dimensions opposite to
their one-dimensional analogues.


title:
Internal Modes of Solitons and Near-Integrable Highly-Dispersive
  Nonlinear Systems

abstract:
  The transition from integrable to non-integrable highly-dispersive nonlinear
models is investigated. The sine-Gordon and $\phi^4$-equations with the
additional fourth-order spatial and spatio-temporal derivatives, describing the
higher dispersion, and with the terms originated from nonlinear interactions
are studied. The exact static and moving topological kinks and soliton-complex
solutions are obtained for a special choice of the equation parameters in the
dispersive systems. The problem of spectra of linear excitations of the static
kinks is solved completely for the case of the regularized equations with the
spatio-temporal derivatives. The frequencies of the internal modes of the kink
oscillations are found explicitly for the regularized sine-Gordon and
$\phi^4$-equations. The appearance of the first internal soliton mode is
believed to be a criterion of the transition between integrable and
non-integrable equations and it is considered as the sufficient condition for
the non-trivial (inelastic) interactions of solitons in the systems.


title: A fluctuation theorem in a random environment

abstract:
  A simple class of chaotic systems in a random environment is considered and
the fluctuation theorem is extended under the assumption of reversibility.


title: Spectral decomposition of 1D Fokker - Planck differential operator

abstract:
  We construct spectral decomposition of 1D Fokker - Planck differential
operator. This reveal solution of Cauchy problem. We develop fundamental
solution of Cauchy problem and compare it with one obtained by other means in
our former work [5].


title: Differential models for 2D turbulence

abstract:
  We present two phenomenological models for 2D turbulence in which the energy
spectrum obeys a nonlinear fourth-order and a second-order differential
equations respectively. Both equations respect the scaling properties of the
original Navier-Stokes equations and it has both the -5/3 inverse-cascade and t
-3 direct-cascade spectra. In addition, the fourth order equation has
Raleigh-Jeans thermodynamic distributions, as exact steady state solutions. We
use the fourth-order model to derive a relation between the direct-cascade and
the inverse-cascade Kolmogorov constants which is in a good qualitative
agreement with the laboratory and numerical experiments. We obtain a steady
state solution where both the enstrophy and the energy cascades are present
simultaneously and we discuss it in context of the Nastrom-Gage spectrum
observed in atmospheric turbulence. We also consider the effect of the bottom
friction onto the cascade solutions, and show that it leads to an additional
decrease and finite-wavenumber cutoffs of the respective cascade spectra.


title:
Critical properties of phase transitions in lattices of coupled logistic
  maps

abstract:
  We numerically demonstrate that collective bifurcations in two-dimensional
lattices of locally coupled logistic maps share most of the defining features
of equilibrium second-order phase transitions. Our simulations suggest that
these transitions between distinct collective dynamical regimes belong to the
universality class of Miller and Huse model with synchronous update.


title:
A note on the relationship between rational and trigonometric solutions
  of the WDVV equations

abstract:
  Legendre transformations provide a natural symmetry on the space of solutions
to the WDVV equations, and more specifically, between different Frobenius
manifolds. In this paper a twisted Legendre transformation is constructed
between solutions which define the corresponding dual Frobenius manifolds. As
an application it is shown that certain trigonometric and rational solutions of
the WDVV equations are related by such a twisted Legendre transform.


title: Nonlinear Dynamics of Quantum Systems and Soliton Theory

abstract:
  We show that space-time evolution of one-dimensional fermionic systems is
described by nonlinear equations of soliton theory. We identify a space-time
dependence of a matrix element of fermionic systems related to the {\it
Orthogonality Catastrophe} or {boundary states} with the $\tau$-function of the
modified KP-hierarchy. The established relation allows to apply the apparatus
of soliton theory to the study of non-linear aspects of quantum dynamics. We
also describe a {\it bosonization in momentum space} - a representation of a
fermion operator by a Bose field in the presence of a boundary state.


title: Stability of Discrete Solitons in the Presence of Parametric Driving

abstract:
  In this brief report, we consider parametrically driven bright solitons in
the vicinity of the anti-continuum limit. We illustrate the mechanism through
which these solitons become unstable due to the collision of the phase mode
with the continuous spectrum, or eigenvelues bifurcating thereof. We show how
this mechanism typically leads to complete destruction of the bright solitary
wave.


title:
Biorthogonal polynomials for 2-matrix models with semiclassical
  potentials

abstract:
  We consider the biorthogonal polynomials associated to the two-matrix model
where the eigenvalue distribution has potentials V_1,V_2 with arbitrary
rational derivative and whose supports are constrained on an arbitrary union of
intervals (hard-edges). We show that these polynomials satisfy certain
recurrence relations with a number of terms d_i depending on the number of
hard-edges and on the degree of the rational functions V_i'. Using these
relations we derive Christoffel-Darboux identities satisfied by the
biorthogonal polynomials: this enables us to give explicit formulae for the
differential equation satisfied by d_i+1 consecutive polynomials, We also
define certain integral transforms of the polynomials and use them to formulate
a Riemann-Hilbert problem for (d_i+1) x (d_i+1) matrices constructed out of the
polynomials and these transforms. Moreover we prove that the
Christoffel-Darboux pairing can be interpreted as a pairing between two dual
Riemann-Hilbert problems.


title: Sufficient set of integrability conditions of an orthonomic system

abstract:
  Every orthonomic system of partial differential equations is known to possess
a finite number of integrability conditions sufficient to ensure the validity
of all. Herewith we offer an efficient algorithm to construct a sufficient set
of integrability conditions free of redundancies.


title:
All-optical switching in a two-channel waveguide with cubic-quintic
  nonlinearity

abstract:
  We consider dynamics of spatial beams in a dual-channel waveguide with
competing cubic and quintic (CQ) nonlinearities. Gradually increasing the power
in the input channel, we identify four different regimes of the pulses coupling
into the cross channel, which alternate three times between full pass and full
stop, thus suggesting three realizations of switching between the channels. As
in the case of the Kerr (solely cubic) nonlinearity, the first two regimes are
the linear one, and one dominated by the self-focusing nonlinearity, with the
beam which, respectively, periodically couples between the channels, or stays
in the input channel. Further increase of the power reveals two novel
transmission regimes, one characterized by balance between the competing
nonlinearities, which again allows full coupling between the channels, and a
final regime dominated by the self-defocusing quintic nonlinearity. In the
latter case, the situation resembles that known for a self-repulsive
Bose-Einstein condensate trapped in a double-well potential, which is
characterized by strong symmetry breaking; accordingly, the beam again abides
in the input channel, contrary to an intuitive expectation that the
self-defocusing nonlinearity would push it into the cross channel. The
numerical results are qualitatively explained by a simple analytical model
based on the variational approximation.


title:
Different Neurons Population Distribution Correlates with
  Topologic-Temporal Dynamic Acoustic Information Flow

abstract:
  It is reported a great variety of functional actions of GABA in auditory
system. Although many studies reports the presence and distribution of GABA
receptors; nevertheless, the studies about the inhibitory GABA-dependent
neurons distribution in the Inferior Culliculus are scarce. We are interested
in studies on the role played by GABAergic neurons in the acoustic information
transmission in the Central Nucleus of Inferior Culliculus. The existence and
distribution of GABAergic neurons in CNIC, could give us understandings on how
the inhibitory actions of neurotransmitters are participating in ways which the
information flow is spatial-temporal associated with the firing synchrony in
each isofrequency region. And with these results, we could achieve some
insights over the emergence of certain mind properties from neurons dynamic
interactions.


title: From synchronization to Lyapunov exponents and back

abstract:
  The goal of this paper is twofold. In the first part we discuss a general
approach to determine Lyapunov exponents from ensemble- rather than
time-averages. The approach passes through the identification of locally stable
and unstable manifolds (the Lyapunov vectors), thereby revealing an analogy
with generalized synchronization. The method is then applied to a periodically
forced chaotic oscillator to show that the modulus of the Lyapunov exponent
associated to the phase dynamics increases quadratically with the coupling
strength and it is therefore different from zero already below the onset of
phase-synchronization. The analytical calculations are carried out for a model,
the generalized special flow, that we construct as a simplified version of the
periodically forced Rossler oscillator.


title: A mesoscopic approach for multi-phase flows in nano-corrugated channels

abstract:
  An approach based on a lattice version of the Boltzmann kinetic equation for
describing multi-phase flows in nano- and micro-corrugated devices is proposed.
We specialize it to describe the wetting/dewetting transition of fluids in
presence of nanoscopic grooves etched on the boundaries. This approach permits
to retain the essential supra-molecular details of fluid-solid interactions
without surrendering -actually boosting- the computational efficiency of
continuum methods. The mesoscopic method is first validated quantitatively
against Molecular Dynamics (MD) results of Cottin-Bizonne et al. [Nature Mater.
2, 237 (2003)] and then applied to more complex situations which are hardly
accessible to MD simulations. The resulting analysis confirms that surface
roughness and capillary effects may conspire to promote a counter-intuitive but
significant reduction of the flow drag with substantial enhancement in the mass
flow rates and slip-lengths in the micrometric range for highly hydrophobic
surfaces.


title:
Stability of Simple Periodic Orbits and Chaos in a Fermi -- Pasta --
  Ulam Lattice

abstract:
  We investigate the connection between local and global dynamics in the Fermi
-- Pasta -- Ulam (FPU) $\beta$ -- model from the point of view of stability of
its simplest periodic orbits (SPOs). In particular, we show that there is a
relatively high $q$ mode $(q=2(N+1)/{3})$ of the linear lattice, having one
particle fixed every two oppositely moving ones (called SPO2 here), which can
be exactly continued to the nonlinear case for $N=5+3m, m=0,1,2,...$ and whose
first destabilization, $E_{2u}$, as the energy (or $\beta$) increases for {\it
any} fixed $N$, practically {\it coincides} with the onset of a ``weak'' form
of chaos preceding the break down of FPU recurrences, as predicted recently in
a similar study of the continuation of a very low ($q=3$) mode of the
corresponding linear chain. This energy threshold per particle behaves like
$\frac{E_{2u}}{N}\propto N^{-2}$. We also follow exactly the properties of
another SPO (with $q=(N+1)/{2}$) in which fixed and moving particles are
interchanged (called SPO1 here) and which destabilizes at higher energies than
SPO2, since $\frac{E_{1u}}{N}\propto N^{-1}$. We find that, immediately after
their first destabilization, these SPOs have different (positive) Lyapunov
spectra in their vicinity. However, as the energy increases further (at fixed
$N$), these spectra converge to {\it the same} exponentially decreasing
function, thus providing strong evidence that the chaotic regions around SPO1
and SPO2 have ``merged'' and large scale chaos has spread throughout the
lattice.


title: Recursion operator for the IGSG equation

abstract:
  In this paper we find the inverse and direct recursion operator for the
intrinsic generalized sine-Gordon equation in any number $n > 2$ of independent
variables. Among the flows generated by the direct operator we identify a
higher-dimensional analogue of the pmKdV equation.


title: Gap solitons in Bragg gratings with a harmonic superlattice

abstract:
  Solitons are studied in a model of a fiber Bragg grating (BG) whose local
reflectivity is subjected to periodic modulation. The superlattice opens an
infinite number of new bandgaps in the model's spectrum. Averaging and
numerical continuation methods show that each gap gives rise to gap solitons
(GSs), including asymmetric and double-humped ones, which are not present
without the superlattice.Computation of stability eigenvalues and direct
simulation reveal the existence of completely stable families of fundamental
GSs filling the new gaps - also at negative frequencies, where the ordinary GSs
are unstable. Moving stable GSs with positive and negative effective mass are
found too.


title: Basis Markov Partitions and Transition Matrices for Stochastic Systems

abstract:
  We analyze dynamical systems subjected to an additive noise and their
deterministic limit. In this work, we will introduce a notion by which a
stochastic system has something like a Markov partition for deterministic
systems. For a chosen class of the noise profiles the Frobenius-Perron operator
associated to the noisy system is exactly represented by a stochastic
transition matrix of a finite size K. This feature allows us to introduce for
these stochastic systems a basis--Markov partition, defined herein,
irrespectively of whether the deterministic system possesses a Markov partition
or not. We show that in the deterministic limit, corresponding to K -->
infinity, the sequence of invariant measures of the noisy systems tends, in the
weak sense, to the invariant measure of the deterministic system. Thus by
introducing a small additive noise one may approximate transition matrices and
invariant measures of deterministic dynamical systems.


title: The Yablonskii - Vorob'ev polynomials for the second Painlev'e hierarchy

abstract:
  Special polynomials associated with rational solutions of the second
Painlev'e equation and other equations of its hierarchy are studied. A new
method, which allows one to construct each family of polynomials is presented.
The structure of the polynomials is established. Formulaes for their
coefficients are found. The degree of every polynomial is obtained. The main
achievement of the method lies in the fact that it enables one to construct the
family of polynomials corresponding to any member of the second Painlev'e
hierarchy. Our approach can be applied for deriving the polynomials related to
rational or algebraic solutions of other nonlinear differential equations.


title:
Spectral fluctuation characterization of random matrix ensembles through
  wavelets

abstract:
  A recently developed wavelet based approach is employed to characterize the
scaling behavior of spectral fluctuations of random matrix ensembles, as well
as complex atomic systems. Our study clearly reveals anti-persistent behavior
and supports the Fourier power spectral analysis. It also finds evidence for
multi-fractal nature in the atomic spectra. The multi-resolution and
localization nature of the discrete wavelets ideally characterizes the
fluctuations in these time series, some of which are not stationary.


title: Singular solutions, momentum maps and computational anatomy

abstract:
  This paper describes the variational formulation of template matching
problems of computational anatomy (CA); introduces the EPDiff evolution
equation in the context of an analogy between CA and fluid dynamics; discusses
the singular solutions for the EPDiff equation and explains why these singular
solutions exist (singular momentum map). Then it draws the consequences of
EPDiff for outline matching problem in CA and gives numerical examples.


title:
Asymptotics of a Class of Operator Determinants with Application to the
  Cylindrical Toda Equations

abstract:
  In work of C. A. Tracy and the author asymptotic formulas were derived for
certain operator determinants which gave solutions to the cylindrical Toda
equations. Later the author considered a more general class of operators which
retained some of the properties of those cited and found analogous asymptotics
for the determinants. These results applied only in what we call the regular
case, when the symbol of an associated convolution operator is nonzero and has
zero index. The present work goes further and establishes asymptotics for a
class of singular cases.


title: Synchronisation schemes for two dimensional discrete systems

abstract:
  In this work we consider two models of two dimensional discrete systems
subjected to three different types of coupling and analyse systematically the
performance of each in realising synchronised states.We find that linear
coupling effectively introduce control of chaos along with
synchronisation,while synchronised chaotic states are possible with an additive
parametric coupling scheme both being equally relevant for specific
applications.The basin leading to synchronisationin the initial value plane and
the choice of parameter values for synchronisation in the parameter plane are
isolatedin each case.


title: Model of Wealth and Goods Dynamics in a Closed Market

abstract:
  A simple computer simulation model of a closed market on a fixed network with
free flow of goods and money is introduced. The model contains only two
variables : the amount of goods and money beside the size of the system. An
initially flat distribution of both variables is presupposed. We show that
under completely random rules, i.e. through the choice of interacting agent
pairs on the network and of the exchange rules that the market stabilizes in
time and shows diversification of money and goods. We also indicate that the
difference between poor and rich agents increases for small markets, as well as
for systems in which money is steadily deduced from the market through
taxation.


title:
Implementation of the Backlund transformations for the Ablowitz-Ladik
  hierarchy

abstract:
  The derivation of the Backlund transformations (BTs) is a standard problem of
the theory of the integrable systems. Here, I discuss the equations describing
the BTs for the Ablowitz-Ladik hierarchy (ALH), which have been already
obtained by several authors. The main aim of this work is to solve these
equations. This can be done in the framework of the so-called functional
representation of the ALH, when an infinite number of the evolutionary
equations are replaced, using the Miwa's shifts, with a few equations linking
tau-functions with different arguments. It is shown that starting from these
equations it is possible to obtain explicit solutions of the BT equations. In
other words, the main result of this work is a presentation of the discrete BTs
as a superposition of an infinite number of evolutionary flows of the
hierarchy. These results are used to derive the superposition formulae for the
BTs as well as pure soliton solutions.


title: The Limit Cycles of Lienard Equations in the Weakly Nonlinear Regime

abstract:
  Li\'enard equations of the form $\ddot{x}+\epsilon f(x)\dot{x}+x=0$, with
$f(x)$ an even function, are considered in the weakly nonlinear regime
($\epsilon\to 0$). A perturbative algorithm for obtaining the number, amplitude
and shape of the limit cycles of these systems is given. The validity of this
algorithm is shown and several examples illustrating its application are given.
In particular, an ${\mathcal O}(\epsilon^8)$ approximation for the amplitude of
the van der Pol limit cycle is explicitly obtained.


title: Topological Entropy of Braids on the Torus

abstract:
  A fast method is presented for computing the topological entropy of braids on
the torus. This work is motivated by the need to analyze large braids when
studying two-dimensional flows via the braiding of a large number of particle
trajectories. Our approach is a generalization of Moussafir's technique for
braids on the sphere. Previous methods for computing topological entropies
include the Bestvina--Handel train-track algorithm and matrix representations
of the braid group. However, the Bestvina--Handel algorithm quickly becomes
computationally intractable for large braid words, and matrix methods give only
lower bounds, which are often poor for large braids. Our method is
computationally fast and appears to give exponential convergence towards the
exact entropy. As an illustration we apply our approach to the braiding of both
periodic and aperiodic trajectories in the sine flow. The efficiency of the
method allows us to explore how much extra information about flow entropy is
encoded in the braid as the number of trajectories becomes large.


title:
Clifford Algebra Derivations of Tau-Functions for Two-Dimensional
  Integrable Models with Positive and Negative Flows

abstract:
  We use a Grassmannian framework to define multi-component tau functions as
expectation values of certain multi-component Fermi operators satisfying simple
bilinear commutation relations on Clifford algebra. The tau functions contain
both positive and negative flows and are shown to satisfy the $2n$-component KP
hierarchy. The hierarchy equations can be formulated in terms of
pseudo-differential equations for $n \times n$ matrix wave functions derived in
terms of tau functions. These equations are cast in form of Sato-Wilson
relations. A reduction process leads to the AKNS, two-component Camassa-Holm
and Cecotti-Vafa models and the formalism provides simple formulas for their
solutions


title:
Quantum Graphs: Applications to Quantum Chaos and Universal Spectral
  Statistics

abstract:
  During the last years quantum graphs have become a paradigm of quantum chaos
with applications from spectral statistics to chaotic scattering and wave
function statistics. In the first part of this review we give a detailed
introduction to the spectral theory of quantum graphs and discuss exact trace
formulae for the spectrum and the quantum-to-classical correspondence. The
second part of this review is devoted to the spectral statistics of quantum
graphs as an application to quantum chaos. Especially, we summarise recent
developments on the spectral statistics of generic large quantum graphs based
on two approaches: the periodic-orbit approach and the supersymmetry approach.
The latter provides a condition and a proof for universal spectral statistics
as predicted by random-matrix theory.


title:
Three Logistic Models for the Ecological and Economic Interactions:
  Symbiosis, Predator-Prey and Competition

abstract:
  If one isolated species (corporation) is supposed to evolve following the
logistic mapping, then we are tempted to think that the dynamics of two species
(corporations) can be expressed by a coupled system of two discrete logistic
equations. As three basic relationships between two species are present in
Nature, namely symbiosis, predator-prey and competition, three different models
are obtained. Each model is a cubic two-dimensional discrete logistic-type
equation with its own dynamical properties: stationary regime, periodicity,
quasi-periodicity and chaos. We also propose that these models could be useful
for thinking in the different interactions happening in the economic world, as
for instance for the competition and the collaboration between corporations.
Furthermore, these models could be considered as the basic ingredients to
construct more complex interactions in the ecological and economic networks.


title: On transition to bursting via deterministic chaos

abstract:
  We study statistical properties of the irregular bursting arising in a class
of neuronal models close to the transition from spiking to bursting. Prior to
the transition to bursting, the systems in this class develop chaotic
attractors, which generate irregular spiking. The chaotic spiking gives rise to
irregular bursting. The duration of bursts near the transition can be very
long. We describe the statistics of the number of spikes and the interspike
interval distributions within one burst as functions of the distance from
criticality.


title:
Structure analysis of two-dimensional nonlinear self-trapped photonic
  lattices in anisotropic photorefractive media

abstract:
  We generate experimentally different types of two-dimensional self-trapped
photonic lattices in a photorefractive medium and analyze the induced
refractive index change using two different methods. One method gives the first
experimental Fourier space analysis of both linear and nonlinear self-trapped
photonic lattices with periodic phase modulation using partially spatially
incoherent multi-band excitation of the lattice modes. The other method
utilizes the waveguiding properties of the lattice to achieve a real space
analysis of the induced refractive index change. The results of both methods
are compared.


title: Stable circulation modes in a dual-core matter-wave soliton laser

abstract:
  We consider a model of a matter-wave laser generating a periodic array of
solitary-wave pulses. The system, a general version of which was recently
proposed in Ref. [5], is composed of two parallel tunnel-coupled cigar-shaped
traps (a reservoir and a lasing cavity), solitons being released through a
valve at one edge of the cavity. We report a stable lasing mode accounted for
by circulations of a narrow soliton in the cavity, which generates an array of
strong pulses (with 1,000 - 10,000 atoms in each, the array's duty cycle ~ 30%)
when the soliton periodically hits the valve.


title: Large-scale anisotropy in scalar turbulence

abstract:
  The effect of anisotropy on the statistics of a passive tracer transported by
a turbulent flow is investigated. We show that under broad conditions an
arbitrarily small amount of anisotropy propagates to the large scales where it
eventually dominates the structure of the concentration field. This result is
obtained analytically in the framework of an exactly solvable model and
confirmed by numerical simulations of scalar transport in two-dimensional
turbulence.


title:
Special polynomials associated with the fourth order analogue to the
  Painlev'e equations

abstract:
  Rational solutions of the fourth order analogue to the Painlev'e equations
are classified. Special polynomials associated with the rational solutions are
introduced. The structure of the polynomials is found. Formulas for their
coefficients and degrees are derived. It is shown that special solutions of the
Fordy - Gibbons, the Caudrey - Dodd - Gibbon and the Kaup - Kupershmidt
equations can be expressed through solutions of the equation studied.


title:
Stationary localized modes in the quintic nonlinear Schrodinger equation
  with a periodic potential

abstract:
  We consider the localized modes (bright solitons) described by
one-dimensional quintic nonlinear Schrodinger equation with a periodic
potential. In the case of attractive nonlinearity we deduce sufficient
conditions for collapse. We show that there exist spatially localized modes
with arbitrarily large number of particles. We study such solutions in the
semi-infinite gap (attractive case) and in the first gap (attractive and
repulsive cases), and show that a nonzero minimum value of the number of
particles is necessary for a localized mode to be created. In the limit of
large negative frequencies (attractive case) we observe "quantization" of the
number of particles of the stationary modes. Such solutions can be interpreted
as coupled "Townes" solitons and appear to be stable. The modes in the first
gap have numbers of particles infinitely growing with frequencies approaching
one of the gap edges, which is explained by the power decay of the modes.
Stability of the localized modes is discussed.


title: Zero-lag long-range synchronization via dynamical relaying

abstract:
  We show that simultaneous synchronization between two delay-coupled
oscillators can be achieved by relaying the dynamics via a third mediating
element, which surprisingly lags behind the synchronized outer elements. The
zero-lag synchronization thus obtained is robust over a considerable parameter
range. We substantiate our claims with experimental and numerical evidence of
these synchronization solutions in a chain of three coupled semiconductor
lasers with long inter-element coupling delays. The generality of the mechanism
is validated in a neuronal model with the same coupling architecture. Thus, our
results show that synchronized dynamical states can occur over long distances
through relaying, without restriction by the amount of delay.


title:
Delayed Feedback and Chaos on the Driven Diode-Terminated Transmission
  Line

abstract:
  A simple model of a distributed, non-linear circuit that produces chaos at
GHz frequencies is introduced and tested experimentally. The model circuit is a
driven diode-terminated transmission line with the transmission line impedance
mismatched to that of the source. Experiments were performed with sinusoidal
driving frequencies of 10 MHz to 1.2 GHz, driving powers of -30 to +50 dBm and
transmission line delay times from 3 to 20 ns. Diode reverse recovery times
ranged from 4 to 100 ns. As a result of many experiments, it was found that
chaotic behavior was strongly dependent on the unbiased, small-signal reactance
of the system as seen by the driving source, and influenced by an applied DC
voltage-bias across the diode. In the experiments that showed period-doubling
and / or chaos, the reverse recovery times of the diodes were on the order of
both the driving period and the delay time of the circuits. Comparisons between
theory and experiment are in general agreement. Chaos produced with a driving
frequency of 1.105 GHz has been observed experimentally.


title:
Bifurcations and Chaos in the Six-Dimensional Turbulence Model of
  Gledzer

abstract:
  The cascade-shell model of turbulence with six real variables originated by
Gledzer is studied numerically using Mathematica 5.1. Periodic, doubly-periodic
and chaotic solutions and the routes to chaos via both frequency-locking and
period-doubling are found by the Poincar\'e plot of the first mode $v_1$. The
circle map on the torus is well approximated by the summation of several
sinusoidal functions. The dependence of the rotation number on the viscosity
parameter is in accordance with that of the sine-circle map. The complicated
bifurcation structure and the revival of a stable periodic solution at the
smaller viscosity parameter in the present model indicates that the turbulent
state may be very sensitive to the Reynolds number.


title:
A Cellular Automata Model with Probability Infection and Spatial
  Dispersion

abstract:
  In this article, we have proposed an epidemic model by using probability
cellular automata theory. The essential mathematical features are analyzed with
the help of stability theory. We have given an alternative modelling approach
for the spatiotemporal system which is more realistic and satisfactory from the
practical point of view. A discrete and spatiotemporal approach are shown by
using cellular automata theory. It is interesting to note that both size of the
endemic equilibrium and density of the individual increase with the increasing
of the neighborhood size and infection rate, but the infections decrease with
the increasing of the recovery rate. The stability of the system around the
positive interior equilibrium have been shown by using suitable Lyapunov
function. Finally experimental data simulation for SARS disease in China and a
brief discussion conclude the paper.


title: Sling effect in collisions of water droplets in turbulent clouds

abstract:
  We describe and evaluate the contribution of sling effect into the collision
rate of the same-size water droplets in turbulent clouds. We show that already
for Stokes numbers exceeding 0.2 the sling effect gives a contribution
comparable to Saffman-Turner contribution, which may explain why the latter
consistently underestimates collision rate (even with the account of
preferential concentration).


title:
Geodesic Flow and Two (Super) Component Analog of the Camassa-Holm
  Equation

abstract:
  We derive the 2-component Camassa-Holm equation and corresponding N=1 super
generalization as geodesic flows with respect to the $H^1$ metric on the
extended Bott-Virasoro and superconformal groups, respectively.


title: On Kernel Formulas and Dispersionless Hirota Equations

abstract:
  We rederive dispersionless Hirota equations of the dispersionless Toda
hierarchy from the method of kernel formula provided by Carroll and Kodama. We
then apply the method to derive dispersionless Hirota equations of the extended
dispersionless BKP(EdBKP) hierarchy proposed by Takasaki. Moreover, we verify
associativity equations (WDVV equations) in the EdBKP hierarchy from
dispersionless Hirota equations and give a realization of associative algebra
with structure constants expressed in terms of residue formula.


title:
Two-pulse solutions in the fifth-order KdV equation : rigorous theory
  and numerical approximations

abstract:
  We revisit existence and stability of two-pulse solutions in the fifth-order
Korteweg--de Vries (KdV) equation with two new results. First, we modify the
Petviashvili method of successive iterations for numerical (spectral)
approximations of pulses and prove convergence of iterations in a neighborhood
of two-pulse solutions. Second, we prove structural stability of embedded
eigenvalues of negative Krein signature in a linearized KdV equation. Combined
with stability analysis in Pontryagin spaces, this result completes the proof
of spectral stability of the corresponding two-pulse solutions. Eigenvalues of
the linearized problem are approximated numerically in exponentially weighted
spaces where embedded eigenvalues are isolated from the continuous spectrum.
Approximations of eigenvalues and full numerical simulations of the fifth-order
KdV equation confirm stability of two-pulse solutions related to the minima of
the effective interaction potential and instability of two-pulse solutions
related to the maxima points.


title:
Predicting equation from Chaotic data by Nonlinear Singular Value
  Decomposition

abstract:
  Singular Value Decomposition can be considered as an effective method for
Signal Processing/especially data compression. In this short paper we
investigate the application of SVD to predict data equation from data. The
method is similar to nonlinear ARMA method for fitting a nonlinear equation to
the data.


title:
Predictions of ultra-harmonic oscillations in coupled arrays of limit
  cycle oscillators

abstract:
  Coupled distinct arrays of nonlinear oscillators have been shown to have a
regime of high frequency, or ultra-harmonic, oscillations that are at multiples
of the natural frequency of individual oscillators. The coupled array
architectures generate an in-phase high-frequency state by coupling with an
array in an anti-phase state. The underlying mechanism for the creation and
stability of the ultra-harmonic oscillations is analyzed. A class of
inter-array coupling is shown to create a stable, in-phase oscillation having
frequency that increases linearly with the number of oscillators, but with an
amplitude that stays fairly constant. The analysis of the theory is illustrated
by numerical simulation of coupled arrays of Stuart-Landau limit cycle
oscillators.


title:
Spatial organization and evolutional period of the epidemic model using
  cellular automata

abstract:
  We investigate epidemic models with spatial structure based on the cellular
automata method. The construction of the cellular automata is from the study by
Weimar and Boon about the reaction-diffusion equations [Phys. Rev. E 49, 1749
(1994)]. Our results show that the spatial epidemic models exhibit the
spontaneous formation of irregular spiral waves at large scales within the
domain of chaos. Moreover, the irregular spiral waves grow stably. The system
also shows a spatial period-2 structure at one dimension outside the domain of
chaos. It is interesting that the spatial period-2 structure will break and
transform into a spatial synchronous configuration in the domain of chaos. Our
results confirm that populations embed and disperse more stably in space than
they do in nonspatial counterparts.


title: Exhaustive percolation on random networks

abstract:
  We consider propagation models that describe the spreading of an attribute,
called "damage", through the nodes of a random network. In some systems, the
average fraction of nodes that remain undamaged vanishes in the large system
limit, a phenomenon we refer to as exhaustive percolation. We derive scaling
law exponents and exact results for the distribution of the number of undamaged
nodes, valid for a broad class of random networks at the exhaustive percolation
transition and in the exhaustive percolation regime. This class includes
processes that determine the set of frozen nodes in random Boolean networks
with indegree distributions that decay sufficiently rapidly with the number of
inputs. Connections between our calculational methods and previous studies of
percolation beginning from a single initial node are also pointed out. Central
to our approach is the observation that key aspects of damage spreading on a
random network are fully characterized by a single function specifying the
probability that a given node will be damaged as a function of the fraction of
damaged nodes. In addition to our analytical investigations of random networks,
we present a numerical example of exhaustive percolation on a directed lattice.


title: Mobility of Discrete Solitons in Quadratically Nonlinear Media

abstract:
  We study the mobility of solitons in second-harmonic-generating lattices.
Contrary to what is known for their cubic counterparts, discrete quadratic
solitons are mobile not only in the one-dimensional (1D) setting, but also in
two dimensions (2D). We identify parametric regions where an initial kick
applied to a soliton leads to three possible outcomes, namely, staying put,
persistent motion, or destruction. For the 2D lattice, it is found that, for
the solitary waves, the direction along which they can sustain the largest kick
and can attain the largest speed is the diagonal. Basic dynamical properties of
the discrete solitons are also discussed in the context of an analytical
approximation, in terms of an effective Peierls-Nabarro potential in the
lattice setting.


title:
Dynamics of subpicosecond dispersion-managed soliton in a fibre: A
  perturbative analysis

abstract:
  A model is studied which describes a propagation of a subpicosecond optical
pulse in dispersion-managed fibre links. In the limit of weak chromatic
dispersion management, the model equation is reduced to a perturbed modified
NLS equation having a nonlinearity dispersion term. By means of the
Riemann--Hilbert problem, a perturbation theory for the soliton of the modified
NLS equation is developed. It is shown in the adiabatic approximation that
there exists a unique possibility to suppress the perturbation-induced shift of
the soliton centre at the cost of proper matching of the soliton width and
nonlinearity dispersion parameter. In the next-order approximation, the
spectral density of the radiation power emitted by a soliton is calculated.


title: Generic N-coupled maps in Bose-Mesner algebra perspective

abstract:
  By choosing a dynamical system with d different couplings, one can rearrange
a system based on the graph with given vertex dependent on the dynamical system
elements. The relation between the dynamical elements (coupling) is replaced by
a relation between the vertexes. Based on the E_0 transverse projection
operator. We addressed synchronization problem of an array of the linearly
coupled map lattices of identical discrete time systems.
  The synchronization rate is determined by the second largest eigenvalue of
the transition probability matrix. Algebraic properties of the Bose-Mesner
algebra with an associated scheme with definite spectrum has been used in order
to study the stability of the coupled map lattice. Associated schemes play a
key role and may lead to analytical methods in studying the stability of the
dynamical systems. The relation between the coupling parameters and the chaotic
region is presented. It is shown that the feasible region is analytically
determined by the number of couplings (i.e, by increasing the number of coupled
maps the feasible region is restricted). It is very easy to apply our criteria
to the system being studied and they encompass a wide range of coupling schemes
including most of the popularly used ones in the literature.


title:
Kinematic studies of transport across an island wake, with application
  to the Canary islands

abstract:
  Transport from nutrient-rich coastal upwellings is a key factor influencing
biological activity in surrounding waters and even in the open ocean. The rich
upwelling in the North-Western African coast is known to interact strongly with
the wake of the Canary islands, giving rise to filaments and other mesoscale
structures of increased productivity. Motivated by this scenario, we introduce
a simplified two-dimensional kinematic flow describing the wake of an island in
a stream, and study the conditions under which there is a net transport of
substances across the wake. For small vorticity values in the wake, it acts as
a barrier, but there is a transition when increasing vorticity so that for
values appropriate to the Canary area, it entrains fluid and enhances
cross-wake transport.


title: A q-analogue of gl_3 hierarchy and q-Painleve VI

abstract:
  A q-analogue of the gl_3 Drinfel'd-Sokolov hierarchy is proposed as a
reduction of the q-KP hierarchy. Applying a similarity reduction and a
q-Laplace transformation to the hierarchy, one can obtain the q-Painleve VI
equation proposed by Jimbo and Sakai.


title:
Shear-Improved Smagorinsky Model for Large-Eddy Simulation of
  Wall-Bounded Turbulent Flows

abstract:
  A shear-improved Smagorinsky model is introduced based on recent results
concerning shear effects in wall-bounded turbulence by Toschi et al. (2000).
The Smagorinsky eddy-viscosity is modified subtracting the magnitude of the
mean shear from the magnitude of the instantaneous resolved strain-rate tensor.
This subgrid-scale model is tested in large-eddy simulations of plane-channel
flows at two different Reynolds numbers. First comparisons with the dynamic
Smagorinsky model and direct numerical simulations, including mean velocity,
turbulent kinetic energy and Reynolds stress profiles, are shown to be
extremely satisfactory. The proposed model, in addition of being physically
sound, has a low computational cost and possesses a high potentiality of
generalization to more complex non-homogeneous turbulent flows.


title: D-dimensional developed MHD turbulence: Double expansion model

abstract:
  Developed magnetohydrodynamic turbulence near two dimensions $d$ up to three
dimensions has been investigated by means of renormalization group approach and
double expansion regularization. A modification of standard minimal subtraction
scheme has been used to analyze the stability of the Kolmogorov scaling regime
which is governed by the renormalization group fixed point. The exact
analytical expressions have been obtained for the fixed points. The
continuation of the universal value of the inverse Prandtl number $u=1.562$
determined at $d=2$ up to $d=3$ restores the value of $u=1.393$ which is known
in the kinetic fixed point from usual $\epsilon$-expansion. The magnetic stable
fixed point has been calculated and its stability region has been also
examined. This point losses stability: (1) below critical value of dimension
$d_c=2.36$ (independently on the $a$-parameter of a magnetic forcing) and, (2)
below the value of $a_c=0.146$ (independently on the dimension).


title:
Similarity Solution of the 3-phase Stefan Problem for Alloys with
  Arbitrary Temperature Dependent Properties

abstract:
  In this paper a 3-phase Stefan problem solution method for 1D semi-infinity
alloy is developed. The problem is first solved for full enthalpy of the system
and then the thermal diffusivity has been eliminated from the divergence
operator by Kirchoff transformation. Moreover, we introduce a similarity
independent variable $\eta=x^{2}/\tau$ and original problem transforms to
ordinary differential equations (ODE) for each phase separately. These ODEs
have Dirichlet's type boundary conditions.


title: Energy Spectra of Developed Turbulencein Helium Superfluids

abstract:
  We suggest a "minimal model" for the 3D turbulent energy spectra in
superfluids, based on their two-fluid description. We start from the
Navier-Stokes equation for the normal fluid and from the coarse-grained
hydrodynamic equation for the superfluid component (obtained from the Euler
equation for the superfluid velocity after averaging over the vortex lines) and
introduce a mutual friction coupling term, proportional to the counterflow
velocity, the average superfluid vorticity and to the temperature dependent
parameter $q=\alpha/(1+\alpha')$, where $\alpha$ and $\alpha'$ denote the
dimensionless parameters characterizing the mutual friction between quantized
vortices and the normal component of the liquid. We then derive the energy
balance equations, taking into account the cross-velocity correlations. We
obtain all asymptotical solutions for normal and superfluid energy spectra for
limiting cases of small/big normal to superfluid density ratio and coupling. We
discuss the applicability limits of our model to superfluid He II and to
$^3$He-B and compare the model predictions with available experimental data.


title: Stochastic Properties of the Frobenius-Perron Operator

abstract:
  In the present paper the Renormalization Group (RG) method is adopted as a
tool for a constructive analysis of the properties of the Frobenius-Perron
Operator. The renormalization group reduction of a generic symplectic map in
the case, where the unperturbed rotation frequency of the map is far from
structural resonances driven by the kick perturbation has been performed in
detail. It is further shown that if the unperturbed rotation frequency is close
to a resonance, the reduced RG map of the Frobenius-Perron operator (or
phase-space density propagator) is equivalent to a discrete Fokker-Planck
equation for the renormalized distribution function. The RG method has been
also applied to study the stochastic properties of the standard Chirikov-Taylor
map.

categories: nlin.CD cond-mat.stat-mech nlin.PS physics.acc-ph


title:
Corrugated surfaces with slow modulation and quasiclassical Weierstrass
  representation

abstract:
  Quasiclassical generalized Weierstrass representation for highly corrugated
surfaces with slow modulation in the three-dimensional space is proposed.
Integrable deformations of such surfaces are described by the dispersionless
Veselov-Novikov hierarchy.


title: Intermittency and Synchronisation in Gumowski-Mira Maps

abstract:
  The Gumowski-Mira map is a 2-dimensional recurrence relation that provide a
large variety of phase space plots resembling fractal patterns of nature. We
investigate the nature of the dynamical states that produce these patterns and
find that they correspond to Type I intermittency near periodic cycles. By
coupling two GM maps, such patterns can be wiped out to give synchronised
periodic states of lower order.The efficiency of the coupling scheme is
established by analysing the error function dynamics.


title:
Stochastic resonance as a filter for signal detection from multisignal
  inputs

abstract:
  We undertake a detailed numerical study of the phenomenon of stochastic
resonance with multisignal inputs. A bistable cubic map is used as the model
and we show that it combines the features of a bistable system and a threshold
system. A study of stochastic resonance in these two setups reveal some
fundamental differences between the two mechanisms with respect to
amplification of a composite input signal. As a practically relevant result, we
show that the phenomenon of stochastic resonance can be used as a filter for
the detection/transmission of the component frequencies in a composite signal.


title: Scale-invariant cellular automata and self-similar Petri nets

abstract:
  Two novel computing models based on an infinite tessellation of space-time
are introduced. They consist of recursively coupled primitive building blocks.
The first model is a scale-invariant generalization of cellular automata,
whereas the second one utilizes self-similar Petri nets. Both models are
capable of hypercomputations and can, for instance, "solve" the halting problem
for Turing machines. These two models are closely related, as they exhibit a
step-by-step equivalence for finite computations. On the other hand, they
differ greatly for computations that involve an infinite number of building
blocks: the first one shows indeterministic behavior whereas the second one
halts. Both models are capable of challenging our understanding of
computability, causality, and space-time.


title:
Explicit solutions of the WDVV equation determined by the "flat"
  hydrodynamic reductions of the Egorov hydrodynamic chains

abstract:
  Classification of the Egorov hydrodynamic chain and corresponding 2+1
quasilinear system is given in the previous paper. In this paper we present a
general construction of explicit solutions for the WDVV equation associated
with Hamiltonian hydrodynamic reductions of these Egorov hydrodynamic chains


title:
A geometric interpretation of the spectral parameter for surfaces of
  constant mean curvature

abstract:
  Considering the kinematics of the moving frame associated with a constant
mean curvature surface immersed in S^3 we derive a linear problem with the
spectral parameter corresponding to elliptic sinh-Gordon equation. The spectral
parameter is related to the radius R of the sphere S^3. The application of the
Sym formula to this linear problem yields constant mean curvature surfaces in
E^3. Independently, we show that the Sym formula itself can be derived by an
appropriate limiting process R -> infinity.


title:
Discretization of multidimensional submanifolds associated with
  Spin-valued spectral problems

abstract:
  We present a large family of Spin(p,q)-valued discrete spectral problems. The
associated discrete nets generated by the so called Sym-Tafel formula are
circular nets (i.e., all elementary quadrilaterals are inscribed into circles).
These nets are discrete analogues of smooth multidimensional immersions in R^m
including isothermic surfaces, Guichard nets, and some other families of
orthogonal nets.


title:
The Darboux-Backlund transformation for the static 2-dimensional
  continuum Heisenberg chain

abstract:
  We construct the Darboux-Backlund transformation for the sigma model
describing static configurations of the 2-dimensional classical continuum
Heisenberg chain. The transformation is characterized by a non-trivial
normalization matrix depending on the background solution. In order to obtain
the transformation we use a new, more general, spectral problem.


title: Pragmatic Information and Gaian Development -- First Thoughts

abstract:
  The scientific community believes in the theory of evolution with a passion
that rivals that of any religious belief. This passion extends beyond the
irrefutable evidence of the fossil record to the familiar claims of survival of
the fittest and random mutation. Yet the theory of natural selection has, to
the knowledge of the present author, never been tested against the alternative
hypothesis that evolution is, in fact, the ongoing development of a single,
world-spanning super-organism. Just what kind of evidence would settle this
question is not clear, so this paper is intended to begin the discussion. It
does so by suggesting how a new, quantitative theory of pragmatic information,
first presented in Weinberger (2002), might detect the widespread temporal and
inter-species connections that a developmental view of evolution would imply.


title:
Variation of Fractal Properties of Two-Component Systems in Their
  Evolution Process

abstract:
  Analysis of experimental kinetic dependences and results of the computer
modeling of pairwise interactions in the heterogeneous system have shown that a
character of its fractal property variation in the evolution process would be
different at distinguished temperature ranges and dependent on the proportion
of reagent concentrations and their initial distribution type.