title:
Stripe-hexagon competition in forced pattern forming systems with broken
  up-down symmetry

abstract:
  We investigate the response of two-dimensional pattern forming systems with a
broken up-down symmetry, such as chemical reactions, to spatially resonant
forcing and propose related experiments. The nonlinear behavior immediately
above threshold is analyzed in terms of amplitude equations suggested for a
$1:2$ and $1:1$ ratio between the wavelength of the spatial periodic forcing
and the wavelength of the pattern of the respective system. Both sets of
coupled amplitude equations are derived by a perturbative method from the
Lengyel-Epstein model describing a chemical reaction showing Turing patterns,
which gives us the opportunity to relate the generic response scenarios to a
specific pattern forming system. The nonlinear competition between stripe
patterns and distorted hexagons is explored and their range of existence,
stability and coexistence is determined. Whereas without modulations hexagonal
patterns are always preferred near onset of pattern formation, single mode
solutions (stripes) are favored close to threshold for modulation amplitudes
beyond some critical value. Hence distorted hexagons only occur in a finite
range of the control parameter and their interval of existence shrinks to zero
with increasing values of the modulation amplitude. Furthermore depending on
the modulation amplitude the transition between stripes and distorted hexagons
is either sub- or supercritical.


title:
A method to discern complexity in two-dimensional patterns generated by
  coupled map lattices

abstract:
  Complex patterns generated by the time evolution of a one-dimensional
digitalized coupled map lattice are quantitatively analyzed. A method for
discerning complexity among the different patterns is implemented. The
quantitative results indicate two zones in parameter space where the dynamics
shows the most complex patterns. These zones are located on the two edges of an
absorbent region where the system displays spatio-temporal intermittency.

categories: nlin.PS cond-mat.dis-nn cs.CG math.DS nlin.CD q-bio.QM


title:
On integrable system on $S^2$ with the second integral quartic in the
  momenta

abstract:
  We consider integrable system on the sphere $S^2$ with an additional integral
of fourth order in the momenta. At the special values of parameters this system
coincides with the Kowalevski-Goryachev-Chaplygin system.


title: Effective Dissipation and Turbulence in Spectrally Truncated Euler Flows

abstract:
  A new transient regime in the relaxation towards absolute equilibrium of the
conservative and time-reversible 3-D Euler equation with high-wavenumber
spectral truncation is characterized. Large-scale dissipative effects, caused
by the thermalized modes that spontaneously appear between a transition
wavenumber and the maximum wavenumber, are calculated using fluctuation
dissipation relations. The large-scale dynamics is found to be similar to that
of high-Reynolds number Navier-Stokes equations and thus to obey (at least
approximately) Kolmogorov scaling.


title: Sine-Gordon Soliton on a Cnoidal Wave Background

abstract:
  The method of Darboux transformation, which is applied on cnoidal wave
solutions of the sine-Gordon equation, gives solitons moving on a cnoidal wave
background. Interesting characteristics of the solution, i.e., the velocity of
solitons and the shift of crests of cnoidal waves along a soliton, are
calculated. Solutions are classified into three types (Type-1A, Type-1B,
Type-2) according to their apparent distinct properties.


title:
Multidimensional Gaussian sums arising from distribution of Birkhoff
  sums in zero entropy dynamical systems

abstract:
  A duality formula, of the Hardy and Littlewood type for multidimensional
Gaussian sums, is proved in order to estimate the asymptotic long time behavior
of distribution of Birkhoff sums $S_n$ of a sequence generated by a skew
product dynamical system on the $\mathbb{T}^2$ torus, with zero Lyapounov
exponents. The sequence, taking the values $\pm 1$, is pairwise independent
(but not independent) ergodic sequence with infinite range dependence. The
model corresponds to the motion of a particle on an infinite cylinder, hopping
backward and forward along its axis, with a transversal acceleration parameter
$\alpha$. We show that when the parameter $\alpha /\pi$ is rational then all
the moments of the normalized sums $E((S_n/\sqrt{n})^k)$, but the second, are
unbounded with respect to n, while for irrational $\alpha /\pi$, with bounded
continuous fraction representation, all these moments are finite and bounded
with respect to n.


title: Optical-parametric-oscillator solitons driven by the third harmonic

abstract:
  We introduce a model of a lossy second-harmonic-generating (chi^2) cavity
externally pumped at the third harmonic, which gives rise to driving terms of a
new type, corresponding to a cross-parametric gain. The equation for the
fundamental-frequency (FF) wave may also contain a quadratic self-driving term,
which is generated by the cubic nonlinearity of the medium. Unlike previously
studied phase-matched models of chi^2 cavities driven at the second harmonic
(SH) or at FF, the present one admits an exact analytical solution for the
soliton, at a special value of the gain parameter. Two families of solitons are
found in a numerical form, and their stability area is identified through
numerical computation of the perturbation eigenvalues (stability of the zero
solution, which is a necessary condition for the soliton's stability, is
investigated in an analytical form). One family is a continuation of the
special analytical solution. At given values of parameters, one soliton is
stable and the other one is not; they swap their stability at a critical value
of the mismatch parameter. The stability of the solitons is also verified in
direct simulations, which demonstrate that the unstable pulse rearranges itself
into the stable one, or into a delocalized state, or decays to zero. A soliton
which was given an initial boost C starts to move but quickly comes to a halt,
if the boost is smaller than a critical value C_cr. If C>C_cr, the boost
destroys the soliton (sometimes, through splitting into two secondary pulses).
Interactions between initially separated solitons are investigated too. It is
concluded that stable solitons always merge into a single one. In the system
with weak loss, it appears in a vibrating form, slowly relaxing to the static
shape. With stronger loss, the final soliton emerges in the stationary form.


title: Wave Functions of the Toda Chain with Boundary Interaction

abstract:
  In this contribution, we give an integral representation of the wave
functions of the quantum N-particle Toda chain with boundary interaction. In
the case of the Toda chain with one-boundary interaction, we obtain the wave
function by an integral transformation from the wave functions of the open Toda
chain. The kernel of this transformation is given explicitly in terms of
\Gamma-functions. The wave function of the Toda chain with two-boundary
interaction is obtained from the previous wave functions by an integral
transformation. In this case, the difference equation for the kernel of the
integral transformation admits separation of variables. The separated
difference equations coincide with the Baxter equation.


title:
Point configurations, Cremona transformations and the elliptic
  difference Painlev\'e equation

abstract:
  A theoretical foundation for a generalization of the elliptic difference
Painlev\'e equation to higher dimensions is provided in the framework of
birational Weyl group action on the space of point configurations in general
position in a projective space. By introducing an elliptic parametrization of
point configurations, a realization of the Weyl group is proposed as a group of
Cremona transformations containing elliptic functions in the coefficients. For
this elliptic Cremona system, a theory of $\tau$-functions is developed to
translate it into a system of bilinear equations of Hirota-Miwa type for the
$\tau$-functions on the lattice.


title: Dynamical scaling and intermittency in shell models of turbulence

abstract:
  We introduce a model for the turbulent energy cascade aimed at studying the
effect of dynamical scaling on intermittency. In particular, we show that by
slowing down the energy transfer mechanism for fixed energy flux, intermittency
decreases and eventually disappears. This result supports the conjecture that
intermittency can be observed only if energy is flowing towards faster and
faster scales of motion.


title: Vorticity cutoff in nonlinear photonic crystals

abstract:
  Using group theory arguments, we demonstrate that, unlike in homogeneous
media, no symmetric vortices of arbitrary order can be generated in
two-dimensional (2D) nonlinear systems possessing a discrete-point symmetry.
The only condition needed is that the non-linearity term exclusively depends on
the modulus of the field. In the particular case of 2D periodic systems, such
as nonlinear photonic crystals or Bose-Einstein condensates in periodic
potentials, it is shown that the realization of discrete symmetry forbids the
existence of symmetric vortex solutions with vorticity higher than two.


title:
Emergent Effective Collusion in an Economy of Perfectly Rational
  Competitors

abstract:
  We consider a simple model of rational agents competing in a single product
market described by simple linear demand curve. Contrary to accepted economic
theory, the agents' production levels synchronise in the absence of conscious
collusion, leading to a downward spiraling of market total production until the
monopoly price level is realised. This is in stark contrast to the standard
predictions of an ideal rational competitive market. Some form of randomness in
the form of agent irrationality, or non-synchronous updates is needed to break
this emergent "collusion"


title:
Breaking a chaos-based secure communication scheme designed by an
  improved modulation method

abstract:
  Recently Bu and Wang [Chaos, Solitons & Fractals 19 (2004) 919] proposed a
simple modulation method aiming to improve the security of chaos-based secure
communications against return-map-based attacks. Soon this modulation method
was independently cryptanalyzed by Chee et al. [Chaos, Solitons & Fractals 21
(2004) 1129], Wu et al. [Chaos, Solitons & Fractals 22 (2004) 367], and
\'{A}lvarez et al. [Chaos, Solitons & Fractals, accepted (2004),
arXiv:nlin.CD/0406065] via different attacks. As an enhancement to the Bu-Wang
method, an improving scheme was suggested by Wu et al. by removing the
relationship between the modulating function and the zero-points. The present
paper points out that the improved scheme proposed by Wu et al. is still
insecure against a new attack. Compared with the existing attacks, the proposed
attack is more powerful and can also break the original Bu-Wang scheme.
Furthermore, it is pointed out that the security of the modulation-based
schemes is not so satisfactory from a pure cryptographical point of view. The
synchronization performance of this class of modulation-based schemes is also
discussed.


title: Inhomogeneous Anisotropic Passive Scalars

abstract:
  We investigate the behaviour of the two-point correlation function in the
context of passive scalars for non homogeneous, non isotropic forcing
ensembles. Exact analytical computations can be carried out in the framework of
the Kraichnan model for each anisotropic sector. It is shown how the
homogeneous solution is recovered at separations smaller than an intrinsic
typical lengthscale induced by inhomogeneities, and how the different Fourier
modes in the centre-of-mass variable recombine themselves to give a ``beating''
(superposition of power laws) described by Bessel functions. The pure power-law
behaviour is restored even if the inhomogeneous excitation takes place at very
small scales.


title:
Quasi-linear Stokes phenomenon for the Hastings-McLeod solution of the
  second Painlev\'e equation

abstract:
  Using the Riemann-Hilbert approach, we explicitly construct the asymptotic
$\Psi$-function corresponding to the solution $y\sim\pm\sqrt{-x/2}$ as
$|x|\to\infty$ to the second Painlev\'e equation $y_{xx}=2y^3+xy-\alpha$. We
precisely describe the exponentially small jump in the dominant solution and
the coefficient asymptotics in its power-like expansion.


title: Models for optical solitons in the two-cycle regime

abstract:
  We derive model equations for optical pulse propagation in a medium described
by a two-level Hamiltonian, without the use of the slowly varying envelope
approximation. Assuming that the resonance frequency of the two-level atoms is
either well above or well below the inverse of the characteristic duration of
the pulse, we reduce the propagation problem to a modified Korteweg-de Vries or
a sine-Gordon equation. We exhibit analytical solutions of these equations
which are rather close in shape and spectrum to pulses in the two-cycle regime
produced experimentally, which shows that soliton-type propagation of the
latter can be envisaged.


title: A topological approach to neural complexity

abstract:
  Considerable efforts in modern statistical physics is devoted to the study of
networked systems. One of the most important example of them is the brain,
which creates and continuously develops complex networks of correlated
dynamics. An important quantity which captures fundamental aspects of brain
network organization is the neural complexity C(X)introduced by Tononi et al.
This work addresses the dependence of this measure on the topological features
of a network in the case of gaussian stationary process. Both anlytical and
numerical results show that the degree of complexity has a clear and simple
meaning from a topological point of view. Moreover the analytical result offers
a straightforward algorithm to compute the complexity than the standard one.


title:
Fine structure of distributions and central limit theorem in diffusive
  billiards

abstract:
  We investigate deterministic diffusion in periodic billiard models, in terms
of the convergence of rescaled distributions to the limiting normal
distribution required by the central limit theorem; this is stronger than the
usual requirement that the mean square displacement grow asymptotically
linearly in time. The main model studied is a chaotic Lorentz gas where the
central limit theorem has been rigorously proved. We study one-dimensional
position and displacement densities describing the time evolution of
statistical ensembles in a channel geometry, using a more refined method than
histograms. We find a pronounced oscillatory fine structure, and show that this
has its origin in the geometry of the billiard domain. This fine structure
prevents the rescaled densities from converging pointwise to gaussian
densities; however, demodulating them by the fine structure gives new densities
which seem to converge uniformly. We give an analytical estimate of the rate of
convergence of the original distributions to the limiting normal distribution,
based on the analysis of the fine structure, which agrees well with simulation
results. We show that using a Maxwellian (gaussian) distribution of velocities
in place of unit speed velocities does not affect the growth of the mean square
displacement, but changes the limiting shape of the distributions to a
non-gaussian one. Using the same methods, we give numerical evidence that a
non-chaotic polygonal channel model also obeys the central limit theorem, but
with a slower convergence rate.


title: Structure formation in electromagnetically driven granular media

abstract:
  We report structure formation in submonolayers of magnetic microparticles
subjected to periodic electrostatic and magnetic excitations. Depending on the
excitation parameters, we observe the formation of a rich variety of
structures: clusters, rings, chains, and networks. The growth dynamics and
shapes of the structures are strongly dependent on the amplitude and frequency
of the external magnetic field. We find that for pure ac magnetic driving at
low densities of particles, the low-frequency magnetic excitation favors
clusters while high frequency excitation favors chains and net-like structures.
An abrupt phase transition from chains to a network phase was observed for a
high density of particles.


title: Soliton Dynamics in Computational Anatomy

abstract:
  Computational anatomy (CA) has introduced the idea of anatomical structures
being transformed by geodesic deformations on groups of diffeomorphisms. Among
these geometric structures, landmarks and image outlines in CA are shown to be
singular solutions of a partial differential equation that is called the
geodesic EPDiff equation. A recently discovered momentum map for singular
solutions of EPDiff yields their canonical Hamiltonian formulation, which in
turn provides a complete parameterization of the landmarks by their canonical
positions and momenta. The momentum map provides an isomorphism between
landmarks (and outlines) for images and singular soliton solutions of the
EPDiff equation. This isomorphism suggests a new dynamical paradigm for CA, as
well as new data representation.


title: Nearest neighbor embedding with different time delays

abstract:
  A nearest neighbor based selection of time delays for phase space
reconstruction is proposed and compared to the standard use of time delayed
mutual information. The possibility of using different time delays for
consecutive dimensions is considered. A case study of numerically generated
solutions of the Lorenz system is used for illustration. The effect of
contamination with various levels of additive Gaussian white noise is
discussed.


title:
Nonlinear Schr\"{o}dinger lattices II: Persistence and Stability of
  Discrete Vortices

abstract:
  We study discrete vortices in the anti-continuum limit of the discrete
two-dimensional nonlinear Schr{\"o}dinger (NLS) equations. The discrete
vortices in the anti-continuum limit represent a finite set of excited nodes on
a closed discrete contour with a non-zero topological charge. Using the
Lyapunov-Schmidt reductions, we find sufficient conditions for continuation and
termination of the discrete vortices for a small coupling constant in the
discrete NLS lattice. An example of a closed discrete contour is considered
that includes the vortex cell (also known as the off-site vortex). We classify
the symmetric and asymmetric discrete vortices that bifurcate from the
anti-continuum limit. We predict analytically and confirm numerically the
number of unstable eigenvalues associated with various families of such
discrete vortices.


title: Epidemic Spreading in Dynamic Small World Networks

abstract:
  In this paper, we use a series of small world networks to simulate the
epidemic spreading in the real world. To make our model more similar to the
real world, we employ a parameter $p_{move}$ to denote its moving probability,
which corresponds with the general mobility of individuals in realistic social
network. The networks keep the same small world properties when they are
varying. And the SIRS model is used to simulate the disease propagation. From
these simulations we see the moving probability of a small world network has a
profound effect on the velocity for the spread of an infection. The
quantitative results show that the characteristic time $\tau$ of infection at
initial stage decreases exponentially with $p_{move}$.


title:
Chaotic dynamics of charged particles in the field of a finite
  non-uniform wave packet

abstract:
  A generalization of the Chirikov-Taylor model is introduced to study the
dynamics of a charged particle in the field of an electrostatic wave packet
with an arbitrary but finite number of harmonics.


title: Large-Scale Coherence and Law of Decay of Two-Dimensional Turbulence

abstract:
  At the short times, the enstrophy $\Omega$ of a two-dimensional flow,
generated by a random Gaussian initial condition decays as $\Omega(t)\propto
t^{-\gamma}$ with $\gamma\approx 0.7$. After that, the flow undergoes
transition to a different state characterized by the magnitude of the decay
exponent $\gamma\approx 0.4$ (Yakhot, Wanderer, Phys.Rev.Lett.{\bf 93}, 154502
\~(2004)). It is shown that the very existence of this transition and various
characteristics of evolving flow crucially depend upon phase correlation
between the large-scale modes containing only a few percent of total enstrophy.


title: Chaos suppression in the parametrically driven Lorenz system

abstract:
  We predict theoretically and verify experimentally the suppression of chaos
in the Lorenz system driven by a high-frequency periodic or stochastic
parametric force. We derive the theoretical criteria for chaos suppression and
verify that they are in a good agreement with the results of numerical
simulations and the experimental data obtained for an analog electronic
circuit.


title:
Coupled-mode theory for spatial gap solitons in optically-induced
  lattices

abstract:
  We develop a coupled-mode theory for spatial gap solitons in the
one-dimensional photonic lattices induced by interfering optical beams in a
nonlinear photorefractive crystal. We derive a novel system of coupled-mode
equations for two counter-propagating probe waves, and find its analytical
solutions for stationary gap solitons. We also predict the existence of moving
(or tilted) gap solitons and study numerically soliton collisions.


title:
A Time-Varying Complex Dynamical Network Model And Its Controlled
  Synchronization Criteria

abstract:
  Today, complex networks have attracted increasing attention from various
fields of science and engineering. It has been demonstrated that many complex
networks display various synchronization phenomena. In this paper, we introduce
a time-varying complex dynamical network model. We then further investigate its
synchronization phenomenon and prove several network synchronization theorems.
Especially, we show that synchronization of such a time-varying dynamical
network is completely determined by the inner-coupling matrix, and the
eigenvalues and the corresponding eigenvectors of the coupling configuration
matrix of the network.


title: Introduction to chaos and diffusion

abstract:
  This contribution is relative to the opening lectures of the ISSAOS 2001
summer school and it has the aim to provide the reader with some concepts and
techniques concerning chaotic dynamics and transport processes in fluids. Our
intention is twofold: to give a self-consistent introduction to chaos and
diffusion, and to offer a guide for the reading of the rest of this volume.


title: Stable Vortex Solitons in Nonlocal Self-Focusing Nonlinear Media

abstract:
  We reveal that spatially localized vortex solitons become stable in
self-focusing nonlinear media when the vortex symmetry-breaking azimuthal
instability is eliminated by a nonlocal nonlinear response. We study the main
properties of different types of vortex beams and discuss the physical
mechanism of the vortex stabilization in spatially nonlocal nonlinear media.


title: Predicting rogue waves in random oceanic sea states

abstract:
  Using the inverse spectral theory of the nonlinear Schrodinger (NLS) equation
we correlate the development of rogue waves in oceanic sea states characterized
by the JONSWAP spectrum with the proximity to homoclinic solutions of the NLS
equation. We find in numerical simulations of the NLS equation that rogue waves
develop for JONSWAP initial data that is ``near'' NLS homoclinic data, while
rogue waves do not occur for JONSWAP data that is ``far'' from NLS homoclinic
data. We show the nonlinear spectral decomposition provides a simple criterium
for predicting the occurrence and strength of rogue waves (PACS: 92.10.Hm,
47.20.Ky, 47.35+i).


title:
Meanders and Reconnection-Collision Sequences in the Standard Nontwist
  Map

abstract:
  New global periodic orbit collision/separatrix reconnection scenarios in the
standard nontwist map in different regions of parameter space are described in
detail, including exact methods for determining reconnection thresholds that
are implemented numerically. The results are compared to a break-up diagram of
shearless invariant curves. The existence of meanders (invariant tori that are
not graphs) is demonstrated numerically for both odd and even period
reconnection for certain regions in parameter space, and some of the
implications on transport are discussed.


title:
Hopf Bifurcation and Chaos in a Single Inertial Neuron Model with Time
  Delay

abstract:
  A delayed differential equation modelling a single neuron with inertial term
is considered in this paper. Hopf bifurcation is studied by using the normal
form theory of retarded functional differential equations. When adopting a
nonmonotonic activation function, chaotic behavior is observed. Phase plots,
waveform plots, and power spectra are presented to confirm the chaoticity.


title: Hopf Bifurcation and Chaos in Tabu Learning Neuron Models

abstract:
  In this paper, we consider the nonlinear dynamical behaviors of some tabu
leaning neuron models. We first consider a tabu learning single neuron model.
By choosing the memory decay rate as a bifurcation parameter, we prove that
Hopf bifurcation occurs in the neuron. The stability of the bifurcating
periodic solutions and the direction of the Hopf bifurcation are determined by
applying the normal form theory. We give a numerical example to verify the
theoretical analysis. Then, we demonstrate the chaotic behavior in such a
neuron with sinusoidal external input, via computer simulations. Finally, we
study the chaotic behaviors in tabu learning two-neuron models, with linear and
quadratic proximity functions respectively.


title:
Codimension-two points in annular electroconvection as a function of
  aspect ratio

abstract:
  We rigorously derive from first principles the generic Landau amplitude
equation that describes the primary bifurcation in electrically driven
convection. Our model accurately represents the experimental system: a weakly
conducting, submicron thick liquid crystal film suspended between concentric
circular electrodes and driven by an applied voltage between its inner and
outer edges. We explicitly calculate the coefficient $g$ of the leading cubic
nonlinearity and systematically study its dependence on the system's
geometrical and material parameters. The radius ratio $\alpha$ quantifies the
film's geometry while a dimensionless group ${\cal P}$, similar to the Prandtl
number, fixes the ratio of the fluid's electrical and viscous relaxation times.
Our calculations show that for fixed $\alpha$, $g$ is a decreasing function of
${\cal P}$, as ${\cal P}$ becomes smaller, and is nearly constant for ${\cal P}
\gtrsim 1$. As ${\cal P} \to 0$, $g \to \infty$. We find that $g$ is a
nontrivial and discontinuous function of $\alpha$. We show that the
discontinuities occur at codimension-two points that are accessed by varying
$\alpha$.


title: Dynamics of a piecewise smooth map with singularity

abstract:
  Experiments observing the liquid surface in a vertically oscillating
container have indicated that modeling the dynamics of such systems require
maps that admit states at infinity. In this paper we investigate the
bifurcations in such a map. We show that though such maps in general fall in
the category of piecewise smooth maps, the mechanisms of bifurcations are quite
different from those in other piecewise smooth maps. We obtain the conditions
of occurrence of infinite states, and show that periodic orbits containing such
states are superstable. We observe period-adding cascade in this system, and
obtain the scaling law of the successive periodic windows.


title:
Isochronism and tangent bifurcation of band edge modes in Hamiltonian
  lattices

abstract:
  In {\em Physica D} {\bf 91}, 223 (1996), results were obtained regarding the
tangent bifurcation of the band edge modes ($q=0,\pi$) of nonlinear Hamiltonian
lattices made of $N$ coupled oscillators. Introducing the concept of {\em
partial isochronism} which characterises the way the frequency of a mode,
$\omega$, depends on its energy, $\epsilon$, we generalize these results and
show how the bifurcation energies of these modes are intimately connected to
their degree of isochronism. In particular we prove that in a lattice of
coupled purely isochronous oscillators ($\omega(\epsilon)$ strictly constant),
the in-phase mode ($q=0$) never undergoes a tangent bifurcation whereas the
out-of-phase mode ($q=\pi$) does, provided the strength of the nonlinearity in
the coupling is sufficient. We derive a discrete nonlinear Schr\"odinger
equation governing the slow modulations of small-amplitude band edge modes and
show that its nonlinear exponent is proportional to the degree of isochronism
of the corresponding orbits. This equation may be seen as a link between the
tangent bifurcation of band edge modes and the possible emergence of localized
modes such as discrete breathers.


title:
Thermodynamic formalism for the Lorentz gas with open boundaries in $d$
  dimensions

abstract:
  A Lorentz gas may be defined as a system of fixed dispersing scatterers, with
a single light particle moving among these and making specular collisions on
encounters with the scatterers. For a dilute Lorentz gas with open boundaries
in $d$ dimensions we relate the thermodynamic formalism to a random flight
problem. Using this representation we analytically calculate the central
quantity within this formalism, the topological pressure, as a function of
system size and a temperature-like parameter $\ba$. The topological pressure is
given as the sum of the topological pressure for the closed system and a
diffusion term with a $\ba$-dependent diffusion coefficient. From the
topological pressure we obtain the Kolmogorov-Sinai entropy on the repeller,
the topological entropy, and the partial information dimension.


abstract:
  We introduce Rayleigh functional for nonlinear systems. It is defined using
the energy functional and the normalization properties of the variables of
variation. The key property of the Rayleigh quotient for linear systems is
preserved in our definition: the extremals of the Rayleigh functional coincide
with the stationary solutions of the Euler-Lagrange equation. Moreover, the
second variation of the Rayleigh functional defines stability of the solution.
This gives rise to a powerful numerical optimization method in the search for
the energy minimizers. It is shown that the well-known imaginary time
relaxation is a special case of our method. To illustrate the method we find
the stationary states of Bose-Einstein condensates in various geometries.
Finally, we show that the Rayleigh functional also provides a simple way to
derive analytical identities satisfied by the stationary solutions of the
critical nonlinear equations. We also show that the functional used in Phys.
Rev. A 66, 036612 (2002) is erroneous.

categories: nlin.PS cond-mat.other nlin.CD physics.comp-ph


title: Additive Noise Induces Front Propagation

abstract:
  The propagation of a front connecting a stable homogeneous state with a
stable periodic state in the presence of additive noise is studied. The mean
velocity was computed both numerically and analitically. The numerics are in
good agreement with the analitical prediction.


title: Weak noise approach to the logistic map

abstract:
  Using a nonperturbative weak noise approach we investigate the interference
of noise and chaos in simple 1D maps. We replace the noise-driven 1D map by an
area-preserving 2D map modelling the Poincare sections of a conserved dynamical
system with unbounded energy manifolds. We analyze the properties of the 2D map
and draw conclusions concerning the interference of noise on the nonlinear time
evolution. We apply this technique to the standard period-doubling sequence in
the logistic map. From the 2D area-preserving analogue we, in addition to the
usual period-doubling sequence, obtain a series of period doubled cycles which
are elliptic in nature. These cycles are spinning off the real axis at
parameters values corresponding to the standard period doubling events.


title:
Towards spectral theory of the Nonstationary Schr\"{o}dinger equation
  with a two-dimensionally perturbed one-dimensional potential

abstract:
  The Nonstationary Schr\"{o}dinger equation with potential being a
perturbation of a generic one-dimensional potential by means of a decaying
two-dimensional function is considered here in the framework of the extended
resolvent approach. The properties of the Jost solutions and spectral data are
investigated.


title:
Length scale competition in soliton bearing equations: A collective
  coordinate approach

abstract:
  We study the phenomenon of length scale competition, an instability of
solitons and other coherent structures that takes place when their size is of
the same order of some characteristic scale of the system in which they
propagate. Working on the framework of nonlinear Klein-Gordon models as a
paradigmatic example, we show that this instability can be understood by means
of a collective coordinate approach in terms of soliton position and width. As
a consequence, we provide a quantitative, natural explanation of the phenomenon
in much simpler terms than any previous treatment of the problem. Our technique
allows to study the existence of length scale competition in most soliton
bearing nonlinear models and can be extended to coherent structures with more
degrees of freedom, such as breathers.

categories: nlin.PS cond-mat.other math.AP physics.class-ph


title: Bethe ansatz for the XXX-S chain with non-diagonal open boundaries

abstract:
  We consider the algebraic Bethe ansatz solution of the integrable and
isotropic XXX-S Heisenberg chain with non-diagonal open boundaries. We show
that the corresponding K-matrices are similar to diagonal matrices with the
help of suitable transformations independent of the spectral parameter. When
the boundary parameters satisfy certain constraints we are able to formulate
the diagonalization of the associated double-row transfer matrix by means of
the quantum inverse scattering method. This allows us to derive explicit
expressions for the eigenvalues and the corresponding Bethe ansatz equations.
We also present evidences that the eigenvectors can be build up in terms of
multiparticle states for arbitrary S.


title: Collection of Master-Slave Synchronized Chaotic Systems

abstract:
  In this work the open-plus-closed-loop (OPCL) method of synchronization is
used in order to synchronize the systems from the Sprott's collection of the
simplest chaotic systems. The method is general and we were looking for the
simplest coupling between master and slave system. The interval of parameters
were synchronization is achieved are obtained analytically using Routh-Hurwitz
conditions. Detailed calculations and numerical simulation are given for the
system I from the Sprott's collection. Working in the same manner for
non-linear systems based on ordinary differential equations the method can be
adopted for the teaching of the topic.


title:
Anomalous scaling of passively advected magnetic field in the presence
  of strong anisotropy

abstract:
  Inertial-range scaling behavior of high-order (up to order N=51) structure
functions of a passively advected vector field has been analyzed in the
framework of the rapid-change model with strong small-scale anisotropy with the
aid of the renormalization group and the operator-product expansion. It has
been shown that in inertial range the leading terms of the structure functions
are coordinate independent, but powerlike corrections appear with the same
anomalous scaling exponents as for the passively advected scalar field. These
exponents depend on anisotropy parameters in such a way that a specific
hierarchy related to the degree of anisotropy is observed. Deviations from
power-law behavior like oscillations or logarithmic behavior in the corrections
to structure functions have not been found.


title:
Entropy production in diffusion-reaction systems: The reactive random
  Lorentz gas

abstract:
  We report the study of a random Lorentz gas with a reaction of isomerization
$A\rightleftharpoons B$ between the two colors of moving particles elastically
bouncing on hard disks. The reaction occurs when the moving particles collide
on catalytic disks which constitute a fraction of all the disks. Under the
dilute-gas conditions, the reaction-diffusion process is ruled by two coupled
Boltzmann-Lorentz equations for the distribution functions of the colors. The
macroscopic reaction-diffusion equations with cross-diffusion terms induced by
the chemical reaction are derived from the kinetic equations. We use a
$H$-theorem of the kinetic theory in order to derive a macroscopic entropy
depending on the gradients of color densities and which has a non-negative
entropy production in agreement with the second law of thermodynamics.


title: The Lie algebraic structure of extended Sutherland models

abstract:
  We disclose the Lie algebraic structure of two extended Sutherland models.
Their Hamiltonians are BC_N, and A_N Sutherland Hamiltonians with some
additional terms. We show that both Hamiltonians can be written in the
quadratic forms of generators of the Lie algebra gl(N+1).


title: Domain wall dynamics in an optical Kerr cavity

abstract:
  An anisotropic (dichroic) optical cavity containing a self-focusing Kerr
medium is shown to display a bifurcation between static --Ising-- and moving
--Bloch-- domain walls, the so-called nonequilibrium Ising-Bloch transition
(NIB). Bloch walls can show regular or irregular temporal behaviour, in
particular, bursting and spiking. These phenomena are interpreted in terms of
the spatio-temporal dynamics of the extended patterns connected by the wall,
which display complex dynamical behaviour as well. Domain wall interaction,
including the formation of bound states is also addressed.


title: Box-ball system with reflecting end

abstract:
  A soliton cellular automaton on a one dimensional semi-infinite lattice with
a reflecting end is presented. It extends a box-ball system on an infinite
lattice associated with the crystal base of U_q(sl_n). A commuting family of
time evolutions are obtained by adapting the K matrices and the double row
construction of transfer matrices in solvable lattice models to a crystal
setting. Factorized scattering among the left and the right moving solitons and
the boundary reflection rule are determined.


title: Analysis of Bifurcations in a Power System Model with Excitation Limits

abstract:
  This paper studies bifurcations in a three node power system when excitation
limits are considered. This is done by approximating the limiter by a smooth
function to facilitate bifurcation analysis. Spectacular qualitative changes in
the system behavior induced by the limiter are illustrated by two case studies.
Period doubling bifurcations and multiple attractors are shown to result due to
the limiter. Detailed numerical simulations are presented to verify the results
and illustrate the nature of the attractors and solutions involved.


title: On dispersionless BKP hierarchy and its reductions

abstract:
  Integrable dispersionless Kadomtsev-Petviashvili (KP) hierarchy of B type is
considered. Addition formula for the $\tau$-function and conformally invariant
equations for the dispersionless BKP (dBKP) hierarchy are derived. Symmetry
constraints for the dBKP hierarchy are studied.


title: Excitability mediated by localized structures

abstract:
  We find and characterize an excitability regime mediated by localized
structures in a dissipative nonlinear optical cavity. The scenario is that
stable localized structures exhibit a Hopf bifurcation to self-pulsating
behavior, that is followed by the destruction of the oscillation in a
saddle-loop bifurcation. Beyond this point there is a regime of excitable
localized structures under the application of suitable perturbations.
Excitability emerges from the spatial dependence since the system does not
exhibit any excitable behavior locally. We show that the whole scenario is
organized by a Takens-Bogdanov codimension-2 bifurcation point.

categories: nlin.PS cond-mat.stat-mech math.DS physics.optics


title:
Controlled observation of a nonequilibrium Ising-Bloch transition in a
  nonlinear optical cavity

abstract:
  We describe the controlled observation of the nonequilibrium Ising-Bloch
transition in a broad area nonlinear optical cavity, namely, a quasi-1D single
longitudinal-mode photorefractive oscilator in a degenerate four-wave mixing
configuration. Our experimental technique allows for the controlled injection
of the domain walls. We use cavity detuning as control parameter and find that
both Ising and Bloch walls can exist for the same detuning values within a
certain interval of detunings, i.e., the Ising-Bloch transition is hysteretic
in our case. A complex Ginzburg-Landau model is used for supporting the
observations.


title: Random Delays and the Synchronization of Chaotic Maps

abstract:
  We investigate the dynamics of an array of logistic maps coupled with random
delay times. We report that for adequate coupling strength the array is able to
synchronize, in spite of the random delays. Specifically, we find that the
synchronized state is a homogeneous steady-state, where the chaotic dynamics of
the individual maps is suppressed. This differs drastically from the
synchronization with instantaneous and fixed-delay coupling, as in those cases
the dynamics is chaotic. Also in contrast with the instantaneous and
fixed-delay cases, the synchronization does not dependent on the connection
topology, depends only on the average number of links per node. We find a
scaling law that relates the distance to synchronization with the randomness of
the delays. We also carry out a statistical linear stability analysis that
confirms the numerical results and provides a better understanding of the
nontrivial roles of random delayed interactions.


title: Changing shapes: adiabatic dynamics of composite solitary waves

abstract:
  We discuss the solitary wave solutions of a particular two-component scalar
field model in two-dimensional Minkowski space. These solitary waves involve
one, two or four lumps of energy. The adiabatic motion of these composite
non-linear non-dispersive waves points to variations in shape.


title: Integrable string and hydrodynamical type models and nonlocal brackets

abstract:
  The closed string model in the background gravity field is considered as a
bi-Hamiltonian system in assumption that string model is the integrable model
for particular kind of the background fields. The dual nonlocal Poisson
brackets(PB), depending of the background fields and of their derivatives, are
obtained. The integrability condition is formulated as the compatibility of the
bi-Hamiltonity condition and the Jacobi identity of the dual PB. It is shown
that the dual brackets and dual Hamiltonians can be obtained from the canonical
PB and from the initial Hamiltonian by imposing the second kind constraints on
the initial dynamical system, on the closed string model in the constant
background fields, as example. The hydrodynamical type equation was obtained.
Two types of the nonlocal brackets are introduced. Constant curvature and
time-dependent metrics are considered. It is shown that the Jacobi identities
for the nonlocal brackets have particular solution for the space-time
coordinates, as matrix representation of the simple Lie group.


title:
Melnikov method approach to control of homoclinic and heteroclinic chaos
  by weak harmonic excitations

abstract:
  A review on the application of Melnikov's method to control homoclinic and
heteroclinic chaos in low-dimensional, non-autonomous and dissipative,
oscillator systems by weak harmonic excitations is presented, including diverse
applications such as chaotic escape from a potential well, chaotic solitons in
Frenkel-Kontorova chains, and chaotic charged particles in the field of an
electrostatic wave packet.


title: Path Integration on Hermitian Hyperbolic Space

abstract:
  In this paper the path integral technique is applied to the quantum motion on
the Hermitian hyperbolic space HH(2). The Schr\"odinger equation on this space
separates in 12 coordinate systems which are closely related to the coordinate
systems on the two-dimensional hyperboloid. For six coordinate systems out of
the twelve it is possible to find a path integral solution.


title: Anomalous transport in Charney-Hasegawa-Mima flows

abstract:
  Transport properties of particles evolving in a system governed by the
Charney-Hasegawa-Mima equation are investigated. Transport is found to be
anomalous with a non linear evolution of the second moments with time. The
origin of this anomaly is traced back to the presence of chaotic jets within
the flow. All characteristic transport exponents have a similar value around
$\mu=1.75$, which is also the one found for simple point vortex flows in the
literature, indicating some kind of universality. Moreover the law
$\gamma=\mu+1$ linking the trapping time exponent within jets to the transport
exponent is confirmed and an accumulation towards zero of the spectrum of
finite time Lyapunov exponent is observed. The localization of a jet is
performed, and its structure is analyzed. It is clearly shown that despite a
regular coarse grained picture of the jet, motion within the jet appears as
chaotic but chaos is bounded on successive small scales.

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


title: Field Theory Approach to Quantum Interference in Chaotic Systems

abstract:
  We consider the spectral correlations of clean globally hyperbolic (chaotic)
quantum systems. Field theoretical methods are applied to compute quantum
corrections to the leading (`diagonal') contribution to the spectral form
factor. Far-reaching structural parallels, as well as a number of differences,
to recent semiclassical approaches to the problem are discussed.


title: Generation of spin-wave dark solitons with phase engineering

abstract:
  We generate experimentally spin-wave envelope dark solitons from rectangular
high-frequency dark input pulses with externally introduced phase shifts in
yttrium-iron garnet magnetic fims. We observe the generation of both odd and
even numbers of magnetic dark solitons when the external phase shift varies.
The experimental results are in a good qualitative agreement with the theory of
the dark-soliton generation in magnetic films developed earlier [Phys. Rev.
Lett. 82, 2583 (1999)].


title: Creative Thought as a nonDarwinian Evolutionary Process

abstract:
  Selection theory requires multiple, distinct, simultaneously-actualized
states. In cognition, each thought or cognitive state changes the 'selection
pressure' against which the next is evaluated; they are not simultaneously
selected amongst. Creative thought is more a matter of honing in a vague idea
through redescribing successive iterations of it from different real or
imagined perspectives; in other words, actualizing potential through exposure
to different contexts. It has been proven that the mathematical description of
contextual change of state introduces a non-Kolmogorovian probability
distribution, and a classical formalism such as selection theory cannot be
used. This paper argues that creative thought evolves not through a Darwinian
process, but a process of context-driven actualization of potential.


title: Lattice Boltzmann method at finite-Knudsen numbers

abstract:
  A modified lattice Boltzmann model with a stochastic relaxation mechanism
mimicking "virtual'' collisions between free-streaming particles and solid
walls is introduced. This modified scheme permits to compute plane channel
flows in satisfactory agreement with analytical results over a broad spectrum
of Knudsen numbers, ranging from the hydrodynamic regime, all the way to
quasi-free flow regimes up to Kn 30.


title: Discrete-symmetry vortices as angular Bloch modes

abstract:
  The most general form for symmetric modes of nonlinear discrete-symmetry
systems with nonlinearity depending on the modulus of the field is presented.
Vortex solutions are demonstrated to behave as Bloch modes characterized by an
angular Bloch momentum associated to a periodic variable, periodicity being
fixed by the order of discrete point-symmetry of the system. The concept of
angular Bloch momentum is thus introduced to generalize the usual definition of
angular momentum to cases where O(2) -symmetry no longer holds. The
conservation of angular Bloch momentum during propagation is demonstrated.


title:
Non-linear deformation and break up of enclaves in a rhyolitic magma: a
  case study from Lipari Island (Southern Italy)

abstract:
  A dome from Lipari Island (Southern Italy) consists of 12 vol. percent of
circular, elongated and folded latitic enclaves hosted in a rhyolitic matrix.
The dm- to cm-scale enclaves are more deformed than the mm-scale blobs. The
critical value of the ratio between the viscous forces, which allow deformation
and eventually break up blobs of latitic magma, and the interfacial tension
forces is larger than 0.29. The Reynolds number is < 5.3. The equivalent radius
and the axial ratio of the enclaves follow power-law distributions. This
feature suggests that the break up and stretching of magmas are non-linear,
scale-invariant, probably cyclic processes. The coexistence of enclaves of
different shape and the self-similar size distributions suggest that chaotic
advection plays a major role in the formation of mingled magmas. Caution must
be used when measuring the finite strain from enclave shapes because they may
break apart during the deformation.


title: A new integrable 3+1 dimensional generalization of the Burgers equation

abstract:
  A new nonlinear 3+1 dimensional evolution equation admitting the Lax pair is
presented. In the case of one spatial dimension, the equation reduces to the
Burgers equation. A method of construction of exact solutions, based on a class
of discrete symmetries of the former equation is developed. These symmetries
reduce to the Cole-Hopf transformation in one-dimensional limit. Some exact
solutions are analyzed, in the physical context of spatial dissipative
structures and shock wave dressing.


title: The Fermi-Pasta-Ulam problem: 50 years of progress

abstract:
  A brief review of the Fermi-Pasta-Ulam (FPU) paradox is given, together with
its suggested resolutions and its relation to other physical problems. We focus
on the ideas and concepts that have become the core of modern nonlinear
mechanics, in their historical perspective. Starting from the first numerical
results of FPU, both theoretical and numerical findings are discussed in close
connection with the problems of ergodicity, integrability, chaos and stability
of motion. New directions related to the Bose-Einstein condensation and quantum
systems of interacting Bose-particles are also considered.

categories: nlin.CD cond-mat.stat-mech physics.hist-ph quant-ph


title:
Detecting synchronization in spatially extended discrete systems by
  complexity measurements

abstract:
  The synchronization of two stochastically coupled one-dimensional cellular
automata (CA) is analyzed. It is shown that the transition to synchronization
is characterized by a dramatic increase of the statistical complexity of the
patterns generated by the difference automaton. This singular behavior is
verified to be present in several CA rules displaying complex behavior.

categories: nlin.CG cond-mat.dis-nn cs.MA math.DS nlin.PS q-bio.QM


title: Stability Properties of Nonhyperbolic Chaotic Attractors under Noise

abstract:
  We study local and global stability of nonhyperbolic chaotic attractors
contaminated by noise. The former is given by the maximum distance of a noisy
trajectory from the noisefree attractor, while the latter is provided by the
minimal escape energy necessary to leave the basin of attraction, calculated
with the Hamiltonian theory of large fluctuations. We establish the important
and counterintuitive result that both concepts may be opposed to each other.
Even when one attractor is globally more stable than another one, it can be
locally less stable. Our results are exemplified with the Holmes map, for two
different sets of parameter, and with a juxtaposition of the Holmes and the
Ikeda maps. Finally, the experimental relevance of these findings is pointed
out.


title: Finite-gap Solutions of the Vortex Filament Equation, I

abstract:
  For the class of quasi-periodic solutions of the vortex filament equation, we
study connections between the algebro-geometric data used for their explicit
construction and the geometry of the evolving curves. We give a complete
description of genus one solutions, including geometrically interesting special
cases such as Euler elastica, constant torsion curves, and self-intersecting
filaments. We also prove generalizations of these connections to higher genus.


title: Self-Organizing Traffic Lights

abstract:
  Steering traffic in cities is a very complex task, since improving efficiency
involves the coordination of many actors. Traditional approaches attempt to
optimize traffic lights for a particular density and configuration of traffic.
The disadvantage of this lies in the fact that traffic densities and
configurations change constantly. Traffic seems to be an adaptation problem
rather than an optimization problem. We propose a simple and feasible
alternative, in which traffic lights self-organize to improve traffic flow. We
use a multi-agent simulation to study three self-organizing methods, which are
able to outperform traditional rigid and adaptive methods. Using simple rules
and no direct communication, traffic lights are able to self-organize and adapt
to changing traffic conditions, reducing waiting times, number of stopped cars,
and increasing average speeds.


title: Anomalous scaling of low-order structure functions of turbulent velocity

abstract:
  It is now believed that the scaling exponents of moments of velocity
increments are anomalous, or that the departures from Kolmogorov's (1941)
self-similar scaling increase nonlinearly with the increasing order of the
moment. This appears to be true whether one considers velocity increments
themselves or their absolute values. However, moments of order lower than 2 of
the absolute values of velocity increments have not been investigated
thoroughly for anomaly. Here, we discuss the importance of the scaling of
non-integer moments of order between +2 and -1, and obtain them from direct
numerical simulations at moderate Reynolds numbers (Taylor microscale Reynolds
numbers $R_\lambda \le$ 450) and experimental data at high Reynolds numbers
($R_\lambda \approx$ 10,000). The relative difference between the measured
exponents and Kolmogorov's prediction increases as the moment order decreases
towards -1, thus showing that the anomaly that is manifest in high-order
moments is present in low-order moments as well. This conclusion provides a
motivation for seeking a theory of anomalous scaling as the order of the moment
vanishes. Such a theory does not have to consider rare events--which may be
affected by non-universal features such as shear--and so may be regarded as
advantageous to consider and develop.


title:
Observation of stable phase jump lines in convection of a twisted
  nematic

abstract:
  We report observations of stable, localized, line-like structures in the
spatially periodic pattern formed by nematic electroconvection, along which the
phase of the pattern jumps by $\pi$. With increasing electric voltage, these
lines form a grid-like structure that goes over into a structure
indistinguishable from the well known grid pattern. We present theoretical
arguments that suggest that the twisted cell geometry we are using is
indirectly stabilizing the phase jump lines, and that the PJL lattice is caused
by an interaction of phase jump lines and a zig-zag instability of the
surrounding pattern.


title:
Classification of polynomial integrable systems of mixed scalar and
  vector evolution equations. I

abstract:
  We perform a classification of integrable systems of mixed scalar and vector
evolution equations with respect to higher symmetries. We consider polynomial
systems that are homogeneous under a suitable weighting of variables. This
paper deals with the KdV weighting, the Burgers (or potential KdV or modified
KdV) weighting, the Ibragimov-Shabat weighting and two unfamiliar weightings.
The case of other weightings will be studied in a subsequent paper. Making an
ansatz for undetermined coefficients and using a computer package for solving
bilinear algebraic systems, we give the complete lists of 2nd order systems
with a 3rd order or a 4th order symmetry and 3rd order systems with a 5th order
symmetry. For all but a few systems in the lists, we show that the system (or,
at least a subsystem of it) admits either a Lax representation or a linearizing
transformation. A thorough comparison with recent work of Foursov and Olver is
made.


title:
Multiple-scale analysis and renormalization for pre-asymptotic scalar
  transport

abstract:
  Pre-asymptotic transport of a scalar quantity passively advected by a
velocity field formed by a large-scale component superimposed to a small-scale
fluctuation is investigated both analytically and by means of numerical
simulations. Exploiting the multiple-scale expansion one arrives at a
Fokker--Planck equation which describes the pre-asymptotic scalar dynamics.
Such equation is associated to a Langevin equation involving a multiplicative
noise and an effective (compressible) drift. For the general case, no explicit
expression for both the effective drift and the effective diffusivity (actually
a tensorial field) can be obtained. We discuss an approximation under which an
explicit expression for the diffusivity (and thus for the drift) can be
obtained. Its expression permits to highlight the important fact that the
diffusivity explicitly depends on the large-scale advecting velocity. Finally,
the robustness of the aforementioned approximation is checked numerically by
means of direct numerical simulations.


title:
The Davey-Stewartson I Equation on the Quarter Plane with Homogeneous
  Dirichlet Boundary Conditions

abstract:
  Dromions are exponentially localised coherent structures supported by
nonlinear integrable evolution equations in two spatial dimensions.In the study
of initial-value problems on the plane, such solutions occur only if one
imposes nontrivial boundary conditions at infinity, a situation of dubious
physical significance. However it is established here that dromions appear
naturally in the study of boundary-value problems. In particular, it is shown
that the long time asymptotics of the solution of the Davey-Stewartson I
equation in the quarter plane with arbitrary initial conditions and with zero
Dirichlet boundary conditions is dominated by dromions. The case of non-zero
Dirichlet boundary conditions is also discussed.


title:
An Equation-Free Approach to Nonlinear Control: Coarse Feedback
  Linearization With Pole-Placement

abstract:
  We present an application of equation-free computation to the coarse-grained
feedback linearization problem of nonlinear systems described by
microscopic/stochastic simulators. Feedback linearization with pole placement
requires the solution of a functional equation involving the macroscopic
(coarse-grained) system model. In the absence of such a closed-form model,
short, appropriately initialized bursts of microscopic simulation are designed
and performed, and their results used to estimate on demand the quantities
required for the numerical solution of the (explicitly unavailable) functional
equation. Our illustrative example is a kinetic Monte Carlo realization of a
simplified heterogeneous catalytic reaction scheme


title:
On the Clark-alpha model of turbulence: global regularity and long--time
  dynamics

abstract:
  In this paper we study a well-known three--dimensional turbulence model, the
filtered Clark model, or Clark-alpha model. This is Large Eddy Simulation (LES)
tensor-diffusivity model of turbulent flows with an additional spatial filter
of width alpha ($\alpha$). We show the global well-posedness of this model with
constant Navier-Stokes (eddy) viscosity. Moreover, we establish the existence
of a finite dimensional global attractor for this dissipative evolution system,
and we provide an anaytical estimate for its fractal and Hausdorff dimensions.
Our estimate is proportional to $(L/l_d)^3$, where $L$ is the integral spatial
scale and $l_d$ is the viscous dissipation length scale. This explicit bound is
consistent with the physical estimate for the number of degrees of freedom
based on heuristic arguments. Using semi-rigorous physical arguments we show
that the inertial range of the energy spectrum for the Clark-$\aa$ model has
the usual $k^{-5/3}$ Kolmogorov power law for wave numbers $k\aa \ll 1$ and
$k^{-3}$ decay power law for $k\aa \gg 1.$ This is evidence that the
Clark$-\alpha$ model parameterizes efficiently the large wave numbers within
the inertial range, $k\aa \gg 1$, so that they contain much less translational
kinetic energy than their counterparts in the Navier-Stokes equations.


title: The Nonlinear Schr\"odinger Equation on the Interval

abstract:
  Let $q(x,t)$ satisfy the Dirichlet initial-boundary value problem for the
nonlinear Schr\"odinger equation on the finite interval, $0 < x < L$, with
$q_{0}(x) = q(x,0)$, $g_{0}(t) = q(0,t)$, $f_{0}(t) = q(L,t)$. Let $g_{1}(t)$
and $f_{1}(t)$ denote the {\it unknown} boundary values $q_{x}(0,t)$ and
$q_{x}(L,t)$, respectively. We first show that these unknown functions can be
expressed in terms of the given initial and boundary conditions through the
solution of a system of nonlinear ODEs. Although the question of the global
existence of solution of this system remains open, it appears that this is the
first time in the literature that such a characterization is explicitely
described for a nonlinear evolution PDE defined on the interval; this result is
the extension of the analogous result of [4] and [6] from the half-line to the
interval. We then show that $q(x,t)$ can be expressed in terms of the solution
of a $2\times 2$ matrix Riemann-Hilbert problem formulated in the complex $k$ -
plane. This problem has explicit $(x,t)$ dependence in the form $\exp[2ikx +
4ik^2t]$, and it has jumps across the real and imaginary axes. The relevant
jump matrices are explicitely given in terms of the spectral data $\{a(k),
b(k)\}$, $\{A(k), B(k)\}$, and $\{\A(k), \B(k)\}$, which in turn are defined in
terms of $q_{0}(x)$, $\{g_{0}(t), g_{1}(t)\}$, and $\{f_{0}(t), f_{1}(t)\}$,
espectively.


title:
The Time Periodic Solution of the Burgers Equation on the Half-Line and
  an Application to Steady Streaming

abstract:
  The phenomenon of steady streaming, or acoustic streaming, is an important
physical phenomenon studied extensively in the literature. Its mathematical
formulation involves the Navier-Stokes equations, thus due to the complexity of
these equations is usually studied heuristically using formal perturbation
expansions. It turns out that the Burgers equation formulated on the half line
provides a simple model of the above phenomenon. The physical situation
corresponds to the solution of the Dirichlet problem on the half-line, which
decays as $x \to \infty$ and which is {\it time periodic}. We show that the
Dirichlet problem, where the usual prescription of the initial condition is now
replaced by the requirement of the time periodicity, yields a well posed
problem. Furthermore, we show that the solution of this problem tends to the
``inner'' and ``outer'' solutions obtained by the perturbation expansions.


title:
Linearizable Initial-Boundary Value Problems for the sine-Gordon
  Equation on the Half-Line

abstract:
  A rigorous methodology for the analysis of initial boundary value problems on
the half-line, $0<x<\infty$, $t>0$, for integrable nonlinear evolution PDEs has
recently appeared in the literature. As an application of this methodology the
solution $q(x,t)$ of the sine-Gordon equation can be obtained in terms of the
solution of a $2\times 2$ matrix Riemann-Hilbert problem. This problem is
formulated in the complex $k$-plane and is uniquely defined in terms of the so
called spectral functions $a(k)$, $b(k)$, and $B(k)/A(k)$. The functions $a(k)$
and $b(k)$ can be constructed in terms of the given initial conditions $q(x,0)$
and $q_t(x,0)$ via the solution of a system of two {\it linear} ODE's, while
for \emph{arbitrary} boundary conditions the functions $A(k)$ and $B(k)$ can be
constructed in terms of the given boundary condition via the solution of a
system of four {\it nonlinear} ODEs. In this paper we analyse two
\emph{particular} boundary conditions: the case of constant Dirichlet data,
$q(0,t) = \chi$, as well as the case that $q_x(0,t)$, $\sin (q(0,t)/2)$, and
$\cos(q(0,t)/2)$ are linearly related by two constants $\chi_1$ and $\chi_2$.
We show that for these particular cases, the system of the above nonlinear ODEs
can be avoided, and $B(k)/A(k)$ can be computed explicitly in terms of
$\{a(k),b(k),\chi\}$ and $\{a(k),b(k), \chi_1, \chi_2\}$ respectively. Thus
these ``linearizable'' initial-boundary value problems can be solved with
absolutely the same level of efficiency as the classical initial value problem
of the line.


title:
Poincare recurrence and measure of hyperbolic and nonhyperbolic chaotic
  attractors

abstract:
  We study Poincare recurrence of chaotic attractors for regions of finite
size. Contrary to the standard case, where the size of the recurrent regions
tends to zero, the measure is not supported anymore solely by unstable periodic
orbits inside it, but also by other special recurrent trajectories, located
outside that region. The presence of the latter leads to a deviation of the
distribution of the Poincare first return times from a Poissonian.
Consequently, by taken into account the contribution of these recurrent
trajectories, a corrected estimate of the measure can be provided. This has
wide experimental implications, as in the laboratory all returns can
exclusively be observed for regions of finite size only.


title: Critical exponents of Nikolaevskii turbulence

abstract:
  We study the spatial power spectra of Nikolaevskii turbulence in
one-dimensional space. First, we show that the energy distribution in
wavenumber space is extensive in nature. Then, we demonstrate that, when
varying a particular parameter, the spectrum becomes qualitatively
indistinguishable from that of Kuramoto-Sivashinsky turbulence. Next, we derive
the critical exponents of turbulent fluctuations. Finally, we argue that in
some previous studies, parameter values for which this type of turbulence does
not appear were mistakenly considered, and we resolve inconsistencies obtained
in previous studies.


title: Dynamics of Passive-Scalar Turbulence

abstract:
  We present the first study of the dynamic scaling or multiscaling of
passive-scalar and passive-vector turbulence. For the Kraichnan version of
passive-scalar and passive-vector turbulence we show analytically, in both
Eulerian and quasi-Lagrangian frameworks, that simple dynamic scaling is
obtained but with different dynamic exponents. By developing the multifractal
model we show that dynamic multiscaling occurs in passive-scalar turbulence
only if the advecting velocity field is itself multifractal. We substantiate
our results by detailed numerical simulations in shell models of passive-scalar
advection.


title: n-body dynamics of stabilized vector solitons

abstract:
  In this work we study the interactions between stabilized Townes solitons. By
means of effective Lagrangian methods, we have found that the interactions
between these solitons are governed by central forces, in a first
approximation. In our numerical simulations we describe different types of
orbits, deflections, trapping and soliton splitting. Splitting phenomena are
also described by finite dimensional reduced models. All these effects could be
used for potential applications of stabilized solitons.


title: Some symmetry classifications of hyperbolic vector evolution equations

abstract:
  Motivated by recent work on integrable flows of curves and 1+1 dimensional
sigma models, several O(N)-invariant classes of hyperbolic equations $u_{tx}
=f(u,u_t,u_x)$ for an $N$-component vector $u(t,x)$ are considered. In each
class we find all scaling-homogeneous equations admitting a higher symmetry of
least possible scaling weight. Sigma model interpretations of these equations
are presented.


title: Univalent functions and integrable systems

abstract:
  We study one-parameter expanding evolution families of simply connected
domains in the complex plane described by infinite systems of evolution
parameters. These evolution parameters in some cases admit Hamiltonian
formulation and lead to integrable systems. One example of such parameters is
complex moments for the Laplacian growth that form a Whitham-Toda integrable
hierarchy. Another example we deal with is related to expanding coefficient
bodies for conformal maps given by L\"owner subordination chains. The
coefficients bodies are proved to form a Liouville partially integrable
Hamiltonian system for each fixed index and the first integrals are obtained.
We also discuss the contact structure of this system.


title: B\"acklund transformations for the rational Lagrange chain

abstract:
  We consider a long--range homogeneous chain where the local variables are the
generators of the direct sum of $N$ $\mathfrak{e}(3)$ interacting Lagrange
tops. We call this classical integrable model rational ``Lagrange chain''
showing how one can obtain it starting from $\mathfrak{su}(2)$ rational Gaudin
models. Moreover we construct one- and two--point integrable maps (B\"acklund
transformations).


title: Maximal superintegrability of Benenti systems

abstract:
  For a class of Hamiltonian systems naturally arising in the modern theory of
separation of variables, we establish their maximal superintegrability by
explicitly constructing the additional integrals of motion.


title:
Hodograph transformations for a Camassa- Holm hierarchy in 2+1
  dimensions

abstract:
  A generalization of the negative Camassa-Holm hierarchy to 2+1 dimensions is
presented under the name CHH(2+1). Several hodograph transformations are
applied in order to transform the hierarchy into a system of coupled CBS
(Calogero-Bogoyavlenskii-Schiff) equations in 2+1 dimensions that pass the
Painleve test. A non-isospectral Lax pair for CHH(2+1) is obtained through the
above mentioned relationship with the CBS spectral problem..


title: Singular manifold method for an equation in 2+1 dimensions

abstract:
  he Singular Manifold Method is presented as an excellent tool to study a 2+1
dimensional equation in despite of the fact that the same method presents
several problems when applied to 1+1 reductions of the same equation.
Nevertheless these problems are solved when the number of dimensions of the
equation is increased.


title: Multicolor vortex solitons in two-dimensional photonic lattices

abstract:
  We report on the existence and stability of multicolor lattice vortex
solitons constituted by coupled fundamental frequency and second-harmonic waves
in optical lattices in quadratic nonlinear media. It is shown that the solitons
are stable almost in the entire domain of their existence, and that the
instability domain decreases with the increase of the lattice depth. We also
show the generation of the solitons, and the feasibility of the concept of
lattice soliton algebra.


title:
Existence, uniqueness and multiplicity of rotating fluxon waves in
  annular Josephson junctions

abstract:
  We prove that the equation modelling an annular Josephson junction has a
rotating fluxon wave for all values of the parameters. We also obtain results
on uniqueness of the rotating fluxon wave in some parameter regimes, and
results on multiplicity of rotating fluxon waves in other parameter regimes.


title: Security problems with a chaos-based deniable authentication scheme

abstract:
  Recently, a new scheme was proposed for deniable authentication. Its main
originality lied on applying a chaos-based encryption-hash parallel algorithm
and the semi-group property of the Chebyshev chaotic map. Although original and
practicable, its insecurity and inefficiency are shown in this paper, thus
rendering it inadequate for adoption in e-commerce.


title: Large-scale energy spectra in surface quasi-geostrophic turbulence

abstract:
  The large-scale energy spectrum in two-dimensional turbulence governed by the
surface quasi-geostrophic (SQG) equation
$$\partial_t(-\Delta)^{1/2}\psi+J(\psi,(-\Delta)^{1/2}\psi) =\mu\Delta\psi+f$$
is studied. The nonlinear transfer of this system conserves the two quadratic
quantities $\Psi_1=<[(-\Delta)^{1/4}\psi]^2>/2$ and
$\Psi_2=<[(-\Delta)^{1/2}\psi]^2>/2$ (kinetic energy), where $<\cdot>$ denotes
a spatial average. The energy density $\Psi_2$ is bounded and its spectrum
$\Psi_2(k)$ is shallower than $k^{-1}$ in the inverse-transfer range. For
bounded turbulence, $\Psi_2(k)$ in the low-wavenumber region can be bounded by
$Ck$ where $C$ is a constant independent of $k$ but dependent on the domain
size. Results from numerical simulations confirming the theoretical predictions
are presented.


title:
Diminishing inverse transfer and non-cascading dynamics in surface
  quasi-geostrophic turbulence

abstract:
  The inverse transfer in two-dimensional turbulence governed by the surface
quasi-geostrophic (SQG) equation is studied. The nonlinear transfer of this
system conserves the two quadratic quantities
$\Psi_1=<|(-\Delta)^{1/4}\psi|^2>/2$ and $\Psi_2=<|(-\Delta)^{1/2}\psi|^2>/2$
(kinetic energy), where $\psi$ is the streamfunction and $<\cdot>$ denotes a
spatial average. In the limit of infinite domain, the kinetic energy density
$\Psi_2$ remains bounded. For power-law inverse-transfer region, the inverse
flux of $\Psi_1$ diminishes as it proceeds toward sufficiently low wavenumbers,
implying that no persistent inverse cascade of $\Psi_1$ is sustainable. The
unrealizability of an inverse cascade of $\Psi_1$ implies that there is no
direct cascade of $\Psi_2$. Hence, the dual-cascade picture which is widely
believed to be realizable in two-dimensional Navier--Stokes turbulence does not
apply to SQG turbulence. Numerical results supporting the theoretical
predictions are presented.


title: Remarks on the KLB theory of two-dimensional turbulence

abstract:
  We study the inverse energy transfer in forced two-dimensional (2D)
Navier--Stokes turbulence in a doubly periodic domain. It is shown that an
inverse energy cascade that carries a nonzero fraction of the injected energy
to the large scales via a power-law energy spectrum $\propto k^{-\alpha}$
requires that $\alpha\ge5/3$. This result is consistent with the classical
theory of 2D turbulence that predicts a $k^{-5/3}$ inverse-cascading range,
thus providing for the first time a rigorous basis for this important feature
of the theory. We derive bounds for the Kolmogorov constant $C$ in the
classical energy spectrum $E(k)=C\epsilon^{2/3}k^{-5/3}$, where $\epsilon$ is
the energy injection rate. Issues related to Kraichnan's conjecture of energy
condensation and to power-law spectra as the quasi-steady dynamics become
steady are discussed.


title: On chaotic behavior of gravitating stellar shells

abstract:
  Motion of two gravitating spherical stellar shells around a massive central
body is considered. Each shell consists of point particles with the same
specific angular momenta and energies. In the case when one can neglect the
influence of gravitation of one ("light") shell onto another ("heavy") shell
("restricted problem") the structure of the phase space is described. The
scaling laws for the measure of the domain of chaotic motion and for the
minimal energy of the light shell sufficient for its escape to infinity are
obtained.


title:
Randomness Evaluation and Hardware Implementation of Nonadditive
  CA-Based Stream Cipher

abstract:
  We shall review the cellular automaton(CA)-based pseudorandom-number
generators (PRNGs), and show that one of these PRNGs can generate high-quality
random numbers which can pass all of the statistical tests provided by the
National Institute of Standards and Technology (NIST). A CA is suitable for
hardware implementation. We demonstrate that the CA-based stream cipher, which
is implemented in the field-programmable gate arrays (FPGA), has a high
encryption speed in a real-time video encryption and decryption system.


title:
A class of equations with peakon and pulson solutions (with an Appendix
  by Harry Braden and John Byatt-Smith)

abstract:
  We consider a family of integro-differential equations depending upon a
parameter $b$ as well as a symmetric integral kernel $g(x)$. When $b=2$ and $g$
is the peakon kernel (i.e. $g(x)=\exp(-|x|)$ up to rescaling) the
dispersionless Camassa-Holm equation results, while the Degasperis-Procesi
equation is obtained from the peakon kernel with $b=3$. Although these two
cases are integrable, generically the corresponding integro-PDE is
non-integrable. However,for $b=2$ the family restricts to the pulson family of
Fringer & Holm, which is Hamiltonian and numerically displays elastic
scattering of pulses. On the other hand, for arbitrary $b$ it is still possible
to construct a nonlocal Hamiltonian structure provided that $g$ is the peakon
kernel or one of its degenerations: we present a proof of this fact using an
associated functional equation for the skew-symmetric antiderivative of $g$.
The nonlocal bracket reduces to a non-canonical Poisson bracket for the peakon
dynamical system, for any value of $b\neq 1$.


title:
Travelling Fronts, Pulses, and Pulse Trains in a 1D discrete
  Reaction-Diffusion System

abstract:
  We follow up an earlier work (briefly reviewed below) to investigate the
temporal stability of an exact travelling front solution, constructed in the
form of an integral expression, for a one-dimensional discrete Nagumo-like
model without recovery. Since the model is a piecewise linear one with an
on-site reaction function involving a Heaviside step function, a
straightforward linearisation around the front solution presents problems, and
we follow an alternative approach in estimating a `stability multiplier' by
looking at the variational problem as a succession of linear evolution of the
perturbations, punctuated with `kicks' of small but finite duration. The
perturbations get damped during the linear evolution, while the kicks amplify
only the perturbations located at specific sites (the `significant
perturbations', see below) with reference to the propagating front. Comparison
is made with results of numerical integration of the reaction-diffusion system
whereby it appears likely that the travelling front is temporally stable for
all parameter values characterising the model for which it exists. We modify
the system by introducing a slow variation of a relevant recovery parameter and
perform a leading order singular perturbation analysis to construct a pulse
solution in the resulting model. In addition, we obtain (in the leading order)
a 1-parameter family of periodic pulse trains for the system, modelling
re-entrant pulses in a one-dimensional ring of excitable cells.


title: Dynamical Properties of nystagmus

abstract:
  By the methods of the time series analysis we investigate human vestibular
and optovestibular nystagmus time series. They can be stationary or
nonstationary and are between the classes of purely periodic or purely chaotic
time series. The amplitudes of the autocorrelation functions of the time series
have an unexpected peak between 7 and 9 seconds on the time axis. The singular
spectrum analysis shows that the important information about the time series is
concentrated in the first four to six principal components. The influence of
the sensory input modality, which can be changed by opening or closing eyes of
the investigated persons, leads to changes in the histogram, but leaves almost
unchanged other important characteristics of the time series such as the
statistical dimension or the positions of the dominant frequencies in the power
spectrum. Thus the behavior of the studied time series shows a presence of
nonlinearities which could play an important role for realization of the
nystagmus phenomenon.


title: On the Generalized Bohm Sheath Criterion in Dusty Plasmas

abstract:
  The paper analyses Bohm criterion for the formation positive ion sheath in
dusty plasmas . The criterion may be derived from the dispersion relation.


title: Two-Ion Dusty Plasma Waves and Landau Damping

abstract:
  The paper analyses the properties of dusty plasmas in the extreme conditions
when the free electrons are absent. The nonlinear Korteveg de Vries equation
with a nonlocal (integral) term in a small parameter approximation is derived.
The conditions are determined when the integral term is essential hence the
Landau damping of two-ion-dusty plasma waves is substantial.


title:
Closed geodesics and billiards on quadrics related to elliptic KdV
  solutions

abstract:
  We consider algebraic geometrical properties of the integrable billiard on a
quadric Q with elastic impacts along another quadric confocal to Q. These
properties are in sharp contrast with those of the ellipsoidal Birkhoff
billiards. Namely, generic complex invariant manifolds are not Abelian
varieties, and the billiard map is no more algebraic. A Poncelet-like theorem
for such system is known. We give explicit sufficient conditions both for
closed geodesics and periodic billiard orbits on Q and discuss their relation
with the elliptic KdV solutions and elliptic Calogero system


title: Motion and wake structure of spherical particles

abstract:
  This paper presents results from a flow visualization study of the wake
structures behind solid spheres rising or falling freely in liquids under the
action of gravity. These show remarkable differences to the wake structures
observed behind spheres held fixed. The two parameters controlling the rise or
fall velocity (i.e., the Reynolds number) are the density ratio between sphere
and liquid and the Galileo number.


title: Miura type transformations and homogeneous spaces

abstract:
  We relate Miura type transformations (MTs) over an evolution system to its
zero-curvature representations with values in Lie algebras g. We prove that
certain homogeneous spaces of g produce MTs and show how to distinguish these
spaces. For a scalar translation-invariant evolution equation this allows to
classify all MTs in terms of homogeneous spaces of the Wahlquist-Estabrook
algebra of the equation. For other evolution systems this allows to construct
some MTs. As an example, we study MTs over the KdV equation, a 5th order
equation of Harry-Dym type, and the coupled KdV-mKdV system of Kersten and
Krasilshchik.


title: The classical dynamics of two-electron atoms near the triple collision

abstract:
  The classical dynamics of two electrons in the Coulomb potential of an
attractive nucleus is chaotic in large parts of the high-dimensional phase
space. Quantum spectra of two-electron atoms, however, exhibit structures which
clearly hint at the existence of approximate symmetries in this system. In a
recent paper,(Phys. Rev. Lett. 93, 054302 (2004)), we presented a study of the
dynamics near the triple collision as a first step towards uncovering the
hidden regularity in the classical dynamics of two electron atoms. The
non-regularisable triple collision singularity is a main source of chaos in
three body Coulomb problems. Here, we will give a more detailed account of our
findings based on a study of the global structure of the stable and unstable
manifolds of the triple collision.


title: Multifractal Behavior of the Korean Stock-market Index KOSPI

abstract:
  We investigate multifractality in the Korean stock-market index KOSPI. The
generalized $q$th order height-height correlation function shows multiscaling
properties. There are two scaling regimes with a crossover time around $t_c
=40$ min. We consider the original data sets and the modified data sets
obtained by removing the daily jumps, which occur due to the difference between
the closing index and the opening index. To clarify the origin of the
multifractality, we also smooth the data through convolution with a Gaussian
function. After convolution we observe that the multifractality disappears in
the short-time scaling regime $t<t_c$, but remains in the long-time scaling
regime $t>t_c$, regardless of whether or not the daily jumps are removed. We
suggest that multifractality in the short-time scaling regime is caused by the
local fluctuations of the stock index. But the multifractality in the long-time
scaling regime appears to be due to the intrinsic trading properties, such as
herding behavior, information outside the market, the long memory of the
volatility, and the nonlinear dynamics of the stock market.

categories: nlin.CD cond-mat.other physics.soc-ph q-fin.ST


title: Morphology changes in the evolution of liquid two-layer films

abstract:
  We consider two thin layers of immiscible liquids on a heated solid
horizontal substrate. The free liquid-liquid and liquid-gas interfaces of such
a two-layer (or bilayer) liquid film may be unstable due to effective molecular
interactions or the Marangoni effect. Using a long wave approximation we derive
coupled evolution equations for the interafce profiles for a general
non-isothermal situation allowing for slip at the substrate. Linear and
nonlinear analyses are performed for isothermal ultrathin layers below 100 nm
thickness under the influence of destabilizing long-range and stabilizing
short-range interactions. Flat films may be unstable to varicose, zigzag or
mixed modes. During the long-time evolution the nonlinear mode type can change
via switching between two different branches of stable stationary solutions or
via coarsening along a single such branch.


title:
Long-wave theory of bounded two-layer films with a free liquid-liquid
  interface: Short- and long-time evolution

abstract:
  We consider two-layers of immiscible liquids confined between an upper and a
lower rigid plate. The dynamics of the free liquid-liquid interface is
described for arbitrary amplitudes by a single evolution equation derived from
the basic hydrodynamic equations using long-wave approximation. After giving
the evolution equation in a general way, we focus on interface instabilities
driven by gravity, thermocapillary and electrostatic fields. First, we study
the linear stability discussing especially the conditions for destabilizing the
system by heating from above or below. Second, we use a variational formulation
of the evolution equation based on an energy functional to predict metastable
states and the long-time pattern morphology (holes, drops or maze structures).
Finally, fully nonlinear three-dimensional numerical integrations are performed
to study the short- and long-time evolution of the evolving patterns. Different
coarsening modes are discussed and long-time scaling exponents are extracted.


title: On integration of the Kowalevski gyrostat and the Clebsch problems

abstract:
  For the Kowalevski gyrostat change of variables similar to that of the
Kowalevski top is done. We establish one to one correspondence between the
Kowalevski gyrostat and the Clebsch system and demonstrate that Kowalevski
variables for the gyrostat practically coincide with elliptic coordinates on
sphere for the Clebsch case. Equivalence of considered integrable systems
allows to construct two Lax matrices for the gyrostat using known rational and
elliptic Lax matrices for the Clebsch model. Associated with these matrices
solutions of the Clebsch system and, therefore, of the Kowalevski gyrostat
problem are discussed. The Kotter solution of the Clebsch system in modern
notation is presented in detail.


title: Multifractal eigenstates of quantum chaos and the Thue-Morse sequence

abstract:
  We analyze certain eigenstates of the quantum baker's map and demonstrate,
using the Walsh-Hadamard transform, the emergence of the ubiquitous Thue-Morse
sequence, a simple sequence that is at the border between quasi-periodicity and
chaos, and hence is a good paradigm for quantum chaotic states. We show a
family of states that are also simply related to Thue-Morse sequence, and are
strongly scarred by short periodic orbits and their homoclinic excursions. We
give approximate expressions for these states and provide evidence that these
and other generic states are multifractal.


title: Innovation as Evolution: Case Study Phylomemetic of Cellphone Designs

abstract:
  Cellular phone is one of the most developing technological artifacts today.
The evolution occurs through random innovation. Our effort is trying to view
the evolution of this artifact from memetics. By constructing a phylomemetic
tree based on cellular phone memes to infer or estimate the evolutionary
history and relationship among cellular phone. We adopt several methods, which
are commonly used in constructing phylogenetic tree, they are UPGMA algorithm
and Parsimony Maximum algorithm to construct cellphone phylomemetic tree.
Therefore we compare with the innovation tree, which is based on serial number
and their appearance time. From phylomemetic tree, we then analyze the process
of a cellular phone innovation through looking out on the cellular phone type
lies in the same cluster. The comparison of the simulation tree result shows a
generally different branching pattern, giving a presumption that innovation in
cellular phone is not really relating with their serial number, but occurs
merely because of random mutation of allomeme design and competes with its
technological development.


title: Local control of Hamiltonian chaos

abstract:
  We review a method of control for Hamiltonian systems which is able to create
smooth invariant tori. This method of control is based on an apt modification
of the perturbation which is small and localized in phase space.


title: On application of fractal analysis to cranial sutures

abstract:
  Fractal exponents ($d$) for human cranial sutures are calculated using the
box counting method. The results were found around $d = 1.5$ (within the range
$1.3\div 1.7$), supporting the random walk model for the suture formation
process. However, the calculated dispersion above the estimated accuracy
suggests that other mechanisms are also present. Similar numbers were obtained
for both the sagittal and coronal sutures, with the coronal sutures displaying
a better scaling. Our results are compared with estimations published by other
authors.


title: Wavelet analysis and scaling properties of time series

abstract:
  We propose a wavelet based method for the characterization of the scaling
behavior of non-stationary time series. It makes use of the built-in ability of
the wavelets for capturing the trends in a data set, in variable window sizes.
Discrete wavelets from the Daubechies family are used to illustrate the
efficacy of this procedure. After studying binomial multifractal time series
with the present and earlier approaches of detrending for comparison, we
analyze the time series of averaged spin density in the 2D Ising model at the
critical temperature, along with several experimental data sets possessing
multi-fractal behavior.


title: The song of the dunes as a self-synchronized instrument

abstract:
  Since Marco Polo (1) it has been known that some sand dunes have the peculiar
ability of emitting a loud sound with a well defined frequency, sometimes for
several minutes. The origin of this sustained sound has remained mysterious,
partly because of its rarity in nature (2). It has been recognized that the
sound is not due to the air flow around the dunes but to the motion of an
avalanche (3), and not to an acoustic excitation of the grains but to their
relative motion (4-7). By comparing several singing dunes and two controlled
experiments, one in the laboratory and one in the field, we here demonstrate
that the frequency of the sound is the frequency of the relative motion of the
sand grains. The sound is produced because some moving grains synchronize their
motions. The existence of a velocity threshold in both experiments further
shows that this synchronization comes from an acoustic resonance within the
flowing layer: if the layer is large enough it creates a resonance cavity in
which grains self-synchronize.


title:
Complexes of stationary domain walls in the resonantly forced
  Ginsburg-Landau equation

abstract:
  The parametrically driven Ginsburg-Landau equation has well-known stationary
solutions -- the so-called Bloch and Neel, or Ising, walls. In this paper, we
construct an explicit stationary solution describing a bound state of two
walls. We also demonstrate that stationary complexes of more than two walls do
not exist.


title:
Parameter mismatch estimation using large deviations from
  synchronization

abstract:
  We present a method to determine the relative parameter mismatch in a
collection of nearly identical chaotic oscillators by measuring large
deviations from the synchronized state. We demonstrate our method with an
ensemble of slightly different circle maps. We discuss how to apply our method
when there is noise, and show an example where the noise intensity is
comparable to the mismatch.


title:
Soliton Solutions for the Non-autonomous Discrete-time Toda Lattice
  Equation

abstract:
  We construct $N$-soliton solution for the non-autonomous discrete-time Toda
lattice equation, which is a generalization of the discrete-time Toda equation
such that the lattice interval with respect to time is an arbitrary function in
time.


title:
A Rich Example of Geometrically Induced Nonlinearity: From Rotobreathers
  and Kinks to Moving Localized Modes and Resonant Energy Transfer

abstract:
  We present an experimentally realizable, simple mechanical system with linear
interactions whose geometric nature leads to nontrivial, nonlinear dynamical
equations. The equations of motion are derived and their ground state
structures are analyzed. Selective ``static'' features of the model are
examined in the context of nonlinear waves including rotobreathers and
kink-like solitary waves. We also explore ``dynamic'' features of the model
concerning the resonant transfer of energy and the role of moving intrinsic
localized modes in the process.


title:
Nonlinear Lattices Generated from Harmonic Lattices with Geometric
  Constraints

abstract:
  Geometrical constraints imposed on higher dimensional harmonic lattices
generally lead to nonlinear dynamical lattice models. Helical lattices obtained
by such a procedure are shown to be described by sine- plus linear-lattice
equations. The interplay between sinusoidal and quadratic potential terms in
such models is shown to yield localized nonlinear modes identified as intrinsic
resonant modes.


title:
Experimental verification of fidelity decay: From perturbative to Fermi
  Golden Rule regime

abstract:
  The scattering matrix was measured for a flat microwave cavity with
classically chaotic dynamics. The system can be perturbed by small changes of
the geometry. We define the "scattering fidelity" in terms of parametric
correlation functions of scattering matrix elements. In chaotic systems and for
weak coupling the scattering fidelity approaches the fidelity of the closed
system. Without free parameters the experimental results agree with random
matrix theory in a wide range of perturbation strengths, reaching from the
perturbative to the Fermi golden rule regime.


title:
Description of compatible differential-geometric Poisson brackets of the
  first order

abstract:
  Compatible local differential-geometric Poisson brackets of the first order
(Dubrovin-Novikov type) are classified by solutions of modified Sinh-Gordon
equation. It was proved by E.V. Ferapontov. In this paper integrable system
describing compatible non-local differential-geometric Poisson brackets of the
first order (Ferapontov type) is presented in case when one metric is flat and
another one has co-dimension 1. This is a reduction of the Cherednik model
(chiral fields).


title:
Classical Dissipation and Asymptotic Equilibrium via Interaction with
  Chaotic Systems

abstract:
  We study the energy flow between a one dimensional oscillator and a chaotic
system with two degrees of freedom in the weak coupling limit. The oscillator's
observables are averaged over an initially microcanonical ensemble of
trajectories of the chaotic system, which plays the role of an environment for
the oscillator. We show numerically that the oscillator's average energy
exhibits irreversible dynamics and `thermal' equilibrium at long times. We use
linear response theory to describe the dynamics at short times and we derive a
condition for the absorption or dissipation of energy by the oscillator from
the chaotic system. The equilibrium properties at long times, including the
average equilibrium energies and the energy distributions, are explained with
the help of statistical arguments. We also check that the concept of
temperature defined in terms of the `volume entropy' agrees very well with
these energy istributions.


title: The Boussinesq equation and Miura type transformations

abstract:
  A direct method for calculation of Miura type transformations via LA pair is
used for the Boussinesq equation. Quadratic Miura type transformations
connected with local weakly-nonlocal (Maltsev-Novikov) Hamiltonian structures.
Modified systems are presented.


title: Explicit integration of the H\'enon-Heiles Hamiltonians

abstract:
  We consider the cubic and quartic He'non-Heiles Hamiltonians with additional
inverse square terms, which pass the Painleve' test for only seven sets of
coefficients. For all the not yet integrated cases we prove the
singlevaluedness of the general solution. The seven Hamiltonians enjoy two
properties: meromorphy of the general solution, which is hyperelliptic with
genus two and completeness in the Painleve' sense (impossibility to add any
term to the Hamiltonian without destroying the Painleve' property).


title:
On $A_{n-1}^{(1)},B_{n}^{(1)}, C_{n}^{(1)}, D_{n}^{(1)},A_{2n}^{(2)},
  A_{2n-1}^{(2)}$ and $D_{n+1}^{(2)}$ Reflection $K$-Matrices

abstract:
  We present the classification of the most general regular solutions to the
boundary Yang-Baxter equations for vertex models associated with
non-exceptional affine Lie algebras. Reduced solutions found by applying a
limit procedure to the general solutions are discussed. We also present the
list of diagonal $K$-matrices. Special cases are considered separately.