title: Nonlinear elastic polymers in random flow

abstract:
  Polymer stretching in random smooth flows is investigated within the
framework of the FENE dumbbell model. The advecting flow is Gaussian and
short-correlated in time. The stationary probability density function of
polymer extension is derived exactly. The characteristic time needed for the
system to attain the stationary regime is computed as a function of the
Weissenberg number and the maximum length of polymers. The transient relaxation
to the stationary regime is predicted to be exceptionally slow in the proximity
of the coil-stretch transition.


title: An approach to chaotic synchronization

abstract:
  This paper deals with the chaotic oscillator synchronization. A new approach
to the synchronization of chaotic oscillators has been proposed. This approach
is based on the analysis of different time scales in the time series generated
by the coupled chaotic oscillators. It has been shown that complete
synchronization, phase synchronization, lag synchronization and generalized
synchronization are the particular cases of the synchronized behavior called as
"time-scale synchronization". The quantitative measure of chaotic oscillator
synchronous behavior has been proposed. This approach has been applied for the
coupled R\"ossler systems and two coupled Chua's circuits.


title: Chimera States in a Ring of Nonlocally Coupled Oscillators

abstract:
  Arrays of identical limit-cycle oscillators have been used to model a wide
variety of pattern-forming systems, such as neural networks, convecting fluids,
laser arrays, and coupled biochemical oscillators. These systems are known to
exhibit rich collective behavior, from synchrony and traveling waves to
spatiotemporal chaos and incoherence. Recently, Kuramoto and his colleagues
reported a strange new mode of organization--here called the chimera state--in
which coherence and incoherence exist side by side in the same system of
oscillators. Such states have never been seen in systems with either local or
global coupling; they are apparently peculiar to the intermediate case of
nonlocal coupling. Here we give an exact solution for the chimera state, for a
one-dimensional ring of phase oscillators coupled nonlocally by a cosine
kernel. The analysis reveals that the chimera is born in a continuous
bifurcation from a spatially modulated drift state, and dies in a saddle-node
collision with an unstable version of itself.


title:
Chaotic synchronization of coupled electron-wave systems with backward
  waves

abstract:
  The chaotic synchronization of two electron-wave media with interacting
backward waves and cubic phase nonlinearity is investigated in the paper. To
detect the chaotic synchronization regime we use a new approach, the so-called
time scale synchronization [Chaos, 14 (3) 603-610 (2004)]. This approach is
based on the consideration of the infinite set of chaotic signals' phases
introduced by means of continuous wavelet transform. The complex space-time
dynamics of the active media and mechanisms of the time scale synchronization
appearance are considered.


title:
Intermittent generalized synchronization in unidirectionally coupled
  chaotic oscillators

abstract:
  A new behavior type of unidirectionally coupled chaotic oscillators near the
generalized synchronization transition has been detected. It has been shown
that the generalized synchronization appearance is preceded by the intermitted
behavior: close to threshold parameter value the coupled chaotic systems
demonstrate the generalized synchronization most of the time, but there are
time intervals during which the synchronized oscillations are interrupted by
non-synchronous bursts. This type of the system behavior has been called
intermitted generalized synchronization (IGS) by analogy with intermitted lag
synchronization (ILS) [Phys. Rev. E \textbf{62}, 7497 (2000)].


title: Synchronization of chaotic oscillator time scales

abstract:
  This paper deals with the chaotic oscillator synchronization. A new approach
to detect the synchronized behaviour of chaotic oscillators has been proposed.
This approach is based on the analysis of different time scales in the time
series generated by the coupled chaotic oscillators. It has been shown that
complete synchronization, phase synchronization, lag synchronization and
generalized synchronization are the particular cases of the synchronized
behavior called as "time--scale synchronization". The quantitative measure of
chaotic oscillator synchronous behavior has been proposed. This approach has
been applied for the coupled Rossler systems.


title: Resolving isospectral "drums" by counting nodal domains

abstract:
  Several types of systems were put forward during the past decades to show
that there exist {\it isospectral} systems which are {\it metrically}
different. One important class consists of Laplace Beltrami operators for pairs
of flat tori in $\mathbb{R}^n$ with $n\geq 4$. We propose that the spectral
ambiguity can be resolved by comparing the nodal sequences (the numbers of
nodal domains of eigenfunctions, arranged by increasing eigenvalues). In the
case of isospectral flat tori in four dimensions - where a 4-parameters family
of isospectral pairs is known- we provide heuristic arguments supported by
numerical simulations to support the conjecture that the isospectrality is
resolved by the nodal count. Thus - one can {\it count} the shape of a drum (if
it is designed as a flat torus in four dimensions...).


title:
Historical remarks to finite-gap integration theory: elementary
  treatment of the theory

abstract:
  In the example of the Schr\"odinger/KdV equation we give elementary treatment
of the theory of finite-gap integration. The concept is equivalent to two kinds
of Liouvillian integrability: quadrature integrability of linear differential
equations with a parameter (spectral problem) and Liouville's integrability of
finite-dimensional Hamiltonian systems (stationary KdV--equations).
  Three key objects in this field: the new explicit formula for the
$\Psi$-function, trace formula and the Jacobi problem provide a complete
solution.
  Appendix contains Russian translation of two papers of J.Drach


title:
Modulational instability for nonlinear Schrodinger equations with a
  periodic potential

abstract:
  We study the stability properties of periodic solutions to the Nonlinear
Schr\"odinger (NLS) equation with a periodic potential. We exploit the
symmetries of the problem, in particular the Hamiltonian structure and the
$\U(1)$ symmetry. We develop a simple sufficient criterion that guarantees the
existence of a modulational instability spectrum along the imaginary axis. In
the case of small amplitude solutions that bifurcate from the band edges of the
linear problem this criterion becomes especially simple. We find that the small
amplitude solutions corresponding to the band edges alternate stability, with
the first band edge being modulationally unstable in the focusing case, the
second band edge being modulationally unstable in the defocusing case, and so
on. This small amplitude result has a nice physical interpretation in terms of
the effective mass of a particle in the periodic potential. We also consider,
in somewhat less detail, some sideband instabilities in the small amplitude
limit. We find that, depending on the Krein signature of the collision, these
can be of one of two types. Finally we illustrate this with some exact
calculations in the case where $V(x)$ is an elliptic function, where all of the
relevant calculations can be done explicitly.


title:
Meromorphic traveling wave solutions of the Kuramoto-Sivashinsky
  equation

abstract:
  We determine all cases when there exists a meromorphic solution of the third
order ODE describing traveling waves solutions of the Kuramoto-Sivashinsky
equation. It turns out that there are no other meromorphic solutions besides
those explicit solutions found by Kuramoto and Kudryashov. The general method
used in this paper, based on Nevanlinna theory, is applicable to finding all
meromorphic solutions of a wide class of non-linear ODE.
  Keywords: Kuramoto and Sivashinsky equation, meromorphic functions, elliptic
functions, Nevanlinna theory.


title:
Numerical Computation of the Stable and Unstable Manifolds of Invariant
  Tori

abstract:
  We develop an iterative technique for computing the unstable and stable
eigenfunctions of the invariant tori of diffeomorphisms. Using the approach of
Jorba, the linearized equations are rewritten as a generalized eigenvalue
problem. Casting the system in this light allows us to take advantage of the
speed of eigenvalue solvers and create an efficient method for finding the
first order approximations to the invariant manifolds of the torus. We present
a numerical scheme based on the power method that can be used to determine the
behavior normal to such tori, and give some examples of the application of the
method. We confirm the qualitative conclusions of the Melnikov calculations of
Lomel\'i and Meiss (2003) for a volume-preserving mapping.


title:
Parametric Representation for the Multisoliton Solution of the
  Camassa-Holm Equation

abstract:
  The parametric representation is given to the multisoliton solution of the
Camassa-Holm equation. It has a simple structure expressed in terms of
determinants. The proof of the solution is carried out by an elementary theory
of determinanats. The large time asymptotic of the solution is derived with the
fomula for the phase shift. The latter reveals a new feature when compared with
the one for the typical soliton solutions. The peakon limit of the phase shift
ia also considered, showing that it reproduces the known result.


title: Reentrant Hexagons in non-Boussinesq Convection

abstract:
  While non-Boussinesq hexagonal convection patterns are well known to be
stable close to threshold (i.e. for Rayleigh numbers $R \approx R_c$), it has
often been assumed that they are always unstable to rolls already for slightly
higher Rayleigh numbers. Using the {\em incompressible} Navier-Stokes equations
for parameters corresponding to water as a working fluid, we perform full
numerical stability analyses of hexagons in the strongly nonlinear regime
($\epsilon\equiv R-R_c/R_c=\mathcal{O}(1)$). We find `reentrant' behavior of
the hexagons, i.e. as $\epsilon$ is increased they can lose and {\it regain}
stability. This can occur for values of $\epsilon$ as low as $\epsilon=0.2$. We
identify two factors contributing to the reentrance: i) the hexagons can make
contact with a hexagon attractor that has been identified recently in the
nonlinear regime even in Boussinesq convection (Assenheimer & Steinberg (1996);
Clever & Busse (1996)) and ii) the non-Boussinesq effects increase with
$\epsilon$. Using direct simulations for circular containers we show that the
reentrant hexagons can prevail even for side-wall conditions that favor
convection in the form of the competing stable rolls. For sufficiently strong
non-Boussinesq effects hexagons become stable even over the whole
$\epsilon$-range considered, $0 \le \epsilon \le 1.5$.


title:
Cluster synchronization in an ensemble of neurons interacting through
  chemical synapses

abstract:
  In networks of periodically firing spiking neurons that are interconnected
with chemical synapses, we analyze cluster state, where an ensemble of neurons
are subdivided into a few clusters, in each of which neurons exhibit perfect
synchronization. To clarify stability of cluster state, we decompose linear
stability of the solution into two types of stabilities: stability of mean
state and stabilities of clusters. Computing Floquet matrices for these
stabilities, we clarify the total stability of cluster state for any types of
neurons and any strength of interactions even if the size of networks is
infinitely large. First, we apply this stability analysis to investigating
synchronization in the large ensemble of integrate-and-fire (IF) neurons. In
one-cluster state we find the change of stability of a cluster, which
elucidates that in-phase synchronization of IF neurons occurs with only
inhibitory synapses. Then, we investigate entrainment of two clusters of IF
neurons with different excitability. IF neurons with fast decaying synapses
show the low entrainment capability, which is explained by a pitchfork
bifurcation appearing in two-cluster state with change of synapse decay time
constant. Second, we analyze one-cluster state of Hodgkin-Huxley (HH) neurons
and discuss the difference in synchronization properties between IF neurons and
HH neurons.


title: On Reversible Cellular Automata with Triplet Local Rules

abstract:
  Bijections between sets may be seen as discrete (or crisp) unitary
transformations used in quantum computations. So discrete quantum cellular
automata are cellular automata with reversible transition functions. This note
studies on 1d reversible cellular automata with triplet local rules.


title: Discrete Physics: a new way to look at cryptography

abstract:
  This paper shows that Physics is very close to the substitution-diffusion
paradigm of symmetric ciphers. Based on this analogy, we propose a new
cryptographic algorithm. Statistical Physics gives design principles to devise
fast, scalable and secure encryption systems. In particular, increasing space
dimension and considering larger data blocks improve both speed and security,
allowing us to reach high throughput (larger than 10Gb/s on dedicated HW). The
physical approach enlarges the way to look at cryptography and is expected to
bring new tools and concepts to better understand and quantify security
aspects.


title:
Gaudin magnet with impurity and its generalized Knizhnik-Zamolodchikov
  equation

abstract:
  This work is concerned with the formulation of the boundary quantum inverse
scattering method for the xxz Gaudin magnet coupled to boundary impurities with
arbitrary exchange constants. The Gaudin magnet is diagonalized by taking a
quasi-classical limit of the inhomogeneous lattice. Using the method proposed
by Babujian, the integral representation for the solution of the
Knizhnik-Zamolodchikov equation is explictly constructed and its rational limit
discussed.


title:
Spatial dispersive shock waves generated in supersonic flow of
  Bose-Einstein condensate past slender body

abstract:
  Supersonic flow of Bose-Einstein condensate past macroscopic obstacles is
studied theoretically. It is shown that in the case of large obstacles the
Cherenkov cone transforms into a stationary spatial shock wave which consists
of a number of spatial dark solitons. Analytical theory is developed for the
case of obstacles having a form of a slender body. This theory explains
qualitatively the properties of such shocks observed in recent experiments on
nonlinear dynamics of condensates of dilute alkali gases.


title: On the dbar-dressing method applicable to heavenly equation

abstract:
  The $\dbar$-dressing scheme based on local nonlinear vector $\dbar$-problem
is developed. It is applicable to multidimensional nonlinear equations for
vector fields, and, after Hamiltonian reduction, to heavenly equation.
Hamiltonian reduction is described explicitely in terms of the $\dbar$-data. An
analogue of Hirota bilinear identity for heavenly equation hierarchy is
introduced, $\tau$-function for the hierarchy is defined. Addition formulae
(generating equations) for the $\tau$-function are found. It is demonstrated
that $\tau$-function for heavenly equation hierarchy is given by the action for
$\dbar$-problem evaluated on the solution of this problem.


title: Approximate Description of the Mandelbrot Set. Thermodynamic Analogy

abstract:
  Analogy between an approximate version of Feigenbaum renormalization group
analysis in complex domain and the phase transition theory of Yang-Lee (based
on consideration of formally complexified thermodynamic values) is discussed.
It is shown that the Julia sets of the renormalization transformation
correspond to the approximation of Mandelbrot set of the original map. New
aspects of analogy between the theory of dynamical systems and the phase
transition theory are uncovered.


title:
A cohomological construction of integrable hierarchies of hydrodynamic
  type

abstract:
  We explain how to use the theory of bidifferential ideals to construct
integrable hierarchies of hydrodynamic type.


title: Zero tension Kardar-Parisi-Zhang equation in (d+1)- Dimensions

abstract:
  The joint probability distribution function (PDF) of the height and its
gradients is derived for a zero tension $d+1$-dimensional Kardar-Parisi-Zhang
(KPZ) equation. It is proved that the height`s PDF of zero tension KPZ equation
shows lack of positivity after a finite time $t_{c}$. The properties of zero
tension KPZ equation and its differences with the case that it possess an
infinitesimal surface tension is discussed. Also potential relation between the
time scale $t_{c}$ and the singularity time scale $t_{c, \nu \to 0}$ of the KPZ
equation with an infinitesimal surface tension is investigated.


title: Projective Synchronization and Control of Unified Chaotic System

abstract:
  The problem of projective synchronization(ps) and control are studied in
modified unified chaotic system which possess partially linearity property. The
desired ratio factor of corresponding subsystem variable could be obtained by
state feedback control. Theoretical analysis and numerical simulations are
provided to illustrate the projective synchronization and the feasibility of
the proposed control method. The effect on projective synchronization caused by
channel noise and parameter mismatch are investigated in detail, the results
showed that parameter mismatch has more effect on projective synchronization
than channel noise does, which may be applied to chaotic secure communications.


title: What does integrability of finite-gap or soliton potentials mean?

abstract:
  In the example of the Schr\"odinger/KdV equation we treat the theory as
equivalence of two concepts of Liouvillian integrability: quadrature
integrability of linear differential equations with a parameter (spectral
problem) and Liouville's integrability of finite-dimensional Hamiltonian
systems (stationary KdV--equations). Three key objects in this field: new
explicit $\Psi$-function, trace formula and the Jacobi problem provide a
complete solution. The $\Theta$-function language is derivable from these
objects and used for ultimate representation of a solution to the inversion
problem. Relations with non-integrable equations are discussed also.


title:
Symbolic Software for the Painleve Test of Nonlinear Ordinary and
  Partial Differential Equations

abstract:
  The automation of the traditional Painleve test in Mathematica is discussed.
The package PainleveTest.m allows for the testing of polynomial systems of
ordinary and partial differential equations which may be parameterized by
arbitrary functions (or constants). Except where limited by memory, there is no
restriction on the number of independent or dependent variables. The package is
quite robust in determining all the possible dominant behaviors of the Laurent
series solutions of the differential equation. The omission of valid dominant
behaviors is a common problem in many implementations of the Painleve test, and
these omissions often lead to erroneous results. Finally, our package is
compared with the other available implementations of the Painleve test.


title:
Tyurin parameters of commuting pairs and infinite dimensional Grassmann
  manifold

abstract:
  Commuting pairs of ordinary differential operators are classified by a set of
algebro-geometric data called ``algebraic spectral data''. These data consist
of an algebraic curve (``spectral curve'') $\Gamma$ with a marked point
$\gamma_\infty$, a holomorphic vector bundle $E$ on $\Gamma$ and some
additional data related to the local structure of $\Gamma$ and $E$ in a
neighborhood of $\gamma_\infty$. If the rank $r$ of $E$ is greater than 1, one
can use the so called ``Tyurin parameters'' in place of $E$ itself. The Tyurin
parameters specify the pole structure of a basis of joint eigenfunctions of the
commuting pair. These data can be translated to the language of an infinite
dimensional Grassmann manifold. This leads to a dynamical system of the
standard exponential flows on the Grassmann manifold, in which the role of
Tyurin parameters and some other parameters is made clear.


title: Chemo-Sensitive Running Droplet

abstract:
  Chemical control of the spontaneous motion of a reactive oil droplet moving
on a glass substrate under an aqueous phase is reported. Experimental results
show that the self-motion of an oil droplet is confined on an acid-treated
glass surface. The transient behavior of oil-droplet motion is also observed
with a high-speed video camera. A mathematical model that incorporates the
effect of the glass surface charge is built based on the experimental
observation of oil-droplet motion. A numerical simulation of this mathematical
model reproduced the essential features concerning confinement within a certain
chemical territory of oil-droplet motion, and also its transient behavior. Our
results may shed light on physical aspects of reactive spreading and a
chemotaxis in living things.


title: Energy Complexity of Software in Embedded Systems

abstract:
  The importance of low power consumption is widely acknowledged due to the
increasing use of portable devices, which require minimizing the consumption of
energy. The energy in a computational system depends heavily on the software
being executed, since it determines the activity in the underlying circuitry.
In this paper we introduce the notion of energy complexity of an algorithm for
estimating the required energy consumption. As test vehicle we employ matrix
multiplication algorithms and from the results it can be observed that energy
complexity in combination with computational complexity, provides an accurate
estimation for the energy consumed in the system.


title: Vortex transmutation

abstract:
  Using group theory arguments and numerical simulations, we demonstrate the
possibility of changing the vorticity or topological charge of an individual
vortex by means of the action of a system possessing a discrete rotational
symmetry of finite order. We establish on theoretical grounds a "transmutation
pass rule'' determining the conditions for this phenomenon to occur and
numerically analize it in the context of two-dimensional optical lattices or,
equivalently, in that of Bose-Einstein condensates in periodic potentials.


title: A General Methodology for Designing Self-Organizing Systems

abstract:
  Our technologies complexify our environments. Thus, new technologies need to
deal with more and more complexity. Several efforts have been made to deal with
this complexity using the concept of self-organization. However, in order to
promote its use and understanding, we must first have a pragmatic understanding
of complexity and self-organization. This paper presents a conceptual framework
for speaking about self-organizing systems. The aim is to provide a methodology
useful for designing and controlling systems developed to solve complex
problems. First, practical notions of complexity and self-organization are
given. Then, starting from the agent metaphor, a conceptual framework is
presented. This provides formal ways of speaking about "satisfaction" of
elements and systems. The main premise of the methodology claims that reducing
the "friction" or "interference" of interactions between elements of a system
will result in a higher "satisfaction" of the system, i.e. better performance.
The methodology discusses different ways in which this can be achieved. A case
study on self-organizing traffic lights illustrates the ideas presented in the
paper.


title:
Identification and Calculation of the Universal Maximum Drag Reduction
  Asymptote by Polymers in Wall Bounded Turbulence

abstract:
  Drag reduction by polymers in wall turbulence is bounded from above by a
universal maximal drag reduction (MDR) velocity profile that is a log-law,
estimated experimentally by Virk as $V^+(y^+)\approx 11.7 \log y^+ -17$. Here
$V^+(y)$ and $y^+$ are the mean streamwise velocity and the distance from the
wall in "wall" units. In this Letter we propose that this MDR profile is an
edge solution of the Navier-Stokes equations (with an effective viscosity
profile) beyond which no turbulent solutions exist. This insight rationalizes
the universality of the MDR and provides a maximum principle which allows an
ab-initio calculation of the parameters in this law without any viscoelastic
experimental input.


title: Phase synchronization from noisy univariate signals

abstract:
  We present methods for detecting phase synchronization of two
unidirectionally coupled, self-sustained noisy oscillators from a signal of the
driven oscillator alone. One method detects soft, another hard phase locking.
Both are applied to the problem of detecting phase synchronization in von
Karman vortex flow meters.


title: Accumulation of embedded solitons in systems with quadratic nonlinearity

abstract:
  Previous numerical studies have revealed the existence of embedded solitons
(ESs) in a class of multi-wave systems with quadratic nonlinearity, families of
which seem to emerge from a critical point in the parameter space, where the
zero solution has a fourfold zero eigenvalue. In this paper, the existence of
such solutions is studied in a three-wave model. An appropriate rescaling casts
the system in a normal form, which is universal for models supporting ESs
through quadratic nonlinearities. The normal-form system contains a single
irreducible parameter $\epsilon $, and is tantamount to the basic model of
type-I second-harmonic generation. An analytical approximation of WKB type
yields an asymptotic formula for the distribution of discrete values of
$\epsilon $ at which the ESs exist. Comparison with numerical results shows
that the asymptotic formula yields an exact value of the scaling index, -6/5,
and a fairly good approximation for the numerical factor in front of the
scaling term.


title:
Differential-geometric approach to the integrability of hydrodynamic
  chains: the Haantjes tensor

abstract:
  The integrability of an m-component system of hydrodynamic type, u_t=V(u)u_x,
by the generalized hodograph method requires the diagonalizability of the mxm
matrix V(u). This condition is known to be equivalent to the vanishing of the
corresponding Haantjes tensor. We generalize this approach to hydrodynamic
chains -- infinite-component systems of hydrodynamic type for which the
infinite matrix V(u) is `sufficiently sparse'. For such systems the Haantjes
tensor is well-defined, and the calculation of its components involves finite
summations only. We illustrate our approach by classifying broad classes of
conservative and Hamiltonian hydrodynamic chains with the zero Haantjes tensor.
We prove that the vanishing of the Haantjes tensor is a necessary condition for
a hydrodynamic chain to possess an infinity of semi-Hamiltonian hydrodynamic
reductions, thus providing an easy-to-verify necessary condition for the
integrability.


title:
Oscillatory convection in binary mixtures: thermodiffusion, solutal
  buoyancy, and advection

abstract:
  The role of thermodiffusive generation of concentration fluctuations via the
Soret effect, their contribution to the buoyancy forces that drive convection,
the advective mixing effect of the latter, and the diffusive homogenisation are
compared and elucidated for oscillatory convection. Numerically obtained
solutions of the field equations in the form of spatially extended relaxed
traveling waves, of standing waves, and of the transient growth of standing
waves and their transition to traveling waves are discussed as well as
spatially localized convective states of traveling waves that are surrounded by
the quiescent fluid.


title: On integrability of finite-gap potentials

abstract:
  For spectral problems, determined by ordinary differential equations, we
consider finite-gap potentials as exact solvable by quadratures in the spirit
of the Picard--Vessio theory and suggest that this class is the only one.
Ideology goes back to works by Drach 1919 but has not been mentioned in the
modern literature. We exhibit new examples and technique for obtaining
necessary ingredients of exact integrability: new formula for the
$\Psi$-function, main trace formula and problem of inversion of Abelian
integrals.


title: Pattern formation in parametric sound generation

abstract:
  Pattern formation of sound is predicted in a driven resonator where
subharmonic generation takes place. A model allowing for diffraction of the
fields (large-aspect ratio limit) is derived by means of the multiple scale
expansions technique. An analysis of the solutions and its stability against
space-dependent perturbations is performed in detail considering the
distinctive peculiarities of the acoustical system. Numerical integration
confirm the analytical predictions, and shows the possibility of patterns in
the form of stripes and squares.


title: Computational Complexity as a Source of Thermodynamic Irreversibility

abstract:
  In spite of the fact that the Newtonian dynsmics of the underlying molecules
do not seem to favor one direction of time over its opposite, the
non-decreasing entropy of macroscopic physical systems provides a unique
direction to 'the arrow of time'. This paper proposes that the directionality
of time arises from the intrinsic computational complexity of molecular
dynamics. In particular, the following question about a hard sphere gas is
proven to be Np-complete: Given a set of input signals, in which TRUE is
represented by an actual sphere trajectory and FALSE is represented by a
trajectory that is not followed because an input signal is not TRUE; a set of
'routing' spheres that follow the same trajectory for all choices of input
signals and that collide with the signal trajectories at pre-specified points;
does there exist a set of inputs that would produce a specified final
configuration? The time asymmetry arises because the computational effort, and
thus the actual time required to determine the final configuration from the
starting configuration grows only linearly with the number of particles, N, but
the computational effort required to determine the answer to the above
Np-complete problem probably grows faster than any polynomial in N. We conclude
by arguing that, as N approaches infinity, the resulting temporal asymmetry is
sufficient to justify the molecular chaos assumption (Stosszahlansatz) used in
deriving the Boltzmann equation.


title:
Gel'fand-Zakharevich Systems and Algebraic Integrability: the Volterra
  Lattice Revisited

abstract:
  In this paper we will discuss some features of the bihamiltonian method for
solving the Hamilton-Jacobi (H-J) equations by Separation of Variables, and
make contact with the theory of Algebraic Complete Integrability and,
specifically, with the Veselov--Novikov notion of algebro-geometric (AG)
Poisson brackets. The "bihamiltonian" method for separating the Hamilton-Jacobi
equations is based on the notion of pencil of Poisson brackets and on the
Gel'fand-Zakharevich (GZ) approach to integrable systems. We will herewith show
how, quite naturally, GZ systems may give rise to AG Poisson brackets, together
with specific recipes to solve the H-J equations. We will then show how this
setting works by framing results by Veselov and Penskoi about the algebraic
integrability of the Volterra lattice within the bihamiltonian setting for
Separation of Variables.


title: Bazhanov-Stroganov model from 3D approach

abstract:
  We apply a 3-dimensional approach to describe a new parametrization of the
L-operators for the 2-dimensional Bazhanov-Stroganov (BS) integrable spin model
related to the chiral Potts model. This parametrization is based on the
solution of the associated classical discrete integrable system. Using a
3-dimensional vertex satisfying a modified tetrahedron equation, we construct
an operator which generalizes the BS quantum intertwining matrix S. This
operator describes the isospectral deformations of the integrable BS model.


title:
Resonance-assisted tunneling in three degrees of freedom without
  discrete symmetry

abstract:
  We study dynamical tunneling in a near-integrable Hamiltonian with three
degrees of freedom. The model Hamiltonian does not have any discrete symmetry.
Despite this lack of symmetry we show that the mixing of near-degenerate
quantum states is due to dynamical tunneling mediated by the nonlinear
resonances in the classical phase space. Identifying the key resonances allows
us to suppress the dynamical tunneling via the addition of weak
counter-resonant terms.


title:
Spontaneously generated waves and obstacles to integrability in
  perturbed evolution equations

abstract:
  The perturbed Burgers and KdV equations are considered. Often, the
perturbation excites waves that are different from the solution one is seeking.
In the case of the Burgers equation, the spontaneously generated wave is also a
solution of the equation. In contrast, in the case of the KdV equation, this
wave is constructed from new (non-KdV) solitons that undergo an elastic
collision around the origin. Their amplitudes have opposite signs, which they
exchange upon collision. The perturbation then contains terms, which represent
coupling between the solution and these spontaneously generated waves. Whereas
the unperturbed equations describe gradient systems, these coupling terms may
be non-gradient. In that case, they turn out to be obstacles to asymptotic
integrability, encountered in the analysis of the solutions of the perturbed
evolution equations.


title:
Gap soliton gating, dissociation, and retrieval via defect mode
  excitation in a resonant photonic crystal

abstract:
  We consider the interaction within a bunch of two coherent optical pulses in
a one dimensional, resonant photonic crystal which includes a defect produced
by a coherent pump. Using numerical methods, the defect is shown to provide a
selective reversible trap for a gap soliton mediated by the long-range
coupling. This opens up new opportunities for signal transmission control and
light localization.


title: Bistability in sine-Gordon: the ideal switch

abstract:
  The sine-Gordon equation, used as the representative nonlinear wave equation,
presents a bistable behavior resulting from nonlinearity and generating
hysteresis properties. We show that the process can be understood in a
comprehensive analytical formulation and that it is a generic property of
nonlinear systems possessing a natural band gap. The approach allows to
discover that sine-Gordon can work as an it ideal switch by reaching a
transmissive regime with vanishing driving amplitude.

categories: nlin.PS cond-mat.stat-mech nlin.SI physics.class-ph


title: Post-critical set and non existence of preserved meromorphic two-forms

abstract:
  We present a family of birational transformations in $ CP_2$ depending on
two, or three, parameters which does not, generically, preserve meromorphic
two-forms. With the introduction of the orbit of the critical set (vanishing
condition of the Jacobian), also called ``post-critical set'', we get some new
structures, some "non-analytic" two-form which reduce to meromorphic two-forms
for particular subvarieties in the parameter space. On these subvarieties, the
iterates of the critical set have a polynomial growth in the \emph{degrees of
the parameters}, while one has an exponential growth out of these subspaces.
The analysis of our birational transformation in $ CP_2$ is first carried out
using Diller-Favre criterion in order to find the complexity reduction of the
mapping. The integrable cases are found. The identification between the
complexity growth and the topological entropy is, one more time, verified. We
perform plots of the post-critical set, as well as calculations of Lyapunov
exponents for many orbits, confirming that generically no meromorphic two-form
can be preserved for this mapping. These birational transformations in $ CP_2$,
which, generically, do not preserve any meromorphic two-form, are extremely
similar to other birational transformations we previously studied, which do
preserve meromorphic two-forms. We note that these two sets of birational
transformations exhibit totally similar results as far as topological
complexity is concerned, but drastically different results as far as a more
``probabilistic'' approach of dynamical systems is concerned (Lyapunov
exponents). With these examples we see that the existence of a preserved
meromorphic two-form explains most of the (numerical) discrepancy between the
topological and probabilistic approach of dynamical systems.


title: B\"acklund transformations for fourth Painlev\'e hierarchies

abstract:
  B\"acklund transformations (BTs) for ordinary differential equations (ODEs),
and in particular for hierarchies of ODEs, are a topic of great current
interest. Here we give an improved method of constructing BTs for hierarchies
of ODEs. This approach is then applied to fourth Painlev\'e ($P_{IV}$)
hierarchies recently found by the same authors [{\em Publ. Res. Inst. Math.
Sci. (Kyoto)} {\bf 37} 327--347 (2001)]. We show how the known pattern of BTs
for $P_{IV}$ can be extended to our $P_{IV}$ hierarchies. Remarkably, the BTs
required to do this are precisely the Miura maps of the dispersive water wave
hierarchy. We also obtain the important result that the fourth Painlev\'e
equation has only one nontrivial fundamental BT, and not two such as is
frequently stated.


title: Dynamic characterisers of spatiotemporal intermittency

abstract:
  We study spatiotemporal intermittency in a system of coupled sine circle
maps. The phase diagram of the system shows parameter regimes where the STI
lies in the directed percolation class, as well as regimes which show pure
spatial intermittency (where the temporal behaviour is regular) which do not
belong to the DP class. Thus, both DP and non-DP behaviour can be seen in the
same system. The signature of DP and non-DP behaviour can be seen in the
dynamic characterisers, viz. the spectrum of eigenvalues of the linear
stability matrix of the evolution equation, as well as in the multifractal
spectrum of the eigenvalue distribution. The eigenvalue spectrum of the system
in the DP regimes is continuous, whereas it shows evidence of level repulsion
in the form of gaps in the spectrum in the non-DP regime. The multifractal
spectrum of the eigenvalue distribution also shows the signature of DP and
non-DP behaviour. These results have implications for the manner in which
correlations build up in extended systems.


title:
Singular limit of Hele-Shaw flow and dispersive regularization of shock
  waves

abstract:
  We study a family of solutions to the Saffman-Taylor problem with zero
surface tension at a critical regime. In this regime, the interface develops a
thin singular finger. The flow of an isolated finger is given by the Whitham
equations for the KdV integrable hierarchy. We show that the flow describing
bubble break-off is identical to the Gurevich-Pitaevsky solution for
regularization of shock waves in dispersive media. The method provides a scheme
for the continuation of the flow through singularites.

categories: nlin.SI cond-mat.soft nlin.PS physics.flu-dyn


title:
Traveling Wave Fronts and Localized Traveling Wave Convection in Binary
  Fluid Mixtures

abstract:
  Nonlinear fronts between spatially extended traveling wave convection (TW)
and quiescent fluid and spatially localized traveling waves (LTWs) are
investigated in quantitative detail in the bistable regime of binary fluid
mixtures heated from below. A finite-difference method is used to solve the
full hydrodynamic field equations in a vertical cross section of the layer
perpendicular to the convection roll axes. Results are presented for
ethanol-water parameters with several strongly negative separation ratios where
TW solutions bifurcate subcritically. Fronts and LTWs are compared with each
other and similarities and differences are elucidated. Phase propagation out of
the quiescent fluid into the convective structure entails a unique selection of
the latter while fronts and interfaces where the phase moves into the quiescent
state behave differently. Interpretations of various experimental observations
are suggested.


title: Synchrony of limit-cycle oscillators induced by random external impulses

abstract:
  The mechanism of phase synchronization between uncoupled limit-cycle
oscillators induced by common external impulsive forcing is analyzed. By
reducing the dynamics of the oscillator to a random phase map, it is shown that
phase synchronization generally occurs when the oscillator is driven by weak
external impulses in the limit of large inter-impulse intervals. The case where
the inter-impulse intervals are finite is also analyzed perturbatively for
small impulse intensity. For weak Poissonian impulses, it is shown that the
phase synchronization persists up to the first order approximation.


title: Multi-Hamiltonian structure of Plebanski's second heavenly equation

abstract:
  We show that Plebanski's second heavenly equation, when written as a
first-order nonlinear evolutionary system, admits multi-Hamiltonian structure.
Therefore by Magri's theorem it is a completely integrable system. Thus it is
an example of a completely integrable system in four dimensions.

categories: nlin.SI gr-qc hep-th math-ph math.DG math.MP


title:
The recurrence time of Dansgaard-Oeschger events and limits on the
  possible periodic component

abstract:
  By comparing the high-resolution isotopic records from the GRIP and NGRIP
icecores, we approximately separate the climate signal from local noise to
obtain an objective criterion for defining Dansgaard-Oeschger events. Our
analysis identifies several additional short lasting events, increasing the
total number of DO events to 27 in the period 12-90 kyr BP. The quasi-regular
occurrence of the DO events could indicate a stochastic or coherent resonance
mechanism governing their origin. From the distribution of waiting times we
obtain a statistical upper bound on the strength of a possible periodic
forcing. This finding indicates that the climate shifts are purely noise driven
with no underlying periodicity.


title:
Replicator dynamics with mutations for games with a continuous strategy
  space

abstract:
  A partial differential equation is derived, describing the replicator
dynamics with mutations of games with a continuous strategy space. This
equation is then applied to continuous versions of symmetric 2x2 games, such as
the Prisoners Dilemma, Hawk-Dove and Coordination games, and to the Ultimatum
Game. In the latter case, we find that adding even a small mutation term to the
replicator equation leads to a solution where the average offer is
significantly larger than zero.


title:
New Cellular Automata associated with the Schroedinger Discrete Spectral
  Problem

abstract:
  New Cellular Automata associated with the Schroedinger discrete spectral
problem are derived. These Cellular Automata possess an infinite (countable)
set of constants of motion.


title: Experimental study of two-dimensional enstrophy cascade

abstract:
  We study the direct enstrophy cascade in a two-dimensional flow generated in
an electromagnetically driven thin layer of fluid. Due to the presence of
bottom friction, the energy spectrum deviates from the classical Kraichnan
prediction $k^{-3}$. We find that the correction to the spectral slope depends
on the thickness on the layer, in agreement with a theoretical prediction based
on the analogy with passive scalar statistics.


title:
All-Optical Generation and Steering of Spatial Solitons in Discrete
  Waveguide Array

abstract:
  We numerically study Stokes beam generation in an array of discrete
waveguides. The feasibility of generation and steering of spatial solitons due
to nonlinear Raman response is demonstrated for the first time


title: Independent Component Analysis of Spatiotemporal Chaos

abstract:
  Two types of spatiotemporal chaos exhibited by ensembles of coupled nonlinear
oscillators are analyzed using independent component analysis (ICA). For
diffusively coupled complex Ginzburg-Landau oscillators that exhibit smooth
amplitude patterns, ICA extracts localized one-humped basis vectors that
reflect the characteristic hole structures of the system, and for nonlocally
coupled complex Ginzburg-Landau oscillators with fractal amplitude patterns,
ICA extracts localized basis vectors with characteristic gap structures.
Statistics of the decomposed signals also provide insight into the complex
dynamics of the spatiotemporal chaos.


title: Poisson integrators

abstract:
  An overview of Hamiltonian systems with noncanonical Poisson structures is
given. Examples of bi-Hamiltonian ode's, pde's and lattice equations are
presented. Numerical integrators using generating functions, Hamiltonian
splitting, symplectic Runge-Kutta methods are discussed for Lie-Poisson systems
and Hamiltonian systems with a general Poisson structure. Nambu-Poisson systems
and the discrete gradient methods are also presented.


title:
Synchronization of spectral components and its regularities in chaotic
  dynamical systems

abstract:
  The chaotic synchronization regime in coupled dynamical systems is
considered. It has been shown, that the onset of synchronous regime is based on
the appearance of the phase relation between interacting chaotic oscillators
frequency components of Fourier spectra. The criterion of synchronization of
spectral components as well as the measure of synchronization have been
discussed. The universal power law has been described. The main results are
illustrated by coupled R\"ossler systems, Van-der-Pol and Van-der-Pol-Duffing
oscillators.


title:
Hamiltonian structures of fermionic two-dimensional Toda lattice
  hierarchies

abstract:
  By exhibiting the corresponding Lax pair representations we propose a wide
class of integrable two-dimensional (2D) fermionic Toda lattice (TL)
hierarchies which includes the 2D N=(2|2) and N=(0|2) supersymmetric TL
hierarchies as particular cases. We develop the generalized graded R-matrix
formalism using the generalized graded bracket on the space of graded operators
with involution generalizing the graded commutator in superalgebras, which
allows one to describe these hierarchies in the framework of the Hamiltonian
formalism and construct their first two Hamiltonian structures. The first
Hamiltonian structure is obtained for both bosonic and fermionic Lax operators
while the second Hamiltonian structure is established for bosonic Lax operators
only.


title:
Scarred Resonances and Steady Probability Distribution in a Chaotic
  Microcavity

abstract:
  We investigate scarred resonances of a stadium-shaped chaotic microcavity. It
is shown that two components with different chirality of the scarring pattern
are slightly rotated in opposite ways from the underlying unstable periodic
orbit, when the incident angles of the scarring pattern are close to the
critical angle for total internal reflection. In addition, the correspondence
of emission pattern with the scarring pattern disappears when the incident
angles are much larger than the critical angle. The steady probability
distribution gives a consistent explanation about these interesting phenomena
and makes it possible to expect the emission pattern in the latter case.


title: Generalized BBV Models for Weighted Complex Networks

abstract:
  We will introduce two evolving models that characterize weighted complex
networks. Though the microscopic dynamics are different, these models are found
to bear a similar mathematical framework, and hence exhibit some common
behaviors, for example, the power-law distributions and evolution of degree,
weight and strength. We also study the nontrivial clustering coefficient C and
tunable degree assortativity coefficient r, depending on specific parameters.
Most results are supported by present empirical evidences, and may provide us
with a better description of the hierarchies and organizational architecture of
weighted networks. Our models have been inspired by the weighted network model
proposed by Alain Barrat et al. (BBV for short), and can be considered as a
meaningful development of their original work.


title:
Freedom in the Expansion and Obstacles to Integrability in
  Multiple-Soliton Solutions of the Perturbed KdV Equation

abstract:
  The construction of a solution of the perturbed KdV equation encounters
obstacles to asymptotic integrability beyond the first order, when the
zero-order approximation is a multiple-soliton wave. In the standard analysis,
the obstacles lead to the loss of integrability of the Normal Form, resulting
in a zero-order term, which does not have the simple structure of the solution
of the unperturbed equation. Exploiting the freedom in the perturbative
expansion, we propose an algorithm that shifts the effect of the obstacles from
the Normal Form to the higher-order terms. The Normal Form then remains
integrable, and the zero-order approximation retains the multiple-soliton
structure of the unperturbed solution. The obstacles are expressed in terms of
symmetries of the unperturbed equation, and decay exponentially away from the
soliton-interaction region. As a result, they generate a bounded correction
term, which decays exponentially away from the origin in the x-t plane. The
computation is performed through second order.


title:
A network analysis of committees in the United States House of
  Representatives

abstract:
  Network theory provides a powerful tool for the representation and analysis
of complex systems of interacting agents. Here we investigate the United States
House of Representatives network of committees and subcommittees, with
committees connected according to ``interlocks'' or common membership. Analysis
of this network reveals clearly the strong links between different committees,
as well as the intrinsic hierarchical structure within the House as a whole. We
show that network theory, combined with the analysis of roll call votes using
singular value decomposition, successfully uncovers political and
organizational correlations between committees in the House without the need to
incorporate other political information.

categories: nlin.AO cs.MA math.ST physics.data-an physics.soc-ph stat.TH


title: Spatial correlations in SIR epidemic models

abstract:
  We investigate the role of global mixing in epidemic processes. We first
construct a simplified model of the SIR epidemic using a realistic population
distribution. Using this model, we examine possible mechanisms for destruction
of spatial correlations, in an attempt to produce correlation curves similar to
those reported recently for real epidemiological data. We find that
introduction of a long-range interaction destroys spatial correlations very
easily if neighbourhood sizes are homogeneous. For inhomogeneous
neighbourhoods, very strong long-range coupling is required to achieve a
similar effect.


title:
Integrable flows and Backlund transformations on extended Stiefel
  varieties with application to the Euler top on the Lie group SO(3)

abstract:
  We show that the $m$-dimensional Euler--Manakov top on $so^*(m)$ can be
represented as a Poisson reduction of an integrable Hamiltonian system on a
symplectic extended Stiefel variety $\bar{\cal V}(k,m)$, and present its Lax
representation with a rational parameter.
  We also describe an integrable two-valued symplectic map $\cal B$ on the
4-dimensional variety ${\cal V}(2,3)$. The map admits two different reductions,
namely, to the Lie group SO(3) and to the coalgebra $so^*(3)$.
  The first reduction provides a discretization of the motion of the classical
Euler top in space and has a transparent geometric interpretation, which can be
regarded as a discrete version of the celebrated Poinsot model of motion and
which inherits some properties of another discrete system, the elliptic
billiard.
  The reduction of $\cal B$ to $so^*(3)$ gives a new explicit discretization of
the Euler top in the angular momentum space, which preserves first integrals of
the continuous system.


title:
Steady-state stabilization due to random delays in maps with
  self-feedback loops and in globally delayed-coupled maps

abstract:
  We study the stability of the fixed-point solution of an array of mutually
coupled logistic maps, focusing on the influence of the delay times,
$\tau_{ij}$, of the interaction between the $i$th and $j$th maps. Two of us
recently reported [Phys. Rev. Lett. {\bf 94}, 134102 (2005)] that if
$\tau_{ij}$ are random enough the array synchronizes in a spatially homogeneous
steady state. Here we study this behavior by comparing the dynamics of a map of
an array of $N$ delayed-coupled maps with the dynamics of a map with $N$
self-feedback delayed loops. If $N$ is sufficiently large, the dynamics of a
map of the array is similar to the dynamics of a map with self-feedback loops
with the same delay times. Several delayed loops stabilize the fixed point,
when the delays are not the same; however, the distribution of delays plays a
key role: if the delays are all odd a periodic orbit (and not the fixed point)
is stabilized. We present a linear stability analysis and apply some
mathematical theorems that explain the numerical results.


title:
Symbolic software for separation of variables in the Hamilton-Jacobi
  equation for the L-systems

abstract:
  We discuss computer implementation of the known algorithm of finding
separation coordinates for the special class of orthogonal separable systems
called L-systems or Benenti systems.


title: Lyapunov Instability versus Relaxation Time in two Coupled Oscillators

abstract:
  We consider the relation between relaxation time and the largest Lyapunov
exponent in a system of two coupled oscillators, one of them being harmonic. It
has been found that in a rather broad region of parameter space, contrary to
the common expectation, both Lyapunov exponent and relaxation time increase as
a function of the total energy. This effect is attributed to the fact that
above a critical value of the total energy, although the Lyapunov exponent
increases, KAM tori appear and the chaotic fraction of phase space decreases.
We examine the required conditions and demonstrate the key role of the
dispersion relation for this behaviour to occur. This study is useful, among
others, in the understanding of the damping of nuclear giant resonances.


title:
Transverse velocities, intermittency and asymmetry in fully developed
  turbulence

abstract:
  Using experimental transverse velocities data for very high Reynolds number
turbulence, we suggest a model describing both formation of intermittency and
asymmetry of turbulence. The model, called "bump-model" is a modification of
ramp-model suggested earlier, S.I. Vainshtein and K.R. Sreenivasan, Phys. Rev.
Lett., 73, 3085 (1994). The connection between asymmetry and intermittency
makes it possible to study the latter with relatively low moments.


title:
Looking at map networks with time delay interactions from a local
  perspective

abstract:
  The evolution of networks of coupled chaotic maps with delayed interactions
can be studied in the usual way by analyzing the evolution of the state of
elements at each iteration time (the "Simulator" point of view), or it can be
analyzed from the point of view of a single element (the "Observer"
perspective) that is receiving delayed information from the other elements in
the system. In the usual"Simulator" timeframe, an absolute time (i.e. the
number of iterations $t$) is adopted to define the system state at each time
$t$. In the"Observer" framework, the state of an element in the system is given
by its state at the "Simulator" time $t-\tau$, where $\tau$ is the information
travel time between that element and the Observer. We emphasize the convenience
of the analysis of the system dynamics in the "Observer" timeframe by showing
that the "Observer" dynamics differs substantially from the one in the
"Simulator" timeframe, and that the system dynamics in the "Observer" timeframe
reflects the proper causality of the interactions among the elements.


title:
Statistical description of eigenfunctions in chaotic and weakly
  disordered systems beyond universality

abstract:
  We present a semiclassical approach to eigenfunction statistics in chaotic
and weakly disordered quantum systems which goes beyond Random Matrix Theory,
supersymmetry techniques, and existing semiclassical methods. The approach is
based on a generalization of Berry's Random Wave Model, combined with a
consistent semiclassical representation of spatial two-point correlations. We
derive closed expressions for arbitrary wavefunction averages in terms of
universal coefficients and sums over classical paths, which contain, besides
the supersymmetry results, novel oscillatory contributions. Their physical
relevance is demonstrated in the context of Coulomb blockade physics.


title: Easily Adaptable Complexity Measure for Finite Time Series

abstract:
  We present a complexity measure for any finite time series. This measure has
invariance under any monotonic transformation of the time series, has a degree
of robustness against noise, and has the adaptability of satisfying almost all
the widely accepted but conflicting criteria for complexity measurements.
Surprisingly, the measure is developed from Kolmogorov complexity, which is
traditionally believed to represent only randomness and to satisfy one
criterion to the exclusion of the others. For familiar iterative systems, our
treatment may imply a heuristic approach to transforming symbolic dynamics into
permutation dynamics and vice versa.


title:
Bifurcation and Chaos in Coupled Ratchets exhibiting Synchronized
  Dynamics

abstract:
  The bifurcation and chaotic behaviour of unidirectionally coupled
deterministic ratchets is studied as a function of the driving force amplitude
($a$) and frequency ($\omega$). A classification of the various types of
bifurcations likely to be encountered in this system was done by examining the
stability of the steady state in linear response as well as constructing a
two-parameter phase diagram in the ($a -\omega$) plane. Numerical explorations
revealed varieties of bifurcation sequences including quasiperiodic route to
chaos. Besides, the familiar period-doubling and crises route to chaos
exhibited by the one-dimensional ratchet were also found. In addition, the
coupled ratchets display symmetry-breaking, saddle-nodes and bubbles of
bifurcations. Chaotic behaviour is characterized by using the sensitivity to
initial condition as well as the Lyapunov exponent spectrum; while a perusal of
the phase space projected in the Poincar$\acute{e}$ cross-section confirms some
of the striking features.


title: Chaos synchronization in gap-junction-coupled neurons

abstract:
  Depending on temperature the modified Hodgkin-Huxley (MHH) equations exhibit
a variety of dynamical behavior including intrinsic chaotic firing. We analyze
synchronization in a large ensemble of MHH neurons that are interconnected with
gap junctions. By evaluating tangential Lyapunov exponents we clarify whether
synchronous state of neurons is chaotic or periodic. Then, we evaluate
transversal Lyapunov exponents to elucidate if this synchronous state is stable
against infinitesimal perturbations. Our analysis elucidates that with weak gap
junctions, stability of synchronization of MHH neurons shows rather complicated
change with temperature. We, however, find that with strong gap junctions,
synchronous state is stable over the wide range of temperature irrespective of
whether synchronous state is chaotic or periodic. It turns out that strong gap
junctions realize the robust synchronization mechanism, which well explains
synchronization in interneurons in the real nervous system.


title: Spectral Form Factor for Chaotic Dynamics in a Weak Magnetic Field

abstract:
  Using semiclassical periodic orbit theory for a chaotic system in a weak
magnetic field, we obtain the form factor predicted by Pandey and Mehta's two
matrix model up to the third order. The third order contribution has a peculiar
term which exists only in the intermediate crossover domain between the GOE
(Gaussian Orthogonal Ensemble) and the GUE (Gaussian Unitary Ensemble)
universality classes. The exact expression is obtained by taking account of the
contribution from encounter regions where orbit loops are connected.


title:
Max-Plus Algebra for Complex Variables and Its Application to Discrete
  Fourier Transformation

abstract:
  A generalization of the max-plus transformation, which is known as a method
to derive cellular automata from integrable equations, is proposed for complex
numbers. Operation rules for this transformation is also studied for general
number of complex variables. As an application, the max-plus transformation is
applied to the discrete Fourier transformation. Stretched coordinates are
introduced to obtain the max-plus transformation whose imaginary part coinsides
with a phase of the discrete Fourier transformation.


title: Shuffling cards, factoring numbers, and the quantum baker's map

abstract:
  It is pointed out that an exactly solvable permutation operator, viewed as
the quantization of cyclic shifts, is useful in constructing a basis in which
to study the quantum baker's map, a paradigm system of quantum chaos. In the
basis of this operator the eigenfunctions of the quantum baker's map are
compressed by factors of around five or more. We show explicitly its connection
to an operator that is closely related to the usual quantum baker's map. This
permutation operator has interesting connections to the art of shuffling cards
as well as to the quantum factoring algorithm of Shor via the quantum order
finding one. Hence we point out that this well-known quantum algorithm makes
crucial use of a quantum chaotic operator, or at least one that is close to the
quantization of the left-shift, a closeness that we also explore
quantitatively.


title: On a transformation between hierarchies of integrable equations

abstract:
  A transforation between a hierarchy of integrable equations arising from the
standard $R$-matrix construction on the algebra of differential operators and a
hierarchy of integrable equations arising from a deformation of the standard
$R$-matrix is given.


title: On a Camassa-Holm type equation with two dependent variables

abstract:
  We consider a generalization of the Camassa Holm (CH) equation with two
dependent variables, called CH2, introduced by Liu and Zhang. We briefly
provide an alternative derivation of it based on the theory of Hamiltonian
structures on (the dual of) a Lie Algebra. The Lie Algebra here involved is the
same algebra underlying the NLS hierarchy. We study the structural properties
of the CH2 hierarchy within the bihamiltonian theory of integrable PDEs, and
provide its Lax representation. Then we explicitly discuss how to construct
classes of solutions, both of peakon and of algebro-geometrical type. We
finally sketch the construction of a class of singular solutions, defined by
setting to zero one of the two dependent variables.


title: Uniform semiclassical trace formula for U(3) --> SO(3) symmetry breaking

abstract:
  We develop a uniform semiclassical trace formula for the density of states of
a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term
$\propto r^4$. This term breaks the U(3) symmetry of the HO, resulting in a
spherical system with SO(3) symmetry. We first treat the anharmonic term in
semiclassical perturbation theory by integration of the action of the perturbed
periodic HO orbits over the manifold $\mathbb{C}$P$^2$ which characterizes
their 4-fold degeneracy. Then we obtain an analytical uniform trace formula
which in the limit of strong perturbations (or high energy) asymptotically goes
over into the correct trace formula of the full anharmonic system with SO(3)
symmetry, and in the limit $\epsilon$ (or energy) $\to 0$ restores the HO trace
formula with U(3) symmetry. We demonstrate that the gross-shell structure of
this anharmonically perturbed system is dominated by the two-fold degenerate
diameter and circular orbits, and {\it not} by the orbits with the largest
classical degeneracy, which are the three-fold degenerate tori with rational
ratios $\omega_r:\omega_\phi=N:M$ of radial and angular frequencies. The same
holds also for the limit of a purely quartic spherical potential $V(r)\propto
r^4$.


title:
Multiple-scale analysis of discrete nonlinear partial difference
  equations: the reduction of the lattice potential KdV

abstract:
  We consider multiple lattices and functions defined on them. We introduce
slow varying conditions for functions defined on the lattice and express the
variation of a function in terms of an asymptotic expansion with respect to the
slow varying lattices.
  We use these results to perform the multiple--scale reduction of the lattice
potential Korteweg--de Vries equation.


title:
Discrete Klein-Gordon models with static kinks free of the
  Peierls-Nabarro potential

abstract:
  For the nonlinear Klein-Gordon type models, we describe a general method of
discretization in which the static kink can be placed anywhere with respect to
the lattice. These discrete models are therefore free of the {\it static}
Peierls-Nabarro potential. Previously reported models of this type are shown to
belong to a wider class of models derived by means of the proposed method. A
relevant physical consequence of our findings is the existence of a wide class
of discrete Klein-Gordon models where slow kinks {\it practically} do not
experience the action of the Peierls-Nabarro potential. Such kinks are not
trapped by the lattice and they can be accelerated by even weak external
fields.


title:
Standard Nearest Neighbor Discretizations of Klein-Gordon Models Cannot
  Preserve Both Energy and Linear Momentum

abstract:
  We consider nonlinear Klein-Gordon wave equations and illustrate that
standard discretizations thereof (involving nearest neighbors) may preserve
either standardly defined linear momentum or total energy but not both. This
has a variety of intriguing implications for the ``non-potential''
discretizations that preserve only the linear momentum, such as the
self-accelerating or self-decelerating motion of coherent structures such as
discrete kinks in these nonlinear lattices.


title:
Does multifractal theory of turbulence have logarithms in the scaling
  relations?

abstract:
  The multifractal theory of turbulence uses a saddle-point evaluation in
determining the power-law behaviour of structure functions. Without suitable
precautions, this could lead to the presence of logarithmic corrections,
thereby violating known exact relations such as the four-fifths law. Using the
theory of large deviations applied to the random multiplicative model of
turbulence and calculating subdominant terms, we explain here why such
corrections cannot be present.


title: Semiclassical transmission across transition states

abstract:
  It is shown that the probability of quantum-mechanical transmission across a
phase space bottleneck can be compactly approximated using an operator derived
from a complex Poincar\'e return map. This result uniformly incorporates
tunnelling effects with classically-allowed transmission and generalises a
result previously derived for a classically small region of phase space.


title: Dynamics of fluctuation of the top location of a sandpile

abstract:
  We investigate the fluctuation of the top location of a sandpile numerically
using the two-dimensional discrete elements method. We feed particles to a
sandpile at a fixed time interval and calculate power spectra from the time
series of the top location. We find that the power spectra are approximated as
power functions, and their exponents increase to -1 through a plateau as the
time interval decreases. For small time interval, avalanches occur continuously
either on the left or right side slope of a sandpile, and the slope on which
avalanches take place switches intermittently. The long time fluctuation of the
top location corresponds to the switchings. For the time series of the
switchings, we discuss the relation between the power spectrum and the
distribution of waiting times based on analytic theories.


title: All-optical switching in rubidium vapor

abstract:
  We report on an all-optical switch that operates at low light levels. It
consists of laser beams counterpropagating through a warm rubidium vapor that
induce an off-axis optical pattern. A switching laser beam causes this pattern
to rotate even when the power in the switching beam is much lower than the
power in the pattern. The observed switching energy density is very low,
suggesting that the switch might operate at the single-photon level with system
optimization. This approach opens the possibility of realizing a single-photon
switch for quantum information networks and for improving transparent optical
telecommunication networks.


title: Translationally invariant discrete kinks from one-dimensional maps

abstract:
  For most discretisations of the $\phi^4$ theory, the stationary kink can only
be centered either on a lattice site or midway between two adjacent sites. We
search for exceptional discretisations which allow stationary kinks to be
centered anywhere between the sites. We show that this translational invariance
of the kink implies the existence of an underlying one-dimensional map
$\phi_{n+1}=F(\phi_n)$. A simple algorithm based on this observation generates
three different families of exceptional discretisations.


title: Stable spatiotemporal solitons in Bessel optical lattices

abstract:
  We investigate the existence and stability of three-dimensional (3D) solitons
supported by cylindrical Bessel lattices (BLs) in self-focusing media. If the
lattice strength exceeds a threshold value, we show numerically, and using the
variational approximation, that the solitons are stable within one or two
intervals of values of their norm. In the latter case, the Hamiltonian-vs.-norm
diagram has a "swallowtail" shape, with three cuspidal points. The model
applies to Bose-Einstein condensates (BECs) and to optical media with saturable
nonlinearity, suggesting new ways of making stable 3D BEC solitons and "light
bullets" of an arbitrary size.


title: Uniform approximation of barrier penetration in phase space

abstract:
  A method to approximate transmission probabilities for a nonseparable
multidimensional barrier is applied to a waveguide model. The method uses
complex barrier-crossing orbits to represent reaction probabilities in phase
space and is uniform in the sense that it applies at and above a threshold
energy at which classical reaction switches on. Above this threshold the
geometry of the classically reacting region of phase space is clearly reflected
in the quantum representation. Two versions of the approximation are applied. A
harmonic version which uses dynamics linearised around an instanton orbit is
valid only near threshold but is easy to use. A more accurate and more widely
applicable version using nonlinear dynamics is also described.


title: Mapping Model of Chaotic Phase Synchronization

abstract:
  A coupled map model for the chaotic phase synchronization and its
desynchronization phenomenon is proposed. The model is constructed by
integrating the coupled kicked oscillator system, kicking strength depending on
the complex state variables. It is shown that the proposed model clearly
exhibits the chaotic phase synchronization phenomenon. Furthermore, we
numerically prove that in the region where the phase synchronization is weakly
broken, the anomalous scaling of the phase difference rotation number is
observed. This proves that the present model belongs to the same universality
class found by Pikovsky et al.. Furthermore, the phase diffusion coefficient in
the de-synchronization state is analyzed.


title: Optimal phase space projection for noise reduction

abstract:
  In this communication we will re-examine the widely studied technique of
phase space projection. By imposing a time domain constraint (TDC) on the
residual noise, we deduce a more general version of the optimal projector,
which includes those appearing in previous literature as subcases but does not
assume the independence between the clean signal and the noise. As an
application, we will apply this technique for noise reduction. Numerical
results show that our algorithm has succeeded in augmenting the signal-to-noise
ratio (SNR) for simulated data from the R\"ossler system and experimental
speech record.


title:
Paraxial light in a Cole-Cole nonlocal medium: integrable regimes and
  singularities

abstract:
  Nonlocal nonlinear Schroedinger-type equation is derived as a model to
describe paraxial light propagation in nonlinear media with different `degrees'
of nonlocality. High frequency limit of this equation is studied under specific
assumptions of Cole-Cole dispersion law and a slow dependence along propagating
direction. Phase equations are integrable and they correspond to dispersionless
limit of Veselov-Novikov hierarchy. Analysis of compatibility among intensity
law (dependence of intensity on the refractive index) and high frequency limit
of Poynting vector conservation law reveals the existence of singular
wavefronts. It is shown that beams features depend critically on the
orientation properties of quasiconformal mappings of the plane. Another class
of wavefronts, whatever is intensity law, is provided by harmonic minimal
surfaces. Illustrative example is given by helicoid surface. Compatibility with
first and third degree nonlocal perturbations and explicit solutions are also
discussed.


title:
Stability analysis of dynamical regimes in nonlinear systems with
  discrete symmetries

abstract:
  We present a theorem that allows to simplify linear stability analysis of
periodic and quasiperiodic nonlinear regimes in N-particle mechanical systems
(both conservative and dissipative) with different kinds of discrete symmetry.
This theorem suggests a decomposition of the linearized system arising in the
standard stability analysis into a number of subsystems whose dimensions can be
considerably less than that of the full system. As an example of such
simplification, we discuss the stability of bushes of modes (invariant
manifolds) for the Fermi-Pasta-Ulam chains and prove another theorem about the
maximal dimension of the above mentioned subsystems.


title: Synchronization and clustering in electroencephalographic signals

abstract:
  The degree of synchronization and the amount of dynamical cluster formation
in electroencephalographic (EEG) signals are characterized by employing two
order parameters introduced in the context of coupled chaotic systems subject
to external noise. These parameters are calculated in EEG signals from a group
of healthy subjects and a group of epileptic patients, including a patient
experiencing an epileptic crisis. The evolution of these parameters shows the
occurrence of intermittent synchronization and clustering in the brain activity
during an epileptic crisis. Significantly, the existence of an instantaneous
maximum of synchronization previous to the onset of a crisis is revealed by
this procedure. The mean values of the order parameters and their standard
deviations are compared between both groups of individuals.


title:
On Some Processes and Distributions in a Collective Model of Investors'
  Behavior

abstract:
  This article considers a model for alternative processes for securities
prices and compares this model with actual return data of several securities.
The distributions of returns that appear in the model can be Gaussian as well
as non-Gaussian; in particular they may have two peaks. We consider a discrete
Markov chain model. This model in some aspects is similar to well-known Ising
model describing ferromagnetics. Namely we consider a set of N investors, each
of whom has either bullish or bearish opinion, denoted by plus or minus
respectively. At every time step each of N investors can change his/her sign.
The probability of a plus becoming a minus and the probability of a minus
becoming a plus depends only on the bullish sentiment described as the number
of bullish investors among the total of N investors. The number of bullish
investors then forms a Markov chain whose transition matrix is calculated
explicitly. The transition matrix of that chain is ergodic and any initial
distribution of bullish investors converges to stationary. Stationary
distributions of bullish investors in this Markov chain model are similar to
continuous distributions of the "theory of social imitation" of Callen and
Shapero. Distributions obtained this way can represent 3 types of market
behavior: one-peaked distribution that is close to Gaussian, transition market
(flattening of the top), and two-peaked distribution.


title:
A new approach to the Darboux-Backlund transformation versus the
  standard dressing method

abstract:
  We present a new approach to the construction of the Darboux matrix. This is
a generalization of the recently formulated method based on the assumption that
the square of the Darboux matrix vanishes for some values of the spectral
parameter. We consider the multisoliton case, the reduction problem and the
discrete case. The relationship between our approach and the standard dressing
method is discussed in detail.


title: Energy localization in two chaotically coupled systems

abstract:
  We set up and analyze a random matrix model to study energy localization and
its time behavior in two chaotically coupled systems. This investigation is
prompted by a recent experimental and theoretical study of Weaver and Lobkis on
coupled elastomechanical systems. Our random matrix model properly describes
the main features of the findings by Weaver and Lobkis. Due to its general
character, our model is also applicable to similar systems in other areas of
physics -- for example, to chaotically coupled quantum dots.


title: Quantum dynamical echo in two-level systems

abstract:
  Evolution of quantum fidelity for two-level systems is studied in the context
of periodic echo. From a general treatment for time independent case, we obtain
a simple condition on the governing Hamiltonians under which the systems
display periodic quantum echo. For a specific time dependent problem the
quantum fidelity is shown to exhibit Rabi oscillation. This may be considered
as a simple mechanism to generate periodic echo, except for a specific initial
superpositional state in which case the fidelity remains invariant.


title: Travelling kinks in discrete phi^4 models

abstract:
  In recent years, three exceptional discretizations of the phi^4 theory have
been discovered [J.M. Speight and R.S. Ward, Nonlinearity 7, 475 (1994); C.M.
Bender and A. Tovbis, J. Math. Phys. 38, 3700 (1997); P.G. Kevrekidis, Physica
D 183, 68 (2003)] which support translationally invariant kinks, i.e. families
of stationary kinks centred at arbitrary points between the lattice sites. It
has been suggested that the translationally invariant stationary kinks may
persist as 'sliding kinks', i.e. discrete kinks travelling at nonzero
velocities without experiencing any radiation damping. The purpose of this
study is to check whether this is indeed the case. By computing the Stokes
constants in beyond-all-order asymptotic expansions, we prove that the three
exceptional discretizations do not support sliding kinks for most values of the
velocity - just like the standard, one-site, discretization. There are,
however, isolated values of velocity for which radiationless kink propagation
becomes possible. There is one such value for the discretization of Speight and
Ward and three 'sliding velocities' for the model of Kevrekedis.


title:
Formation of clumps and patches in self-aggregation of finite size
  particles

abstract:
  New model equations are derived for dynamics of self-aggregation of
finite-size particles. Differences from standard Debye-Huckel and Keller-Segel
models are: a) the mobility $\mu$ of particles depends on the locally-averaged
particle density and b) linear diffusion acts on that locally-averaged particle
density. The cases both with and without diffusion are considered here.
Surprisingly, these simple modifications of standard models allow progress in
the analytical description of evolution as well as the complete analysis of
stationary states. When $\mu$ remains positive, the evolution of collapsed
states in our model reduces exactly to finite-dimensional dynamics of
interacting particle clumps. Simulations show these collapsed (clumped) states
emerging from smooth initial conditions, even in one spatial dimension. If
$\mu$ vanishes for some averaged density, the evolution leads to spontaneous
formation of \emph{jammed patches} (weak solution with density having compact
support). Simulations confirm that a combination of these patches forms the
final state for the system.


title:
Exact Equal Time Statistics of Orszag-McLaughlin Dynamics By The Hopf
  Characteristic Functional Approach

abstract:
  By employing Hopf's functional method, we find the exact characteristic
functional for a simple nonlinear dynamical system introduced by Orszag.
Steady-state equal-time statistics thus obtained are compared to direct
numerical simulation. The solution is both non-trivial and strongly
non-Gaussian.


title: Lattice system of interacting spins in the thermodynamical limit

abstract:
  In this paper we investigate some particular spin lattice (a higher
dimensional generalization of a spin chain) related to Zamolodchikov model, in
the limit when both sizes of the lattice tend to infinity. An infinite set of
bilinear equations, describing a distribution of eigenvalues of infinite set of
mutually commuting operators, is derived. The distribution for the maximal
eigenvalues is obtained explicitly. The way to obtain the excitations is
discussed.


title: Generalized synchronization: a modified system approach

abstract:
  The universal mechanism resulting in the generalized synchronization regime
arising in the chaotic oscillators with the dissipative coupling has been
described. The reasons of the generalized synchronization occurrence may be
clarified by means of a modified system approach. The main results are
illustrated by unidirectionally coupled Rossler systems, Rossler and Lorenz
systems and logistic maps.


title: Proof of Nishida's conjecture on anharmonic lattices

abstract:
  We prove Nishida's 1971 conjecture stating that almost all low-energetic
motions of the anharmonic Fermi-Pasta-Ulam lattice with fixed endpoints are
quasi-periodic. The proof is based on the formal computations of Nishida, the
KAM theorem, discrete symmetry considerations and an algebraic trick that
considerably simplifies earlier results.


title:
Aspects of the Scattering and Impedance Properties of Chaotic Microwave
  Cavities

abstract:
  We consider the statistics of the impedance of a chaotic microwave cavity
coupled to a single port. We remove the non-universal effects of the coupling
from the experimental data using the radiation impedance obtained directly from
the experiments. We thus obtain the normalized impedance whose Probability
Density Function (PDF) is predicted to be universal in that it depends only on
the loss (quality factor) of the cavity. We find that impedance fluctuations
decrease with increasing loss. The results apply to scattering measurements on
any wave chaotic system.


title:
Differential-like Chosen Cipher Attack on A Spatiotemporally Chaotic
  Cryptosystem

abstract:
  The combinative applications of one-way coupled map lattice (OCML) and some
simple algebraic operations have demonstrated to be able to construct the best
known chaotic cryptosystem with high practical security, fast encryption speed,
and excellent robustness against channel noise. In this paper, we propose a
differential-like chosen cipher attack to break the prototypical system
cooperating with INT and MOD operations. This cryptographic method exploits the
weakness that the high-dimensional cryptosystem degenerates to be
one-dimensional under constant driving, therefore, is no more sensitive to the
slight perturbation on the driving after convergence. The experimental results
show that this method can successfully extract the key within just hundreds of
iterations. To the best of our knowledge, it is the first time to present
successful cryptanalysis on such a cryptosystem. we also make some suggestions
to improve the security in future versions.


title: Characteristic Algebras of Fully Discrete Hyperbolic Type Equations

abstract:
  The notion of the characteristic Lie algebra of the discrete hyperbolic type
equation is introduced. An effective algorithm to compute the algebra for the
equation given is suggested. Examples and further applications are discussed.


title: Types and Forms of Emergence

abstract:
  The knowledge of the different types of emergence is essential if we want to
understand and master complex systems in science and engineering, respectively.
This paper specifies a universal taxonomy and comprehensive classification of
the major types and forms of emergence in Multi-Agent Systems, from simple
types of intentional and predictable emergence in machines to more complex
forms of weak, multiple and strong emergence.


title: sl_2 Gaudin model with Jordanian twist

abstract:
  sl_2 Gaudin model with Jordanian twist is studied. This system can be
obtained as the semiclassical limit of the XXX spin chain deformed by the
Jordanian twist. The appropriate creation operators that yield the Bethe states
of the Gaudin model and consequently its spectrum are defined. Their
commutation relations with the generators of the corresponding loop algebra as
well as with the generating function of integrals of motion are given. The
inner products and norms of Bethe states and the relation to the solutions of
the Knizhnik-Zamolodchikov equations are discussed.


title: Chaos in computer performance

abstract:
  Modern computer microprocessors are composed of hundreds of millions of
transistors that interact through intricate protocols. Their performance during
program execution may be highly variable and present aperiodic oscillations. In
this paper, we apply current nonlinear time series analysis techniques to the
performances of modern microprocessors during the execution of prototypical
programs. Our results present pieces of evidence strongly supporting that the
high variability of the performance dynamics during the execution of several
programs display low-dimensional deterministic chaos, with sensitivity to
initial conditions comparable to textbook models. Taken together, these results
show that the instantaneous performances of modern microprocessors constitute a
complex (or at least complicated) system and would benefit from analysis with
modern tools of nonlinear and complexity science.

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


title: Statistics of quantum recurrences in the Hilbert space

abstract: This paper has been withdrawn by the authors due to a crucial error.


title:
A generalized model of active media with a set of interacting
  pacemakers: Application to the heart beat analysis

abstract:
  We propose a quite general model of active media by consideration of the
interaction between pacemakers via their phase response curves. This model
describes a network of pulse oscillators coupled by their response to the
internal depolarization of mutual stimulations.
  First, a macroscopic level corresponding to an arbitrary large number of
oscillatory elements coupled globally is considered. As a specific and
important case of the proposed model, the bidirectional interaction of two
cardiac nodes is described. This case is generalized by means of an additional
pacemaker, which can be expounded as an external stimulater. The behavior of
such a system is analyzed. Second, the microscopic level corresponding to the
representation of cardiac nodes by one-- and two--dimensional lattices of pulse
oscillators coupled via the nearest neighbors is described. The model is a
universal one in the sense that on its basis one can easily construct discrete
distributed media of active elements, which interact via phase response curves.


title:
Exact Analysis of the Adiabatic Invariants in Time-Dependent Harmonic
  Oscillator

abstract:
  The theory of adiabatic invariants has a long history and important
applications in physics but is rarely rigorous. Here we treat exactly the
general time-dependent 1-D harmonic oscillator, $\ddot{q} + \omega^2(t) q=0$
which cannot be solved in general. We follow the time-evolution of an initial
ensemble of phase points with sharply defined energy $E_0$ and calculate
rigorously the distribution of energy $E_1$ after time $T$, and all its
moments, especially its average value $\bar{E_1}$ and variance $\mu^2$. Using
our exact WKB-theory to all orders we get the exact result for the leading
asymptotic behaviour of $\mu^2$.


title:
Instabilities of multi-hump vector solitons in coupled nonlinear
  Schroedinger equations

abstract:
  Spectral stability of multi-hump vector solitons in the Hamiltonian system of
coupled nonlinear Schr\"{o}dinger (NLS) equations is investigated both
analytically and numerically. Using the closure theorem for the negative index
of the linearized Hamiltonian, we classify all possible bifurcations of
unstable eigenvalues in the systems of coupled NLS equations with cubic and
saturable nonlinearities. We also determine the eigenvalue spectrum numerically
by the shooting method. In case of cubic nonlinearities, all multi-hump vector
solitons in the non-integrable model are found to be linearly unstable. In case
of saturable nonlinearities, stable multi-hump vector solitons are found in
certain parameter regions, and some errors in the literature are corrected.


abstract:
  Multiple permanent-wave trains in nonlinear systems are constructed by the
asymptotic tail-matching method. Under some general assumptions, simple
criteria for the construction are presented. Applications to fourth-order
systems and coupled nonlinear Schr\"odinger equations are discussed.


title:
A tail-matching method for the linear stability of multi-vector-soliton
  bound states

abstract:
  Linear stability of multi-vector-soliton bound states in the coupled
nonlinear Schr\"odinger equations is analyzed using a new tail-matching method.
Under the condition that individual vector solitons in the bound states are
wave-and-daughter-waves and widely separated, small eigenvalues of these bound
states that bifurcate from the zero eigenvalue of single vector solitons are
calculated explicitly. It is found that unstable eigenvalues from phase-mode
bifurcations always exist, thus the bound states are always linearly unstable.
This tail-matching method is simple, but it gives identical results as the
Karpman-Solev'ev-Gorshkov-Ostrovsky method.


abstract:
  Complete eigenfunctions of linearized integrable equations expanded around an
arbitrary solution are obtained for the Ablowitz-Kaup-Newell-Segur (AKNS)
hierarchy and the Korteweg-de Vries (KdV) hierarchy. It is shown that the
linearization operators and the recursion operator which generates the
hierarchy are commutable. Consequently, eigenfunctions of the linearization
operators are precisely squared eigenfunctions of the associated eigenvalue
problem. Similar results are obtained for the adjoint linearization operators
as well. These results make a simple connection between the direct
soliton/multi-soliton perturbation theory and the inverse-scattering based
perturbation theory for these hierarchy equations.


title:
Anomalous Scaling of Structure Functions and Dynamic Constraints on
  Turbulence Simulations

abstract:
  The connection between anomalous scaling of structure functions
(intermittency) and numerical methods for turbulence simulations is discussed.
It is argued that the computational work for direct numerical simulations (DNS)
of fully developed turbulence increases as $Re^{4}$, and not as $Re^{3}$
expected from Kolmogorov's theory, where $Re$ is a large-scale Reynolds number.
Various relations for the moments of acceleration and velocity derivatives are
derived. An infinite set of exact constraints on dynamically consistent subgrid
models for Large Eddy Simulations (LES) is derived from the Navier-Stokes
equations, and some problems of principle associated with existing LES models
are highlighted.


title: Stochastic Resonance in Underdamped, Bistable Systems

abstract:
  We carry out a detailed numerical investigation of stochastic resonance in
underdamped systems in the non-perturbative regime. We point out that an
important distinction between stochastic resonance in overdamped and
underdamped systems lies in the lack of dependence of the amplitude of the
noise-averaged trajectory on the noise strength, in the latter case. We provide
qualitative explanations for the observed behavior and show that signatures
such as the initial decay and long-time oscillatory behaviour of the temporal
correlation function and peaks in the noise and phase averaged power spectral
density, clearly indicate the manifestation of resonant behaviour in noisy,
underdamped bistable systems in the weak to moderate noise regime.


title:
Correlation functions of impedance and scattering matrix elements in
  chaotic absorbing cavities

abstract:
  Wave scattering in chaotic systems with a uniform energy loss (absorption) is
considered. Within the random matrix approach we calculate exactly the energy
correlation functions of different matrix elements of impedance or scattering
matrices for systems with preserved or broken time-reversal symmetry. The
obtained results are valid at any number of arbitrary open scattering channels
and arbitrary absorption. Elastic enhancement factors (defined through the
ratio of the corresponding variance in reflection to that in transmission) are
also discussed.


title:
Fermionic one- and two-dimensional Toda lattice hierarchies and their
  bi-Hamiltonian structures

abstract:
  By exhibiting the corresponding Lax pair representations we propose a wide
class of integrable two-dimensional (2D) fermionic Toda lattice (TL)
hierarchies which includes the 2D N=(2|2) and N=(0|2) supersymmetric TL
hierarchies as particular cases. Performing their reduction to the
one-dimensional case by imposing suitable constraints we derive the
corresponding 1D fermionic TL hierarchies. We develop the generalized graded
R-matrix formalism using the generalized graded bracket on the space of graded
operators with an involution generalizing the graded commutator in
superalgebras, which allows one to describe these hierarchies in the framework
of the Hamiltonian formalism and construct their first two Hamiltonian
structures. The first Hamiltonian structure is obtained for both bosonic and
fermionic Lax operators while the second Hamiltonian structure is established
for bosonic Lax operators only. We propose the graded modified Yang-Baxter
equation in the operator form and demonstrate that for the class of graded
antisymmetric R-matrices it is equivalent to the tensor form of the graded
classical Yang-Baxter equation.


title: On the mobility and efficiency of mechanical systems

abstract:
  The definition of a mobilized system and its efficiency are introduced. The
existence of an optimal (maximally efficient) system is proved by an
application of Young measures and compensated compactness.


title: Chaotic Dynamics of N-degree of Freedom Hamiltonian Systems

abstract:
  We investigate the connection between local and global dynamics of two
N-degree of freedom Hamiltonian systems with different origins describing
one-dimensional nonlinear lattices: The Fermi-Pasta-Ulam (FPU) model and a
discretized version of the nonlinear Schrodinger equation related to
Bose-Einstein Condensation (BEC). We study solutions starting in the vicinity
of simple periodic orbits (SPOs) representing in-phase (IPM) and out-of-phase
motion (OPM), which are known in closed form and whose linear stability can be
analyzed exactly. Our results verify that as the energy E increases for fixed
N, beyond the destabilization threshold of these orbits, all positive Lyapunov
exponents exhibit a transition between two power laws, occurring at the same
value of E. The destabilization energy E_c per particle goes to zero as N goes
to infinity following a simple power-law. However, using SALI, a very efficient
indicator we have recently introduced for distinguishing order from chaos, we
find that the two Hamiltonians have very different dynamics near their stable
SPOs: For example, in the case of the FPU system, as the energy increases for
fixed N, the islands of stability around the OPM decrease in size, the orbit
destabilizes through period-doubling bifurcation and its eigenvalues move
steadily away from -1, while for the BEC model the OPM has islands around it
which grow in size before it bifurcates through symmetry breaking, while its
real eigenvalues return to +1 at very high energies. Still, when calculating
Lyapunov spectra, we find for the OPMs of both Hamiltonians that the Lyapunov
exponents decrease following an exponential law and yield extensive
Kolmogorov--Sinai entropies per particle, in the thermodynamic limit of fixed
energy density E/N with E and N arbitrarily large.


title: Estimating von-Karman's constant from Homogeneous Turbulence

abstract:
  A celebrated universal aspect of wall-bounded turbulent flows is the von
Karman log-law-of-the-wall, describing how the mean velocity in the streamwise
direction depends on the distance from the wall. Although the log-law is known
for more than 75 years, the von Karman constant governing the slope of the
log-law was not determined theoretically. In this Letter we show that the
von-Karman constant can be estimated from homogeneous turbulent data, i.e.
without information from wall-bounded flows.