title: Cascades of Failure and Extinction in Evolving Complex Systems

abstract:
  There is empirical evidence from a range of disciplines that as the
connectivity of a network increases, we observe an increase in the average
fitness of the system. But at the same time, there is an increase in the
proportion of failure/extinction events which are extremely large. The
probability of observing an extreme event remains very low, but it is markedly
higher than in the system with lower degrees of connectivity. We give examples
from complex systems such as outages in the US power grid, the robustness
properties of cell biology networks, and trade links and the propagation of
both currency crises and disease. We consider networks which are populated by
agents which are heterogeneous in terms of their fitness for survival. The
network evolves over time, and in each period agents take self-interested
decisions to increase their fitness for survival to form alliances which
increase the connectivity of the network. The network is subjected to external
negative shocks both with respect to the size of the shock and the spatial
impact of the shock. We examine the size/frequency distribution of extinctions
and how this distribution evolves as the connectivity of the network grows. The
results are robust with respect to the choice of statistical distribution of
the shocks. We find that increasing the number of connections causes an
increase in the average fitness of agents, yet at the same time makes the
system as whole more vulnerable to catastrophic failure/extinction events on an
near-global scale.


title: Kraichnan flow in a square: an example of integrable chaos

abstract:
  The Kraichnan flow provides an example of a random dynamical system
accessible to an exact analysis. We study the evolution of the infinitesimal
separation between two Lagrangian trajectories of the flow. Its long-time
asymptotics is reflected in the multiplicative large deviation regime of the
statistics of stretching exponents. In the flow in a two-dimensional periodic
square where the anisotropy persists at small scales, the calculation of the
large deviation rate function of the stretching exponents reduces to the study
of the ground state energy of an integrable periodic Schroedinger operator of
the Lame type. The underlying integrability permits to explicitly exhibit the
non-Gaussianity of the multiplicative large deviations, to analyze the
time-scales at which the large deviation regime sets in and to identify the
general scenario for the appearance of multiplicative large deviations and the
restrictions on its applicability.


title:
On existence of dark solitons in cubic-quintic nonlinear Schr\"{o}dinger
  equation with a periodic potential

abstract:
  A proof of existence of stationary dark soliton solutions of the
cubic-quintic nonlinear Schr\"{o}dinger equation with a periodic potential is
given. It is based on the interpretation of the dark soliton as a heteroclinic
on the Poincar\'e map.


title: Integrability of the Egorov hydrodynamic type systems

abstract:
  Integrability criterion for the Egorov hydrodynamic type systems is
presented. The general solution by generalized hodograph method is found.
Examples are given


title: Newton polygons for finding exact solutions

abstract:
  A method for finding exact solutions of nonlinear differential equations is
presented. Our method is based on the application of the Newton polygons
corresponding to nonlinear differential equations. It allows one to express
exact solutions of the equation studied through solutions of another equation
using properties of the basic equation itself. The ideas of power geometry are
used and developed. Our approach has a pictorial rendition, which is is
illustrative and effective. The method can be also applied for finding
transformations between solutions of the differential equations. To demonstrate
the method application exact solutions of several equations are found. These
equations are: the Korteveg - de Vries - Burgers equation, the generalized
Kuramoto - Sivashinsky equation, the fourth - order nonlinear evolution
equation, the fifth - order Korteveg - de Vries equation, the modified Korteveg
- de Vries equation of the fifth order and nonlinear evolution equation of the
sixth order for the turbulence description. Some new exact solutions of
nonlinear evolution equations are given.


title: Macroscopic parameters of Fokker-Planck flows

abstract:
  The aim of this work is to investigate properties of solutions of Fokker -
Planck equation in the context of continuum mechanics. We show that average
quantities, calculated for these solutions approximately satisfy equations of
isothermal motion of viscous ideal gas.


title:
Discrete Breathers in Two-Dimensional Anisotropic Nonlinear Schrodinger
  lattices

abstract:
  We study the structure and stability of discrete breathers (both pinned and
mobile) in two-dimensional nonlinear anisotropic Schrodinger lattices. Starting
from a set of identical one-dimensional systems we develop the continuation of
the localized pulses from the weakly coupled regime (strongly anisotropic) to
the homogeneous one (isotropic). Mobile discrete breathers are seen to be a
superposition of a localized mobile core and an extended background of
two-dimensional nonlinear plane waves. This structure is in agreement with
previous results on onedimensional breather mobility. The study of the
stability of both pinned and mobile solutions is performed using standard
Floquet analysis. Regimes of quasi-collapse are found for both types of
solutions, while another kind of instability (responsible for the discrete
breather fission) is found for mobile solutions. The development of such
instabilities is studied, examining typical trajectories on the unstable
nonlinear manifold.


title: Generalized Quantum Baker Maps as perturbations of a simple kernel

abstract:
  We present a broad family of quantum baker maps that generalize the proposal
of Schack and Caves to any even Hilbert space with arbitrary boundary
conditions. We identify a structure, common to all maps consisting of a simple
kernel perturbed by diffraction effects. This "essential" baker's map has a
different semiclassical limit and can be diagonalized analytically for Hilbert
spaces spanned by qubits. In all cases this kernel provides an accurate
approximation to the spectral properties - eigenvalues and eigenfunctions - of
all the different quantizations.


title: Gauge Theory for Finite-Dimensional Dynamical Systems

abstract:
  Gauge theory is a well-established concept in quantum physics,
electrodynamics, and cosmology. This theory has recently proliferated into new
areas, such as mechanics and astrodynamics. In this paper, we discuss a few
applications of gauge theory in finite-dimensional dynamical systems with
implications to numerical integration of differential equations. We distinguish
between rescriptive and descriptive gauge symmetry. Rescriptive gauge symmetry
is, in essence, re-scaling of the independent variable, while descriptive gauge
symmetry is a Yang-Mills-like transformation of the velocity vector field,
adapted to finite-dimensional systems. We show that a simple gauge
transformation of multiple harmonic oscillators driven by chaotic processes can
render an apparently "disordered" flow into a regular dynamical process, and
that there exists a remarkable connection between gauge transformations and
reduction theory of ordinary differential equations. Throughout the discussion,
we demonstrate the main ideas by considering examples from diverse engineering
and scientific fields, including quantum mechanics, chemistry, rigid-body
dynamics and information theory.


title: On an Irreducible Theory of Complex Systems

abstract:
  In the paper we present results to develop an irreducible theory of complex
systems in terms of self-organization processes of prime integer relations.
Based on the integers and controlled by arithmetic only the self-organization
processes can describe complex systems by information not requiring further
explanations. Important properties of the description are revealed. It points
to a special type of correlations that do not depend on the distances between
parts, local times and physical signals and thus proposes a perspective on
quantum entanglement. Through a concept of structural complexity the
description also computationally suggests the possibility of a general
optimality condition of complex systems. The computational experiments indicate
that the performance of a complex system may behave as a concave function of
the structural complexity. A connection between the optimality condition and
the majorization principle in quantum algorithms is identified. A global
symmetry of complex systems belonging to the system as a whole, but not
necessarily applying to its embedded parts is presented. As arithmetic fully
determines the breaking of the global symmetry, there is no further need to
explain why the resulting gauge forces exist the way they do and not even
slightly different.


title: Lyapunov exponents of heavy particles in turbulence

abstract:
  Lyapunov exponents of heavy particles and tracers advected by homogeneous and
isotropic turbulent flows are investigated by means of direct numerical
simulations. For large values of the Stokes number, the main effect of inertia
is to reduce the chaoticity with respect to fluid tracers. Conversely, for
small inertia, a counter-intuitive increase of the first Lyapunov exponent is
observed. The flow intermittency is found to induce a Reynolds number
dependency for the statistics of the finite time Lyapunov exponents of tracers.
Such intermittency effects are found to persist at increasing inertia.


title: Darboux transformations for a 6-point scheme

abstract:
  We introduce (binary) Darboux transformation for general differential
equation of the second order in two independent variables. We present a
discrete version of the transformation for a 6-point difference scheme. The
scheme is appropriate to solving a hyperbolic type initial-boundary value
problem. We discuss several reductions and specifications of the
transformations as well as construction of other Darboux covariant schemes by
means of existing ones. In particular we introduce a 10-point scheme which can
be regarded as the discretization of self-adjoint hyperbolic equation.


title:
Spiral-wave Dynamics Depends Sensitively on nhomogeneities in
  Mathematical Models of Ventricular Tissue

abstract:
  Every sixth death in industrialised countries occurs because of cardiac
arrhythmias like ventricular tachycardia (VT) and ventricular fibrillation
(VF). There is growing consensus that VT is associated with an unbroken spiral
wave of electrical activation on cardiac tissue but VF with broken waves,
spiral turbulence, spatiotemporal chaos and rapid, irregular activation. Thus
spiral-wave activity in cardiac tissue has been studied extensively.
Nevertheless many aspects of such spiral dynamics remain elusive because of the
intrinsically high-dimensional nature of the cardiac-dynamical system. In
particular, the role of tissue heterogeneities in the stability of cardiac
spiral waves is still being investigated. Experiments with conduction blocks in
cardiac tissue yield a variety of results: some suggest that blocks can
eliminate VF partially or completely, leading to VT or quiescence, but others
show that VF is unaffected by obstacles. We propose theoretically that this
variety of results is a natural manifestation of a fractal boundary that must
separate the basins of the attractors associated, respectively, with VF and VT.
We substantiate this with extensive numerical studies of Panfilov and Luo-Rudy
I models, where we show that the suppression of VF depends sensitively on the
position, size, and nature of the inhomogeneity.


title: Pulse vaccination in the periodic infection rate SIR epidemic model

abstract:
  A pulse vaccination SIR model with periodic infection rate $\beta (t)$ have
been proposed and studied. The basic reproductive number $R_0$ is defined. The
dynamical behaviors of the model are analyzed with the help of persistence,
bifurcation and global stability. It has been shown that the infection-free
periodic solution is globally stable provided $R_0 < 1$ and is unstable if
$R_0>1$. Standard bifurcation theory have been used to show the existence of
the positive periodic solution for the case of $R_0 \to1^+$. Finally, the
numerical simulations have been performed to show the uniqueness and the global
stability of the positive periodic solution of the system.


title: A New Lorenz System Parameter Determination Method and Applications

abstract:
  This paper describes how to determine the parameter values of the chaotic
Lorenz system from one of its variables waveform. The geometrical properties of
the system are used firstly to reduce the parameter search space. Then, a
synchronization-based approach, with the help of the same geometrical
properties as coincidence criteria, is implemented to determine the parameter
values with the wanted accuracy. The method is not affected by a moderate
amount of noise in the waveform. As way of example of its effectiveness, the
method is applied to figure out directly from the ciphertext the secret keys of
two-channel chaotic cryptosystems using the variable $z$ as a synchronization
signal, based on the ultimate state projective chaos synchronization.


title:
Lorenz System Parameter Determination and Application to Break the
  Security of Two-channel Chaotic Cryptosystems

abstract:
  This paper describes how to determine the parameter values of the chaotic
Lorenz system used in a two-channel cryptosystem. The geometrical properties of
the Lorenz system are used firstly to reduce the parameter search space, then
the parameters are exactly determined, directly from the ciphertext, through
the minimization of the average jamming noise power created by the encryption
process.


title: Reconnection of Unstable/Stable Manifolds of the Harper Map

abstract:
  The Harper map is one of the simplest chaotic systems exhibiting reconnection
of invariant manifolds. The method of asymptotics beyond all orders (ABAO) is
used to construct unstable/stable manifolds of the Harper map. By enlarging the
neighborhood of a singularity, the perturbative solution of the unstable
manifold is expressed as a Borel summable asymptotic expansion in a sector
including $t=-\infty$ and is analytically continued to the other sectors, where
the solution acquires new terms describing heteroclinic tangles. When the
parameter changes to the reconnection threshold, the unstable/stable manifolds
are shown to acquire new oscillatory portion corresponding to the heteroclinic
tangle after the reconnection.


title:
State Transitions and the Continuum Limit for a 2D Interacting,
  Self-Propelled Particle System

abstract:
  We study a class of swarming problems wherein particles evolve dynamically
via pairwise interaction potentials and a velocity selection mechanism. We find
that the swarming system undergoes various changes of state as a function of
the self-propulsion and interaction potential parameters. In this paper, we
utilize a procedure which, in a definitive way, connects a class of
individual-based models to their continuum formulations and determine criteria
for the validity of the latter. H-stability of the interaction potential plays
a fundamental role in determining both the validity of the continuum
approximation and the nature of the aggregation state transitions. We perform a
linear stability analysis of the continuum model and compare the results to the
simulations of the individual-based one.


title:
Chaotic dynamics of resting ventilatory flow in humans assessed through
  noise titration

abstract:
  The mammalian ventilatory behavior exhibits nonlinear dynamics as reflected
by certain nonlinearity or complexity indicators (e.g. correlation dimension,
approximate entropy, Lyapunov exponents...) but this is not sufficient to
determine its possible chaotic nature. To address this, we applied the noise
titration technique, previously shown to discern and quantify chaos in short
and noisy time series, to ventilatory flow recordings obtained in quietly
breathing normal humans. Nine subjects (8 men and 1 woman, 24-42 yrs) were
studied during 15-minute epochs of ventilatory steady-state (10.1 +/- 3.0
breaths/minute, tidal volume 0.63 +/- 0.2L). Noise titration applied to the
unfiltered signals subsampled at 5 Hz detected nonlinearity in all cases (noise
limit 20.2 +/- 12.5%). Noise limit values were weakly correlated to the
correlation dimension and the largest Lyapunov exponent of the signals. This
study shows that the noise titration approach evidences a chaotic dimension to
the behavior of ventilatory flow over time in normal humans during tidal
breathing.


title: Method of Asymptotics beyond All Orders and Restriction on Maps

abstract:
  The method of asymptotics beyond all orders (ABAO) is known to be a useful
tool to investigate separatrix splitting of several maps. For a class of
simplectic maps, the form of maps is shown to be restricted by the conditions
for the ABAO method to work well. More over, we check that the standard map,
H\' enon map and the cubic map satisfy the restrcitions.


title: Scarring by homoclinic and heteroclinic orbits

abstract:
  In addition to the well known scarring effect of periodic orbits, we show
here that homoclinic and heteroclinic orbits, which are cornerstones in the
theory of classical chaos, also scar eigenfunctions of classically chaotic
systems when associated closed circuits in phase space are properly quantized,
thus introducing strong quantum correlations. The corresponding quantization
rules are also established. This opens the door for developing computationally
tractable methods to calculate eigenstates of chaotic systems.


title: Analytic Model of the Universal Structure of Turbulent Boundary Layers

abstract:
  Turbulent boundary layers exhibit a universal structure which nevertheless is
rather complex, being composed of a viscous sub-layer, a buffer zone, and a
turbulent log-law region. In this letter we present a simple analytic model of
turbulent boundary layers which culminates in explicit formulae for the
profiles of the mean velocity, the kinetic energy and the Reynolds stress as a
function of the distance from the wall. The resulting profiles are in close
quantitative agreement with measurements over the entire structure of the
boundary layer, without any need of re-fitting in the different zones.


title:
On the structure of $(2+1)$--dimensional commutative and noncommutative
  integrable equations

abstract:
  We develop the symbolic representation method to derive the hierarchies of
$(2+1)$-dimensional integrable equations from the scalar Lax operators and to
study their properties globally. The method applies to both commutative and
noncommutative cases in the sense that the dependent variable takes its values
in ${\mathbb C}$ or a noncommutative associative algebra. We prove that these
hierarchies are indeed quasi-local in the commutative case as conjectured by
Mikhailov and Yamilov in 1998. We propose a ring extension based on the
symbolic representation. As examples, we give noncommutative versions of KP,
mKP and Boussinesq equations.


title:
Strength distributions and symmetry breaking in coupled microwave
  billiards

abstract:
  Flat microwave cavities can be used to experimentally simulate quantum
mechanical systems. By coupling two such cavities, we study the equivalent to
the symmetry breaking in quantum mechanics. As the coupling is tunable, we can
measure resonance strength distributions as a function of the symmetry
breaking. We analyze the data employing a qualitative model based on Random
Matrix Theory (RMT) and show that the results derived from the strength
distribution are consistent with those previously obtained from spectral
statistics.


title: Clustering of heavy particles in the inertial range of turbulence

abstract:
  A statistical description of heavy particles suspended in incompressible
rough self-similar flows is developed. It is shown that, differently from
smooth flows, particles do not form fractal clusters. They rather distribute
inhomogeneously with a statistics that only depends on a local Stokes number,
given by the ratio between the particles' response time and the turnover time
associated to the observation scale. Particle clustering is reduced when
increasing the fluid roughness. Heuristic arguments supported by numerics are
used to explain this effect in terms of the algebraic tails of the probability
density function of the velocity difference between two particles. These tails
are a signature of events during which particle couples approach each other
very closely.


title: q-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy

abstract:
  Using the determinant representation of gauge transformation operator, we
have shown that the general form of $\tau$ function of the $q$-KP hierarchy is
a q-deformed generalized Wronskian, which includes the q-deformed Wronskian as
a special case. On the basis of these, we study the q-deformed constrained KP
($q$-cKP) hierarchy, i.e. $l$-constraints of $q$-KP hierarchy. Similar to the
ordinary constrained KP (cKP) hierarchy, a large class of solutions of $q$-cKP
hierarchy can be represented by q-deformed Wronskian determinant of functions
satisfying a set of linear $q$-partial differential equations with constant
coefficients. We obtained additional conditions for these functions imposed by
the constraints. In particular, the effects of $q$-deformation ($q$-effects) in
single $q$-soliton from the simplest $\tau$ function of the $q$-KP hierarchy
and in multi-$q$-soliton from one-component $q$-cKP hierarchy, and their
dependence of $x$ and $q$, were also presented. Finally, we observe that
$q$-soliton tends to the usual soliton of the KP equation when $x\to 0$ and
$q\to 1$, simultaneously.


title: An integrable hierarchy with a perturbed Henon-Heiles system

abstract:
  We consider an integrable scalar partial differential equation (PDE) that is
second order in time. By rewriting it as a system and applying the
Wahlquist-Estabrook prolongation algebra method, we obtain the zero curvature
representation of the equation, which leads to a Lax representation in terms of
an energy-dependent Schr\"{o}dinger spectral problem of the type studied by
Antonowicz and Fordy. The solutions of this PDE system, and of its associated
hierarchy of commuting flows, display weak Painlev\'e behaviour, i.e. they have
algebraic branching. By considering the travelling wave solutions of the next
flow in the hierarchy, we find an integrable perturbation of the case (ii)
Henon-Heiles system which has the weak Painlev\'{e} property. We perform
separation of variables for this generalized Henon-Heiles system, and describe
the corresponding solutions of the PDE.


title:
Clusters die hard: Time-correlated excitation in the Hamiltonian Mean
  Field model

abstract:
  The Hamiltonian Mean Field (HMF) model has a low-energy phase where $N$
particles are trapped inside a cluster. Here, we investigate some properties of
the trapping/untrapping mechanism of a single particle into/outside the
cluster. Since the single particle dynamics of the HMF model resembles the one
of a simple pendulum, each particle can be identified as a high-energy particle
(HEP) or a low-energy particle (LEP), depending on whether its energy is above
or below the separatrix energy. We then define the trapping ratio as the ratio
of the number of LEP to the total number of particles and the
``fully-clustered'' and ``excited'' dynamical states as having either no HEP or
at least one HEP. We analytically compute the phase-space average of the
trapping ratio by using the Boltzmann-Gibbs stable stationary solution of the
Vlasov equation associated with the $N \to \infty$ limit of the HMF model. The
same quantity, obtained numerically as a time average, is shown to be in very
good agreement with the analytical calculation. Another important feature of
the dynamical behavior of the system is that the dynamical state changes
transitionally: the ``fully-clustered'' and ``excited'' states appear in turn.
We find that the distribution of the lifetime of the ``fully-clustered'' state
obeys a power law. This means that clusters die hard, and that the excitation
of a particle from the cluster is not a Poisson process and might be controlled
by some type of collective motion with long memory. Such behavior should not be
specific of the HMF model and appear also in systems where {\it itinerancy}
among different ``quasi-stationary'' states has been observed. It is also
possible that it could mimick the behavior of transient motion in molecular
clusters or some observed deterministic features of chemical reactions.


title:
Power expansions for the self-similar solutions of the modified
  Savada-Kotera equation

abstract:
  The fourth-order ordinary differential equation, defining new transcendents,
is studied. The self-similar solutions of the Kaup-Kupershmidt and
Savada-Kotera equations are shown to be found taking its solutions into
account. Equation studied belongs to the class of fourth-order analogues of the
Painlev\'{e} equations. All the power and non-power asymptotic forms and
expansions near points $z=0$, $z=\infty$ and near arbitrary point $z=z_0$ are
found by means of power geometry methods. The exponential additions to the
solutions of studied equation are also determined.


title: Small scale statistics of viscoelastic turbulence

abstract:
  The small scale statistics of homogeneous isotropic turbulence of dilute
polymer solutions is investigated by means of direct numerical simulations of a
simplified viscoelastic fluid model. It is found that polymers only partially
suppress the turbulent cascade below the Lumley scale, leaving a remnant energy
flux even for large elasticity. As a consequence, fluid acceleration in
viscoelastic flows is reduced with respect to Newtonian turbulence, whereas its
rescaled probability density is left unchanged. At large scales the velocity
field is found to be unaffected by the presence of polymers.


title: A synthesis and a practical approach to complex systems

abstract:
  This document is both a synthesis of current notions about complex systems,
and a practical approach description. A disambiguation is proposed and exposes
possible reasons for controversies related to causation and emergence.
Theoretical considerations about simulations are presented. A justification is
then given for the development of practical tools and techniques for the
investigation of complex systems. A methodology for the usage of these tools is
finally suggested, illustrated by application examples.


title: Time delay in the Kuramoto model with bimodal frequency distribution

abstract:
  We investigate the effects of a time-delayed all-to-all coupling scheme in a
large population of oscillators with natural frequencies following a bimodal
distribution. The regions of parameter space corresponding to synchronized and
incoherent solutions are obtained both numerically and analytically for
particular frequency distributions. In particular we find that bimodality
introduces a new time scale that results in a quasiperiodic disposition of the
regions of incoherence.


title: On the Integrability of a Class of Nonlinear Dispersive Wave Equations

abstract:
  We investigate the integrability of a class of 1+1 dimensional models
describing nonlinear dispersive waves in continuous media, e.g. cylindrical
compressible hyperelastic rods, shallow water waves, etc. The only completely
integrable cases coincide with the Camassa-Holm and Degasperis-Procesi
equations.


title: Integrable dispersionless KdV hierarchy with sources

abstract:
  An integrable dispersionless KdV hierarchy with sources (dKdVHWS) is derived.
Lax pair equations and bi-Hamiltonian formulation for dKdVHWS are formulated.
Hodograph solution for the dispersionless KdV equation with sources (dKdVWS) is
obtained via hodograph transformation. Furthermore, the dispersionless
Gelfand-Dickey hierarchy with sources (dGDHWS) is presented.


title:
Convective stabilization of a Laplacian moving boundary problem with
  kinetic undercooling

abstract:
  We study the shape stability of disks moving in an external Laplacian field
in two dimensions. The problem is motivated by the motion of ionization fronts
in streamer-type electric breakdown. It is mathematically equivalent to the
motion of a small bubble in a Hele-Shaw cell with a regularization of kinetic
undercooling type, namely a mixed Dirichlet-Neumann boundary condition for the
Laplacian field on the moving boundary. Using conformal mapping techniques,
linear stability analysis of the uniformly translating disk is recast into a
single PDE which is exactly solvable for certain values of the regularization
parameter. We concentrate on the physically most interesting exactly solvable
and non-trivial case. We show that the circular solutions are linearly stable
against smooth initial perturbations. In the transformation of the PDE to its
normal hyperbolic form, a semigroup of automorphisms of the unit disk plays a
central role. It mediates the convection of perturbations to the back of the
circle where they decay. Exponential convergence to the unperturbed circle
occurs along a unique slow manifold as time $t\to\infty$. Smooth temporal
eigenfunctions cannot be constructed, but excluding the far back part of the
circle, a discrete set of eigenfunctions does span the function space of
perturbations. We believe that the observed behaviour of a convectively
stabilized circle for a certain value of the regularization parameter is
generic for other shapes and parameter values. Our analytical results are
illustrated by figures of some typical solutions.


title: Bifurcations of discrete breathers in a diatomic Fermi-Pasta-Ulam chain

abstract:
  Discrete breathers are time-periodic, spatially localized solutions of the
equations of motion for a system of classical degrees of freedom interacting on
a lattice. Such solutions are investigated for a diatomic Fermi-Pasta-Ulam
chain, i. e., a chain of alternate heavy and light masses coupled by anharmonic
forces. For hard interaction potentials, discrete breathers in this model are
known to exist either as ``optic breathers'' with frequencies above the optic
band, or as ``acoustic breathers'' with frequencies in the gap between the
acoustic and the optic band. In this paper, bifurcations between different
types of discrete breathers are found numerically, with the mass ratio m and
the breather frequency omega as bifurcation parameters. We identify a period
tripling bifurcation around optic breathers, which leads to new breather
solutions with frequencies in the gap, and a second local bifurcation around
acoustic breathers. These results provide new breather solutions of the FPU
system which interpolate between the classical acoustic and optic modes. The
two bifurcation lines originate from a particular ``corner'' in parameter space
(omega,m). As parameters lie near this corner, we prove by means of a center
manifold reduction that small amplitude solutions can be described by a
four-dimensional reversible map. This allows us to derive formally a continuum
limit differential equation which characterizes at leading order the
numerically observed bifurcations.


title: Can one count the shape of a drum?

abstract:
  Sequences of nodal counts store information on the geometry (metric) of the
domain where the wave equation is considered. To demonstrate this statement, we
consider the eigenfunctions of the Laplace-Beltrami operator on surfaces of
revolution. Arranging the wave functions by increasing values of the
eigenvalues, and counting the number of their nodal domains, we obtain the
nodal sequence whose properties we study. This sequence is expressed as a trace
formula, which consists of a smooth (Weyl-like) part which depends on global
geometrical parameters, and a fluctuating part which involves the classical
periodic orbits on the torus and their actions (lengths). The geometrical
content of the nodal sequence is thus explicitly revealed.


title: Excitability in a nonlinear magnetoacoustic resonator

abstract:
  We report a nonlinear acoustic system displaying excitability. The considered
system is a magnetostrictive material where acoustic waves are parametrically
generated. For a set of parameters, the system presents homoclinic and
heteroclinic dynamics, whose boundaries define a excitability domain. The
excitable behaviour is characterized by analyzing the response of the system to
different external stimuli. Single spiking and bursting regimes have been
identified.


title:
Harmonic maps, Backlund-Darboux transformations and "line soliton"
  analogs

abstract:
  Harmonic maps from $\BR^2$ or one-connected domain ${\O}\subset \BR^2$ into
$GL(m, \BC)$ and $U(m)$ are treated. The GBDT version of the B\"acklund-Darboux
transformation is applied to the case of the harmonic maps. A new general
formula on the GBDT transformations of the Sym-Tafel immersions is derived. A
class of the harmonic maps similar in certain ways to line-solitons is obtained
explicitly and studied.


title: Generalised Recurrence Plot Analysis for Spatial Data

abstract:
  Recurrence plot based methods are highly efficient and widely accepted tools
for the investigation of time series or one-dimensional data. We present an
extension of the recurrence plots and their quantifications in order to study
recurrent structures in higher-dimensional spatial data. The capability of this
extension is illustrated on prototypical 2D models. Next, the tested and proved
approach is applied to assess the bone structure from CT images of human
proximal tibia. We find that the spatial structures in trabecular bone become
more self-similar during the bone loss in osteoporosis.


title:
Casualty Dynamics in Wars and Terrorism and the Scale-Free Organization
  of Social Systems

abstract:
  In this paper I propose a 'mechanism' for the explanation of power-law
characteristics of casualty dynamics in inter-state wars, intra-state wars and
terrorist attacks: the scale-free physical organization of social systems.
Other explanations - self-organized criticality (Cederman, 2003) and the
redistribution of total attack capabilities (Johnson et al. 2006) - do not
provide a consistent framework for the power-law characteristics of casualty
dynamics. The development in time of the power-law characteristics of casualty
dynamics during wars and conflicts provides clues for the 'functioning' of
social systems which are targeted, and/or for the (in)effectiveness and
strategies of actors using force (violence) against these social systems.


title:
The generalized Davey-Stewartson equations, its Kac-Moody-Virasoro
  symmetry algebra and relation to DS equations

abstract:
  We compute the Lie symmetry algebra of the generalized Davey-Stewartson (GDS)
equations and show that under certain conditions imposed on parameters in the
system it is infinite-dimensional and isomorphic to that of the standard
integrable Davey-Stewartson equations which is known to have a very specific
Kac-Moody-Virasoro loop algebra structure. We discuss how the Virasoro part of
this symmetry algebra can be used to construct new solutions, which are of
vital importance in demonstrating existence of blow-up profiles, from known
ones using Lie subgroup of transformations generated by three-dimensional
subalgebras, namely $\Sl(2,\mathbb{R})$. We further discuss integrability
aspects of GDS equations.


title: On a class of third order mappings with two rational invariants

abstract:
  A novel family of integrable third order maps is presented. Each map
possesses, by construction, a pair of rational invariants and a commuting map
from the same class. The 3-dimensional invariant curve is parametrized, in
general, by an elliptic curve.


title:
Energy evolution in time-dependent harmonic oscillator with arbitrary
  external forcing

abstract:
  The classical Hamiltonian system of time-dependent harmonic oscillator driven
by the arbitrary external time-dependent force is considered. Exact analytical
solution of the corresponding equations of motion is constructed in the
framework of the technique (Robnik M, Romanovski V G, J. Phys. A: Math. Gen.
{\bf 33} (2000) 5093) based on WKB approach. Energy evolution for the ensemble
of uniformly distributed w.r.t. the canonical angle initial conditions on the
initial invariant torus is studied. Exact expressions for the energy moments of
arbitrary order taken at arbitrary time moment are analytically derived.
Corresponding characteristic function is analytically constructed in the form
of infinite series and numerically evaluated for certain values of the system
parameters. Energy distribution function is numerically obtained in some
particular cases. In the limit of small initial ensemble's energy the relevant
formula for the energy distribution function is analytically derived.


title: A Model of Intra-seasonal Oscillations in the Earth atmosphere

abstract:
  We suggest a way of rationalizing an intra-seasonal oscillations (IOs) of the
Earth atmospheric flow as four meteorological relevant triads of interacting
planetary waves, isolated from the system of all the rest planetary waves.
  Our model is independent of the topography (mountains, etc.) and gives a
natural explanation of IOs both in the North and South Hemispheres. Spherical
planetary waves are an example of a wave mesoscopic system obeying discrete
resonances that also appears in other areas of physics.


title:
Fay-like identities of the Toda Lattice Hierarchy and its dispersionless
  limit

abstract:
  In this paper, we derive the Fay-like identities of tau function for the Toda
lattice hierarchy from the bilinear identity. We prove that the Fay-like
identities are equivalent to the hierarchy. We also show that the
dispersionless limit of the Fay-like identities are the dispersionless Hirota
equations of the dispersionless Toda hierarchy.


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

abstract:
  The B\"{a}cklund transformations between the constrained dispersionless KP
hierarchy (cdKPH) and the constrained dispersionless mKP hieararchy (cdmKPH)
and between the dispersionless KP hieararchy with self-consistent sources
(dKPHSCS) and the dispersionless mKP hieararchy with self-consistent sources
(dmKPHSCS) are constructed. The auto-B\"{a}cklund transformations for the
cdmKPH and for the dmKPHSCS are also formulated.


title:
Ignition and Front Propagation in Polymer Electrolyte Membrane Fuel
  Cells

abstract:
  Water produced in a Polymer Electrolyte Membrane (PEM) fuel cell enhances
membrane proton conductivity; this positive feedback loop can lead to current
ignition. Using a segmented anode fuel cell we study the effect of gas phase
convection and membrane diffusion of water on the spatiotemporal nonlinear
dynamics - localized ignition and front propagation - in the cell. Co-current
gas flow causes ignition at the cell outlet, and membrane diffusion causes the
front to slowly propagate to the inlet; counter-current flow causes ignition in
the interior of the cell, with the fronts subsequently spreading towards both
inlets. These instabilities critically affect fuel cell performance.


title:
Algebro-Geometric Constraints on Solitons with Respect to Quasi-Periodic
  Backgrounds

abstract:
  We investigate the algebraic conditions the scattering data of short-range
perturbations of quasi-periodic finite-gap Jacobi operators have to satisfy. As
our main result we provide the Poisson-Jensen-type formula for the transmission
coefficient in terms of Abelian integrals on the underlying hyperelliptic
Riemann surface and give an explicit condition for its single-valuedness. In
addition, we establish trace formulas which relate the scattering data to the
conserved quantities in this case.


title: Prequantum chaos: Resonances of the prequantum cat map

abstract:
  Prequantum dynamics has been introduced in the 70' by
Kostant-Souriau-Kirillov as an intermediate between classical and quantum
dynamics. In common with the classical dynamics, prequantum dynamics transports
functions on phase space, but add some phases which are important in quantum
interference effects. In the case of hyperbolic dynamical systems, it is
believed that the study of the prequantum dynamics will give a better
understanding of the quantum interference effects for large time, and of their
statistical properties. We consider a linear hyperbolic map M in SL(2,Z) which
generates a chaotic dynamics on the torus. This dynamics is lifted on a
prequantum fiber bundle. This gives a unitary prequantum (partially hyperbolic)
map. We calculate its resonances and show that they are related with the
quantum eigenvalues. A remarkable consequence is that quantum dynamics emerges
from long time behaviour of prequantum dynamics. We present trace formulas, and
discuss perspectives of this approach in the non linear case.


title: Periodic structure of spin-transfer current in ferromagnetic multilayers

abstract:
  We show that the drift-diffusion mechanism in a normal-metal layer in
combination with the resonance electron-magnon interactions at
ferromagnet-normal interface of F-N-F heterostucture creates spatial
instability modes and, out of these modes, a quasi-stable periodic structure of
spin-transfer d.c. current can arise with certain channel step and
step-to-radius ratio. The ferromagnetic resonance conditions determine
spin-transfer current density. Independent nano-oscillators creating
intersecting arrays of channels can phase-lock on sub-micrometer distance,
which depends on multilayer geometry and applied fields. By decreasing the
layer thickness, the number of channels affected by each independent
d.c.-current source and their radius may be diminished. Phase-locking of
multiple independent nano-oscillators can be used for enhancement of output
power.


title:
The Effects of Lagrangian vs. Population Dynamics on Plankton Patchiness
  Generation

abstract:
  The relative importance of Lagrangian and population dynamics on spatial
pattern formation in the distribution of plankton near the ocean's surface is
investigated. Phytoplankton and zooplankton are treated as biologically
interacting tracers that are passively advected by a divergence-free
two-dimensional nonsteady velocity field. The time-dependence of this field is
assumed to be quasiperiodic, which extends the analysis presented beyond
standard chaotic advection. Various forms of predator--prey interactions,
including complex interactions, are considered. Numerical simulations
illustrate how Lagrangian dynamics, which is characterized by a mixed phase
space with coexisting regular and chaotic motion regions, influences plankton
patchiness generation depending on the nature of the biological interactions.


title: Runup of nonlinear asymmetric waves on a plane beach

abstract:
  The problem of the long wave runup on a beach is discussed in the framework
of the rigorous solutions of the nonlinear shallow-water theory. The key and
novel moment here is the analysis of the runup of a certain class of asymmetric
waves, the face slope steepness of which exceeds the back slope steepness.
Shown is that the runup height increases when the relative face slope steepness
increases whereas the rundown weakly depends on the steepness. The results
partially explain why the tsunami waves with the steep front (as it was for the
2004 tsunami in the Indian Ocean) penetrate deeper into inland compared with
symmetric waves of the same height and length.


title:
Long-time signatures of short-time dynamics in decaying quantum-chaotic
  systems

abstract:
  We analyze the decay of classically chaotic quantum systems in the presence
of fast ballistic escape routes on the Ehrenfest time scale. For a continuous
excitation process, the form factor of the decay cross section deviates from
the universal random-matrix result on the Heisenberg time scale, i.e. for times
much larger than the time for ballistic escape. We derive an exact analytical
description and compare our results with numerical simulations for a dynamical
model.


title: Self-similarity in Laplacian Growth

abstract:
  We consider Laplacian Growth of self-similar domains in different geometries.
Self-similarity determines the analytic structure of the Schwarz function of
the moving boundary. The knowledge of this analytic structure allows us to
derive the integral equation for the conformal map. It is shown that solutions
to the integral equation obey also a second order differential equation which
is the one dimensional Schroedinger equation with the sinh inverse square
potential. The solutions, which are expressed through the Gauss hypergeometric
function, characterize the geometry of self-similar patterns in a wedge. We
also find the potential for the Coulomb gas representation of the self-similar
Laplacian growth in a wedge and calculate the corresponding free energy.


title:
Coisotropic deformations of associative algebras and dispersionless
  integrable hierarchies

abstract:
  The paper is an inquiry of the algebraic foundations of the theory of
dispersionless integrable hierarchies, like the dispersionless KP and modified
KP hierarchies and the universal Whitham's hierarchy of genus zero. It stands
out for the idea of interpreting these hierarchies as equations of coisotropic
deformations for the structure constants of certain associative algebras. It
discusses the link between the structure constants and the Hirota's tau
function, and shows that the dispersionless Hirota's bilinear equations are,
within this approach, a way of writing the associativity conditions for the
structure constants in terms of the tau function. It also suggests a simple
interpretation of the algebro-geometric construction of the universal Whitham's
equations of genus zero due to Krichever.


title: Psi-Series Solution of Fractional Ginzburg-Landau Equation

abstract:
  One-dimensional Ginzburg-Landau equations with derivatives of noninteger
order are considered. Using psi-series with fractional powers, the solution of
the fractional Ginzburg-Landau (FGL) equation is derived. The leading-order
behaviours of solutions about an arbitrary singularity, as well as their
resonance structures, have been obtained. It was proved that fractional
equations of order $alpha$ with polynomial nonlinearity of order $s$ have the
noninteger power-like behavior of order $\alpha/(1-s)$ near the singularity.


title:
The Painleve Test and Reducibility to the Canonical Forms for
  Higher-Dimensional Soliton Equations with Variable-Coefficients

abstract:
  The general KdV equation (gKdV) derived by T. Chou is one of the famous (1+1)
dimensional soliton equations with variable coefficients. It is well-known that
the gKdV equation is integrable. In this paper a higher-dimensional gKdV
equation, which is integrable in the sense of the Painleve test, is presented.
A transformation that links this equation to the canonical form of the
Calogero-Bogoyavlenskii-Schiff equation is found. Furthermore, the form and
similar transformation for the higher-dimensional modified gKdV equation are
also obtained.


title: A note on the superintegrability of the Toda lattice

abstract:
  The superintegrability of the non-periodic Toda lattice is explained in the
framework of systems written in action-angles coordinates. Moreover, a simpler
form of the first integrals is given.


title: Electromagnetically induced switching of ferroelectric thin films

abstract:
  We analyze the interaction of an electromagnetic spike (one cycle) with a
thin layer of ferroelectric medium with two equilibrium states. The model is
the set of Maxwell equations coupled to the undamped Landau-Khalatnikov
equation, where we do not assume slowly varying envelopes. From linear
scattering theory, we show that low amplitude pulses can be completely
reflected by the medium. Large amplitude pulses can switch the ferroelectric.
Using numerical simulations and analysis, we study this switching for long and
short pulses, estimate the switching times and provide useful information for
experiments.


title:
On the proper reconstruction of complex dynamical systems spoilt by
  strong measurement noise

abstract:
  This article reports on a new approach to properly analyze time series of
dynamical systems which are spoilt by the simultaneous presence of dynamical
noise and measurement noise. It is shown that even strong external measurement
noise as well as dynamical noise which is an intrinsic part of the dynamical
process can be quantified correctly, solely on the basis of measured times
series and proper data analysis. Finally real world data sets are presented
pointing out the relevance of the new approach.


title:
Classification of integrable Hamiltonian hydrodynamic chains associated
  with Kupershmidt's brackets

abstract:
  We characterize a class of integrable Hamiltonian hydrodynamic chains, based
on the necessary condition for the integrability provided by the vanishing of
the Haantjes tensor. We prove that the vanishing of the first few components of
the Haantjes tensor is already sufficiently restrictive, and allows a complete
description of the corresponding Hamiltonian densities. In each of the cases we
were able to explicitly construct a generating function for conservation laws,
thus establishing the integrability.


title: Analyticity of the SRB measure for a class of simple Anosov flows

abstract:
  We consider perturbations of the Hamiltonian flow associated with the
geodesic flow on a surface of constant negative curvature. We prove that, under
a small perturbation, not necessarely of Hamiltonian character, the SRB measure
associated to the flow exists and is analytic in the strength of the
perturbation. An explicit example of "thermostatted" dissipative dynamics is
constructed.


title:
Spiral Instabilities in Rayleigh-B\'enard Convection under Localized
  Heating

abstract:
  We study from the numerical point of view, instabilities developed in a fluid
layer with a free surface, in a cylindrical container which is
non-homogeneously heated from below. In particular we consider the case in
which the applied heat is localized around the origin. An axysimmetric basic
state appears as soon a non-zero horizontal temperature gradient is imposed.
The basic state may bifurcate to different solutions depending on vertical and
lateral temperature gradients and on the shape of the heating function. We find
different kinds of instabilities: extended patterns growing on the whole domain
which include those known as targets and spirals waves. Spirals are present
even for infinite Prandtl number. Localized structures both at the origin and
at the outer part of the cylinder may appear either as Hopf or stationary
bifurcations. An overview of the developed instabilities as a function of the
dimesionless parameters is reported in this article.


title: Reynolds number dependence of drag reduction by rod-like polymers

abstract:
  We present experimental and theoretical results addressing the Reynolds
number (Re) dependence of drag reduction by sufficiently large concentrations
of rod-like polymers in turbulent wall-bounded flows. It is shown that when Re
is small the drag is {\em enhanced}. On the other hand when Re increases the
drag is reduced and eventually the Maximal Drag Reduction (MDR) asymptote is
attained. The theory is shown to be in excellent agreement with experiments,
rationalizing and explaining all the universal and the non-universal aspects of
drag reduction by rod-like polymers.


title: Universality classes in Burgers turbulence

abstract:
  We establish necessary and sufficient conditions for the shock statistics to
approach self-similar form in Burgers turbulence with L\'{e}vy process initial
data. The proof relies upon an elegant closure theorem of Bertoin and Carraro
and Duchon that reduces the study of shock statistics to Smoluchowski's
coagulation equation with additive kernel, and upon our previous
characterization of the domains of attraction of self-similar solutions for
this equation.


title:
Propagation of localized optical waves in media with dispersion, in
  dispersionless media and in vacuum. Non-diffracting pulses

abstract:
  The applied method of the amplitude envelopes give us the possibility to
describe a new class of amplitude equations governing the propagation of
optical pulses in media with dispersion, dispersionless media and vacuum. We
normalized these amplitude equations and obtained five dimensionless parameters
that determine different linear and nonlinear regimes of the optical pulses
evolution. Surprisingly, in linear regime the normalized amplitude equations
for media with dispersion and the amplitude equations in dispersionless media
and vacuum are equal with precise - material constants. The equations were
solved for pulses with low intensity (linear regime), using the method of
Fourier transforms. One unexpected new result was the relative stability of
light bullets and light disks and the significant reduction of their
diffraction enlargement. It is important to emphasize here the case of light
disks, which turn out to be practically diffractionless over distances of more
than hundred kilometers.


title:
Modulated Amplitude Waves in Collisionally Inhomogeneous Bose-Einstein
  Condensates

abstract:
  We investigate the dynamics of an effectively one-dimensional Bose-Einstein
condensate (BEC) with scattering length $a$ subjected to a spatially periodic
modulation, $a=a(x)=a(x+L)$. This "collisionally inhomogeneous" BEC is
described by a Gross-Pitaevskii (GP) equation whose nonlinearity coefficient is
a periodic function of $x$. We transform this equation into a GP equation with
constant coefficient $a$ and an additional effective potential and study a
class of extended wave solutions of the transformed equation. For weak
underlying inhomogeneity, the effective potential takes a form resembling a
superlattice, and the amplitude dynamics of the solutions of the
constant-coefficient GP equation obey a nonlinear generalization of the Ince
equation. In the small-amplitude limit, we use averaging to construct
analytical solutions for modulated amplitude waves (MAWs), whose stability we
subsequently examine using both numerical simulations of the original GP
equation and fixed-point computations with the MAWs as numerically exact
solutions. We show that "on-site" solutions, whose maxima correspond to maxima
of $a(x)$, are significantly more stable than their "off-site" counterparts.

categories: nlin.PS cond-mat.other math.DS physics.atom-ph


title: Fractal Properties of Anomalous Diffusion in Intermittent Maps

abstract:
  An intermittent nonlinear map generating subdiffusion is investigated.
Computer simulations show that the generalized diffusion coefficient of this
map has a fractal, discontinuous dependence on control parameters. An amended
continuous time random walk theory well approximates the coarse behavior of
this quantity in terms of a continuous function. This theory also reproduces a
full suppression of the strength of diffusion, which occurs at the dynamical
phase transition from one type of diffusive behavior to another. Similarly, the
probability density function of this map exhibits a nontrivial fine structure
while its coarse functional form is governed by a time fractional diffusion
equation. A more detailed understanding of the irregular structure of the
generalized diffusion coefficient is provided by an anomalous Taylor-Green-Kubo
formula establishing a relation to de Rham-type fractal functions.


title: Bright solitons in asymmetrically trapped Bose-Einstein condensate

abstract:
  We study the dynamics of bright solitons in a Bose-Einstein condensate (BEC)
confined in a highly asymmetric trap. While working within the f ramework of a
variational approach we carry out the stability analysis o f BEC solitons
against collapse. When the number of atoms in the soliton exceeds a critical
number $N_c$, it undergoes the so called primary col lapse. We find an
analytical expression for $N_c$ in terms of appropriat e experimental
quantities that are used to produce and confine the conde nsate. We further
demonstrate that, in the geometry of the problem consi dered, the width of the
soliton varies inversely as the number of consti tuent atoms.


title: On Coherent Optical Pulse Propagation in One-Dimensional Bragg Grating

abstract:
  The propagation of the solitary waves in the Bragg grating formed by array of
thin dielectric films is considered. We assume that the thin films of contain
the resonant molecules, which are evolved according to two-level atoms model,
which is used to description of the coherent optical pulses propagation. There
the alternative derivation of the Mantsyzov's equations is represented.


title:
Analytical description of the coherent structures within the hyperbolic
  generalization of Burgers equation

abstract:
  We present new periodic, kink-like and soliton-like travelling wave solutions
to the hyperbolic generalization of Burgers equation. To obtain them, we employ
the classical and generalized symmetry methods and the ansatz-based approach


title:
Non-ergodicity of the motion in three dimensional steep repelling
  dispersing potentials

abstract:
  It is demonstrated numerically that smooth three degrees of freedom
Hamiltonian systems which are arbitrarily close to three dimensional strictly
dispersing billiards (Sinai billiards) have islands of effective stability, and
hence are non-ergodic. The mechanism for creating the islands are corners of
the billiard domain.


title: Coherent vector pi-pulse in optical amplifiers

abstract:
  We obtain an exact vector solitary solution for the amplification of an
optical pulse with a time width short compared with both population and
polarization decay time. This dissipative soliton results from the balance
between the gain from inverted resonant two-level atoms and the linear loss of
the host material. We suppose that the excited state of the active centers is
degenerate on the projection of the angular moment. Numerical simulations
demonstrate the stability of these vector dissipative solitons in the presence
of both linear birefringence and group velocity dispersion of the host
material.


title: Chaotic mixing and transport in a meandering jet flow

abstract:
  Mixing and transport of passive particles are studied in a simple kinematic
model of a meandering jet flow motivated by the problem of lateral mixing and
transport in the Gulf Stream. We briefly discuss a model streamfunction,
Hamiltonian advection equations, stationary points, and bifurcations. The phase
portrait of the chosen model flow in the moving reference frame consists of a
central eastward jet, chains of northern and southern circulations, and
peripheral westward currents. Under a periodic perturbation of the meander's
amplitude, the topology of the phase space is complicated by the presence of
chaotic layers and chains of oscillatory and ballistic islands with sticky
boundaries immersed into a stochastic sea. Typical chaotic trajectories of
advected particles are shown to demonstrate a complicated behavior with long
flights in both the directions of motion intermittent with trapping in the
circulation cells being stuck to the boundaries of vortex cores and resonant
islands. Transport is asymmetric in the sense that mixing between the
circulations and the peripheral currents is, in general, different from mixing
between the circulations and the jet. The transport properties are
characterized by probability distribution functions (PDFs) of durations and
lengths of flights. Both the PDFs exhibit at their tails power-law decay with
different values of exponents.


title:
Dielectric catastrophe at the magnetic field induced insulator to metal
  transition in Pr1-xCaxMnO3 (x=0.30, 0.37) crystals

abstract:
  The dielectric permittivity and resistivity have been measured simultaneously
as a function of magnetic field in Pr1-xCaxMnO3 crystals with different doping.
A huge increase of dielectric permittivity was detected near percolation
threshold. The dielectric and conductive properties are found to be mutually
correlated throughout insulator to metal transition evidencing the dielectric
catastrophe phenomenon. Data are analyzed in a framework of Maxwell-Garnett
theory and the Mott-Hubbard theory attributed to the role of strong Coulomb
interactions.


title: Synchronization by dynamical relaying in electronic circuit arrays

abstract:
  We experimentally study the synchronization of two chaotic electronic
circuits whose dynamics is relayed by a third parameter-matched circuit, to
which they are coupled bidirectionally in a linear chain configuration. In a
wide range of operating parameters, this setup leads to synchronization between
the outer circuits, while the relaying element remains unsynchronized. The
specifics of the synchronization differ with the coupling level: for low
couplings a state of intermittent synchronization between the outer circuits
coexists with one of antiphase synchronization. Synchronization becomes in
phase for moderate couplings, and for strong coupling identical synchronization
is observed between the outer elements, which are themselves synchronized in a
generalized way with the relaying element. In the latter situation, the middle
element displays a triple scroll attractor that is not possible to obtain when
the chaotic oscillator is isolated.


title: Scaling properties of $q$-breathers in nonlinear acoustic lattices

abstract:
  Recently $q$-breathers - time-periodic solutions which localize in the space
of normal modes and maximize the energy density for some mode vector $q_0$ -
were obtained for finite nonlinear lattices. We scale these solutions together
with the size of the system to arbitrarily large lattices. We generalize
previously obtained analytical estimates of the localization length of
$q$-breathers. The first finding is that the degree of localization depends
only on intensive quantities and is size independent. Secondly a critical wave
vector $k_m$ is identified, which depends on one effective nonlinearity
parameter. $q$-breathers minimize the localization length at $k_0=k_m$ and
completely delocalize in the limit $k_0 \to 0$.


title: Lagrangian particle paths and ortho-normal quaternion frames

abstract:
  Experimentalists now measure intense rotations of Lagrangian particles in
turbulent flows by tracking their trajectories and Lagrangian-average velocity
gradients at high Reynolds numbers. This paper formulates the dynamics of an
orthonormal frame attached to each Lagrangian fluid particle undergoing
three-axis rotations, by using quaternions in combination with Ertel's theorem
for frozen-in vorticity. The method is applicable to a wide range of Lagrangian
flows including the three-dimensional Euler equations and its variants such as
ideal MHD. The applicability of the quaterionic frame description to Lagrangian
averaged velocity gradient dynamics is also demonstrated.


title:
On a new fixed point of the renormalization group operator for
  area-preserving maps

abstract:
  The breakup of the shearless invariant torus with winding number
$\omega=\sqrt{2}-1$ is studied numerically using Greene's residue criterion in
the standard nontwist map. The residue behavior and parameter scaling at the
breakup suggests the existence of a new fixed point of the renormalization
group operator (RGO) for area-preserving maps. The unstable eigenvalues of the
RGO at this fixed point and the critical scaling exponents of the torus at
breakup are computed.


title:
Using dimension reduction to improve outbreak predictability of
  multistrain diseases

abstract:
  Multistrain diseases have multiple distinct coexisting serotypes (strains).
For some diseases, such as dengue fever, the serotypes interact by
antibody-dependent enhancement (ADE), in which infection with a single serotype
is asymptomatic, but contact with a second serotype leads to higher viral load
and greater infectivity. We present and analyze a dynamic compartmental model
for multiple serotypes exhibiting ADE. Using center manifold techniques, we
show how the dynamics rapidly collapses to a lower dimensional system. Using
the constructed reduced model, we can explain previously observed synchrony
between certain classes of primary and secondary infectives (Schwartz et al.,
Phys. Rev. E 72: 066201, 2005). Additionally, we show numerically that the
center manifold equations apply even to noisy systems. Both deterministic and
stochastic versions of the model enable prediction of asymptomatic individuals
that are difficult to track during an epidemic. We also show how this technique
may be applicable to other multistrain disease models, such as those with
cross-immunity.


title:
Controlling transitions in a Duffing oscillator by sweeping parameters
  in time

abstract:
  We consider a high-$Q$ Duffing oscillator in a weakly non-linear regime with
the driving frequency $\sigma$ varying in time between $\sigma_i$ and
$\sigma_f$ at a characteristic rate $r$. We found that the frequency sweep can
cause controlled transitions between two stable states of the system. Moreover,
these transitions are accomplished via a transient that lingers for a long time
around the third, unstable fixed point of saddle type. We propose a simple
explanation for this phenomenon and find the transient life-time to scale as
$-(\ln{|r-r_c|})/\lambda_r$ where $r_c$ is the critical rate necessary to
induce a transition and $\lambda_r$ is the repulsive eigenvalue of the saddle.
Experimental implications are mentioned.


title:
Generalized Synchronization in Ginzburg-Landau Equations with Local
  Coupling

abstract:
  The establishment of generalized chaotic synchronization in Ginzburg-Landau
equations unidirectionally coupled at discrete points of space (local coupling)
has been studied. It is shown that generalized syn-chronization regimes are
also established with this type of coupling, but the necessary intensity of
coupling issignificantly higher than that in the case of a spatially
homogeneous coupling


title: The spectral form factor near the Ehrenfest-time

abstract:
  We calculate the Ehrenfest-time dependence of the leading quantum correction
to the spectral form factor of a ballistic chaotic cavity using periodic orbit
theory. For the case of broken time-reversal symmetry, our result differs from
that previously obtained using field-theoretic methods [Tian and Larkin, Phys.
Rev. B 70, 035305 (2004)]. The discrepancy shows that short-time regularization
procedures dramatically affect physics near the Ehrenfest-time.


title: A Spatially Extended Model for Residential Segregation

abstract:
  In this paper we analyze urban spatial segregation phenomenon in terms of the
income distribution over a population, and inflationary parameter weighting the
evolution of housing prices. For this, we develop a discrete, spatially
extended model based in a multi--agent approach. In our model, the mobility of
socioeconomic agents is driven only by the housing prices. Agents exchange
location in order to fit their status to the cost of their housing. On the
other hand, the price of a particular house changes depends on the status of
its tenant, and on the neighborhood mean lodging cost, weighted by a control
parameter. The agent's dynamics converges to a spatially organized
configuration, whose regularity we measured by using an entropy--like
indicator. With this simple model we found a nontrivial dependence of
segregation on both, the initial inequality of the socioeconomic agents and the
inflationary parameter. In this way we supply an explanatory model for the
segregation--inequality thesis putted forward by Douglas Massey.


title: Modeling Time Series Data of Real Systems

abstract:
  Dynamics of complex systems is studied by first considering a chaotic time
series generated by Lorenz equations and adding noise to it. The trend (smooth
behavior) is separated from fluctuations at different scales using wavelet
analysis and a prediction method proposed by Lorenz is applied to make out of
sample predictions at different regions of the time series. The prediction
capability of this method is studied by considering several improvements over
this method. We then apply this approach to a real financial time series. The
smooth time series is modeled using techniques of non linear dynamics. Our
results for predictions suggest that the modified Lorenz method gives better
predictions compared to those from the original Lorenz method. Fluctuations are
analyzed using probabilistic considerations.


title: Dynamical systems on infinitely sheeted Riemann surfaces

abstract:
  This paper is part of a program that aims to understand the connection
between the emergence of chaotic behaviour in dynamical systems in relation
with the multi-valuedness of the solutions as functions of complex time $\tau$.
In this work we consider a family of systems whose solutions can be expressed
as the inversion of a single hyperelliptic integral. The associated Riemann
surface ${\mathcal R}$ is known to be an infinitely sheeted covering of the
complex time plane, ramified at an infinite set of points whose projection in
the $\tau$-plane is dense. The main novelty of this paper is that the
geometrical structure of these infinitely sheeted Riemann surfaces is described
in great detail, which allows to study global properties of the flow such as
asymptotic behaviour of the solutions, periodic orbits and their stability or
sensitive dependence on initial conditions. The results are then compared with
a numerical integration of the equations of motion. Following the recent
approach of Calogero, the real time trajectories of the system are given by
paths on $\mathcal R$ that are projected to a circle on the complex plane
$\tau$. Due to the branching of $\mathcal R$, the solutions may have different
periods or may not be periodic at all.


title: Modeling Time Series of Real Systems using Genetic Programming

abstract:
  Analytic models of two computer generated time series (Logistic map and
Rossler system) and two real time series (ion saturation current in Aditya
Tokamak plasma and NASDAQ composite index) are constructed using Genetic
Programming (GP) framework. In each case, the optimal map that results from
fitting part of the data set also provides a very good description of rest of
the data. Predictions made using the map iteratively range from being very good
to fair.


title:
Formation and light guiding properties of dark solitons in
  one-dimensional waveguide arrays

abstract:
  We report on the formation of dark discrete solitons in a nonlinear periodic
system consisting of evanescently-coupled channel waveguides that are
fabricated in defocusing lithium niobate. Localized nonlinear dark modes
displaying a phase jump in the center that is located either on-channel (mode
A) or in-between channels (mode B) are formed, which is to our knowledge the
first experimental observation of mode B. By numerical simulations we find that
the saturable nature of the nonlinearity is responsible for the improved
stability of mode B. The ability of the induced refractive index structures to
guide light of a low-power probe beam is demonstrated.


title:
Newtonian dynamics in the plane corresponding to straight and cyclic
  motions on the hyperelliptic curve $\mu^2=\nu^n-1, n\in{\Bbb Z}$: ergodicity,
  isochrony, periodicity and fractals

abstract:
  We study the complexification of the one-dimensional Newtonian particle in a
monomial potential. We discuss two classes of motions on the associated Riemann
surface: the rectilinear and the cyclic motions, corresponding to two different
classes of real and autonomous Newtonian dynamics in the plane. The rectilinear
motion has been studied in a number of papers, while the cyclic motion is much
less understood. For small data, the cyclic time trajectories lead to
isochronous dynamics. For bigger data the situation is quite complicated;
computer experiments show that, for sufficiently small degree of the monomial,
the motion is generically periodic with integer period, which depends in a
quite sensitive way on the initial data. If the degree of the monomial is
sufficiently high, computer experiments show essentially chaotic behaviour. We
suggest a possible theoretical explanation of these different behaviours. We
also introduce a one-parameter family of 2-dimensional mappings, describing the
motion of the center of the circle, as a convenient representation of the
cyclic dynamics; we call such mapping the center map. Computer experiments for
the center map show a typical multi-fractal behaviour with periodicity islands.
Therefore the above complexification procedure generates dynamics amenable to
analytic treatment and possessing a high degree of complexity.


title: Spectral-discrete solitons and localization in frequency space

abstract:
  We report families of discrete optical solitons in frequency space, or
spectral-discrete solitons existing in a dispersive Raman medium, where
individual side-bands are coupled by coherence. The associated time-domain
patterns correspond to either trains of ultrashort pulses, or weakly modulated
waves. We describe the physics behind the spectral localization and study
soliton bifurcations, stability and dynamics.


title:
Freedom in Expansion and Asymptotic Integrability of Perturbed Evolution
  Equations

abstract:
  It is shown that the emergence of obstacles to asymptotic integrability in
the analysis of perturbed evolution equations may, often, be a consequence of
the manner, in which the freedom in the ex-pansion is exploited in the
derivation of the equations. Algorithms exist, which yield perturbed evolution
equations that are devoid of the obstacles for cases, in which, traditionally,
obstacles are encountered. The derivation of the perturbed KdV equation for two
physical systems (propagation of small amplitude disturbances on a shallow
fluid layer, and the ion acoustic wave equations in Plasma Physics), where a
second-order obstacle is anticipated, and of the Burgers equation
(one-dimensional propagation of weak shock waves in an ideal gas), where a
first-order obstacle is an-ticipated, is examined. In all cases, the
anticipated obstacles to integrability can be avoided.


title: Gaussian paradox and clustering in intermittent turbulent signals

abstract:
  A relation between intermittency and clustering phenomena in velocity field
has been revealed for homogeneous fluid turbulence. It is described how the
intermittency exponent can be split into sum of two other exponents. One of
these exponents (cluster-exponent) characterizes clustering of the
'zero'-crossing points in nearly Gaussian velocity field and another exponent
is related to the tails of the velocity probability distribution. The
cluster-exponent is uniquely determined by the energy spectrum of the nearly
Gaussian velocity field and entire dependence of the intermittency exponent on
Reynolds number is determined by the cluster-exponent.


title: Resonance-assisted decay of nondispersive wave packets

abstract:
  We present a quantitative semiclassical theory for the decay of nondispersive
electronic wave packets in driven, ionizing Rydberg systems. Statistically
robust quantities are extracted combining resonance assisted tunneling with
subsequent transport across chaotic phase space and a final ionization step.


title: Measurement of entropy production rate in compressible turbulence

abstract:
  The rate of change of entropy $\dot S$ is measured for a system of particles
floating on the surface of a fluid maintained in a turbulent steady state. The
resulting coagulation of the floaters allows one to relate $\dot S$ to the
velocity divergence and to the Lyapunov exponents characterizing the behavior
of this system. The quantities measured from experiments and simulations are
found to agree well with the theoretical predictions.


title:
Test of the Fluctuation Relation in lagrangian turbulence on a free
  surface

abstract:
  The statistics of lagrangian velocity divergence are studied for an assembly
of particles in compressible turbulence on a free surface. Under an appropriate
definition of entropy, the two-dimensional lagrangian velocity divergence of a
particle trajectory represents the local entropy rate, a random variable. The
statistics of this rate are shown to be in agreement with the fluctuation
relation (FR) over a limited range. The probability distribution functions
(PDFs) obtained in this analysis exhibit features different from those observed
in previous experimental tests.


title:
Wave packet autocorrelation functions for quantum hard-disk and
  hard-sphere billiards in the high-energy, diffraction regime

abstract:
  We consider the time evolution of a wave packet representing a quantum
particle moving in a geometrically open billiard that consists of a number of
fixed hard-disk or hard-sphere scatterers. Using the technique of multiple
collision expansions we provide a first-principle analytical calculation of the
time-dependent autocorrelation function for the wave packet in the high-energy
diffraction regime, in which the particle's de Broglie wave length, while being
small compared to the size of the scatterers, is large enough to prevent the
formation of geometric shadow over distances of the order of the particle's
free flight path. The hard-disk or hard-sphere scattering system must be
sufficiently dilute in order for this high-energy diffraction regime to be
achievable. Apart from the overall exponential decay, the autocorrelation
function exhibits a generally complicated sequence of relatively strong peaks
corresponding to partial revivals of the wave packet. Both the exponential
decay (or escape) rate and the revival peak structure are predominantly
determined by the underlying classical dynamics. A relation between the escape
rate, and the Lyapunov exponents and Kolmogorov-Sinai entropy of the
counterpart classical system, previously known for hard-disk billiards, is
strengthened by generalization to three spatial dimensions. The results of the
quantum mechanical calculation of the time-dependent autocorrelation function
agree with predictions of the semiclassical periodic orbit theory.


title: Dynamics of Epidemics

abstract:
  This article examines how diseases on random networks spread in time. The
disease is described by a probability distribution function for the number of
infected and recovered individuals, and the probability distribution is
described by a generating function. The time development of the disease is
obtained by iterating the generating function. In cases where the disease can
expand to an epidemic, the probability distribution function is the sum of two
parts; one which is static at long times, and another whose mean grows
exponentially. The time development of the mean number of infected individuals
is obtained analytically. When epidemics occur, the probability distributions
are very broad, and the uncertainty in the number of infected individuals at
any given time is typically larger than the mean number of infected
individuals.


title: Degenerate dispersive equations arising in the study of magma dynamics

abstract:
  An outstanding problem in Earth science is understanding the method of
transport of magma in the Earth's mantle. Models for this process, transport in
a viscously deformable porous media, give rise to scalar degenerate,
dispersive, nonlinear wave equations. We establish a general local
well-posedness for a physical class of data (roughly $H^1$) via fixed point
methods. The strategy requires positive lower bounds on the solution. This is
extended to global existence for a subset of possible nonlinearities by making
use of certain conservation laws associated with the equations. Furthermore, we
construct a Lyapunov energy functional, which is locally convex about the
uniform state, and prove (global in time) nonlinear dynamic stability of the
uniform state for any choice of nonlinearity. We compare the dynamics to that
of other problems and discuss open questions concerning a larger range of
nonlinearities, for which we conjecture global existence.


title:
Wavelet Analysis of Cycle-to-Cycle Pressure Variations in an Internal
  Combustion Engine

abstract:
  Using a continuous wavelet transform we have analyzed the cycle-to-cycle
variations of pressure in an internal combustion engine. The time series of
maximum pressure variations are examined for different loading and their
wavelet power spectrum is calculated for each load. From the wavelet power
spectrum we detected the presence of long, intermediate and short-term
periodicities in the pressure signal. It is found that depending on the load,
the long and intermediate-term periodicities may span several cycles, whereas
the short-period oscillations tend to appear intermittently. Knowledge of these
periodicities may be useful to develop effective control strategies for
efficient combustion.


title:
A nonlocal connection between certain linear and nonlinear ordinary
  differential equations/oscillators

abstract:
  We explore a nonlocal connection between certain linear and nonlinear
ordinary differential equations (ODEs), representing physically important
oscillator systems, and identify a class of integrable nonlinear ODEs of any
order. We also devise a method to derive explicit general solutions of the
nonlinear ODEs. Interestingly, many well known integrable models can be
accommodated into our scheme and our procedure thereby provides further
understanding of these models.


title: Vibrations of a Pendulum with Oscillating Support and Extra Torque

abstract:
  The motion of a driven planar pendulum with vertically periodically
oscillating point of suspension and under the action of an additional constant
torque is investigated. We study the influence of the torque strength on the
transition to chaotic motions of the pendulum using Melnikov's analysis.


title: Energy flux fluctuations in a finite volume of turbulent flow

abstract:
  The flux of turbulent kinetic energy from large to small spatial scales is
measured in a small domain B of varying size R. The probability distribution
function of the flux is obtained using a time-local version of Kolmogorov's
four-fifths law. The measurements, made at a moderate Reynolds number, show
frequent events where the flux is backscattered from small to large scales,
their frequency increasing as R is decreased. The observations are corroborated
by a numerical simulation based on the motion of many particles and on an
explicit form of the eddy damping.


title:
Where surface physics and fluid dynamics meet: rupture of an amphiphile
  layer by fluid flow

abstract:
  We investigate the fluctuating pattern created by a jet of fluid impingent
upon an amphiphile-covered surface. This microscopically thin layer is
initially covered with 50 $\mu$m floating particles so that the layer can be
visualized. A vertical jet of water located below the surface and directed
upward drives a hole in this layer. The hole is particle-free and is surrounded
by the particle-laden amphiphile region. The jet ruptures the amphiphile layer
creating a particle-free region that is surrounded by the particle-covered
surface. The aim of the experiment is to understand the (fluctuating) shape of
the ramified interface between the particle-laden and particle-free regions.


title: Phase lock and rotational motion of a parametric pendulum

abstract:
  The effect of noise on a rotational mode of a pendulum excited kinematically
in vertical direction has been analyzed. We have shown that for a weak noise
transitions from oscillations to rotations and vice versa are possible. For a
moderate noise level dynamics of the system is governed by a combination of the
excitation amplitude and stochastic component. Consequently for stronger noise
the rotational solution as an independent sychonized mode has vanished.


title: Dissipative solitons which cannot be trapped

abstract:
  In this paper we study the behavior of dissipative solitons in systems with
high order nonlinear dissipation and show how they cannot survive under the
effect of trapping potentials both of rigid wall type or asymptotically
increasing ones. This provides an striking example of a soliton which cannot be
trapped and only survives to the action of a weak potential.


title:
Spot deformation and replication in the two-dimensional
  Belousov-Zhabotinski reaction in water-in-oil microemulsion

abstract:
  In the limit of large diffusivity ratio, spot-like solutions in the
two-dimensional Belousov-Zhabotinski reaction in water-in-oil microemulsion are
studied. It is shown analytically that such spots undergo an instability as the
diffusivity ratio is decreased. An instability threshold is derived. For spots
of small radius, it is shown that this instability leads to a spot splitting
into precisely two spots. For larger spots, it leads to deformation, fingering
patterns and space-filling curves. Numerical simulations are shown to be in
close agreement with the analytical predictions.


title: Simultaneous and Sequential Synchronisation in Arrays

abstract:
  We discuss the possibility of simultaneous and sequential synchronisation in
vertical and horizontal arrays of unidirectionally coupled discrete systems.
This is realized for the specific case of two dimensional Gumowski-Mira maps.
The synchronised state can be periodic,thereby bringing in control of chaos, or
chaotic for carefully chosen parameters of the participating units. The
synchronised chaotic state is further characterised using variation of the time
of synchronisation with coupling coefficient, size of the array etc. In the
case of the horizontal array, the total time of synchronisation can be
controlled by increasing the coupling coefficient step wise in small bunch of
units.


title: Spectral decomposition of 3D Fokker - Planck differential operator

abstract:
  We construct spectral decomposition of 3D Fokker - Planck differential
operator in this paper. We use the decomposition to obtain solution of Cauchy
problem - and especially the fundamental solution. Then we use the
decomposition to calculate macroscopic parameters of Fokker - Planck flow.


title:
Using the Fractal Attrition Equation to Construct a Metamodel of the
  Mana Cellular Automaton Combat Model

abstract:
  In this report the authors examine the possibility of using the Fractal
Attrition Equation as a metamodel to describe outcomes of cellular automaton
combat models. This Fractal Attrition Equation has been proposed as a
replacement for the Lanchester equation. Unlike Lanchester's equation, it is
based on a measurement of the spatial distribution of forces involved in a
battle, and incorporates this by use of the concept of the fractal dimension.
In this report, the form of the expected Loss-Exchange-Ratio function based on
this equation is determined. It is shown how this function can be used as a
Metamodel to describe the outcome of some cellular automaton models. While this
is not an exhaustive proof of the validity of the equation, the case discussed
does display interesting features which should be further investigated. This is
particularly so given the earlier work of the authors in demonstrating that the
Fractal Attrition Equation explains certain features of historical combat data.


title: Elliptic solutions to a generalized BBM equation

abstract:
  An approach is proposed to obtain some exact explicit solutions in terms of
the Weierstrass' elliptic function $\wp$ to a generalized Benjamin-Bona-Mahony
(BBM) equation. Conditions for periodic and solitary wave like solutions can be
expressed compactly in terms of the invariants of $\wp$. The approach unifies
recently established ad-hoc methods to a certain extent. Evaluation of a
balancing principle simplifies the application of this approach.


title: Stability of Periodic Soliton Equations under Short Range Perturbations

abstract:
  We consider the stability of (quasi-)periodic solutions of soliton equations
under short range perturbations and give a complete description of the long
time asymptotics in this situation. We show that, apart from the phenomenon of
the solitons travelling on the quasi-periodic background, the perturbed
solution asymptotically approaches a modulated solution. We use the Toda
lattice as a model but the same methods and ideas are applicable to all soliton
equations in one space dimension.
  More precisely, let $g$ be the genus of the hyperelliptic Riemann surface
associated with the unperturbed solution. We show that the $n/t$-pane contains
$g+2$ areas where the perturbed solution is close to a quasi-periodic solution
in the same isospectral torus. In between there are $g+1$ regions where the
perturbed solution is asymptotically close to a modulated lattice which
undergoes a continuous phase transition (in the Jacobian variety) and which
interpolates between these isospectral solutions. In the special case of the
free solution ($g=0$) the isospectral torus consists of just one point and we
recover the classical result.
  Both the solutions in the isospectral torus and the phase transition are
explicitly characterized in terms of Abelian integrals on the underlying
hyperelliptic Riemann surface.


title: Bianchi surfaces. Integrability in arbitrary parametrization

abstract:
  We discuss integrability of normal field equations of arbitrary parametrised
Bianchi surfaces. A novel geometric definition of Bianchi surfaces is presented
as well as B\"acklund transformation for the normal field equations in
arbitrary chosen surface parametrization.


title: Evolution operators for quantum chains

abstract:
  Discrete-time evolution operators in integrable quantum lattice models are
sometimes more fundamental objects then Hamiltonians. In this paper we study an
evolution operator for the one-dimensional integrable q-deformed Bose gas with
XXZ-type impurities and find its spectrum. Evolution operators give a new
interpretation of known integrable systems, for instance our system describes
apparently a simplest laser with a clear resonance peak in the spectrum.


title: Passive tracer in a slowly decorrelating random flow with a large mean

abstract:
  We consider the movement of a particle advected by a random flow of the form
$\vv+\delta \bF(\vx)$, with $\vv\in\R^d$ a constant drift, $\bF(\vx)$ -- the
fluctuation -- given by a zero mean, stationary random field and $\delta\ll 1$
so that the drift dominates over the fluctuation. The two-point correlation
matrix $\bR(\vx)$ of the random field decays as $|\vx|^{2\alpha-2}$, as
$|\vx|\to+\infty$ with $\alpha<1$. The Kubo formula for the effective diffusion
coefficient obtained in \cite{kp79} for rapidly decorrelating fields diverges
when $1/2\le\alpha<1$. We show formally that on the time scale
$\delta^{-1/\alpha}$ the deviation of the trajectory from its mean
$\by(t)=\vx(t)-\vv t$ converges to a fractional Brownian motion $B_\alpha(t)$
in this range of the exponent $\alpha$. We also prove rigorously upper and
lower bounds which show that $\E[|\by(t)|^2]$ converges to zero for times
$t\ll\delta^{-1/\alpha}$ and to infinity on time scales $t\gg
\delta^{-1/\alpha}$ as $\delta\to 0$ when $\alpha\in(1/2,1)$. On the other
hand, when $\alpha<1/2$ non-trivial behavior is observed on the time-scale
$O(\delta^{-2})$.


title:
Reciprocal transformations for Stackel-related Liouville integrable
  systems

abstract:
  We consider the St\"ackel transform, also known as the coupling-constant
metamorphosis, which under certain conditions turns a Hamiltonian dynamical
system into another such system and preserves the Liouville integrability. We
show that the corresponding transformation for the equations of motion is
nothing but the reciprocal transformation of a special form and we investigate
the properties of this transformation. This result is further applied for the
study of the $k$-hole deformations of the Benenti systems or more general seed
systems.


title: An Artificial Neural Net approach to forecast the population of India

abstract:
  Present paper endeavors to forecast the population of India through
Artificial Neural Network. A non-linear Artificial Neural Net model has been
developed and the prediction has been found to be sufficiently accurate. It has
been found that the model is performing more efficiently in predicting female
population than the male population. Results have been presented graphically.


title:
Via Hexagons to Squares in Ferrofluids: Experiments on Hysteretic
  Surface Transformations under Variation of the Normal Magnetic Field

abstract:
  We report on different surface patterns on magnetic liquids following the
Rosensweig instability. We compare the bifurcation from the flat surface to a
hexagonal array of spikes with the transition to squares at higher fields. From
a radioscopic mapping of the surface topography we extract amplitudes and
wavelengths. For the hexagon--square transition, which is complex because of
coexisting domains, we tailor a set of order parameters like peak--to--peak
distance, circularity, angular correlation function and pattern specific
amplitudes from Fourier space. These measures enable us to quantify the smooth
hysteretic transition. Voronoi diagrams indicate a pinning of the domains. Thus
the smoothness of the transition is roughness on a small scale.


title: Extracting Multidimensional Phase Space Topology from Periodic Orbits

abstract:
  We establish a hierarchical ordering of periodic orbits in a strongly coupled
multidimensional Hamiltonian system. Phase space structures can be
reconstructed quantitatively from the knowledge of periodic orbits alone. We
illustrate our findings for the hydrogen atom in crossed electric and magnetic
fields.


title: Self-Similar Solutions of the Non-Strictly Hyperbolic Whitham Equations

abstract:
  We study the Whitham equations for the fifth order KdV equation. The
equations are neither strictly hyperbolic nor genuinely nonlinear. We are
interested in the solution of the Whitham equations when the initial values are
given by a step function. We classify the step like initial data into eight
different types. We construct self-similar solutions for each type.


title: Two-dimensional nonlocal multisolitons

abstract:
  We study the bound states of two-dimensional bright solitons in nonlocal
nonlinear media. The general properties and stability of these multisolitary
structures are investigated analytically and numerically. We have found that a
steady bound state of coherent nonrotating and rotating solitary structures
(azimuthons) can exist above some threshold power. A dipolar nonrotating
multisoliton occurs to be stable within the finite range of the beam power.
Azimuthons turn out to be stable if the beam power exceeds some threshold
value. The bound states of three or four nonrotating solitons appear to be
unstable.


title: Discrete surface solitons in two dimensions

abstract:
  We investigate fundamental localized modes in 2D lattices with an edge
(surface). Interaction with the edge expands the stability area for ordinary
solitons, and induces a difference between perpendicular and parallel dipoles;
on the contrary, lattice vortices cannot exist too close to the border.
Furthermore, we show analytically and numerically that the edge stabilizes a
novel wave species, which is entirely unstable in the uniform lattice, namely,
a "horseshoe" soliton, consisting of 3 sites. Unstable horseshoes transform
themselves into a pair of ordinary solitons.


title: Chaotic Dynamics in Optimal Monetary Policy

abstract:
  There is by now a large consensus in modern monetary policy. This consensus
has been built upon a dynamic general equilibrium model of optimal monetary
policy as developed by, e.g., Goodfriend and King (1997), Clarida et al.
(1999), Svensson (1999) and Woodford (2003). In this paper we extend the
standard optimal monetary policy model by introducing nonlinearity into the
Phillips curve. Under the specific form of nonlinearity proposed in our paper
(which allows for convexity and concavity and secures closed form solutions),
we show that the introduction of a nonlinear Phillips curve into the structure
of the standard model in a discrete time and deterministic framework produces
radical changes to the major conclusions regarding stability and the efficiency
of monetary policy. We emphasize the following main results: (i) instead of a
unique fixed point we end up with multiple equilibria; (ii) instead of
saddle--path stability, for different sets of parameter values we may have
saddle stability, totally unstable equilibria and chaotic attractors; (iii) for
certain degrees of convexity and/or concavity of the Phillips curve, where
endogenous fluctuations arise, one is able to encounter various results that
seem intuitively correct. Firstly, when the Central Bank pays attention
essentially to inflation targeting, the inflation rate has a lower mean and is
less volatile; secondly, when the degree of price stickiness is high, the
inflation rate displays a larger mean and higher volatility (but this is
sensitive to the values given to the parameters of the model); and thirdly, the
higher the target value of the output gap chosen by the Central Bank, the
higher is the inflation rate and its volatility.


title:
Hypergeometric Solutions to the q-Painlev\'e Equation of Type
  $(A_1+A_1')^{(1)}$

abstract:
  A class of classical solutions to the $q$-Painlev\'e equation of type
$(A_1+A_1')^{(1)}$ (a $q$-difference analog of the Painlev\'e II equation) is
constructed in a determinantal form with basic hypergeometric function
elements. The continuous limit of this $q$-Painlev\'e equation to the
Painlev\'e II equation and its hypergeometric solutions are discussed. The
continuous limit of these hypergeometric solutions to the Airy function is
obtained through a uniform asymptotic expansion of their integral
representation.


title:
Combined effects of small scale anisotropy and compressibility on
  anomalous scaling of a passive scalar

abstract:
  Model of a passive scalar field advected by the compressible Gaussian
strongly anisotropic velocity field with the covariance $\propto
\delta(t-t^{\prime})|{\bf x}-{\bf x^{\prime}}|^{2\epsilon}$ is studied by using
the field theoretic renormalization group and the operator product expansion.
The inertial-range stability of the corresponding scaling regime is
established. The anomalous scaling of the single-time structure functions is
studied and the corresponding anomalous exponents are calculated. Their
dependence on the compressibility parameter and anisotropy parameters is
analyzed. It is shown that, as in the isotropic case, the presence of
compressibility leads to the decreasing of the critical dimensions of the
important composite operators, i.e., the anomalous scaling is more pronounced
in the compressible systems. All calculations are done to the first order in
$\epsilon$.