title:
Nonlinear transfer and spectral distribution of energy in $\alpha$
  turbulence

abstract:
  Two-dimensional turbulence governed by the so-called $\alpha$ turbulence
equations, which include the surface quasi-geostrophic equation ($\alpha=1$),
the Navier--Stokes system ($\alpha=2$), and the governing equation for a
shallow flow on a rotating domain driven by a uniform internal heating
($\alpha=3$), is studied here in both the unbounded and doubly periodic
domains. This family of equations conserves two inviscid invariants (energy and
enstrophy in the Navier--Stokes case), the dynamics of which are believed to
undergo a dual cascade. It is shown that an inverse cascade can exist in the
absence of a direct cascade and that the latter is possible only when the
inverse transfer rate of the inverse-cascading quantity approaches its own
injection rate. Constraints on the spectral exponents in the wavenumber ranges
lower and higher than the injection range are derived. For Navier--Stokes
turbulence with moderate Reynolds numbers, the realization of an inverse energy
cascade in the complete absence of a direct enstrophy cascade is confirmed by
numerical simulations.


title: Extensivity of two-dimensional turbulence

abstract:
  This study is concerned with how the attractor dimension of the
two-dimensional Navier--Stokes equations depends on characteristic length
scales, including the system integral length scale, the forcing length scale,
and the dissipation length scale. Upper bounds on the attractor dimension
derived by Constantin--Foias--Temam are analysed. It is shown that the optimal
attractor-dimension estimate grows linearly with the domain area (suggestive of
extensive chaos), for a sufficiently large domain, if the kinematic viscosity
and the amplitude and length scale of the forcing are held fixed. For
sufficiently small domain area, a slightly ``super-extensive'' estimate becomes
optimal. In the extensive regime, the attractor-dimension estimate is given by
the ratio of the domain area to the square of the dissipation length scale
defined, on physical grounds, in terms of the average rate of shear. This
dissipation length scale (which is not necessarily the scale at which the
energy or enstrophy dissipation takes place) can be identified with the
dimension correlation length scale, the square of which is interpreted,
according to the concept of extensive chaos, as the area of a subsystem with
one degree of freedom. Furthermore, these length scales can be identified with
a ``minimum length scale'' of the flow, which is rigorously deduced from the
concept of determining nodes.


title:
Freezing of Nonlinear Bloch Oscillations in the Generalized Discrete
  Nonlinear Schrodinger Equation

abstract:
  The dynamics in a nonlinear Schrodinger chain in an homogeneous electric
field is studied. We show that discrete translational invariant
integrability-breaking terms can freeze the Bloch nonlinear oscillations and
introduce new faster frequencies in their dynamics. These phenomena are studied
by direct numerical integration and through an adiabatic approximation. The
adiabatic approximation allows a description in terms of an effective potential
that greatly clarifies the phenomenon.


title: A simple model for self organization of bipartite networks

abstract:
  We suggest a minimalistic model for directed networks and suggest an
application to injection and merging of magnetic field lines. We obtain a
network of connected donor and acceptor vertices with degree distribution
$1/s^2$, and with dynamical reconnection events of size $\Delta s$ occurring
with frequency that scale as $1/\Delta s^3$. This suggest that the model is in
the same universality class as the model for self organization in the solar
atmosphere suggested by Hughes et al.(PRL {\bf 90} 131101).


title: Self Organized Scale-Free Networks from Merging and Regeneration

abstract:
  We consider the self organizing process of merging and regeneration of
vertices in complex networks and demonstrate that a scale-free degree
distribution emerges in a steady state of such a dynamics. The merging of
neighbor vertices in a network may be viewed as an optimization of efficiency
by minimizing redundancy. It is also a mechanism to shorten the distance and
thus decrease signaling times between vertices in a complex network. Thus the
merging process will in particular be relevant for networks where these issues
related to global signaling are of concern.


title: Transversality for a Class of 3D Oscillators via Gyrostat Equations

abstract:
  The class of 3D oscillators of interest includes the modified Brockett, Chua,
Duffing, Ueda, modified Kapitaniak, generalized Lorenz, forced Lorenz, Rossler
and YSVO oscillators. The homoclinic orbits of a symmetric gyrostat with wheels
under torque-free motions are first exploited. The effects of the small
external perturbation torques upon the rotational motions of the forced
symmetric gyrostat are investigated using the equation of the Melnikov
integral. The real zeros of the Melnikov integral determine the transversality
of the homoclinic orbits leading to a necessary condition for the existence of
chaos. The equations of the 3D oscillators are then reduced to the Euler
equations of the perturbed rotational motions of symmetric gyrostats.
Algorithms are established to compute the required parameters for the gyrostat
to represent the 3D oscillators at initiating the transversality. These
parameters include the angular momenta of the wheels and the principal moments
of inertia. The existence of real zeros of the Melnikov integral for the
symmetric gyrostat implies the existence of transversal intersections of the
perturbed solutions of the 3D oscillators. The 4th order Runge-Kutta algorithm
is utilized to simulate and crosscheck the long-term chaotic behaviors of the
dynamical systems.


title: Geometric Phase and Classical-Quantum Correspondence

abstract:
  We study the geometric phase factors underlying the classical and the
corresponding quantum dynamics of a driven nonlinear oscillator exhibiting
chaotic dynamics. For the classical problem, we compute the geometric phase
factors associated with the phase space trajectories using Frenet-Serret
formulation. For the corresponding quantum problem, the geometric phase
associated with the time evolution of the wave function is computed. Our
studies suggest that the classical geometric phase may be related to the the
difference in the quantum geometric phases between two neighboring eigenstates.


title: Cubic Pencils and Painlev\'e Hamiltonians

abstract:
  We present a simple heuristic method to derive the Painlev\'e differential
equations from the corresponding geometry of rational surafces. We also give a
direct relationship between the cubic pencils and Seiberg-Witten curves.


abstract:
  Convenient parameterizations of matrices in terms of vectors transform
(certain classes of) matrix equations into covariant (hence rotation-invariant)
vector equations. Certain recently introduced such parameterizations are
tersely reviewed, and new ones introduced.


title: Integrable systems of quartic oscillators. II

abstract:
  Several completely integrable, indeed solvable, Hamiltonian many-body
problems are exhibited, characterized by Newtonian equations of motion
("acceleration equal force"), with linear and cubic forces, in N-dimensional
space (N being an arbitrary positive integer, with special attention to N=2,
namely motions in a plane, and N=3, namely motions in ordinary
three-dimensional space). All the equations of motion are written in covariant
form ("N-vector equal N-vector"), entailing their rotational invariance. The
corresponding Hamiltonians are of normal type, with the kinetic energy
quadratic in the canonical momenta, and the potential energy quadratic and
quartic in the canonical coordinates.


title: Rayleigh-Benard Convection in Large-Aspect-Ratio Domains

abstract:
  The coarsening and wavenumber selection of striped states growing from random
initial conditions are studied in a non-relaxational, spatially extended, and
far-from-equilibrium system by performing large-scale numerical simulations of
Rayleigh-B\'{e}nard convection in a large-aspect-ratio cylindrical domain with
experimentally realistic boundaries. We find evidence that various measures of
the coarsening dynamics scale in time with different power-law exponents,
indicating that multiple length scales are required in describing the time
dependent pattern evolution. The translational correlation length scales with
time as $t^{0.12}$, the orientational correlation length scales as $t^{0.54}$,
and the density of defects scale as $t^{-0.45}$. The final pattern evolves
toward the wavenumber where isolated dislocations become motionless, suggesting
a possible wavenumber selection mechanism for large-aspect-ratio convection.


title: Chemical turbulence equivalent to Nikolavskii turbulence

abstract:
  We find evidence that a certain class of reaction-diffusion systems can
exhibit chemical turbulence equivalent to Nikolaevskii turbulence. The
distinctive characteristic of this type of turbulence is that it results from
the interaction of weakly stable long-wavelength modes and unstable
short-wavelength modes. We indirectly study this class of reaction-diffusion
systems by considering an extended complex Ginzburg-Landau (CGL) equation that
was previously derived from this class of reaction-diffusion systems. First, we
show numerically that the power spectrum of this CGL equation in a particular
regime is qualitatively quite similar to that of the Nikolaevskii equation.
Then, we demonstrate that the Nikolaevskii equation can in fact be obtained
from this CGL equation through a phase reduction procedure applied in the
neighborhood of a codimension-two Turing--Benjamin-Feir point.


title:
Standing wave oscillations in binary mixture convection: from onset via
  symmetry breaking to period doubling into chaos

abstract:
  Oscillatory solution branches of the hydrodynamic field equations describing
convection in the form of a standing wave (SW) in binary fluid mixtures heated
from below are determined completely for several negative Soret coefficients.
Galerkin as well as finite-difference simulations were used. They were
augmented by simple control methods to obtain also unstable SW states. For
sufficiently negative Soret coefficients unstable SWs bifurcate subcritically
out of the quiescent conductive state. They become stable via a saddle-node
bifurcation when lateral phase pinning is exerted. Eventually their invariance
under time-shift by half a period combined with reflexion at midheight of the
fluid layer gets broken. Thereafter they terminate by undergoing a
period-doubling cascade into chaos.


title: Finite-dimensional reductions of the discrete Toda chain

abstract:
  The problem of construction of integrable boundary conditions for the
discrete Toda chain is considered. The restricted chains for properly chosen
closure conditions are reduced to the well known discrete Painlev\'e equations
$dP_{III}$, $dP_{V}$, $dP_{VI}$. Lax representations for these discrete
Painlev\'e equations are found.


title:
Dirac quantization of the massless Thirring model energy-momentum tensor
  anomaly

abstract:
  The Dirac method of quantizing Hamiltonian systems with constraints is
applied to the massless Thirring model. We solve the quantum Hamiltonian
equation for the energy-momentum tensor and obtain a violation of the classical
conservation law.A previously noticed problem with the equal-time
anticommutators can be fixed using this Hamiltonian method.


title:
Statistics of active vs. passive advections in magnetohydrodynamic
  turbulence

abstract:
  Active turbulent advection is considered in the context of
magneto-hydrodynamics. In this case, an auxiliary passive field bears no
apparent connection to the active field. The scaling properties of the two
fields are different. In the framework of a shell model, we show that the
two-point structure function of the passive field has a unique zero mode,
characterizing the scaling of this field only. In other words, the existence of
statistical invariants for the decaying passive field carries no information on
the scaling properties of the active field.


title:
Classical projected phase space density of billiards and its relation to
  the quantum Neumann spectrum

abstract:
  A comparison of classical and quantum evolution usually involves a
quasi-probability distribution as a quantum analogue of the classical phase
space distribution. In an alternate approach that we adopt here, the classical
density is projected on to the configuration space. We show that for billiards,
the eigenfunctions of the coarse-grained projected classical evolution operator
are identical to a first approximation to the quantum Neumann eigenfunctions.
However, even though there exists a correspondence between the respective
eigenvalues, their time evolutions differ. This is demonstrated numerically for
the stadium and lemon shaped billiards.


title:
Transition to hexagonal pattern under the variation of intrinsic length
  scales of a reaction diffusion system

abstract:
  The intrinsic length scales of a reaction diffusion system (Gierer-Meinhardt
model)is varied by quasi-statically changing the diffusion constant of the
activator and a transition from rolls to hexagon is detected. The transition is
hysteretic or first order like. From stability analysis, we also analytically
show the possibility of such transitions.


title:
Multifractal statistics of Lagrangian velocity and acceleration in
  turbulence

abstract:
  The statistical properties of velocity and acceleration fields along the
trajectories of fluid particles transported by a fully developed turbulent flow
are investigated by means of high resolution direct numerical simulations. We
present results for Lagrangian velocity structure functions, the acceleration
probability density function and the acceleration variance conditioned on the
instantaneous velocity. These are compared with predictions of the multifractal
formalism and its merits and limitations are discussed.


title:
Phase instabilities generated by parametric modulation in reaction
  diffusion systems

abstract:
  Effect of external periodic force on an oscillatory order in a reaction
diffusion system (Gierer Meinhardt model) has been investigated. The 2:1
resonance situation is found susceptible for the generation of a band of phase
instabilities. These phase instabilities, captured on multiple time scales,
produces a mismatch between the oscillation frequency of reacting species.


title: Lagrangian singularities of steady two-dimensional flow

abstract:
  The Lagrangian complex-space singularities of the steady Eulerian flow with
stream function $\sin x_1 \cos x_2$ are studied by numerical and analytical
methods. The Lagrangian singular manifold is analytic. Its minimum distance
from the real domain decreases logarithmically at short times and exponentially
at large times.


title: Factorization of the current algebra and integrable top-like systems

abstract:
  A hierarchy of integrable hamiltonian nonlinear ODEs is associated with any
decomposition of the Lie algebra of Laurent series with coefficients being
elements of a semi-simple Lie algebra into a sum of the subalgebra consisting
of the Taylor series and some complementary subalgebra. In the case of the Lie
algebra $so(3)$ our scheme covers all classical integrable cases in the
Kirchhoff problem of the motion of a rigid body in an ideal fluid. Moreover,
the construction allows us to generate integrable deformations for known
integrable models.


title:
Comment on "Shadowability of Statistical Averages in Chaotic Systems" by
  Y.C. Lai, Z. Liu, G.W. Wei, and C.H. Lai, Phys. Rev. Lett. 89, 184101

abstract:
  Lai {\it et al.} \cite{Lai:2002} investigate systems with a stable periodic
orbit and a coexisting chaotic saddle. They claim that, by adding white
Gaussian noise (GN), averages change with an algebraic scaling law above a
certain noise threshold and argue that this leads to a breakdown of
shadowability of averages. Here, we show that (i) shadowability is not well
defined and even if it were, no breakdown occurs. We clarify misconceptions on
(ii) thresholds for GN. We further point out (iii) misconceptions on the effect
of noise on averages. Finally, we show that (iv) the lack of a proper threshold
can lead to any (meaningless) scaling exponent.


title: Quasi-Scarred Resonances in a Spiral-Shaped Microcavity

abstract:
  We study resonance patterns of a spiral-shaped dielectric microcavity with
chaotic ray dynamics. Many resonance patterns of this microcavity, with
refractive indices $n=2$ and 3, exhibit strong localization of simple geometric
shape, and we call them {\em quasi-scarred resonances} in the sense that there
is, unlike the conventional scarring, no underlying periodic orbits. It is
shown that the formation of quasi-scarred pattern can be understood in ter ms
of ray dynamical probability distributions and wave properties like uncertainty
and interference.


title:
Fractal properties of the diffusion coefficient in a simple
  deterministic dynamical system: a numerical study

abstract:
  Using a numerical library for arbitrary precision arithmetic I study the
irregular dependence of the diffusion coefficient on the slope of a piecewise
linear map defining a dynamical system. I find that the graph of the diffusion
coefficient as a function of the slope has the fractal dimension 1, but the
convergence to this limit is slowed down by logarithmic corrections. The
exponent controlling this correction depends on the slope and is either 1 or 2
depending on existence and properties of a Markov partition.


title: The Strange Eigenmode in Lagrangian Coordinates

abstract:
  For a distribution advected by a simple chaotic map with diffusion, the
"strange eigenmode" is investigated from the Lagrangian (material) viewpoint
and compared to its Eulerian (spatial) counterpart. The eigenmode embodies the
balance between diffusion and exponential stretching by a chaotic flow. It is
not strictly an eigenmode in Lagrangian coordinates, because its spectrum is
rescaled exponentially rapidly.


title:
Separation of variables and B\"acklund transformations for the symmetric
  Lagrange top

abstract:
  We construct the 1- and 2-point integrable maps (B\"acklund transformations)
for the symmetric Lagrange top. We show that the Lagrange top has the same
algebraic Poisson structure that belongs to the $sl(2)$ Gaudin magnet. The
2-point map leads to a real time-discretization of the continuous flow.
Therefore, it provides an integrable numerical scheme for integrating the
physical flow. We illustrate the construction by few pictures of the discrete
flow calculated in MATLAB.


title: Breaking an encryption scheme based on chaotic Baker map

abstract:
  In recent years, a growing number of cryptosystems based on chaos have been
proposed, many of them fundamentally flawed by a lack of robustness and
security. This paper describes the security weaknesses of a recently proposed
cryptographic algorithm with chaos at the physical level. It is shown that the
security is trivially compromised for practical implementations of the
cryptosystem with finite computing precision and for the use of the iteration
number n as the secret key. Some possible countermeasures to enhance the
security of the chaos-based cryptographic algorithm are also discussed.


title: Adaptive Synchronization in Coupled Dynamic Networks

abstract:
  This paper studies synchronization in coupled nonlinear dynamic networks with
unknown parameters. Adaptation can be added to one or several elements in the
network, while preserving the global synchronization conditions derived in
previously. This implies that new nodes can be added to the network without
prior knowledge of the individual dynamics, and that nodes in an existing
network have the ability to recover dynamic information if temporarily lost. In
addition, when the individual elements feature sufficiently rich stable
dynamics, as e.g. in the case of oscillators, then adaptation actually leads to
an exact estimation of the unknown parameters. Different kinds of leaders are
also discussed in this context - one type of leader can specify overall
trajectories for the network, while another can concurrently specify dynamic
parameters.


title:
Optical manipulation of intrinsic localized vibrational energy in
  cantilever arrays

abstract:
  Optically-induced real-time impurity modes are used to shepherd intrinsic
localized vibrational modes (discrete breathers) along micromechanical arrays
via either attractive or replulsive interactions. Adding an electrode to the
cantilever array provides control of the sign of lattice anharmonicity, hence
allowing both hard and soft nonlinearities to be studied. A number of dynamical
effects are demonstrated and explained, including the optical tweezing of
localized vibrational energy in a nonlinear lattice.


title: Analysis of Sunspot Number Fluctuations

abstract:
  Monthly averages of the sunspot number visible on the sun, observed from
  1749, Zurich Observatory, and from 1848 other observatories, have been
analyzed. This time signal presents a frequency power spectra with a clear
$1/f^\alpha$ behavior with $\alpha\simeq 0.8 \pm 0.2$. The well known cycle of
approximately 11 years, clearly present in the spectrum, does not produce a
sensible distortion of that behavior. The eventual characterization of the
sunspot time series as a fractal is analyzed by means of the detrended
fluctuation analysis. The jump size distribution of the signal is also studied.


title: Intermediate statistics in quantum maps

abstract:
  We present a one-parameter family of quantum maps whose spectral statistics
are of the same intermediate type as observed in polygonal quantum billiards.
Our central result is the evaluation of the spectral two-point correlation form
factor at small argument, which in turn yields the asymptotic level
compressibility for macroscopic correlation lengths.


title:
On the Classification of Scalar Non-Polynomial Evolution Equations:
  Quasilinearity

abstract:
  We prove that, for $m\ge 7$, scalar evolution equations of the form
$u_t=F(x,t,u,...,u_m)$ which admit a nontrivial conserved density of order
$m+1$ are linear in $u_m$. The existence of such conserved densities is a
necesary condition for integrability in the sense of admitting a formal
symmetry, hence integrable scalar evolution equations of order $m\ge 7$ are
quasilinear.


title:
Epidemiology Through Cellular Automata: Case of Study Avian Influenza in
  Indonesia

abstract:
  This paper performs the utilization of cellular automata computational
analysis as the dynamic model of spatial epidemiology. Here, explored
elementary aspects of cellular automata and its application in analyzing
contagious disease, in this case avian influenza disease in Indonesia.
Computational model is built and map-based simulation is performed using
several simplified data of such transportation through sea in Indonesia, and
its accordance with poultries in Indonesia, with initial condition of notified
avian influenza infected area in Indonesia. The initial places are Pekalongan,
West Java, East Java, and several regions in Sumatera. The result of simulation
is showing the spreading-rate of influenza and in simple way and describing
possible preventive action through isolation of infected areas as a major step
of preventing pandemic.


title: Hypergeometric solutions to the q-Painlev\'e equations

abstract:
  Hypergeometric solutions to seven q-Painlev\'e equations in Sakai's
classification are constructed. Geometry of plane curves is used to reduce the
q-Painlev\'e equations to the three-term recurrence relations for
q-hypergeometric functions.


title:
Three-Wave Modulational Stability and Dark Solitons in a Quadratic
  Nonlinear Waveguide with Grating

abstract:
  We consider continuous-wave (CW) states and dark solitons (DSs) in a system
of two fundamental-frequency (FF) and one second-harmonic (SH) waves in a
planar waveguide with the quadratic nonlinearity, the FF components being
linearly coupled by resonant reflections on the Bragg grating. We demonstrate
that, in contrast with the usual situation in quadratic spatial-domain models,
CW states with the phase shift between the FF and SH components are
modulationally stable in a broad parameter region in this system, provided that
the CW wavenumber does not belong to the system's spectral gap. Stationary
fundamental DSs are found numerically, and are also constructed by means of a
specially devised analytical approximation. Bound states of two and three DSs
are found too. The fundamental DSs and two-solitons bound states are stable in
all the cases when the CW background is stable, which is shown by dint of
calculation of the corresponding eigenvalues, and verified in direct
simulations. Tilted DSs are found too. They attain a maximum contrast at a
finite value of the tilt, that does not depend on the phase mismatch. At a
maximum value of the tilt, which grows with the mismatch, the DS merges into
the CW background. Interactions between the tilted solitons are shown to be
completely elastic.


title: Quantum chaos and the double-slit experiment

abstract:
  We report on the numerical simulation of the double-slit experiment, where
the initial wave-packet is bounded inside a billiard domain with perfectly
reflecting walls. If the shape of the billiard is such that the classical ray
dynamics is regular, we obtain interference fringes whose visibility can be
controlled by changing the parameters of the initial state. However, if we
modify the shape of the billiard thus rendering classical (ray) dynamics fully
chaotic, the interference fringes disappear and the intensity on the screen
becomes the (classical) sum of intensities for the two corresponding one-slit
experiments. Thus we show a clear and fundamental example in which transition
to chaotic motion in a deterministic classical system, in absence of any
external noise, leads to a profound modification in the quantum behaviour.


title:
Understanding Anomalous Transport in Intermittent Maps: From Continuous
  Time Random Walks to Fractals

abstract:
  We show that the generalized diffusion coefficient of a subdiffusive
intermittent map is a fractal function of control parameters. A modified
continuous time random walk theory yields its coarse functional form and
correctly describes a dynamical phase transition from normal to anomalous
diffusion marked by strong suppression of diffusion. Similarly, the probability
density of moving particles is governed by a time-fractional diffusion equation
on coarse scales while exhibiting a specific fine structure. Approximations
beyond stochastic theory are derived from a generalized Taylor-Green-Kubo
formula.


title:
Stability of low-dimensional bushes of vibrational modes in the
  Fermi-Pasta-Ulam chains

abstract:
  Bushes of normal modes represent the exact excitations in nonlinear physical
systems with discrete symmetries [Physica D117 (1998) 43]. The present paper is
the continuation of our previous paper [Physica D166 (2002) 208], where these
dynamical objects of a new type were discussed for the monoatomic nonlinear
chains. Here, we develop a simple crystallographic method for finding bushes in
nonlinear chains and investigate stability of one-dimensional and
two-dimensional vibrational bushes for both FPU-alpha and FPU-beta models, in
particular, of those revealed recently in [Physica D175 (2003) 31].


title: Agent-based Model Construction In Financial Economic System

abstract:
  The paper gives picture of enrichment to economic and financial system
analysis using agent-based models as a form of advanced study for financial
economic data post-statistical-data analysis and micro-simulation analysis.
Theoretical exploration is carried out by using comparisons of some usual
financial economy system models frequently and popularly used in econophysics
and computational finance. Primitive model, which consists of agent
microsimulation with fundamentalist strategy, chartist, and noise, was
established with an expectation of adjusting micro-simulation analysis upon
stock market in Indonesia. The result of simulation showing how financial
economy data resulted analysis using statistical tools such as data
distribution and central limit theorem, and several other macro-financial
analysis tools previously shown (Situngkir & Surya, 2003b). This paper is ended
with several further possible advancements from the model built.


title: The Structural Dynamics of Corruption: Artificial Society Approach

abstract:
  Corruption has been an important issue as it becomes obstacle to achieve the
better and more efficient economic governmental system. The paper defines
corruption in two ways, as state capture and administrative corruption to grasp
the quintessence of the corruption cases modeled in dynamical computational
social system. The result of experiments through simulation is provided in
order to construct an understanding of structural properties of corruption,
giving way to consider corruption not as an isolated phenomenon, but
conclusively, as an interdisciplinary problem and should be handled in holistic
perspectives.


title:
Exact nonstationary solutions to the mean-field equations of motion for
  two-component Bose-Einstein condensates in periodic potentials

abstract:
  We study the dynamics of two-component Bose-Einstein condensates in periodic
potentials in one dimension. Elliptic potentials which have the sinusoidal
optical potential as a special case are considered. We construct exact
nonstationary solutions to the mean-field equations of motion. Among the
solutions are two types of temporally-periodic solutions -- in one type there
are condensate oscillations between neighboring potential wells, while in the
other the condensates oscillate from side to side within the wells. Our
numerical studies of the stability of these solutions suggests the existence of
one-parameter families of stable nonstationary solutions.


title: Exponentially Localized Solutions of Mel'nikov Equation

abstract:
  The Mel'nikov equation is a (2+1) dimensional nonlinear evolution equation
admitting boomeron type solutions. In this paper, after showing that it
satisfies the Painlev\'{e} property, we obtain exponentially localized dromion
type solutions from the bilinearized version which have not been reported so
far. We also obtain more general dromion type solutions with spatially varying
amplitude as well as induced multi-dromion solutions.


title:
Controlling spatiotemporal chaos in oscillatory reaction-diffusion
  systems by time-delay autosynchronization

abstract:
  Diffusion-induced turbulence in spatially extended oscillatory media near a
supercritical Hopf bifurcation can be controlled by applying global time-delay
autosynchronization. We consider the complex Ginzburg-Landau equation in the
Benjamin-Feir unstable regime and analytically investigate the stability of
uniform oscillations depending on the feedback parameters. We show that a
noninvasive stabilization of uniform oscillations is not possible in this type
of systems. The synchronization diagram in the plane spanned by the feedback
parameters is derived. Numerical simulations confirm the analytical results and
give additional information on the spatiotemporal dynamics of the system close
to complete synchronization.


title:
"Doubled" generalized Landau-Lifshiz hierarchies and special quasigraded
  Lie algebras

abstract:
  Using special quasigraded Lie algebras we obtain new hierarchies of
integrable nonlinear vector equations admitting zero-curvature representations.
Among them the most interesting is extension of the generalized Landau-Lifshitz
hierarchy which we call "doubled" generalized Landau-Lifshiz hierarchy. This
hierarchy can be also interpreted as an anisotropic vector generalization of
"modified" Sine-Gordon hierarchy or as a very special vector generalization of
so(3) anisotropic chiral field hierarchy.


title: Powers of the Governmental State as Feedback Control Dynamic System

abstract:
  Democracy in a state is possibly a gain to have the government that
represents the whole citizens. But the main element of the democratic system is
the ability of the governmental functions in the state to act properly in order
to gain the citizen wants. The simulation presented in this paper shows how the
rule-making, rule-application, and rule-adjudication functions work such ways
and how they work to have the public wants. The model is the second order
feedback control dynamic system where the rule-making and rule-application
function placed in the forward path and the rule-adjudication placed at
backward path of the system. The rule-making function assumed to be the
function that accentuate the result of public inquiries and presented as a gain
function. The rule-application and the rule-adjudication are modeled as an
exponential function which response is lowering the entropy of the disordered
state conditions by the policies that output. The possible noise that came from
the inability of the government system to work properly is also presented here.
The government system that succeed the gain the same as the public wants is the
optimum government that wanted to be achieved.


title:
Numerical analysis of the existence and stability of nonlinear
  excitations in a parametric model of ferromagnetic chain

abstract:
  A parametrized spin model was recently introduced and intended for
one-dimensional ferromagnets with a deformable Zeeman energy. This model is
revisited and given more realistic interpretation in terms of a model for
ferromagnetic systems with nonconvex anisotropies. A main virtue of the
improved form is its exact reduction to the discrete Remoissenet-Peyrard model,
i.e. a parametrized version of the Takeno-Homma's discrete sine-Gordon model.
The spin-wave phase of the improved parametrized spin model is investigated
assuming both harmonic and anharmonic excitations. Intrinsic-self-localized
modes, regarded as zone-boundary breather spin waves, are pointed out by
simulating the nonlinear difference equations describing the spin equilibrium
positions in the chain, and are shown to exist irrespective of values of the
model parameter. Domain-wall textures of the model are also numerically
examined in terms of kink solitons and with regard to the parametrization.


title: Radial solitons in armchair carbon nanotubes

abstract:
  Radial solitons are investigated in armchair carbon nanotubes using a
generalized Lennard-Jones potential. The radial solitons are found in terms of
moving kink defects whose velocity obeys a dispersion relation. Effects of
lattice discreteness on the shape of kink defects are examined by estimating
the Peierls stress. Results suggest that the typical size for an unpinned kink
phase is of the order of a lattice spacing.


title:
Formation and Destruction of Autocatalytic Sets in an Evolving Network
  Model

abstract:
  I analyse a model of an evolving network represented as a directed graph;
each node corresponds to one molecular species and the links to catalytic
interactions between species. Over short timescales the graph remains fixed
while relative populations of the molecular species change according to a set
of coupled differential equations. Over long timescales the system is subject
to periodic perturbations, each of which adds one new node to the graph, with
random links to other nodes, and removes one node with the least relative
population. Starting from a sparse random graph, a small autocatalytic set
(ACS) inevitably forms and then grows by accreting nodes until it spans the
entire graph. The resultant fully autocatalytic graph, whose probability of
forming by pure chance is very small, nevertheless forms in this model in an
average time that grows only logarithmically with the size of the system. ACSs
can also get destroyed, often accompanied by the sudden extinction of a large
number of species. I show that the largest of the extinction events in this
model are caused by one of three mechanisms, each of which produces a specific
discontinuous change in the graph's topology. The model is analytically
tractable: two theorems are proved which determine the set of nodes with least
relative population in the attractor, for any given graph. This in turn can be
used to analytically demonstrate the inevitability of the formation and growth
of ACSs and calculate the associated timescales. Finally, I show that the
formation and growth of ACSs is robust to the relaxation of many of the
idealizations made to enhance the analytical tractability of the model.


title: Integrable equations in nonlinear geometrical optics

abstract:
  Geometrical optics limit of the Maxwell equations for nonlinear media with
the Cole-Cole dependence of dielectric function and magnetic permeability on
the frequency is considered. It is shown that for media with slow variation
along one axis such a limit gives rise to the dispersionless Veselov-Novikov
equation for the refractive index. It is demonstrated that the Veselov-Novikov
hierarchy is amenable to the quasiclassical DBAR-dressing method. Under more
specific requirements for the media, one gets the dispersionless
Kadomtsev-Petviashvili equation. Geometrical optics interpretation of some
solutions of the above equations is discussed.


title: Integrable Quasiclassical Deformations of Algebraic Curves

abstract:
  A general scheme for determining and studying integrable deformations of
algebraic curves is presented. The method is illustrated with the analysis of
the hyperelliptic case. An associated multi-Hamiltonian hierarchy of systems of
hydrodynamic type is characterized.


title: On exact summations in long-range interactions

abstract:
  In this work, simple exact results are presented for summations in
two-particle potential with long-range interactions. Polygamma function is used
to evaluate summations. Results are found when a periodic media is consider.
Periodic boundary conditions are applied by symmetric repetitions of a central
cell. Contributions over all space are used in the problem. The potential
depends strongly on the size of the system; however, forces are convergents
anywhere.


title: Manipulating Consciousness

abstract:
  Manipulation of the effects of consciousness by external influence on the
human brain is considered in the context of the nonlinear dynamical modeling of
interaction between automatic and conscious processes.


title: Nonlocal brackets and integrable string models

abstract:
  The closed string model in the background gravity field is considered as the
bi-Hamiltonian system in assumption that string model is the integrable model
for particular kind of the background fields. The dual nonlocal Poisson
brackets, de pending of the background fields and of there derivatives, are
obtained. The integrability condition is formulated as compatibility of the
bi-Hamiltonity con dition and the Jacobi identity of the dual Poisson bracket.
Two types of the non local brackets are introduced. Constant curvature and
time-dependent metrics are considered, as example. It is, shown that the Jacobi
identities for the non local brackets have particular solution for the
space-time coordinates, as matrix representation of the simple Lie group.


title: Majority Orienting Model for the Oscillation of Market Price

abstract:
  The present paper introduces a majority orienting model in which the dealers'
behavior changes based on the influence of the price to show the oscillation of
stock price in the stock market. We show the oscillation of the price for the
model by applying the van der Pol equation which is a deterministic
approximation of our model.


title: Dirac reduction of dual Poisson-presymplectic pairs

abstract:
  A new notion of a dual Poisson-presymplectic pair is introduced and its
properties are examined. The procedure of Dirac reduction of Poisson operators
onto submanifolds proposed by Dirac is in this paper embedded in a geometric
procedure of reduction of dual Poisson-presymplectic pairs. The method
presented generalizes those used by Marsden and Ratiu for reductions of Poisson
manifolds. Two examples are given.


title:
Estimation of System Parameters in Discrete Dynamical Systems from Time
  Series

abstract:
  We propose a simple method to estimate the parameters involved in discrete
dynamical systems from time series. The method is based on the concept of
controlling chaos by constant feedback. The major advantages of the method are
that it needs a minimal number of time series data and is applicable to
dynamical systems of any dimension. The method also works extremely well even
in the presence of noise in the time series. The method is specifically
illustrated by means of logistic and Henon maps.


title:
A Computational Procedure to Detect a New Type of High Dimensional
  Chaotic Saddle and its Application to the 3-D Hill's Problem

abstract:
  A computational procedure that allows the detection of a new type of
high-dimensional chaotic saddle in Hamiltonian systems with three degrees of
freedom is presented. The chaotic saddle is associated with a so-called
normally hyperbolic invariant manifold (NHIM). The procedure allows to compute
appropriate homoclinic orbits to the NHIM from which we can infer the existence
a chaotic saddle. NHIMs control the phase space transport across an equilibrium
point of saddle-centre-...-centre stability type, which is a fundamental
mechanism for chemical reactions, capture and escape, scattering, and, more
generally, ``transformation'' in many different areas of physics. Consequently,
the presented methods and results are of broad interest. The procedure is
illustrated for the spatial Hill's problem which is a well known model in
celestial mechanics and which gained much interest e.g. in the study of the
formation of binaries in the Kuiper belt.


title:
A Discrete Variational Approach for Investigation of Stationary
  Localized States In A Discrete Nonlinear Schr$\ddot{\rm {\bf {o}}}$dinger
  Equation, Named IN-DNLS

abstract:
  IN-DNLS, considered here is a countable infinite set of coupled one
dimensional nonlinear ordinary differential difference equations with a tunable
nonlinearity parameter, $\nu$. This equation is continuous in time and discrete
in space with lattice translational invariance and has global gauge invariance.
When $\nu = 0$, it reduces to the famous integrable Ablowitz - Ladik (AL)
equation. Otherwise it is nonintegrable. The formation of unstaggered and
staggered stationary localized states (SLS) in IN-DNLS is studied here using
discrete variational method. The appropriate functional is derived and its
equivalence to the effective Lagrangian is established. From the physical
consideration, the ansatz of SLS is assumed to have the functional form of
stationary soliton of AL equation. So, the ansatz contains three optimizable
parameters, defining width ($\beta^{-1})$, maximum amplitude and its position
($\sqrt\Psi$, $x_{0}$). Four possible situations are considered. An unstaggered
SLS can be either on-site peaked $(x_{0} = 0.0)$ or inter-site peaked $(x_{0} =
0.5)$. On the other hand, a staggered SLS can be either Sievers-Takeno (ST)
like mode $(x_{0} = 0.0)$, or Page(P) like mode $(x_{0} = 0.5)$. It is shown
here that unstable SLS arises due to incomplete consideration of the problem.
In the exact calculation, there exists no unstable mode. The width of an
unstaggered SLS of either type decreases with increasing $\nu > 0$.
Furthermore, on-site peaked state is found to be energetically stable. These
results are explained using the effective mass picture. For the staggered SLS,
the existence of ST like mode and P like mode is shown to be a fundamental
property of a system, described by IN-DNLS. Their properties are also
investigated. For large width and small amplitude SLS, the known asymptotic
result for the amplitude is obtained. Further scope and possible extensions of
this work are discussed.


title:
New aspects of integrability of force-free Duffing-van der Pol
  oscillator and related nonlinear systems

abstract:
  In this letter we show that the force-free Duffing-van der Pol oscillator is
completely integrable for a specific parametric choice. We derive a general
solution for this parametric choice. Further, we describe a procedure to
construct the transformation which removes the time dependent part from the
first integral and provide the general solution by quadrature. The procedure is
shown to have a wider applicability through additional examples. We also show
that through our method one can deduce linearizing transformations in a simple
and straightforward way and illustrate it with a specific example.


title:
Direct Construction of a Dividing Surface of Minimal Flux for
  Multi-Degree-of-Freedom Systems: The Equivalence of Conventional and
  Variational Transition State Theory

abstract:
  The fundamental assumption of conventional transition state theory is the
existence of a dividing surface having the property that trajectories
originating in reactants must cross the surface only once and then proceed to
products. Recently it has been shown how to construct a dividing surface in
phase space for Hamiltonian systems with an arbitrary (but finite) number of
degrees of freedom having the property that trajectories only cross once
locally. In this letter we provide an argument showing that the flux across
this dividing surface is a minimum with respect to certain types of variations
of the dividing surface. In this sense, conventional transition state theory is
shown to be equivalent to variational transition state theory.


title: Cellular Automata: Wolfram's Metaphors for Complex Systems

abstract: A brief introduction to Wolfram's work on cellular automata.


title:
Protocol Requirements for Self-organizing Artifacts: Towards an Ambient
  Intelligence

abstract:
  We discuss which properties common-use artifacts should have to collaborate
without human intervention. We conceive how devices, such as mobile phones,
PDAs, and home appliances, could be seamlessly integrated to provide an
"ambient intelligence" that responds to the user's desires without requiring
explicit programming or commands. While the hardware and software technology to
build such systems already exists, as yet there is no standard protocol that
can learn new meanings. We propose the first steps in the development of such a
protocol, which would need to be adaptive, extensible, and open to the
community, while promoting self-organization. We argue that devices,
interacting through "game-like" moves, can learn to agree about how to
communicate, with whom to cooperate, and how to delegate and coordinate
specialized tasks. Thus, they may evolve a distributed cognition or collective
intelligence capable of tackling complex tasks.


title:
Nonlinear Dynamics of Moving Curves and Surfaces: Applications to
  Physical Systems

abstract:
  The subject of moving curves (and surfaces) in three dimensional space (3-D)
is a fascinating topic not only because it represents typical nonlinear
dynamical systems in classical mechanics, but also finds important applications
in a variety of physical problems in different disciplines. Making use of the
underlying geometry, one can very often relate the associated evolution
equations to many interesting nonlinear evolution equations, including soliton
possessing nonlinear dynamical systems. Typical examples include dynamics of
filament vortices in ordinary and superfluids, spin systems, phases in
classical optics, various systems encountered in physics of soft matter, etc.
Such interrelations between geometric evolution and physical systems have
yielded considerable insight into the underlying dynamics. We present a
succinct tutorial analysis of these developments in this article, and indicate
further directions. We also point out how evolution equations for moving
surfaces are often intimately related to soliton equations in higher
dimensions.


title: Experimental simulation of quantum graphs by microwave networks

abstract:
  We present the results of experimental and theoretical study of irregular,
tetrahedral microwave networks consisting of coaxial cables (annular
waveguides) connected by T-joints. The spectra of the networks were measured in
the frequency range 0.0001-16 GHz in order to obtain their statistical
properties such as the integrated nearest neighbor spacing distribution and the
spectral rigidity. The comparison of our experimental and theoretical results
shows that microwave networks can simulate quantum graphs with time reversal
symmetry. In particular, we use the spectra of the microwave networks to study
the periodic orbits of the simulated quantum graphs. We also present
experimental study of directional microwave networks consisting of coaxial
cables and Faraday isolators for which the time reversal symmetry is broken. In
this case our experimental results indicate that spectral statistics of
directional microwave networks deviate from predictions of Gaussian orthogonal
ensembles (GOE) in random matrix theory approaching, especially for small
eigenfrequency spacing s, results for Gaussian unitary ensembles (GUE).
Experimental results are supported by the theoretical analysis of directional
graphs.


title: Lyapunov Modes in Hard-Disk Systems

abstract:
  We consider simulations of a 2-dimensional gas of hard disks in a rectangular
container and study the Lyapunov spectrum near the vanishing Lyapunov
exponents. To this spectrum are associated ``eigen-directions'', called
Lyapunov modes. We carefully analyze these modes and show how they are
naturally associated with vector fields over the container. We also show that
the Lyapunov exponents, and the coupled dynamics of the modes (where it exists)
follow linear laws, whose coefficients only depend on the density of the gas,
but not on aspect ratio and very little on the boundary conditions.


title:
Periodically Varying Externally Imposed Environmental Effects on
  Population Dynamics

abstract:
  Effects of externally imposed periodic changes in the environment on
population dynamics are studied with the help of a simple model. The
environmental changes are represented by the temporal and spatial dependence of
the competition terms in a standard equation of evolution. Possible
applications of the analysis are on the one hand to bacteria in Petri dishes
and on the other to rodents in the context of the spread of the Hantavirus
epidemic. The analysis shows that spatio-temporal structures emerge, with
interesting features which depend on the interplay of separately controllable
aspects of the externally imposed environmental changes.


title: Percolation of New Product Critical Market Penetration

abstract:
  A simulation of new product market penetration in a social environment is
performed, using a spintronic model, where each element of a 3D network
interacts with its first neighbors. Agents are assumed to be rational, with a
perfect market foresight.
  Unitary production cost decreases when consumption is increased. Simulations
indicate that social interaction is the most important factor for new product
market penetration as compared to the consumer readiness to pay a higher price.
Besides the critical exponent of the nucleation of new consumers is computed,
signing a phase transition characterized by the build up of new consumers
intermediate clusters and this critical exponent is compared to others
belonging to several critical phenomena.


title:
Simple analytical model for entire turbulent boundary layer over flat
  plane: from viscous and mixing layers to turbulent logarithmic region

abstract:
  We discuss a simple analytical model of the turbulent boundary layer (TBL)
over flat plane. The model offers an analytical description of the profiles of
mean velocity and turbulent activity in the entire boundary region, from the
viscous sub-layer, through the buffer layer further into the log-law turbulent
region. In contrast to various existing interpolation formulas the model allows
one to generalize the description of simple TBL of a Newtonian fluid for more
complicated flows of turbulent suspensions laden with heavy particles, bubbles,
long-chain polymers, to include the gravity acceleration, etc.


title: Ecolab, Webworld and self-organisation

abstract:
  Ecolab and Webworld are both models of evolution produced by adding evolution
to ecological equations. They differ primarily in the form of the ecological
equations. Both models are self-organised to a state where extinctions balance
speciations. However, Ecolab shows evidence of this self-organised state being
critical, whereas Webworld does not. This paper examines the self-organised
states of these two models and suggest the likely cause of the difference. Also
the lifetime distribution for a mean field version of Ecolab is computed,
showing that the fat tail of the distribution is due to coevolutionary adaption
of the species.


title: Tierra's missing neutrality: case solved

abstract:
  The concept of neutral evolutionary networks being a significant factor in
evolutionary dynamics was first proposed by Huynen {\em et al.} about 7 years
ago. In one sense, the principle is easy to state -- because most mutations to
an organism are deleterious, one would expect that neutral mutations that don't
affect the phenotype will have disproportionately greater representation
amongst successor organisms than one would expect if each mutation was equally
likely. So it was with great surprise that I noted neutral mutations being very
rare in a visualisation of phylogenetic trees generated in {\em Tierra}, since
I already knew that there was a significant amount of neutrality in the Tierra
genotype-phenotype map. It turns out that competition for resources between
host and parasite inhibits neutral evolution.


title: Reductions of integrable equations. Dihedral group

abstract:
  We discuss algebraic and analytic structure of rational Lax operators. With
algebraic reductions of Lax equations we associate a reduction group - a group
of twisted automorphisms of the corresponding infinite dimensional Lie algebra.
We present a complete study of dihedral reductions for sl(2,C) Lax operators
with simple poles and corresponding integrable equations. In the last section
we give three examples of dihedral reductions for sl(N,C) Lax operators.


title: Anisotropy in Turbulent Flows and in Turbulent Transport

abstract:
  We discuss the problem of anisotropy and intermittency in statistical theory
of high Reynolds-number turbulence (and turbulent transport). We present a
detailed description of the new tools that allow effective data analysis and
systematic theoretical studies such as to separate isotropic from anisotropic
aspects of turbulent statistical fluctuations. Employing the invariance of the
equations of fluid mechanics to all rotations, we show how to decompose the
(tensorial) statistical objects in terms of the irreducible representation of
the SO(3) symmetry group. For the case of turbulent advection of passive scalar
or vector fields, this decomposition allows rigorous statements to be made: (i)
the scaling exponents are universal, (ii) the isotropic scaling exponents are
always leading, (iii) the anisotropic scaling exponents form a discrete
spectrum which is strictly increasing as a function of the anisotropic degree.
Next we explain how to apply the SO(3) decomposition to the statistical
Navier-Stokes theory. We show how to extract information about the scaling
behavior in the isotropic sector. Doing so furnishes a systematic way to assess
the universality of the scaling exponents in this sector, clarifying the
anisotropic origin of the many measurements that claimed the opposite. A
systematic analysis of Direct Numerical Simulations and of experiments provides
a strong support to the proposition that also for the non-linear problem there
exists foliation of the statistical theory into sectors of the symmetry group.
The exponents appear universal in each sector, and again strictly increasing as
a function of the anisotropic degreee.


title:
Temperature measurement in the convective and segregated vibrated bed of
  powder : A numerical study

abstract:
  In numerically simulated vibrated beds of powder, we measure temperature
under convection by the generalized Einstein's relation. The spatial
temperature distribution turns out to be quite uniform except for the boundary
layers. In addition to this, temperature remains uniform even if segregation
occurs. This suggests the possibility that there exists some "thermal
equilibrium state" even in a vibrated bed of powder. This finding may lead to a
unified view of the dynamic steady state of granular matter.


title: Diffusion of passive scalar in a finite-scale random flow

abstract:
  We consider a solvable model of the decay of scalar variance in a
single-scale random velocity field. We show that if there is a separation
between the flow scale k_flow^{-1} and the box size k_box^{-1}, the decay rate
lambda ~ (k_box/k_flow)^2 is determined by the turbulent diffusion of the
box-scale mode. Exponential decay at the rate lambda is preceded by a transient
powerlike decay (the total scalar variance ~ t^{-5/2} if the Corrsin invariant
is zero, t^{-3/2} otherwise) that lasts a time t~1/\lambda. Spectra are sharply
peaked at k=k_box. The box-scale peak acts as a slowly decaying source to a
secondary peak at the flow scale. The variance spectrum at scales intermediate
between the two peaks (k_box<<k<<k_flow) is ~ k + a k^2 + ... (a>0). The mixing
of the flow-scale modes by the random flow produces, for the case of large
Peclet number, a k^{-1+delta} spectrum at k>>k_flow, where delta ~ lambda is a
small correction. Our solution thus elucidates the spectral make up of the
``strange mode,'' combining small-scale structure and a decay law set by the
largest scales.

categories: nlin.CD astro-ph physics.ao-ph physics.flu-dyn


title: Bosonic Reduction of Susy Generalized Harry Dym Equation

abstract:
  In this paper we construct the two component supersymmetric generalized Harry
Dym equation which is integrable and study various properties of this model in
the bosonic limit. In particular, in the bosonic limit we obtain a new
integrable system which, under a hodograph transformation, reduces to a coupled
three component system. We show how the Hamiltonian structure transforms under
a hodograph transformation and study the properties of the model under a
further reduction to a two component system. We find a third Hamiltonian
structure for this system (which has been shown earlier to be a bi-Hamiltonian
system) making this a genuinely tri-Hamiltonian system. The connection of this
system to the modified dispersive water wave equation is clarified. We also
study various properties in the dispersionless limit of our model.


title:
Advancing density waves and phase transitions in a velocity dependent
  randomization traffic cellular automaton

abstract:
  Within the class of stochastic cellular automata models of traffic flows, we
look at the velocity dependent randomization variant (VDR-TCA) whose parameters
take on a specific set of extreme values. These initial conditions lead us to
the discovery of the emergence of four distinct phases. Studying the
transitions between these phases, allows us to establish a rigorous
classification based on their tempo-spatial behavioral characteristics. As a
result from the system's complex dynamics, its flow-density relation exhibits a
non-concave region in which forward propagating density waves are encountered.
All four phases furthermore share the common property that moving vehicles can
never increase their speed once the system has settled into an equilibrium.


title: Entropic nonextensivity as a measure of time series complexity

abstract:
  Information entropy is applied to the analysis of time series generated by
dynamical systems. Complexity of a temporal or spatio-temporal signal is
defined as the difference between the sum of entropies of the local linear
regions of the trajectory manifold and the entropy of the globally linearized
manifold. When the entropies are Tsallis entropies the complexity is
characterized by the value of q.


title: Symmetry, Equivalence and Integrable Classes of Abel Equations

abstract:
  We suggest an approach for description of integrable cases of the Abel
equations. It is based on increasing of the order of equations up to the second
one and using equivalence transformations for the corresponding second-order
ordinary differential equations. The problem of linearizability of the
equations under consideration is discussed.


title:
On Persistence and Stability of some Biological Systems with Cross
  Diffusion

abstract:
  The concept of cross diffusion is applied to some biological systems. The
conditions for persistence and Turing instability in the presence of cross
diffusion are derived. Many examples including: predator-prey, epidemics (with
and without delay), hawk-dove-retaliate and prisoner's dilemma games are given.


title:
On the r-th dispersionless Toda hierarchy I: Factorization problem,
  symmetries and some solutions

abstract:
  For a family of Poisson algebras, parametrized by by an integer number r, and
an associated Lie algebraic splitting, we consider the factorization of given
canonical transformations. In this context we rederive the recently found r-th
dispersionless modified KP hierachies and r-th dispersionless Dym hierarchies,
giving a new Miura map among them. We also found a new integrable hierarchy
which we call the r-th dispersionless Toda hierarchy. Moreover, additional
symmetries for these hierarchies are studied in detail and new symmetries
depending on arbitrary functions are explicitly constructed for the r-th
dispersionless KP, r-th dispersionless Dym and r-th dispersionless Toda
equations. Some solutions are derived by examining the imposition of a time
invariance to the potential r-th dispersionless Dym equation, for which a
complete integral is presented and therefore an appropriate envelope leads to a
general solution. Symmetries and Miura maps are applied to get new solutions
and solutions of the r-th dispesionless modified KP equation.


title: Cooperative equilibria in the finite iterated prisoner's dilemma

abstract:
  Nash equilibria are defined using uncorrelated behavioural or mixed joint
probability distributions effectively assuming that players of bounded
rationality must discard information to locate equilibria. We propose instead
that rational players will use all the information available in correlated
distributions to constrain payoff function topologies and gradients to generate
novel "constrained" equilibria, each one a backwards induction pathway
optimizing payoffs in the constrained space. In the finite iterated prisoner's
dilemma, we locate constrained equilibria maximizing payoffs via cooperation
additional to the unconstrained (Nash) equilibrium maximizing payoffs via
defection. Our approach clarifies the usual assumptions hidden in backwards
induction.


title: The dynamics of opinion in hierarchical organizations

abstract:
  We study the mutual influence of authority and persuasion in the flow of
opinion. Many social organizations are characterized by a hierarchical
structure where the propagation of opinion is asymmetric. In the normal flow of
opinion formation a high-rank agent uses its authority (or its persuasion when
necessary) to impose its opinion on others. However, agents with no authority
may only use the force of its persuasion to propagate their opinions. In this
contribution we describe a simple model with no social mobility, where each
agent belongs to a class in the hierarchy and has also a persuasion capability.
The model is studied numerically for a three levels case, and analytically
within a mean field approximation, with a very good agreement between the two
approaches. The stratum where the dominant opinion arises from is strongly
dependent on the percentage of agents in each hierarchy level, and we obtain a
phase diagram identifying the relative frequency of prevailing opinions. We
also find that the time evolution of the conflicting opinions polarizes after a
short transient.


title: Sign-symmetry of temperature structure functions

abstract:
  New scalar structure functions with different sign-symmetry properties are
defined. These structure functions possess different scaling exponents even
when their order is the same. Their scaling properties are investigated for
second and third orders, using data from high-Reynolds-number atmospheric
boundary layer. It is only when structure functions with disparate
sign-symmetry properties are compared can the extended self-similarity detect
two different scaling ranges that may exist, as in the example of convective
turbulence.


title: Quasi-linear Stokes phenomenon for the Painlev\'e first equation

abstract:
  Using the Riemann-Hilbert approach, the $\Psi$-function corresponding to the
solution of the first Painleve equation, $y_{xx}=6y^2+x$, with the asymptotic
behavior $y\sim\pm\sqrt{-x/6}$ as $|x|\to\infty$ is constructed. The
exponentially small jump in the dominant solution and the coefficient
asymptotics in the power-like expansion to the latter are found.


title: Lyapunov instabilities of Lennard-Jones fluids

abstract:
  Recent work on many particle system reveals the existence of regular
collective perturbations corresponding to the smallest positive Lyapunov
exponents (LEs), called hydrodynamic Lyapunov modes. Until now, however, these
modes are only found for hard core systems. Here we report new results on
Lyapunov spectra and Lyapunov vectors (LVs) for Lennard-Jones fluids. By
considering the Fourier transform of the coordinate fluctuation density
$u^{(\alpha)}(x,t)$, it is found that the LVs with $\lambda \approx 0$ are
highly dominated by a few components with low wave-numbers.
  These numerical results provide strong evidence that hydrodynamic Lyapunov
modes do exist in soft-potential systems, although the collective Lyapunov
modes are more vague than in hard-core systems. In studying the density and
temperature dependence of these modes, it is found that, when the value of
Lyapunov exponent $\lambda^{(\alpha)}$ is plotted as function of the dominant
wave number $k_{max}$ of the corresponding LV, all data from simulations with
different densities and temperatures collapse onto a single curve. This shows
that the dispersion relation $\lambda^{(\alpha)}$ vs. $k_{max}$ for
hydrodynamical Lyapunov modes appears to be universal irrespective of the
particle density and temperature of the system.
  Despite the wave-like character of the LVs, no step-like structure exists in
the Lyapunov spectrum of the systems studied here, in contrast to the hard-core
case. Further numerical simulations show that the finite-time LEs fluctuate
strongly. We have also investigated localization features of LVs and propose a
new length scale to characterize the Hamiltonian spatio-temporal chaotic
states.


title: Static and Dynamic Correlations in Many-Particle Lyapunov Vectors

abstract:
  We introduce static and dynamic correlation functions for the spatial
densities of Lyapunov vector fluctuations. They enable us to show, for the
first time, the existence of hydrodynamic Lyapunov modes in chaotic
many-particle systems with soft core interactions, which indicates universality
of this phenomenon. Our investigations for Lennard-Jones fluids yield, in
addition to the Lyapunov exponent - wave vector dispersion, the collective
dynamic excitations of a given Lyapunov vector. In the limit of purely
translational modes the static and dynamic structure factor are recovered.


title: Moving breathers in bent DNA with realistic parameters

abstract:
  Recent papers have considered moving breathers (MBs) in DNA models including
long range interaction due to the dipole moments of the hydrogen bonds. We have
recalculated the value of the charge transfer when hydrogen bonds stretch using
quantum chemical methods which takes into account the whole nucleoside pairs.
We explore the consequences of this value on the properties of MBs, including
the range of frequencies for which they exist and their effective masses. They
are able to travel through bending points with fairly large curvatures provided
that their kinetic energy is larger than a minimum energy which depends on the
curvature. These energies and the corresponding velocities are also calculated
in function of the curvature.


title:
Discrete breathers for understanding reconstructive mineral processes at
  low temperatures

abstract:
  Reconstructive transformations in layered silicates need a high tem- perature
in order to be observed. However, very recently, some systems have been found
where transformation can be studied at temperatures 600 C below the lowest
experimental results previously reported, including sol-gel methods. We explore
the possible relation with the existence of intrinsic localized modes, known as
discrete breathers. We construct a model for nonlinear vibrations within the
cation layer, obtain their parameters and calculate them numerically, obtaining
their energies. Their statistics shows that although there are far less
breathers than phonons, there are much more above the activation energy, being
therefore a good candidate to explain the reconstructive transformations at low
temperature.


title: Lie Point Symmetries for Reduced Ermakov Systems

abstract:
  Reduced Ermakov systems are defined as Ermakov systems restricted to the
level surfaces of the Ermakov invariant. The condition for Lie point symmetries
for reduced Ermakov systems is solved yielding four infinite families of
systems. It is shown that SL(2,R) always is a group of point symmetries for the
reduced Ermakov systems. The theory is applied to a model example and to the
equations of motion of an ion under a generalized Paul trap.


title: Metrics for more than two points at once

abstract:
  The conventional definition of a topological metric over a space specifies
properties that must be obeyed by any measure of "how separated" two points in
that space are. Here it is shown how to extend that definition, and in
particular the triangle inequality, to concern arbitrary numbers of points.
Such a measure of how separated the points within a collection are can be
bootstrapped, to measure "how separated" from each other are two (or more)
collections. The measure presented here also allows fractional membership of an
element in a collection. This means it directly concerns measures of ``how
spread out" a probability distribution over a space is. When such a measure is
bootstrapped to compare two collections, it allows us to measure how separated
two probability distributions are, or more generally, how separated a
distribution of distributions is.


title:
Linear differential equations to solve nonlinear mechanical problems: A
  novel approach

abstract:
  Often a non-linear mechanical problem is formulated as a non-linear
differential equation. A new method is introduced to find out new solutions of
non-linear differential equations if one of the solutions of a given non-linear
differential equation is known. Using the known solution of the non-linear
differential equation, linear differential equations are set up. The solutions
of these linear differential equations are found using standard techniques.
Then the solutions of the linear differential equations are put into non-linear
differential equations and checked whether these solutions are also solutions
of the original non-linear differential equation. It is found that many
solutions of the linear differential equations are also solutions of the
original non-linear differential equation.


title: The Lyapunov spectrum of the many-dimensional dilute random Lorentz gas

abstract:
  For a better understanding of the chaotic behavior of systems of many moving
particles it is useful to look at other systems with many degrees of freedom.
An interesting example is the high-dimensional Lorentz gas, which, just like a
system of moving hard spheres, may be interpreted as a dynamical system
consisting of a point particle in a high-dimensional phase space, moving among
fixed scatterers. In this paper, we calculate the full spectrum of Lyapunov
exponents for the dilute random Lorentz gas in an arbitrary number of
dimensions. We find that the spectrum becomes flatter with increasing
dimensionality. Furthermore, for fixed collision frequency the separation
between the largest Lyapunov exponent and the second largest one increases
logarithmically with dimensionality, whereas the separations between Lyapunov
exponents of given indices not involving the largest one, go to fixed limits.


title: On Selfish Memes

abstract:
  We present the formal definition of meme in the sense of the equivalence
between memetics and the theory of cultural evolution. From the formal
definition we find that culture can be seen analytically and persuade that
memetic gives important role in the exploration of sociological theory,
especially in the cultural studies. We show that we are not allowed to assume
meme as smallest information unit in cultural evolution in general, but it is
the smallest information we use on explaining cultural evolution. We construct
a computational model and do simulation in advance presenting the selfish meme
power-law distributed. The simulation result shows that the contagion of meme
as well as cultural evolution is a complex adaptive system. Memetics is the
system and art of importing genetics to social sciences.


title:
Normal and seminormal forms of sl(3)-valued zero curvature
  representations

abstract:
  We find normal and seminormal forms for a sl(3)-valued zero curvature
representation (ZCR). We prove a theorem about reducibility of ZCR's, which
says that if one of the matrix in a ZCR (A,B) falls to a proper subalgebra of
sl(3), then the second matrix either falls to the same subalgebra or the ZCR is
almost trivial. In the end of this paper we show examples of ZCR's and their
normal forms.


title: Singularity analysis of a spherical Kadomtsev-Petviashvili equation

abstract:
  The (2+1)-dimensional spherical Kadomtsev-Petviashvili (SKP) equation of
J.-K. Xue [Phys. Lett. A 314:479-483 (2003)] fails the Painleve test for
integrability at the highest resonance, where a nontrivial compatibility
condition for recursion relations appears. This compatibility condition,
however, is sufficiently weak and thus allows the SKP equation to possess an
integrable (1+1)-dimensional reduction, which is detected by the Weiss method
of truncated singular expansions.

categories: nlin.SI math-ph math.AP math.MP physics.plasm-ph


title: Weyl's law and quantum ergodicity for maps with divided phase space

abstract:
  For a general class of unitary quantum maps, whose underlying classical phase
space is divided into several invariant domains of positive measure, we
establish analogues of Weyl's law for the distribution of eigenphases. If the
map has one ergodic component, and is periodic on the remaining domains, we
prove the Schnirelman-Zelditch-Colin de Verdiere Theorem on the
equidistribution of eigenfunctions with respect to the ergodic component of the
classical map (quantum ergodicity). We apply our main theorems to quantised
linked twist maps on the torus. In the Appendix, S. Zelditch connects these
studies to some earlier results on `pimpled spheres' in the setting of
Riemannian manifolds. The common feature is a divided phase space with a
periodic component.


title:
What does the nonextensive parameter q stand for in self-gravitating
  systems ?

abstract:
  It is natural important question for us to ask what the nonextensive
parameter stands for when Tsallis statistics is applied to the self-gravitating
systems. In this paper, some properties of the nonextensive parameter and
Tsallis equilibrium distribution for the self-gravitating system are discussed
in the framework of nonextensive kinetic theory. On the basis of the solid
mathematical foundation, the nonextensive parameter can be expressed by a
formula with temperature gradient and the gravitational potential and can be
presented the physical meaning with regard to the non-isothermal
(nonequilibrium stationary state) nature of the systems with long-range
interactions. We come to the conclusion that Tsallis equilibrium distribution
is corresponding to the physical state of self-gravitating system at the
hydrostatic equilibrium.

categories: nlin.AO astro-ph cond-mat.stat-mech nlin.CD


abstract:
  The Backlund transformations for the Nizhnik-Novikov-Veselov equation are
presented. It is shown that these transformations can be iterated and that the
resulting sequence can be described by the Volterra equations. The
relationships between the Nizhnik-Novikov-Veselov equation and the Volterra
hierarchy are discussed.


title:
Mixing structures in the Mediterranean Sea from Finite-Size Lyapunov
  Exponents

abstract:
  We characterize horizontal mixing and transport structures in the surface
circulation of the Mediterranean Sea, as obtained from a primitive equation
circulation model. We calculate the Finite Size Lyapunov Exponents (FSLEs) of
the velocity data set, which gives a direct measure of the local stirring. By
proper election of the FSLE parameters, we focus on the mesoscale structures,
locating a number of vortices embedded in an intricate network of
high-stretching lines. These lines control transport in the system. At the edge
of the vortices, a dense tangle of line intersections appears, identifying
strong mixing. The spatial distribution of FSLEs, averaged over one year,
allows to classify areas in the Mediterranean basin according by their mixing
activity. The space average of FSLEs on selected geographical regions gives a
measure for quantifying and comparing the mixing seasonal variability.


title: Tip-splitting evolution in the idealized Saffman-Taylor problem

abstract:
  We derive a formula describing the evolution of tip-splittings of
Saffman-Taylor fingers in a Hele-Shaw cell, at zero surface tension.


title: Statistical Theory of Magnetohydrodynamic Turbulence: Recent Results

abstract:
  In this review article we will describe recent developments in statistical
theory of magnetohydrodynamic (MHD) turbulence. Kraichnan and Iroshnikov first
proposed a phenomenology of MHD turbulence where Alfven time-scale dominates
the dynamics, and the energy spectrum E(k) is proportional to k^{-3/2}. In the
last decade, many numerical simulations show that spectral index is closer to
5/3, which is Kolmogorov's index for fluid turbulence. We review recent
theoretical results based on anisotropy and Renormalization Groups which
support Kolmogorov's scaling for MHD turbulence.
  Energy transfer among Fourier modes, energy flux, and shell-to-shell energy
transfers are important quantities in MHD turbulence. We report recent
numerical and field-theoretic results in this area. Role of these quantities in
magnetic field amplification (dynamo) are also discussed. There are new
insights into the role of magnetic helicity in turbulence evolution. Recent
interesting results in intermittency, large-eddy simulations, and shell models
of magnetohydrodynamics are also covered.

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


title:
Nonlinear stability of oscillatory wave fronts in chains of coupled
  oscillators

abstract:
  We present a stability theory for kink propagation in chains of coupled
oscillators and a new algorithm for the numerical study of kink dynamics. The
numerical solutions are computed using an equivalent integral equation instead
of a system of differential equations. This avoids uncertainty about the impact
of artificial boundary conditions and discretization in time. Stability results
also follow from the integral version. Stable kinks have a monotone leading
edge and move with a velocity larger than a critical value which depends on the
damping strength.


title: Single polymer dynamics: coil-stretch transition in a random flow

abstract:
  By quantitative studies of statistics of polymer stretching in a random flow
and of a flow field we demonstrate that the stretching of polymer molecules in
a 3D random flow occurs rather sharply via the coil-stretch transition at the
value of the criterion close to theoretically predicted.


title: Interaction of Ising-Bloch fronts with Dirichlet Boundaries

abstract:
  We study the Ising-Bloch bifurcation in two systems, the Complex Ginzburg
Landau equation (CGLE) and a FitzHugh Nagumo (FN) model in the presence of
spatial inhomogeneity introduced by Dirichlet boundary conditions. It is seen
that the interaction of fronts with boundaries is similar in both systems,
establishing the generality of the Ising-Bloch bifurcation. We derive reduced
dynamical equations for the FN model that explain front dynamics close to the
boundary. We find that front dynamics in a highly non-adiabatic (slow front)
limit is controlled by fixed points of the reduced dynamical equations, that
occur close to the boundary.


title: A Quantization of Box-Ball Systems

abstract:
  An L operator is presented related to an infinite dimensional limit of the
fusion R matrices for U_q(A^{(1)}_{n-1}) and U_q(D^{(1)}_n). It is factorized
into the local propagation operators which quantize the deterministic dynamics
of particles and antiparticles in the soliton cellular automata known as the
box-ball systems and their generalizations. Some properties of the dynamical
amplitudes are also investigated.


title: Controlling Fast Chaos in Delay Dynamical Systems

abstract:
  We introduce a novel approach for controlling fast chaos in time-delay
dynamical systems and use it to control a chaotic photonic device with a
characteristic time scale of ~12 ns. Our approach is a prescription for how to
implement existing chaos control algorithms in a way that exploits the system's
inherent time-delay and allows control even in the presence of substantial
control-loop latency (the finite time it takes signals to propagate through the
components in the controller). This research paves the way for applications
exploiting fast control of chaos, such as chaos-based communication schemes and
stabilizing the behavior of ultrafast lasers.


title:
A Nonliearly Dispersive Fifth Order Integrable Equation and its
  Hierarchy

abstract:
  In this paper, we study the properties of a nonlinearly dispersive integrable
system of fifth order and its associated hierarchy. We describe a Lax
representation for such a system which leads to two infinite series of
conserved charges and two hierarchies of equations that share the same
conserved charges. We construct two compatible Hamiltonian structures as well
as their Casimir functionals. One of the structures has a single Casimir
functional while the other has two. This allows us to extend the flows into
negative order and clarifies the meaning of two different hierarchies of
positive flows. We study the behavior of these systems under a hodograph
transformation and show that they are related to the Kaup-Kupershmidt and the
Sawada-Kotera equations under appropriate Miura transformations. We also
discuss briefly some properties associated with the generalization of second,
third and fourth order Lax operators.


title:
Parameter mismatches,variable delay times and synchronization in
  time-delayed systems

abstract:
  We investigate synchronization between two unidirectionally linearly coupled
chaotic non-identical time-delayed systems and show that parameter mismatches
are of crucial importance to achieve synchronization. We establish that
independent of the relation between the delay time in the coupled systems and
the coupling delay time, only retarded synchronization with the coupling delay
time is obtained. We show that with parameter mismatch or without it neither
complete nor anticipating synchronization occurs. We derive existence and
stability conditions for the retarded synchronization manifold. We demonstrate
our approach using examples of the Ikeda and Mackey-Glass models. Also for the
first time we investigate chaos synchronization in time-delayed systems with
variable delay time and find both existence and sufficient stability conditions
for the retarded synchronization manifold with the coupling delay lag time.
Also for the first time we consider synchronization between two
unidirectionally coupled chaotic multi-feedback Ikeda systems and derive
existence and stability conditions for the different anticipating, lag, and
complete synchronization regimes.


title:
Wave-number Selection by Target Patterns and Side Walls in
  Rayleigh-Benard Convection

abstract:
  We present experimental results for Rayleigh-Benard convection patterns in a
cylindrical container with static side-wall forcing induced by a heater. This
forcing stabilized a pattern of concentric rolls (a target pattern) with the
central roll (the umbilicus) at the center of the cell after a jump from the
conduction to the convection state. A quasi-static increase of the control
parameter (epsilon) beyond 0.8 caused the umbilicus of the pattern to move off
center. As observed by others, a further quasi-static increase of epsilon up to
15.6 caused a sequence of transitions. Each transition began with the
displacement of the umbilicus and then proceeded with the loss of one
convection roll at the umbilicus and the return of the umbilicus to a location
near the center of the cell. Alternatively, with decreasing epsilon new rolls
formed at the umbilicus but large umbilicus displacements did not occur. In
addition to quantitative measurements of the umbilicus displacement, we
determined and analyzed the entire wave-director field of each image. The wave
numbers varied in the axial direction, with minima at the umbilicus and at the
cell wall and a maximum at a radial position close to 2/3 Gamma. The wave
numbers at the maximum showed hysteretic jumps at the transitions, but on
average agreed well with the theoretical predictions for the wave numbers
selected in the far field of an infinitely extended target pattern.


title:
Time-oscillating Lyapunov modes and auto-correlation functions for
  quasi-one-dimensional systems

abstract:
  The time-dependent structure of the Lyapunov vectors corresponding to the
steps of Lyapunov spectra and their basis set representation are discussed for
a quasi-one-dimensional many-hard-disk systems. Time-oscillating behavior is
observed in two types of Lyapunov modes, one associated with the time
translational invariance and another with the spatial translational invariance,
and their phase relation is specified. It is shown that the longest period of
the Lyapunov modes is twice as long as the period of the longitudinal momentum
auto-correlation function. A simple explanation for this relation is proposed.
This result gives the first quantitative connection between the Lyapunov modes
and an experimentally accessible quantity.


title:
Adaptive time-delay hyperchaos synchronization in laser diodes subject
  to optical feedback(s)

abstract:
  In this paper a proposal is made of an adaptive coupling function for
achieving synchronization between two lasers subject to optical feedback. Such
a control scheme requires knowledge of the systems' parameters. For the first
time we demonstrate that when these parameters are not available on-line
parameter estimation can be applied.Generalisation of the approach to the
multi-feedback systems is also presented.


title:
Surrogate Test to Distinguish between Chaotic and Pseudoperiodic Time
  Series

abstract:
  In this communication a new algorithm is proposed to produce surrogates for
pseudoperiodic time series. By imposing a few constraints on the noise
components of pseudoperiodic data sets, we devise an effective method to
generate surrogates. Unlike other algorithms, this method properly copes with
pseudoperiodic orbits contaminated with linear colored observational noise. We
will demonstrate the ability of this algorithm to distinguish chaotic orbits
from pseudoperiodic orbits through simulation data sets from theR\"{o}ssler
system. As an example of application of this algorithm, we will also employ it
to investigate a human electrocardiogram (ECG) record.


title:
Resonant Interactions in Rotating Homogeneous Three-dimensional
  Turbulence

abstract:
  Direct numerical simulations of three-dimensional (3D) homogeneous turbulence
under rapid rigid rotation are conducted to examine the predictions of resonant
wave theory for both small Rossby number and large Reynolds number. The
simulation results reveal that there is a clear inverse energy cascade to the
large scales, as predicted by 2D Navier-Stokes equations for resonant
interactions of slow modes. As the rotation rate increases, the
vertically-averaged horizontal velocity field from 3D Navier-Stokes converges
to the velocity field from 2D Navier-Stokes, as measured by the energy in their
difference field. Likewise, the vertically-averaged vertical velocity from 3D
Navier-Stokes converges to a solution of the 2D passive scalar equation. The
energy flux directly into small wave numbers in the $k_z=0$ plane from
non-resonant interactions decreases, while fast-mode energy concentrates closer
to that plane. The simulations are consistent with an increasingly dominant
role of resonant triads for more rapid rotation.


title: Diffusion in a stochastic magnetic field

abstract:
  We consider a stochastic differential equation for a charged particle in a
stochastic magnetic field, known as A-Langevin equation. The solution of the
equation is found, and the Lagrange velocity correlation function is calculated
in Corrsin approximation. A corresponding diffusion constant is estimated. We
observe different transport regimes, such as quasilinear- or Bohm-type
diffusion, depending on the parameters of plasma.


title:
Temporal chaos versus spatial mixing in reaction-advection-diffusion
  systems

abstract:
  We develop a theory describing the transition to a spatially homogeneous
regime in a mixing flow with a chaotic in time reaction. The transverse
Lyapunov exponent governing the stability of the homogeneous state can be
represented as a combination of Lyapunov exponents for spatial mixing and
temporal chaos. This representation, being exact for time-independent flows and
equal P\'eclet numbers of different components, is demonstrated to work
accurately for time-dependent flows and different P\'eclet numbers.


title: Detecting order and chaos in Hamiltonian systems by the SALI method

abstract:
  We use the Smaller Alignment Index (SALI) to distinguish rapidly and with
certainty between ordered and chaotic motion in Hamiltonian flows. This
distinction is based on the different behavior of the SALI for the two cases:
the index fluctuates around non--zero values for ordered orbits, while it tends
rapidly to zero for chaotic orbits. We present a detailed study of SALI's
behavior for chaotic orbits and show that in this case the SALI exponentially
converges to zero, following a time rate depending on the difference of the two
largest Lyapunov exponents $\sigma_1$, $\sigma_2$ i.e. $SALI \propto
e^{-(\sigma_1-\sigma_2)t}$. Exploiting the advantages of the SALI method, we
demonstrate how one can rapidly identify even tiny regions of order or chaos in
the phase space of Hamiltonian systems of 2 and 3 degrees of freedom.


title:
Solitons on nanotubes and fullerenes as solutions of a modified
  non-linear Schroedinger equation

abstract:
  Fullerenes and nanotubes consist of a large number of carbon atoms sitting on
the sites of a regular lattice. For pratical reasons it is often useful to
approximate the equations on this lattice in terms of the continuous equation.
At the moment, the best candidate for such an equation is the modified
non-linear Schroedinger equation. In this paper, we study the modified
non-linear Schroedinger equation, which arises as continuous equation in a
system describing an excitation on a hexagonal lattice. This latter system can
e.g. describe electron-phonon interaction on fullerene related structures such
as the buckminster fullerene and nanotubes. Solutions of this modified
non-linear Schroedinger equation, which have solitonic character, can be
constructed using an Ansatz for the wave function, which has time and azimuthal
angle dependence introduced previously in the study of spinning boson stars and
Q-balls. We study these solutions on a sphere, a disc and on a cylinder.
  Our construction suggests that non-spinning as well as spinning solutions,
which have a wave function with an arbitrary number of nodes, exist. We find
that this property is closely related to the series of well-known mathematical
functions, namely the Legendre functions when studying the equation on a
sphere, the Bessel functions when studying the equation on a disc and the
trigonometric functions, respectively, when studying the equation on a
cylinder.


title:
Analysis of dynamical tunnelling experiments with a Bose-Einstein
  condensate

abstract:
  Dynamical tunnelling is a quantum phenomenon where a classically forbidden
process occurs, that is prohibited not by energy but by another constant of
motion. The phenomenon of dynamical tunnelling has been recently observed in a
sodium Bose-Einstein condensate. We present a detailed analysis of these
experiments using numerical solutions of the three dimensional Gross-Pitaevskii
equation and the corresponding Floquet theory. We explore the parameter
dependency of the tunnelling oscillations and we move the quantum system
towards the classical limit in the experimentally accessible regime.


title:
Relation between shear parameter and Reynolds number in statistically
  stationary turbulent shear flows

abstract:
  Studies of the relation between the shear parameter S^* and the Reynolds
number Re are presented for a nearly homogeneous and statistically stationary
turbulent shear flow. The parametric investigations are in line with a
generalized perspective on the return to local isotropy in shear flows that was
outlined recently [Schumacher, Sreenivasan and Yeung, Phys. Fluids, vol.15, 84
(2003)]. Therefore, two parameters, the constant shear rate S and the level of
initial turbulent fluctuations as prescribed by an energy injection rate
epsilon_{in}, are varied systematically. The investigations suggest that the
shear parameter levels off for larger Reynolds numbers which is supported by
dimensional arguments. It is found that the skewness of the transverse
derivative shows a different decay behavior with respect to Reynolds number
when the sequence of simulation runs follows different pathways across the
two-parameter plane. The study can shed new light on different interpretations
of the decay of odd order moments in high-Reynolds number experiments.


title: Power Law Signature in Indonesian Legislative Election 1999-2004

abstract:
  We analyzed the distribution of the result of Indonesian 1999 and 2004
legislative election in order to have the statistical properties or any
stylized facts. The paper shows that the analysis results the power-law
signature persistently in the election of the House of Representative in 1999
and 2004 and more clearly in the result of Regional Representative Council that
held for the first time in 2004. It shows that the socio-political system is a
complex system constituted by interacting citizens and accentuates universality
that the social evolution dynamically turns to be self-organized in critical
state.


title: A Graphical User Interface to Simulate Classical Billiard Systems

abstract:
  Classical billiards constitute an important class of dynamical systems. They
have not only been in used in mathematical disciplines such as ergodic theory,
but their properties demonstrate fundamental physical phenomena that can be
observed in laboratory settings. This document provides instructions for a
Matlab module that simulates classical billiard systems. It is intended to be
used as both a research and teaching tool. At present, the program efficiently
simulates tables that are constructed entirely from line segments and
elliptical arcs. It functions less reliably for tables with more complex
boundary components. The program and documentation can be downloaded from
\textit{http://www.math.gatech.edu/$\sim$mason/papers/}.

categories: nlin.CD cond-mat.other math-ph math.DS math.MP physics.atom-ph physics.pop-ph


title: Chaos synchronization in the multi-feedback Ikeda model

abstract:
  We investigate synchronization between two unidirectionally coupled chaotic
multi-feedback Ikeda systems and find both the existence and stability
conditions for anticipating, lag, and complete synchronizations.Generalization
of the approach to a wide class of nonlinear systems is also presented.


title: Hierarchical Taxonomy in Multi-Party System

abstract:
  We propose the use of hierarchical taxonomy to analyze the legislative
election results as a model of multi-party system to show the robustness in
political system. As an example we use the result of Indonesian legislative
election 2004 is analyzed with certain comparative with the previous one
(1999). We construct the graph theoretical analysis by finding the Euclidean
distances among political parties. The distances are then treated in
ultrametric spaces by using the minimum spanning tree algorithm. By having the
Indonesian hierarchical taxonomy model of political parties we show some
patterns emerging the pattern agrees with the classical anthropological
analysis of socio-political system in Indonesia. This fact accentuates a
character of robustness in Indonesian political society as a self-organized
system evolves to critical state. Some small perturbations i.e.: different
voting process resulting the same pattern and occasions statistically, emerges
from the social structure based upon political streams: Islamic, secular,
traditional, and some complements of all.


title:
Fractal dimension of transport coefficients in a deterministic dynamical
  system

abstract:
  In many low-dimensional dynamical systems transport coefficients are very
irregular, perhaps even fractal functions of control parameters. To analyse
this phenomenon we study a dynamical system defined by a piece-wise linear map
and investigate the dependence of transport coefficients on the slope of the
map. We present analytical arguments, supported by numerical calculations,
showing that both the Minkowski-Bouligand and Hausdorff fractal dimension of
the graphs of these functions is 1 with a logarithmic correction, and find that
the exponent $\gamma$ controlling this correction is bounded from above by 1 or
2, depending on some detailed properties of the system. Using numerical
techniques we show local self-similarity of the graphs. The local
self-similarity scaling transformations turn out to depend (irregularly) on the
values of the system control parameters.