title:
Localized Structures in Nonlinear Lattices with Diffusive Coupling and
  External Driving

abstract:
  We study the stabilization of localized structures by discreteness in
one-dimensional lattices of diffusively coupled nonlinear sites. We find that
in an external driving field these structures may lose their stability by
either relaxing to a homogeneous state or nucleating a pair of oppositely
moving fronts. The corresponding bifurcation diagram demonstrates a cusp
singularity. The obtained analytic results are in good quantitative agreement
with numerical simulations.


title: A Potential of Incoherent Attraction Between Multidimensional Solitons

abstract:
  We obtain analytical expressions for an effective potential of interaction
between two- and three-dimensional (2D and 3D) solitons (including the case of
2D vortex solitons) belonging to two different modes which are incoherently
coupled by cross-phase modulation. The derivation is based on calculation of
the interaction term in the full Hamiltonian of the system. An essential
peculiarity is that, in the 3D case, as well as in the case of 2D solitons with
unequal masses, the main contribution to the interaction potential originates
from a vicinity of one or both solitons, similarly to what was recently found
in the 2D and 3D single-mode systems, while in the case of identical 2D
solitons, the dominating area covers all the space between the solitons. Unlike
the single-mode systems,_stable_ bound states of mutually orbiting solitons are
shown to be possible in the bimodal system.


title: Buckling Cascade of Thin Plates: Forms, Constraints and Similarity

abstract:
  We experimentally study compression of thin plates in rectangular boxes with
variable height. A cascade of buckling is generated. It gives rise to a
self-similar evolution of elastic reaction of plates with box height which
surprisingly exhibits repetitive vanishing and negative stiffness. These
features are understood from properties of Euler's equation for elastica.


title: Discrete Nonlinear Schr{\"o}dinger Breathers in a Phonon Bath

abstract:
  We study the dynamics of the discrete nonlinear Schr{\"o}dinger lattice
initialized such that a very long transitory period of time in which standard
Boltzmann statistics is insufficient is reached. Our study of the nonlinear
system locked in this {\em non-Gibbsian} state focuses on the dynamics of
discrete breathers (also called intrinsic localized modes). It is found that
part of the energy spontaneously condenses into several discrete breathers.
Although these discrete breathers are extremely long lived, their total number
is found to decrease as the evolution progresses. Even though the total number
of discrete breathers decreases we report the surprising observation that the
energy content in the discrete breather population increases. We interpret
these observations in the perspective of discrete breather creation and
annihilation and find that the death of a discrete breather cause effective
energy transfer to a spatially nearby discrete breather. It is found that the
concepts of a multi-frequency discrete breather and of internal modes is
crucial for this process. Finally, we find that the existence of a discrete
breather tends to soften the lattice in its immediate neighborhood, resulting
in high amplitude thermal fluctuation close to an existing discrete breather.
This in turn nucleates discrete breather creation close to a already existing
discrete breather.


title: Traveling wave solutions in the Burridge-Knopoff model

abstract:
  The slider-block Burridge-Knopoff model with the Coulomb friction law is
studied as an excitable medium. It is shown that in the continuum limit the
system admits solutions in the form of the self-sustained shock waves traveling
with constant speed which depends only on the amount of the accumulated stress
in front of the wave. For a wide class of initial conditions the behavior of
the system is determined by these shock waves and the dynamics of the system
can be expressed in terms of their motion. The solutions in the form of the
periodic wave trains and sources of counter-propagating waves are analyzed. It
is argued that depending on the initial conditions the system will either tend
to synchronize or exhibit chaotic spatiotemporal behavior.


title: Two-color nonlinear localized photonic modes

abstract:
  We analyze second-harmonic generation (SHG) at a thin effectively quadratic
nonlinear interface between two linear optical media. We predict multistability
of SHG for both plane and localized waves, and also describe two-color
localized photonic modes composed of a fundamental wave and its second harmonic
coupled together by parametric interaction at the interface.


title:
Quasi-Solitons in Dissipative Systems and Exactly Solvable Lattice
  Models

abstract:
  A system of first-order differential-difference equations with time lag
describes the formation of density waves, called as quasi-solitons for
dissipative systems in this paper. For co-moving density waves, the system
reduces to some exactly solvable lattice models. We construct a shock-wave
solution as well as one-quasi-soliton solution, and argue that there are
pseudo-conserved quantities which characterize the formation of the co-moving
waves. The simplest non-trivial one is given to discuss the presence of a
cascade phenomena in relaxation process toward the pattern formation.


title:
Existence and stability of hole solutions to complex Ginzburg-Landau
  equations

abstract:
  We consider the existence and stability of the hole, or dark soliton,
solution to a Ginzburg-Landau perturbation of the defocusing nonlinear
Schroedinger equation (NLS), and to the nearly real complex Ginzburg-Landau
equation (CGL). By using dynamical systems techniques, it is shown that the
dark soliton can persist as either a regular perturbation or a singular
perturbation of that which exists for the NLS. When considering the stability
of the soliton, a major difficulty which must be overcome is that eigenvalues
may bifurcate out of the continuous spectrum, i.e., an edge bifurcation may
occur. Since the continuous spectrum for the NLS covers the imaginary axis, and
since for the CGL it touches the origin, such a bifurcation may lead to an
unstable wave. An additional important consideration is that an edge
bifurcation can happen even if there are no eigenvalues embedded in the
continuous spectrum. Building on and refining ideas first presented in Kapitula
and Sandstede (Physica D, 1998) and Kapitula (SIAM J. Math. Anal., 1999), we
show that when the wave persists as a regular perturbation, at most three
eigenvalues will bifurcate out of the continuous spectrum. Furthermore, we
precisely track these bifurcating eigenvalues, and thus are able to give
conditions for which the perturbed wave will be stable. For the NLS the results
are an improvement and refinement of previous work, while the results for the
CGL are new. The techniques presented are very general and are therefore
applicable to a much larger class of problems than those considered here.


title: Near Critical Reflection of Internal Waves

abstract:
  Using a matched asymptotic expansion we analyze the two-dimensional, near-
critical reflection of a weakly nonlinear, internal gravity wave from a sloping
boundary in a uniformly stratified fluid. Taking a distinguished limit in which
the amplitude of the incident wave, the dissipation, and the departure from
criticality are all small, we obtain a reduced description of the dynamics.
This simplification shows how either dissipation or transience heals the
singularity which is presented by the classical solution in the precisely
critical case. In the inviscid critical case, an explicit solution of the
initial value problem shows that the buoyancy perturbation and the along-slope
velocity both grow linearly with time, while the scale of the reflected
disturbance is reduced as $1/t$. During the course of this scale reduction, the
stratification is `overturned' and the Miles-Howard condition for stratified
shear flow stability is violated. However, for all slope angles, the
`overturning' occurs before the Miles-Howard stability condition is violated
and so we argue that the first instability is convective. Solutions of the
simplified dynamics resemble certain experimental visualizations of the
reflection process.


title:
On-off Intermittency in Stochastically Driven Electrohydrodynamic
  Convection in Nematics

abstract:
  We report on-off intermittency in electroconvection of nematic liquid
crystals driven by a dichotomous stochastic electric voltage. With increasing
voltage amplitude we observe laminar phases of undistorted director state
interrupted by shorter bursts of spatially regular stripes. Near a critical
value of the amplitude the distribution of the duration of laminar phases is
governed over several decades by a power law with exponent -3/2. The
experimental findings agree with simulations of the linearized
electrohydrodynamic equations near the sample stability threshold.


title:
Sources, sinks and wavenumber selection in coupled CGL equations and
  experimental implications for counter-propagating wave systems

abstract:
  We study the coupled complex Ginzburg-Landau (CGL) equations for traveling
wave systems in the regime where sources and sinks separate patches of left and
right-traveling waves. We show that sources and sinks are the important
coherent structures that organize much of the dynamical properties of traveling
wave systems. We present in detail the framework to analyze these coherent
structures. Our counting arguments for the multiplicities of these structures
show that independently of the coefficients of the CGL, there exists a
symmetric stationary source solution, which sends out waves with a unique
frequency and wave number. Sinks, on the other hand, occur in two-parameter
families, and play an essentially passive role. Simulations show that sources
can send out stable waves, convectively unstable waves, or absolutely unstable
waves. We show that there exists an additional dynamical regime where both
single- and bimodal states are unstable; the ensuing chaotic states have no
counterpart in single amplitude equations. A third dynamical mechanism is
associated with the fact that the width of the sources does not show simple
scaling with the growth rate epsilon. In particular, when the group velocity
term dominates over the linear growth term, no stationary source can exist, but
sources displaying nontrivial dynamics can survive here. Our results are easily
accessible by experiments, and we advocate a study of the sources and sinks as
a means to probe traveling wave systems and compare theory and experiment.


title: Multi-Phase Patterns in Periodically Forced Oscillatory Systems

abstract:
  Periodic forcing of an oscillatory system produces frequency locking bands
within which the system frequency is rationally related to the forcing
frequency. We study extended oscillatory systems that respond to uniform
periodic forcing at one quarter of the forcing frequency (the 4:1 resonance).
These systems possess four coexisting stable states, corresponding to uniform
oscillations with successive phase shifts of $\pi/2$. Using an amplitude
equation approach near a Hopf bifurcation to uniform oscillations, we study
front solutions connecting different phase states. These solutions divide into
two groups: $\pi$-fronts separating states with a phase shift of $\pi$ and
$\pi/2$-fronts separating states with a phase shift of $\pi/2$. We find a new
type of front instability where a stationary $\pi$-front ``decomposes'' into a
pair of traveling $\pi/2$-fronts as the forcing strength is decreased. The
instability is degenerate for an amplitude equation with cubic nonlinearities.
At the instability point a continuous family of pair solutions exists,
consisting of $\pi/2$-fronts separated by distances ranging from zero to
infinity. Quintic nonlinearities lift the degeneracy at the instability point
but do not change the basic nature of the instability. We conjecture the
existence of similar instabilities in higher 2n:1 resonances (n=3,4,..) where
stationary $\pi$-fronts decompose into n traveling $\pi/n$-fronts. The
instabilities designate transitions from stationary two-phase patterns to
traveling 2n-phase patterns. As an example, we demonstrate with a numerical
solution the collapse of a four-phase spiral wave into a stationary two-phase
pattern as the forcing strength within the 4:1 resonance is increased.


title:
Laplacian Growth I: Finger Competition and Formation of a Single
  Saffman-Taylor Finger without Surface Tension: An Exact Result

abstract:
  We study the exact non-singular zero-surface tension solutions of the
Saffman-Taylor problem for all times. We show that all moving logarithmic
singularities a_k(t) in the complex plane \omega = e^{i\phi}, where \phi is the
stream function, are repelled from the origin, attracted to the unit circle and
eventually coalesce. This pole evolution describes essentially all the
dynamical features of viscous fingering in the Hele-Shaw cell observed by
Saffman and Taylor [Proc. R. Soc. A 245, 312 (1958)], namely tip-splitting,
multi-finger competition, inverse cascade, and subsequent formation of a single
Saffman-Taylor finger.


title: Three dimensional bright vortex soliton

abstract:
  Using the method of separation of variables, we developed a vector
nonparaxial theory for the nonlinear wave equations in strong field
approximation. We found that exact localized vortex soliton solution exists for
the nonlinear 3D+1 vector wave equation and for 3D+1 vector nonlinear
Schr\"{o}dinger equation. This method is applicable for angular functions,
which satisfy additional conditions. It is shown that exact vortex solitary
wave exists only for solution with eigenvalue of momentum L=1


title: Soliton-Complex Dynamics in Strongly Dispersive Medium

abstract:
  The concept of soliton complex in a nonlinear dispersive medium is proposed.
It is shown that strongly interacting identical topological solitons in the
medium can form bound soliton complexes which move without radiation. This
phenomenon is considered to be universal and applicable to various physical
systems. The soliton complex and its "excited" states are described
analytically and numerically as solutions of nonlinear dispersive equations
with the fourth and higher spatial or mixed derivatives. The dispersive
sine-Gordon, double and triple sine-Gordon, and piecewise-linear models are
studied in detail. Mechanisms and conditions of the formation of soliton
complexes, and peculiarities of their stationary dynamics are investigated. A
phenomenological approach to the description of the complexes and the
classification of all the possible complex states are proposed. Some examples
of physical systems, where the phenomenon can be experimentally observed, are
briefly discussed.


title: Excitation Thresholds for Nonlinear Localized Modes on Lattices

abstract:
  Breathers are spatially localized and time periodic solutions of extended
Hamiltonian dynamical systems. In this paper we study excitation thresholds for
(nonlinearly dynamically stable) ground state breather or standing wave
solutions for networks of coupled nonlinear oscillators and wave equations of
nonlinear Schr\"odinger (NLS) type. Excitation thresholds are rigorously
characterized by variational methods. The excitation threshold is related to
the optimal (best) constant in a class of discr ete interpolation inequalities
related to the Hamiltonian energy. We establish a precise connection among $d$,
the dimensionality of the lattice, $2\sigma+1$, the degree of the nonlinearity
and the existence of an excitation threshold for discrete nonlinear
Schr\"odinger systems (DNLS).
  We prove that if $\sigma\ge 2/d$, then ground state standing waves exist if
and only if the total power is larger than some strictly positive threshold,
$\nu_{thresh}(\sigma, d)$. This proves a conjecture of Flach, Kaldko& MacKay in
the context of DNLS. We also discuss upper and lower bounds for excitation
thresholds for ground states of coupled systems of NLS equations, which arise
in the modeling of pulse propagation in coupled arrays of optical fibers.


title: 3D+1 Parametric Bright Vortex Solitons. Optical Mesons

abstract:
  Using the method of separation of variables, we developed a vector
nonparaxial theory from the nonlinear wave equations in strong field
approximation of a Kerr media. Investigating three waves on different
frequencies, which satisfied the condition 2w3=w1+w2, we found that exact
localized vortex parametric soliton solutions existed for the set of four
nonlinear 3D+1vector wave equations. The solutions are obtained for a fixed
angle between the main frequencies and the signal waves A=60 deg. This method
is applicable for angular functions, which satisfy additional conditions. It is
shown that exact parametric vortex solitary waves exist for solution with
eigenrotation momentum L=1. The method is generalized for arbitrary number of
signal waves appearing symmetrically in pairs in respect to w3. The existence
of such type of vortex solitons, in the case of degenerate four-wave mixing is
discussed. As all of the waves are localized and have momentum L=1, they are
called optical mesons.


title: Disclination vortices in elastic media

abstract:
  The vortex-like solutions are studied in the framework of the gauge model of
disclinations in elastic continuum. A complete set of model equations with
disclination driven dislocations taken into account is considered. Within the
linear approximation an exact solution for a low-angle wedge disclination is
found to be independent from the coupling constants of the theory. As a result,
no additional dimensional characteristics (like the core radius of the defect)
are involved. The situation changes drastically for 2\pi vortices where two
characteristic lengths, l_\phi and l_W, become of importance. The asymptotical
behaviour of the solutions for both singular and nonsingular 2\pi vortices is
studied. Forces between pairs of vortices are calculated.


title: Extended parametric resonances in nonlinear Schrodinger systems

abstract:
  We study an example of exact parametric resonance in a extended system ruled
by nonlinear partial differential equations of nonlinear Schr\"odinger type. It
is also conjectured how related models not exactly solvable should behave in
the same way. The results have applicability in recent experiments in
Bose-Einstein condensation and to classical problems in Nonlinear Optics.


title:
Mechanisms of spatial current-density instabilities in $p^+ - p^- - n -
  p^+ -n^{++}$ structures

abstract:
  Semiconductor $p^+ - p^- - n - p^+ - n^{++}$ structures with large junction
and contact areas are treated as 1 \times 2-dimensional active media, in which
self-organized pattern formation can be expected. The local bistable behavior
of the structures may emanate from two different mechanisms both governed by a
nonlinear current feedback-loop between the electrons and holes injected from
the outer layers. By considering the device to be composed of an active
subsystem with negative differential resistance and a passive resistive layer
with positive differential resistance an analytical approach is suggested to
understand and describe the corresponding physical mechanisms in a
self-consistent way. Analytical solutions of the derived model equations allow
a description of homogeneous stationary states and yield explicit expressions
of the current-density vs. voltage characteristics of the whole structure and
its subsystems. A stability analysis of the homogeneous states with respect to
two-dimensional transversal harmonic fluctuations is performed for the two
cases under study. The resulting dispersion relations allow two different types
of instability. While the first one is of Ridley's type which is characteristic
for any spatially extended electrical system with negative differential
resistance, the second type can be considered as a solid-state analogue of
Turing's instability known as a generic instability mechanism which may lead,
e. g., to the formation of periodic patterns.


title: Soliton Interaction with an External Traveling Wave

abstract:
  The dynamics of soliton pulses in the Nonlinear Schrodinger Equation (NLSE)
driven by an external Traveling wave is studied analytically and numerically.
The Hamiltonian structure of the system is used to show that, in the adiabatic
approximation for a single soliton, the problem is integrable despite the large
number of degrees of freedom. Fixed points of the system are found, and their
linear stability is investigated. The fixed points correspond to a Doppler
shifted resonance between the external wave and the soliton. The structure and
topological changes of the phase space of the soliton parameters as functions
of the strength of coupling are investigated. A physical derivation of the
driven NLSE is given in the context of optical pulse propagation in asymmetric,
twin-core optical fibers. The results can be applied to soliton stabilization
and amplification.


title:
Chaotic behaviour of nonlinear waves and solitons of perturbed Korteweg
  - de Vries equation

abstract:
  This paper considers properties of nonlinear waves and solitons of
Korteweg-de Vries equation in the presence of external perturbation. For
time-periodic hamiltonian perturbation the width of the stochastic layer is
calculated. The conclusions about chaotic behaviour in long-period waves and
solitons are inferred. Obtained theoretical results find experimental
confirmation in experiments with the propagation of ion-acoustic waves in
plasma.


title: Interplay between Coherence and Incoherence in Multi-Soliton Complexes

abstract:
  We analyze photo-refractive incoherent soliton beams and their interactions
in Kerr-like nonlinear media. The field in each of M incoherently interacting
components is calculated using an integrable set of coupled nonlinear
Schrodinger equations. In particular, we obtain a general N-soliton solution,
describing propagation of multi-soliton complexes and their collisions. The
analysis shows that the evolution of such higher-order soliton beams is
determined by coherent and incoherent contributions from fundamental solitons.
Common features and differences between these internal interactions are
revealed and illustrated by numerical examples.


title:
Spatiotemporal chaotic dynamics of solitons with internal structure in
  the presence of finite-width inhomogeneities

abstract:
  We present an analytical and numerical study of the Klein-Gordon kink-soliton
dynamics in inhomogeneous media. In particular, we study an external field that
is almost constant for the whole system but that changes its sign at the center
of coordinates and a localized impurity with finite-width. The soliton solution
of the Klein-Gordon-like equations is usually treated as a structureless
point-like particle. A richer dynamics is unveiled when the extended character
of the soliton is taken into account. We show that interesting spatiotemporal
phenomena appear when the structure of the soliton interacts with finite-width
inhomogeneities. We solve an inverse problem in order to have external
perturbations which are generic and topologically equivalent to well-known
bifurcation models and such that the stability problem can be solved exactly.
We also show the different quasiperiodic and chaotic motions the soliton
undergoes as a time-dependent force pumps energy into the traslational mode of
the kink and relate these dynamics with the excitation of the shape modes of
the soliton.


title: Optical Vortex Solitons in Parametric Wave Mixing

abstract:
  We analyze two-component spatial optical vortex solitons supported by
parametric wave mixing processes in a nonlinear bulk medium. We study two
distinct cases of such localised waves, namely, parametric vortex solitons due
to phase-matched second-harmonic generation in an optical medium with competing
quadratic and cubic nonlinear response, and vortex solitons in the presence of
third-harmonic generation in a cubic medium. We find, analytically and
numerically, the structure of two-component vortex solitons, and also
investigate modulational instability of their plane-wave background. In
particular, we predict and analyze in detail novel types of vortex solitons, a
`halo-vortex', consisting of a two-component vortex core surrounded by a bright
ring of its harmonic field, and a `ring-vortex' soliton which is a vortex in a
harmonic field that guides a ring-like localized mode of the
fundamental-frequency field.


title: Bekki-Nozaki Amplitude Holes in Hydrothermal Nonlinear Waves

abstract:
  We present and analyze experimental results on the dynamics of hydrothermal
waves occuring in a laterally-heated fluid layer. We argue that the large-scale
modulations of the waves are governed by a one-dimensional complex
Ginzburg-Landau equation (CGLE). We determine quantitatively all the
coefficients of this amplitude equation using the localized amplitude holes
observed in the experiment, which we show to be well described as Bekki-Nozaki
hole solutions of the CGLE.


title: The moment method in general Nonlinear Schrodinger Equations

abstract:
  In this paper we develop a new approximation method valid for a wide family
of nonlinear wave equations of Nonlinear Schr\"odinger type. The result is a
reduced set of ordinary differential equations for a finite set of parameters
measuring global properties of the solutions, named momenta. We prove that
these equations provide exact results in some relevant cases and show how to
impose reasonable approximations that can be regarded as a perturbative
approach and as an extension of the time dependent variational method.


title:
Stability of Compacton Solutions of Fifth-Order Nonlinear Dispersive
  Equations

abstract:
  We consider fifth-order nonlinear dispersive $K(m,n,p)$ type equations to
study the effect of nonlinear dispersion. Using simple scaling arguments we
show, how, instead of the conventional solitary waves like solitons, the
interaction of the nonlinear dispersion with nonlinear convection generates
compactons - the compact solitary waves free of exponential tails. This
interaction also generates many other solitary wave structures like cuspons,
peakons, tipons etc. which are otherwise unattainable with linear dispersion.
Various self similar solutions of these higher order nonlinear dispersive
equations are also obtained using similarity transformations. Further, it is
shown that, like the third-order nonlinear $K(m,n)$ equations, the fifth-order
nonlinear dispersive equations also have the same four conserved quantities and
further even any arbitrary odd order nonlinear dispersive $K(m,n,p...)$ type
equations also have the same three (and most likely the four) conserved
quantities. Finally, the stability of the compacton solutions for the
fifth-order nonlinear dispersive equations are studied using linear stability
analysis. From the results of the linear stability analysis it follows that,
unlike solitons, all the allowed compacton solutions are stable, since the
stability conditions are satisfied for arbitrary values of the nonlinear
parameters.

categories: patt-sol nlin.PS nlin.SI quant-ph solv-int


title: Spatial Optical Solitons due to Multistep Cascading

abstract:
  We introduce a novel class of parametric optical solitons supported
simultaneously by two second-order nonlinear cascading processes,
second-harmonic generation and sum-frequency mixing. We obtain, analytically
and numerically, the solutions for three-wave spatial solitons and show that
the presence of an additional cascading mechanism can change dramatically the
properties and stability of two-wave quadratic solitary waves.


title: Lie-Group Approach to Perturbative Renormalization-Group Method

abstract:
  The Lie-group approach to the perturbative renormalization group (RG) method
is developed to obtain an asymptotic solutions of both autonomous and
non-autonomous ordinary differential equations. Reduction of some partial
differetial equations to typical RG equations is also achieved by this approach
and a simple recipe for providing RG equations is presented.


title: Two-color multistep cascading and parametric soliton-induced waveguides

abstract:
  We introduce the concept of two-color multistep cascading for vectorial
parametric wave mixing in optical media with quadratic (second-order or chi-2)
nonlinear response. We demonstrate that the multistep cascading allows
light-guiding-light effects with quadratic spatial solitons. With the help of
the so-called `almost exact' analytical solutions, we describe the properties
of parametric waveguides created by two-wave quadratic solitons.


title: Soliton tunneling with sub-barrier kinetic energies

abstract:
  We investigate (theoretically and numerically) the dynamics of a soliton
moving in an asymmetrical potential well with a finite barrier. For large
values of the width of the well, the width of the barrier and/or the height of
the barrier, the soliton behaves classically. On the other hand, we obtain the
conditions for the existence of soliton tunneling with sub-barrier kinetic
energies. We apply these results to the study of soliton propagation in
disordered systems.


title:
Resonance phenomena of a solitonlike extended object in a bistable
  potential

abstract:
  We investigate the dynamics of a soliton that behaves as an extended
particle. The soliton motion in an effective bistable potential can be chaotic
in a similar way as the Duffing oscillator. We generalize the concept of
geometrical resonance to spatiotemporal systems and apply it to design a
nonfeedback mechanism of chaos control using localized perturbations.We show
the existence of solitonic stochastic resonance.


title:
Discrete breathers in systems with homogeneous potentials - analytic
  solutions

abstract:
  We construct lattice Hamiltonians with homogeneous interaction potentials
which allow for explicit breather solutions. Especially we obtain exponentially
localized solutions for $d$-dimensional lattices with $d=2,3$.


title: Stability of multi-hump optical solitons

abstract:
  We demonstrate that, in contrast with what was previously believed,
multi-hump solitary waves can be stable. By means of linear stability analysis
and numerical simulations, we investigate the stability of two- and three-hump
solitary waves governed by incoherent beam interaction in a saturable medium,
providing a theoretical background for the experimental results reported by M.
Mitchell, M. Segev, and D. Christodoulides [Phys. Rev. Lett. v. 80, p. 4657
(1998)].


title: Fracture Patterns Induced by Desiccation in a Thin Layer

abstract:
  We study a theoretical model of mud cracks, that is, the fracture patterns
resulting from the contraction with drying in a thin layer of a mixture of
granules and water. In this model, we consider the slip on the bottom of this
layer and the relaxation of the elastic field that represents deformation of
the layer. Analysis of the one-dimensional model gives results for the crack
size that are consistent with experiments. We propose an analytical method of
estimation for the growth velocity of a simple straight crack to explain the
very slow propagation observed in actual experiments. Numerical simulations
reveal the dependence of qualitative nature of the formation of crack patterns
on material properties.


title: Logarithmically Slow Expansion of Hot Bubbles in Gases

abstract:
  We report logarithmically slow expansion of hot bubbles in gases in the
process of cooling. A model problem first solved, when the temperature has
compact support. Then temperature profile decaying exponentially at large
distances is considered. The periphery of the bubble is shown to remain
essentially static ("glassy") in the process of cooling until it is taken over
by a logarithmically slowly expanding "core". An analytical solution to the
problem is obtained by matched asymptotic expansion. This problem gives an
example of how logarithmic corrections enter dynamic scaling.

categories: patt-sol nlin.PS physics.flu-dyn physics.plasm-ph


title:
Impurity-induced stabilization of solitons in arrays of parametrically
  driven nonlinear oscillators

abstract:
  Chains of parametrically driven, damped pendula are known to support
soliton-like clusters of in-phase motion which become unstable and seed
spatiotemporal chaos for sufficiently large driving amplitudes. We show that
the pinning of the soliton on a "long" impurity (a longer pendulum) expands
dramatically its stability region whereas "short" defects simply repel solitons
producing effective partition of the chain. We also show that defects may
spontaneously nucleate solitons.


title:
Long-range interacting solitons: pattern formation and nonextensive
  thermostatistics

abstract:
  The nonlinear Klein-Gordon equation with a different potential that satisfies
the degeneracy properties discussed in this paper possesses solitonic solutions
that interact with long-range forces. We generalize the Ginzburg-Landau
equation in such a way that the topological defects supported by this equation
present long-range interaction both in D = 1 and D > 1. Finally, we construct a
system of two equations with two complex order parameters in such a way that
the interaction forces between the topological defects decay so slowly that the
system enters the nonextensivity regime.


title: Soliton structure dynamics in inhomogeneous media

abstract:
  We show that soliton interaction with finite-width inhomogeneities can
activate a great number of soliton internal modes. We obtain the exact
stationary soliton solution in the presence of inhomogeneities and solve
exactly the stability problem. We present a Karhunen-Loeve analysis of the
soliton structure dynamics as a time-dependent force pumps energy into the
traslational mode of the kink. We show the importance of the internal modes of
the soliton as they can generate shape chaos for the soliton as well as cases
in which the first shape mode leads the dynamics.


title:
Existence threshold for the ac-driven damped nonlinear Schr\"odinger
  solitons

abstract:
  It has been known for some time that solitons of the externally driven,
damped nonlinear Schr\"odinger equation can only exist if the driver's
strength, $h$, exceeds approximately $(2/ \pi) \gamma$, where $\gamma$ is the
dissipation coefficient. Although this perturbative result was expected to be
correct only to the leading order in $\gamma$, recent studies have demonstrated
that the formula $h_{thr}= (2 /\pi) \gamma$ gives a remarkably accurate
description of the soliton's existence threshold prompting suggestions that it
is, in fact, exact. In this note we evaluate the next order in the expansion of
$h_{thr}(\gamma)$ showing that the actual reason for this phenomenon is simply
that the next-order coefficient is anomalously small: $h_{thr}=(2/ \pi) \gamma
+ 0.002 \gamma^3$. Our approach is based on a singular perturbation expansion
of the soliton near the turning point; it allows to evaluate $h_{thr}(\gamma)$
to all orders in $\gamma$ and can be easily reformulated for other perturbed
soliton equations.


title:
Quadratic solitary waves in a counterpropagating quasi-phase-matched
  configuration

abstract:
  We demonstrate the possibility of self-trapping of optical beams by use of
quasi phase matching in a counterpropagating configuration in quadratic media.
We also show the predominant stability of these spatial self-guided beams and
estimate the power level required for their experimental observation.


title: Stability of multi-parameter solitons: Asymptotic approach

abstract:
  General asymptotic approach to the stability problem of multi-parameter
solitons in Hamiltonian systems $i\partial E_n/\partial z=\delta H/\delta
E_n^*$ has been developed. It has been shown that asymptotic study of the
soliton stability can be reduced to the calculation of a certain sequence of
the determinants, where the famous determinant of the matrix consisting from
the derivatives of the system invariants with respect to the soliton parameters
is just the first in the series. The presented approach gives first analytical
criterion for the oscillatory instability and also predicts novel stationary
instability. Higher order approximations allow to calculate corresponding
eigenvalues with arbitrary accuracy.


title:
Interaction of cavity solitons in degenerate optical parametric
  oscillators

abstract:
  Numerical studies together with asymptotic and spectral analysis establish
regimes where soliton pairs in degenerate optical parametric oscillators fuse,
repel, or form bound states. A novel bound state stabilized by coupled internal
oscillations is predicted.


title:
Modulational instability of solitary waves in non-degenerate three-wave
  mixing: The role of phase symmetries

abstract:
  We show how the analytical approach of Zakharov and Rubenchik [Sov. Phys.
JETP {\bf 38}, 494 (1974)] to modulational instability (MI) of solitary waves
in the nonlinear Schr\"oedinger equation (NLS) can be generalised for models
with two phase symmetries. MI of three-wave parametric spatial solitons due to
group velocity dispersion (GVD) is investigated as a typical example of such
models. We reveal a new branch of neck instability, which dominates the usual
snake type MI found for normal GVD. The resultant nonlinear evolution is
thereby qualitatively different from cases with only a single phase symmetry.


title:
Modulational instability of bright solitary waves in incoherently
  coupled nonlinear Schr\"odinger equations

abstract:
  We present a detailed analysis of the modulational instability (MI) of
ground-state bright solitary solutions of two incoherently coupled nonlinear
Schr\"odinger equations. Varying the relative strength of cross-phase and
self-phase effects we show existence and origin of four branches of MI of the
two-wave solitary solutions. We give a physical interpretation of our results
in terms of the group velocity dispersion (GVD) induced polarization dynamics
of spatial solitary waves. In particular, we show that in media with normal GVD
spatial symmetry breaking changes to polarization symmetry breaking when the
relative strength of the cross-phase modulation exceeds a certain threshold
value. The analytical and numerical stability analyses are fully supported by
an extensive series of numerical simulations of the full model.


title:
Instabilities of Higher-Order Parametric Solitons. Filamentation versus
  Coalescence

abstract:
  We investigate stability and dynamics of higher-order solitary waves in
quadratic media, which have a central peak and one or more surrounding rings.
We show existence of two qualitatively different behaviours. For positive phase
mismatch the rings break up into filaments which move radially to initial ring.
For sufficient negative mismatches rings are found to coalesce with central
peak, forming a single oscillating filament.


title: Instabilities of Hexagonal Patterns with Broken Chiral Symmetry

abstract:
  Three coupled Ginzburg-Landau equations for hexagonal patterns with broken
chiral symmetry are investigated. They are relevant for the dynamics close to
onset of rotating non-Boussinesq or surface-tension-driven convection. Steady
and oscillatory, long- and short-wave instabilities of the hexagons are found.
For the long-wave behavior coupled phase equations are derived. Numerical
simulations of the Ginzburg-Landau equations indicate bistability between
spatio-temporally chaotic patterns and stable steady hexagons. The chaotic
state can, however, not be described properly with the Ginzburg-Landau
equations.


title: Soliton Interactions in Perturbed Nonlinear Schroedinger Equations

abstract:
  We use multiscale perturbation theory in conjunction with the inverse
scattering transform to study the interaction of a number of solitons of the
cubic nonlinear Schroedinger equation under the influence of a small correction
to the nonlinear potential. We assume that the solitons are all moving with the
same velocity at the initial instant; this maximizes the effect each soliton
has on the others as a consequence of the perturbation. Over the long time
scales that we consider, the amplitudes of the solitons remain fixed, while
their center of mass coordinates obey Newton's equations with a force law for
which we present an integral formula. For the interaction of two solitons with
a quintic perturbation term we present more details since symmetries -- one
related to the form of the perturbation and one related to the small number of
particles involved -- allow the problem to be reduced to a one-dimensional one
with a single parameter, an effective mass. The main results include
calculations of the binding energy and oscillation frequency of nearby solitons
in the stable case when the perturbation is an attractive correction to the
potential and of the asymptotic "ejection" velocity in the unstable case.
Numerical experiments illustrate the accuracy of the perturbative calculations
and indicate their range of validity.


title:
Dispersion relations to oscillatory reaction-diffusion systems with the
  self-consistent flow

abstract:
  Dispersion curves to a oscillatory reaction-diffusion system with the
self-consistent flow have obtained by means of numerical calculations. The flow
modulates the shape of dispersion curves and characteristics of traveling
waves. The point of inflection which separates the dispersion curves into two
branches corresponding to trigger and phase waves, moves according to the value
of the advection constant. The dynamics of phase wave in
reaction-diffusion-advection equations has been studied by limit cycle
perturbations. The dispersion relation obtained from the phase equation shows
that the competition between diffusion and advection constants modulates the
oscillation frequency from the bulk oscillation in the long-wave dynamics. Such
a competition implies that phase waves with the flow have a wider variety of
dynamics than waves without the flow.


title: Modelling the dynamics of turbulent floods

abstract:
  Consider the dynamics of turbulent flow in rivers, estuaries and floods.
Based on the widely used k-epsilon model for turbulence, we use the techniques
of centre manifold theory to derive dynamical models for the evolution of the
water depth and of vertically averaged flow velocity and turbulent parameters.
This new model for the shallow water dynamics of turbulent flow: resolves the
vertical structure of the flow and the turbulence; includes interaction between
turbulence and long waves; and gives a rational alternative to classical models
for turbulent environmental flows.


title:
Electric Nusselt number characterization of electroconvection in nematic
  liquid crystals

abstract:
  We develop a characterization method of electroconvection structures in a
planar nematic liquid crystal layer by a study of the electric current
transport. Because the applied potential difference has a sinusoidal time
dependence, we define two electric Nusselt numbers corresponding to the
in-phase and out-of-phase components of the current. These Nusselt numbers are
predicted theoretically using a weakly nonlinear analysis of the standard
model. Our measurements of the electric current confirm that both numbers vary
linearly with the distance from onset until the occurence of secondary
instabilities; these instabilities also have a distinct Nusselt number
signature. A systematic comparison between our theoretical and experimental
results, using no adjusted parameters, demonstrates reasonable agreement. This
represents a quantitative test of the standard model completely independent
from traditional, optical techniques of studying electroconvection.


title: Curvature-induced symmetry breaking in nonlinear Schrodinger models

abstract:
  We consider a curved chain of nonlinear oscillators and show that the
interplay of curvature and nonlinearity leads to a symmetry breaking when an
asymmetric stationary state becomes energetically more favorable than a
symmetric stationary state. We show that the energy of localized states
decreases with increasing curvature, i.e. bending is a trap for nonlinear
excitations. A violation of the Vakhitov-Kolokolov stability criterium is found
in the case where the instability is due to the softening of the Peierls
internal mode.


title: Dynamics of localized structures in vector waves

abstract:
  Dynamical properties of topological defects in a twodimensional complex
vector field are considered. These objects naturally arise in the study of
polarized transverse light waves. Dynamics is modeled by a Vector Complex
Ginzburg-Landau Equation with parameter values appropriate for linearly
polarized laser emission. Creation and annihilation processes, and
selforganization of defects in lattice structures, are described. We find
"glassy" configurations dominated by vectorial defects and a melting process
associated to topological-charge unbinding.


title: Quasiperiodic Envelope Solitons

abstract:
  We analyse nonlinear wave propagation and cascaded self-focusing due to
second-harmonic generation in Fibbonacci optical superlattices and introduce a
novel concept of nonlinear physics, the quasiperiodic soliton, which describes
spatially localized self-trapping of a quasiperiodic wave. We point out a link
between the quasiperiodic soliton and partially incoherent spatial solitary
waves recently generated experimentally.


title:
Selfsimilar Domain Growth, Localized Structures and Labyrinthine
  Patterns in Vectorial Kerr Resonators

abstract:
  We study domain growth in a nonlinear optical system useful to explore
different scenarios that might occur in systems which do not relax to
thermodynamic equilibrium. Domains correspond to equivalent states of different
circular polarization of light. We describe three dynamical regimes: a
coarsening regime in which dynamical scaling holds with a growth law dictated
by curvature effects, a regime in which localized structures form, and a regime
in which polarization domain walls are modulationally unstable and the system
freezes in a labyrinthine pattern.


title: Bifurcation Phenomena in Optimal Velocity Model for Traffic Flows

abstract:
  In the optimal velocity model with a time lag, we show that there appear
multiple exact solutions in some ranges of car density, describing a uniform
flow, a stable and an unstable congested flows. This establishes the presence
of subcritical Hopf bifurcations. Our analytic results have far-reaching
implications for traffic flows such as hysteresis phenomena associated with
discontinuous transitions between uniform and congested flows.


title: Crystallization Kinetics in the Swift--Hohenberg Model

abstract:
  It is shown numerically and analytically that the front propagation process
in the framework of the Swift-Hohenberg model is determined by periodic
nucleation events triggered by the explosive growth of the localized
zero-eigenvalue mode of the corresponding linear problem. We derive the
evolution equation for this mode using asymptotic analysis, and evaluate the
time interval between nucleation events, and hence the front speed. In the
presence of noise, we derive the velocity exponent of ``thermally activated''
front propagation (creep) beyond the pinning threshold.


title:
Bilateral symmetry breaking in a nonlinear Fabry-Perot cavity exhibiting
  optical tristability

abstract:
  We show the existence of a region in the parameter space that defines the
field dynamics in a Fabry-Perot cylindrical cavity, where three output stable
stationary states of the light are possible for a given localized incident
field. Two of these states do not preserve the bilateral (i.e. left-right)
symmetry of the entire system. These broken-symmetry states are the
high-transmission nonlinear modes of the system. We also discuss how to excite
these states.


title: Longwave Interface Instability In Two-Fluid Vibrational Flow

abstract:
  We consider longwave mode of the interface instability in the system
comprising of two immiscible fluid layers. The fluids fill out plane horizontal
cavity which is subjected to horizontal harmonic vibration. The analysis is
performed within the framework of "high frequency of the vibration"
approximation and the averaging procedure. The nonlinear equation (having the
form of Newton's second law) for the amplitude of interface deformation is
obtained by means of multiple scales method. It is shown that (in addition to
previously detected quasistationary periodic solutions) the equation has a
class of quasistationary solitary solutions.


title:
Renormalization study of two-dimensional convergent solutions of the
  porous medium equation

abstract:
  In the focusing problem we study a solution of the porous medium equation
$u_t=\Delta (u^m)$ whose initial distribution is positive in the exterior of a
closed non-circular two dimensional region, and zero inside. We implement a
numerical scheme that renormalizes the solution each time that the average size
of the empty region reduces by a half. The initial condition is a function with
circular level sets distorted with a small sinusoidal perturbation of wave
number $k\geq 3$. We find that for nonlinearity exponents m smaller than a
critical value which depends on k, the solution tends to a self-similar regime,
characterized by rounded polygonal interfaces and similarity exponents that
depend on m and on the discrete rotational symmetry number k. For m greater
than the critical value, the final form of the interface is circular.


title:
Universal Algebraic Relaxation of Velocity and Phase in Pulled Fronts
  generating Periodic or Chaotic States

abstract:
  We investigate the asymptotic relaxation of so-called pulled fronts
propagating into an unstable state. The ``leading edge representation'' of the
equation of motion reveals the universal nature of their propagation mechanism
and allows us to generalize the universal algebraic velocity relaxation of
uniformly translating fronts to fronts, that generate periodic or even chaotic
states. Such fronts in addition exhibit a universal algebraic phase relaxation.
We numerically verify our analytical predictions for the Swift-Hohenberg and
the Complex Ginzburg Landau equation.


title:
Stratified spatiotemporal chaos in anisotropic reaction-diffusion
  systems

abstract:
  Numerical simulations of two dimensional pattern formation in an anisotropic
bistable reaction-diffusion medium reveal a new dynamical state, stratified
spatiotemporal chaos, characterized by strong correlations along one of the
principal axes. Equations that describe the dependence of front motion on the
angle illustrate the mechanism leading to stratified chaos.


title: Approximate solutions and scaling transformations for quadratic solitons

abstract:
  We study quadratic solitons supported by two- and three-wave parametric
interactions in chi-2 nonlinear media. Both planar and two-dimensional cases
are considered. We obtain very accurate, 'almost exact', explicit analytical
solutions, matching the actual bright soliton profiles, with the help of a
specially-developed approach, based on analysis of the scaling properties.
Additionally, we use these approximations to describe the linear tails of
solitary waves which are related to the properties of the soliton bound states.


title:
Long-Lived Localized Field Configurations in Small Lattices: Application
  to Oscillons

abstract:
  Long-lived localized field configurations such as breathers, oscillons, or
more complex objects naturally arise in the context of a wide range of
nonlinear models in different numbers of spatial dimensions. We present a
numerical method, which we call the {\it adiabatic damping method}, designed to
study such configurations in small lattices. Using 3-dimensional oscillons in
$\phi^4$ models as an example, we show that the method accurately (to a part in
10^5 or better) reproduces results obtained with static or dynamically
expanding lattices, dramatically cutting down in integration time. We further
present new results for 2-dimensional oscillons, whose lifetimes would be
prohibitively long to study with conventional methods.

categories: patt-sol cond-mat hep-lat hep-ph nlin.PS physics.comp-ph


title: Dissipation in ferrofluids: Mesoscopic versus hydrodynamic theory

abstract:
  Part of the field dependent dissipation in ferrofluids occurs due to the
rotational motion of the ferromagnetic grains relative to the viscous flow of
the carrier fluid. The classical theoretical description due to Shliomis uses a
mesoscopic treatment of the particle motion to derive a relaxation equation for
the non-equilibrium part of the magnetization. Complementary, the hydrodynamic
approach of Liu involves only macroscopic quantities and results in dissipative
Maxwell equations for the magnetic fields in the ferrofluid. Different stress
tensors and constitutive equations lead to deviating theoretical predictions in
those situations, where the magnetic relaxation processes cannot be considered
instantaneous on the hydrodynamic time scale. We quantify these differences for
two situations of experimental relevance namely a resting fluid in an
oscillating oblique field and the damping of parametrically excited surface
waves. The possibilities of an experimental differentiation between the two
theoretical approaches is discussed.


title:
Diffusion-induced vortex filament instability in 3-dimensional excitable
  media

abstract:
  We studied the stability of linear vortex filaments in 3-dimensional (3D)
excitable media, using both analytical and numerical methods. We found an
intrinsic 3D instability of vortex filaments that is diffusion-induced, and is
due to the slower diffusion of the inhibitor. This instability can result
either in a single helical filament or in chaotic scroll breakup, depending on
the specific kinetic model. When the 2-dimensional dynamics were in the chaotic
regime, filament instability occurred via on-off intermittency, a failure of
chaos synchronization in the third dimension.


title:
Multi-Bunch Solutions of Differential-Difference Equation for Traffic
  Flow

abstract:
  Newell-Whitham type car-following model with hyperbolic tangent optimal
velocity function in a one-lane circuit has a finite set of the exact solutions
for steady traveling wave, which expressed by elliptic theta function. Each
solution of the set describes a density wave with definite number of
car-bunches in the circuit. By the numerical simulation, we observe a
transition process from a uniform flow to the one-bunch analytic solution,
which seems to be an attractor of the system. In the process, the system shows
a series of cascade transitions visiting the configurations closely similar to
the higher multi-bunch solutions in the set.


title: A Particle Model of Rolling Grain Ripples Under Waves

abstract:
  A simple model is presented for the formation of rolling grain ripples on a
flat sand bed by the oscillatory flow generated by a surface wave. An equation
of motion is derived for the individual ripples, seen as "particles", on the
otherwise flat bed. The model account for the initial apperance of the ripples,
the subsequent coarsening of the ripples and the final equilibrium state. The
model is related to physical parameters of the problem, and an analytical
approximation for the equilibrium spacing of the ripples is developed. It is
found that the spacing between the ripples scale with the square-root of the
non-dimensional shear stress (the Shields parameter) on a flat bed. The results
of the model are compared with measurements, and reasonable agreement between
the model and the measurements is demonstrated.

categories: patt-sol cond-mat.stat-mech nlin.PS physics.flu-dyn


title:
Influence of four-wave mixing and walk-off on the self-focusing of
  coupled waves

abstract:
  Four-wave mixing and walk-off between two optical beams are investigated for
fo cusing Kerr media. It is shown that four-wave mixing reinforces the
self-focusi ng of mutually-trapped waves by lowering their power threshold for
collapse, on ly when their phase mismatch is small. On the contrary, walk-off
inhibits the c ollapse by detrapping the beams, whose partial centroids
experience nonlinear o scillations.


title:
Wave Number of Maximal Growth in Viscous Magnetic Fluids of Arbitrary
  Depth

abstract:
  An analytical method within the frame of linear stability theory is presented
for the normal field instability in magnetic fluids. It allows to calculate the
maximal growth rate and the corresponding wave number for any combination of
thickness and viscosity of the fluid. Applying this method to magnetic fluids
of finite depth, these results are quantitatively compared to the wave number
of the transient pattern observed experimentally after a jump--like increase of
the field. The wave number grows linearly with increasing induction where the
theoretical and the experimental data agree well. Thereby a long-standing
controversy about the behaviour of the wave number above the critical magnetic
field is tackled.


title: Linear and nonlinear waveguides induced by optical vortex solitons

abstract:
  We study, numerically and analytically, linear and nonlinear waveguides
induced by optical vortex solitons in a Kerr medium. Both fundamental and
first-order guided modes are analyzed, as well as the cases of effectively
defocusing and focusing nonlinearity.


title:
Abnormal Rolls and Regular Arrays of Disclinations in Homeotropic
  Electroconvection

abstract:
  We present the first quantitative verification of an amplitude description
for systems with (nearly) spontaneously broken isotropy, in particular for the
recently discovered abnormal-roll states. We also obtain a conclusive picture
of the 3d director configuration in a spatial period doubling phenomenon
involving disclination loops (CRAZY rolls). The first observation of two
Lifshitz frequencies in electroconvection is reported.


title: Discrete stochastic modeling of calcium channel dynamics

abstract:
  We propose a simple discrete stochastic model for calcium dynamics in living
cells. Specifically, the calcium concentration distribution is assumed to give
rise to a set of probabilities for the opening/closing of channels which
release calcium thereby changing those probabilities. We study this model in
one dimension, analytically in the mean-field limit of large number of channels
per site N, and numerically for small N. As the number of channels per site is
increased, the transition from a non-propagating region of activity to a
propagating one changes in nature from one described by directed percolation to
that of deterministic depinning in a spatially discrete system. Also, for a
small number of channels a propagating calcium wave can leave behind a novel
fluctuation-driven state, in a parameter range where the limiting deterministic
model exhibits only single pulse propagation.


title: Planform selection in two-layer Benard-Marangoni convection

abstract:
  Benard-Marangoni convection in a system of two superimposed liquids is
investigated theoretically. Extending previous studies the complete
hydrodynamics of both layers is treated and buoyancy is consistently taken into
account. The planform selection problem between rolls, squares and hexagons is
investigated by explicitly calculating the coefficients of an appropriate
amplitude equation from the parameters of the fluids. The results are compared
with recent experiments on two-layer systems in which squares at onset have
been reported.


title:
Dynamics of a Single Peak of the Rosensweig Instability in a Magnetic
  Fluid

abstract:
  To describe the dynamics of a single peak of the Rosensweig instability a
model is proposed which approximates the peak by a half-ellipsoid atop a layer
of magnetic fluid. The resulting nonlinear equation for the height of the peak
leads to the correct subcritical character of the bifurcation for static
induction. For a time-dependent induction the effects of inertia and damping
are incorporated. The results of the model show qualitative agreement with the
experimental findings, as in the appearance of period doubling, trebling, and
higher multiples of the driving period. Furthermore a quantitative agreement is
also found for the parameter ranges of frequency and induction in which these
phenomena occur.


abstract:
  The Cross-Newell equations for hexagons and triangles are derived for general
real gradient systems, and are found to be in flux-divergence form. Specific
examples of complex governing equations that give rise to hexagons and
triangles and which have Lyapunov functionals are also considered, and explicit
forms of the Cross-Newell equations are found in these cases. The general
nongradient case is also discussed; in contrast with the gradient case, the
equations are not flux-divergent. In all cases, the phase stability boundaries
and modes of instability for general distorted hexagons and triangles can be
recovered from the Cross-Newell equations.


title:
Solitons in anharmonic chains with ultra-long-range interatomic
  interactions

abstract:
  We study the influence of long-range interatomic interactions on the
properties of supersonic pulse solitons in anharmonic chains. We show that in
the case of ultra-long-range (e.g., screened Coulomb) interactions three
different types of pulse solitons coexist in a certain velocity interval: one
type is unstable but the two others are stable. The high-energy stable soliton
is broad and can be described in the quasicontinuum approximation. But the
low-energy stable soliton consists of two components, short-range and
long-range ones, and can be considered as a bound state of these components.


title: Crossover from a square to a hexagonal pattern in Faraday surface waves

abstract:
  We report on surface wave pattern formation in a Faraday experiment operated
at a very shallow filling level, where modes with a subharmonic and harmonic
time dependence interact. Associated with this distinct temporal behavior are
different pattern selection mechanisms, favoring squares or hexagons,
respectively. In a series of bifurcations running through a pair of
superlattices the surface wave pattern transforms between the two incompatible
symmetries. The close analogy to 2D and 3D crystallography is pointed out.


title: Instanton solutions in the problem of wrinkled flame front dynamics

abstract:
  The statistics of wrinkling flame front is invetigated by the quantum filed
theory methods. We dwell on the WKB approximation in the functional integral
which is analogous to the Wyld functional integral in turbulence. The main
contribution to statistics is due to a coupled field-force configuration. This
configuration is related to a kink between metastable exact pole solutions of
the Syvashinsky equation. These kinks are responsible for both the formation of
new cusps and the rapid power-law acceleration of the mean flame-front. The
problem of asymptotic stability of the solutions is discussed.


title:
Development and geometry of isotropic and directional shrinkage crack
  patterns

abstract:
  We have studied shrinkage crack patterns which form when a thin layer of an
alumina/water slurry dries. Both isotropic and directional drying were studied.
The dynamics of the pattern formation process and the geometric properties of
the isotropic crack patterns are similar to what is expected from recent
models, assuming weak disorder. There is some evidence for a gradual increase
in disorder as the drying layer become thinner, but no sudden transition, in
contrast to what has been seen in previous experiments. The morphology of the
crack patterns is influenced by drying gradients and front propagation effects,
with sharp gradients having a strong orienting and ordering effect.


title: Surface tension-driven convection patterns in two liquid layers

abstract:
  Two superposed liquid layers display a variety of convective phenomena that
are inaccessible in the traditional system where the upper layer is a gas. We
consider several pairs of immiscible liquids. Once the liquids have been
selected, the applied temperature difference and the depths of the layers are
the only independent control parameters. Using a perfluorinated hydrocarbon and
silicone oil system, we have made the first experimental observation of
convection with the top plate hotter than the lower plate. Since the system is
stably stratified, this convective flow is solely due to thermocapillary
forces. We also have found oscillatory convection at onset in an acetonitrile
and n-hexane system heated from below.


title:
Stability boundaries of roll and square convection in binary fluid
  mixtures with positive separation ratio

abstract:
  Rayleigh-B\'{e}nard convection in horizontal layers of binary fluid mixtures
heated from below with realistic horizontal boundary conditions is studied
theoretically using multi-mode Galerkin expansions. For positive separation
ratios the main difference between the mixtures and pure fluids lies in the
existence of stable three dimensional patterns near onset in a wide range of
the parameter space. We evaluated the stationary solutions of roll, crossroll,
and square convection and we determined the location of the stability
boundaries for many parameter combinations thereby obtaining the Busse balloon
for roll and square patterns.


title: Origin of Multikinks in Dispersive Nonlinear Systems

abstract:
  We develop {\em the first analytical theory of multikinks} for strongly {\em
dispersive nonlinear systems}, considering the examples of the weakly discrete
sine-Gordon model and the generalized Frenkel-Kontorova model with a piecewise
parabolic potential. We reveal that there are no $2\pi$-kinks for this model,
but there exist {\em discrete sets} of $2\pi N$-kinks for all N>1. We also show
their bifurcation structure in driven damped systems.


title: Time resolved pattern evolution in a large aperture laser

abstract:
  We have measured quasi-instantaneous transverse patterns in a broad aperture
laser. Non-ordered patterns yielding to boundary determined regular structures
in progressive time-integrated recording are observed. The linear analysis and
numerical integration of the full Maxwell-Bloch equations allow us to interpret
the features of the experiment. We show that this system being far from
threshold cannot be fully understood with a perturbative model.


title: Kink dynamics in a novel discrete sine-Gordon system

abstract:
  A spatially-discrete sine-Gordon system with some novel features is
described. There is a topological or Bogomol'nyi lower bound on the energy of a
kink, and an explicit static kink which saturates this bound. There is no
Peierls potential barrier, and consequently the motion of a kink is simpler,
especially at low speeds. At higher speeds, it radiates and slows down.


title: Vector solitons in (2+1) dimensions

abstract:
  We address the problem of existence and stability of vector spatial solitons
formed by two incoherently interacting optical beams in bulk Kerr and saturable
media. We identify families of (2+1)-dimensional two-mode self-trapped beams,
with and without a topological charge, and describe their properties
analytically and numerically.


title: Defect Chaos of Oscillating Hexagons in Rotating Convection

abstract:
  Using coupled Ginzburg-Landau equations, the dynamics of hexagonal patterns
with broken chiral symmetry are investigated, as they appear in rotating
non-Boussinesq or surface-tension-driven convection. We find that close to the
secondary Hopf bifurcation to oscillating hexagons the dynamics are well
described by a single complex Ginzburg-Landau equation (CGLE) coupled to the
phases of the hexagonal pattern. At the bandcenter these equations reduce to
the usual CGLE and the system exhibits defect chaos. Away from the bandcenter a
transition to a frozen vortex state is found.


title: Dipole-Mode Vector Solitons

abstract:
  We find a new type of optical vector soliton that originates from trapping of
a dipole mode by a soliton-induced waveguide. These solitons, which appear as a
consequence of the vector nature of the two component system, are more stable
than the previously found optical vortex-mode solitons and represent a new type
of extremely robust nonlinear vector structure.


title:
1/f noise in spatially extended systems with order-disorder phase
  transitions

abstract:
  Noise power spectra in spatially extended dynamical systems are investigated,
using as a model the Complex Ginzburg-Landau equation with a stochastic term.
Analytical and numerical investigations show that the temporal noise spectra
are of 1/f^a form, where a=2-D/2 with D the spatial dimension of the system.
This suggests that nonequilibrium order-disorder phase transitions may play a
role for the universally observed 1/f noise.

categories: patt-sol cond-mat.stat-mech nlin.PS physics.data-an


title:
On the Properties of Two Pulses Propagating Simultaneously in Different
  Dispersion Regimes in a Nonlinear Planar Waveguide

abstract:
  Properties of two pulses propagating simultaneously in different dispersion
regimes, anomalous and normal, in a Kerr-type planar waveguide are studied in
the framework of the nonlinear Schroedinger equation. Catastrophic
self-focusing and spatio-temporal splitting of the pulses is investigated. For
the limiting case when the dispersive term of the pulse propagating in the
normal dispersion regime can be neglected an indication of a possibility of a
stable self-trapped propagation of both pulses is obtained.


title:
Formation and Pinch-off of Viscous Droplets in the Absence of Surface
  Tension: an Exact Result

abstract:
  Within a class of exact time-dependent non-singular N-logarithmic solutions
(Mineev-Weinstein and Dawson, Phys. Rev. E 50, R24 (1994); Dawson and
Mineev-Weinstein, Phys. Rev. E 57, 3063 (1998)), we have found solutions which
describe the development and pinching off of viscous droplets in the Hele-Shaw
cell in the absence of surface tension.


title: Pattern formation in inclined layer convection

abstract:
  We report experiments on thermally driven convection in an inclined layer of
large aspect ratio in a fluid of Prandtl number $\sigma \approx 1$. We observed
a number of new nonlinear, mostly spatio-temporally chaotic, states. At small
angles of inclination we found longitudinal rolls, subharmonic oscillations,
Busse oscillations, undulation chaos, and crawling rolls. At larger angles, in
the vicinity of the transition from buoyancy- to shear-driven instability, we
observed drifting transverse rolls, localized bursts, and drifting bimodals.
For angles past vertical, when heated from above, we found drifting transverse
rolls and switching diamond panes.


title:
Pulse Shepherding and Multi-Channel Soliton Transmission in
  Bit-Parallel-Wavelength Optical Fiber Links

abstract:
  We study bit-parallel-wavelength (BPW) pulse transmission in multi-channel
single-mode optical fiber links for high-performance computer networks. We
develop a theory of the pulse shepherding effect earlier discovered in
numerical simulations, and also describe the families of the BPW solitons and
bifurcation cascades in a system of N coupled nonlinear Schr\"odinger
equations.


title: Capillary-gravity wave transport over spatially random drift

abstract:
  We derive transport equations for the propagation of water wave action in the
presence of a static, spatially random surface drift. Using the Wigner
distribution $\W(\x,\k,t)$ to represent the envelope of the wave amplitude at
position $\x$ contained in waves with wavevector $\k$, we describe surface wave
transport over static flows consisting of two length scales; one varying
smoothly on the wavelength scale, the other varying on a scale comparable to
the wavelength. The spatially rapidly varying but weak surface flows augment
the characteristic equations with scattering terms that are explicit functions
of the correlations of the random surface currents. These scattering terms
depend parametrically on the magnitudes and directions of the smoothly varying
drift and are shown to give rise to a Doppler coupled scattering mechanism. The
Doppler interaction in the presence of slowly varying drift modifies the
scattering processes and provides a mechanism for coupling long wavelengths
with short wavelengths. Conservation of wave action (CWA), typically derived
for slowly varying drift, is extended to systems with rapidly varying flow. At
yet larger propagation distances, we derive from the transport equations, an
equation for wave energy diffusion. The associated diffusion constant is also
expressed in terms of the surface flow correlations. Our results provide a
formal set of equations to analyse transport of surface wave action, intensity,
energy, and wave scattering as a function of the slowly varying drifts and the
correlation functions of the random, highly oscillatory surface flows.


title: We can know more in double-slit experiment

abstract:
  We show that we can know more than the orthodox view does, as one example, we
make a new analysis about double-slit experiment, and demonstrate that we can
measure the objective state of the particles passing through the two slits
while not destroying the interference pattern, the measurement method is to use
protective measurement.


title: Tentative statistical interpretation of non-equilibrium entropy

abstract:
  We suggest a certain statistical interpretation for the entropy produced in
driven thermodynamic processes. The exponential function of half irreversible
entropy re-weights the probability of the standard Ornstein-Uhlenbeck-type
thermodynamic fluctuations.(We add a proof of the standard Fluctuation Theorem
which represents a more natural interpretation.)


title: Single-Pass Lazer Polarization of Ultrarelativistic Positrons

abstract:
  The new method for producing of the polarized relativistic positrons is
suggested. A beam of unpolarized positrons accelerated up to a few GeV can be
polarized during a head-on collision with an intense circularly polarized lazer
wave. After a multiple Compton backscattering process the initial positrons may
lose a substantial part of its energy and, as consequence, may acquire the
significant longitudinal polarization. The simple formulas for the final
positron energy and polarization degree depended on the laser flash parameters
have been obtained. The comparison of efficiences for the suggested technique
and known ones is carried out. Some advantages of the new method were shown.


title:
An asymptotic form of the reciprocity theorem with applications in x-ray
  scattering

abstract:
  The emission of electromagnetic waves from a source within or near a
non-trivial medium (with or without boundaries, crystalline or amorphous, with
inhomogeneities, absorption and so on) is sometimes studied using the
reciprocity principle. This is a variation of the method of Green's functions.
If one is only interested in the asymptotic radiation fields the generality of
these methods may actually be a shortcoming: obtaining expressions valid for
the uninteresting near fields is not just a wasted effort but may be
prohibitively difficult. In this work we obtain a modified form the reciprocity
principle which gives the asymptotic radiation field directly. The method may
be used to obtain the radiation from a prescribed source, and also to study
scattering problems. To illustrate the power of the method we study a few
pedagogical examples and then, as a more challenging application we tackle two
related problems. We calculate the specular reflection of x rays by a rough
surface and by a smoothly graded surface taking polarization effects into
account. In conventional treatments of reflection x rays are treated as scalar
waves, polarization effects are neglected. This is a good approximation at
grazing incidence but becomes increasingly questionable for soft x rays and UV
at higher incidence angles.
  PACs: 61.10.Dp, 61.10.Kw, 03.50.De

categories: physics.class-ph cond-mat.mtrl-sci physics.ed-ph physics.gen-ph physics.optics


title: Temporal correlations and neural spike train entropy

abstract:
  Sampling considerations limit the experimental conditions under which
information theoretic analyses of neurophysiological data yield reliable
results. We develop a procedure for computing the full temporal entropy and
information of ensembles of neural spike trains, which performs reliably for
limited samples of data. This approach also yields insight upon the role of
correlations between spikes in temporal coding mechanisms. The method, when
applied to recordings from complex cells of the monkey primary visual cortex,
results in lower RMS error information estimates in comparison to a `brute
force' approach.


title:
The preliminary results of fast neutron flux measurements in the DULB
  laboratory at Baksan

abstract:
  One of the main sources of a background in underground physics experiments
(such as the investigation of solar neutrino flux, neutrino oscillations,
neutrinoless double beta decay, and the search for annual and daily Cold Dark
Matter particle flux modulation) are fast neutrons originating from the
surrounding rocks. The measurements of fast neutron flux in the new DULB
Laboratory situated at a depth of 4900 m w.e. in the Baksan Neutrino
Observatory have been performed. The relative neutron shielding properties of
several commonly available natural materials were investigated too. The
preliminary results obtained with a high-sensitive fast neutron spectrometer at
the level of sensitivity of about 10^(-7) neutron/ (cm^2 sec) are presented and
discussed.


title:
A semi-classical over-barrier model for charge exchange between highly
  charged ions and one-optical electron atoms

abstract:
  Absolute total cross sections for electron capture between slow, highly
charged ions and alkali targets have been recently measured. It is found that
these cross sections follow a scaling law with the projectile charge which is
different from the one previously proposed basing on a classical over-barrier
model (OBM) and verified using rare gases and molecules as targets. In this
paper we develop a "semi-classical" (i.e. including some quantal features) OBM
attempting to recover experimental results. The method is then applied to
ion-hydrogen collisions and compared with the result of a sophisticated
quantum-mechanical calculation. In the former case the accordance is very good,
while in the latter one no so satisfactory results are found. A qualitative
explanation for the discrepancies is attempted.


title:
An Exact Approach to the Oscillator Radiation Process in an Arbitrarily
  Large Cavity

abstract:
  Starting from a solution of the problem of a mechanical oscillator coupled to
a scalar field inside a reflecting sphere of radius $R$, we study the behaviour
of the system in free space as the limit of an arbitrarily large radius in the
confined solution. From a mathematical point of view we show that this way of
facing the problem is not equivalent to consider the system {\it a} {\it
priori} embedded in infinite space. In particular, the matrix elements of the
transformation turning the system to principal axis, do not tend to
distributions in the limit of an arbitrarily large sphere as it should be the
case if the two procedures were mathematically equivalent. Also, we introduce
"dressed" coordinates which allow an exact description of the oscillator
radiation process for any value of the coupling, strong or weak. In the case of
weak coupling, we recover from our exact expressions the well known decay
formulas from perturbation theory.


title: Spectrum of atomic radiation at sudden perturbation

abstract:
  A general expression for the spectrum of photons emitted by atom at sudden
perturbation is obtained. Some concrete examples of application of the obtained
result are considered. The conclusion about the coherence of radiation of the
atomic electrons under the such influences is made. PACS numbers: 32.30.*


title: The Hydration Number of Li+ in Liquid Water

abstract:
  A theoretical treatment based upon the quasi-chemical theory of solutions
predicts the most probable number of water neighbors in the inner shell of a
Li+ ion in liquid water to be four. The instability of a six water molecule
inner sphere complex relative to four-coordinated structures is confirmed by an
`ab initio' molecular dynamics calculation. A classical Monte Carlo simulation
equilibrated 26 water molecules with a rigid six-coordinated Li(H2O)6+ complex
with periodic boundary conditions in aqueous solution. With that initial
configuration for the molecular dynamics, the six-coordinated structure relaxed
into four-coordinated arrangements within 112 fs and stabilized. This
conclusion differs from prior interpretations of neutron and X-ray scattering
results on aqueous solutions.


title: From quantum motion to classical motion - seeking the lost reality

abstract:
  We show that the natural motion of particles in continuous space-time (CSTM)
is not classical continuous motion (CCM), but one kind of essentially
discontinuous motion, the wave function in quantum mechanics is the very
mathematical complex describing this kind of motion, and Schrodinger equation
is just its simplest nonrelativistic motion equation, we call such motion
quantum discontinuous motion or quantum motion; furthermore, we show that, when
considering gravity the space-time will be essentially discrete, and the motion
in discrete space-time (DSTM) will naturally result in the collapse process of
the wave function, this finally brings about the appearance of classical
continuous motion (CCM) in macroscopic world.


title: Everyone can understand quantum mechanics

abstract:
  We show that everyone can understand quantum mechanics, only if he rejects
the following prejudice, namely classical continuous motion (CCM) is the only
possible and objective motion of particles.


title: Photo-induced intermolecular charge transfer in porphyrin complexes

abstract:
  Optical excitation of the sequential supermolecule H_2P-ZnP-Q induces an
electron transfer from the free-base porphyrin (H_2P) to the quinone (Q) via
the zinc porphyrin (ZnP). This process is modeled by equations of motion for
the reduced density matrix which are solved numerically and approximately
analytically. These two solutions agree very well in a great region of
parameter space. It is shown that for the majority of solvents the electron
transfer occurs with the superexchange mechanism.


title: Using atomic interference to probe atom-surface interaction

abstract:
  We show that atomic interference in the reflection from two suitably
polarized evanescent waves is sensitive to retardation effects in the
atom-surface interaction for specific experimental parameters. We study the
limit of short and long atomic de Broglie wavelength. The former case is
analyzed in the semiclassical approximation (Landau-Zener model). The latter
represents a quantum regime and is analyzed by solving numerically the
associated coupled Schroedinger equations. We consider a specific experimental
scheme and show the results for rubidium (short wavelength) and the much
lighter meta-stable helium atom (long wavelength). The merits of each case are
then discussed.


title: New tests for a singularity of ideal MHD

abstract:
  Analysis using new calculations with 3 times the resolution of the earlier
linked magnetic flux tubes confirms the transition from singular to saturated
growth rate reported by Grauer and Marliani \cite{GrauerMar99} for the
incompressible cases is confirmed. However, all of the secondary tests point to
a transition back to stronger growth rate at a different location at late
times. Similar problems in ideal hydrodynamics are discussed, pointing out that
initial negative results eventually led to better initial conditions that did
show evidence for a singularity of Euler. Whether singular or near-singular
growth in ideal MHD is eventually shown, this study could have bearing on fast
magnetic reconnection, high energy particle production and coronal heating.


title: Inelastic semiclassical Coulomb scattering

abstract:
  We present a semiclassical S-matrix study of inelastic collinear
electron-hydrogen scattering. A simple way to extract all necessary information
from the deflection function alone without having to compute the stability
matrix is described. This includes the determination of the relevant Maslov
indices. Results of singlet and triplet cross sections for excitation and
ionization are reported. The different levels of approximation -- classical,
semiclassical, and uniform semiclassical -- are compared among each other and
to the full quantum result.


title: Hierarchy of time scales and quasitrapping in the N-atom micromaser

abstract:
  We study the dynamics of the reduced density matrix(RDM) of the field in the
micromaser. The resonator is pumped by N-atomic clusters of two-level atoms. At
each given instant there is only one cluster in the cavity. We find the
conditions of the independent evolution of the matrix elements of RDM belonging
to a (sub)diagonal of the RDM, i.e. conditions of the diagonal invariance for
the case of pumping by N-atomic clusters. We analyze the spectrum of the
evolution operator of the RDM and discover the existence of the quasitrapped
states of the field mode. These states exist for a wide range of number of
atoms in the cluster as well as for a broad range of relaxation rates. We
discuss the hierarchy of dynamical processes in the micromaser and find an
important property of the field states corresponding to the quasi-equilibrium:
these states are close to either Fock states or to a superposition of the Fock
states. A possibility to tune the distribution function of photon numbers is
discussed.


title:
Approaching the parameter estimation quality of maximum likelihood via
  generalized moments

abstract:
  A simple criterion is presented for a practical construction of generalized
moments that allow one to approach the theoretical Rao-Cramer limit for
parameter estimation while avoiding the complexity of the maximum likelihood
method in the cases of complicated probability distributions and/or very large
event samples.


title: Why Occam's Razor

abstract:
  Ensemble theories have received a lot of interest recently as a means of
explaining a lot of the detailed complexity observed in reality by a vastly
simpler description ``every possibility exists'' and a selection principle
({\em Anthropic Principle}) ``we only observe that which is consistent with our
existence''. In this paper I show why, in an ensemble theory of the universe,
we should be inhabiting one of the elements of that ensemble with least
information content that satisfies the anthropic principle. This explains the
effectiveness of aesthetic principles such as Occam's razor in predicting
usefulness of scientific theories. I also show, with a couple of reasonable
assumptions about the phenomenon of consciousness, the linear structure of
quantum mechanics can be derived.


title: Evolution in the Multiverse

abstract:
  In the {\em Many Worlds Interpretation} of quantum mechanics, the range of
possible worlds (or histories) provides variation, and the Anthropic Principle
is a selective principle analogous to natural selection. When looked on in this
way, the ``process'' by which the laws and constants of physics is determined
not too different from the process that gave rise to our current biodiversity,
i.e. Darwinian evolution. This has implications for the fields of SETI and
Artificial Life, which are based on a philosophy of the inevitability of life.


title: Quantum Monte Carlo Methods in Statistical Mechanics

abstract:
  This paper deals with the optimization of trial states for the computation of
dominant eigenvalues of operators and very large matrices. In addition to
preliminary results for the energy spectrum of van der Waals clusters, we
review results of the application of this method to the computation of
relaxation times of independent relaxation modes at the Ising critical point in
two dimensions.


title:
Measurement of mechanical vibrations excited in aluminium resonators by
  0.6 GeV electrons

abstract:
  We present measurements of mechanical vibrations induced by 0.6 GeV electrons
impinging on cylindrical and spherical aluminium resonators. To monitor the
amplitude of the resonator's vibrational modes we used piezoelectric ceramic
sensors, calibrated by standard accelerometers. Calculations using the
thermo-acoustic conversion model, agree well with the experimental data, as
demonstrated by the specific variation of the excitation strengths with the
absorbed energy, and with the traversing particles' track positions. For the
first longitudinal mode of the cylindrical resonator we measured a conversion
factor of 7.4 +- 1.4 nm/J, confirming the model value of 10 nm/J. Also, for the
spherical resonator, we found the model values for the L=2 and L=1 mode
amplitudes to be consistent with our measurement. We thus have confirmed the
applicability of the model, and we note that calculations based on the model
have shown that next generation resonant mass gravitational wave detectors can
only be expected to reach their intended ultra high sensitivity if they will be
shielded by an appreciable amount of rock, where a veto detector can reduce the
background of remaining impinging cosmic rays effectively.

categories: physics.ins-det astro-ph hep-ph physics.gen-ph


title: Scattering of positronium by H, He, Ne, and Ar

abstract:
  The low-energy scattering of ortho positronium (Ps) by H, He, Ne, and Ar
atoms has been investigated in the coupled-channel framework by using a
recently proposed time-reversal-symmetric nonlocal electron-exchange model
potential with a single parameter $C$. For H and He we use a three-Ps-state
coupled-channel model and for Ar and Ne we use a static-exchange model. The
sensitivity of the results is studied with respect to the parameter $C$.
Present low-energy cross sections for He, Ne and Ar are in good agreement with
experiment.

categories: physics.atom-ph cond-mat nucl-th physics.atm-clus physics.chem-ph quant-ph


title: Forecast and event control: On what is and what cannot be possible

abstract:
  Consequences of the basic and most evident consistency requirement-that
measured events cannot happen and not happen at the same time-are shortly
reviewed. Particular emphasis is given to event forecast and event control. As
a consequence, particular, very general bounds on the forecast and control of
events within the known laws of physics are derived. These bounds are of a
global, statistical nature and need not affect singular events or groups of
events.


title: Innovators and Interpreters: The Historic Role of Women in Science

abstract:
  Until this century, the number of working female scientists has been
indeterminate. Prevailing wisdom indicates that women, historically, have not
excelled in the mathematics and sciences, for various reasons. These range from
societal pressures to marry and bear children, to a lack of systematic
scientific education for females, to the lack of opportunity in institutions
and industry. Women, until comparatively recently, were not in control of their
own financial lives, and were therefore dependent upon the goodwill of a
husband, father or brother, should they attempt to enter academic life. Many
times, their accomplishments, and the accomplishments of these collaborating
relatives, become so merged as to become indistinguishable. Nevertheless, with
all these factors working against them, history records an occasional bright
star. Their diaries, memoirs and correspondence detail both the similarities
and the differences between their roles and the roles of modern female
scientists, in their own minds, and in the estimation of those closest to them.
There exists, in science, a dichotomy between the desire to understand one's
universe, and the desire to change the understanding of others. These two
fundamental desires lead future scientists to the discipline. Historically, the
role of women has largely been interpretive, rather than innovative, by their
own estimation. But is interpretation the "natural" role of women scientists?


title: Newtownian Relativity, Gravity, and Cosmology

abstract:
  Well-known to specialists but little-known to the wider audience is that
Newtonian gravity can be understood as geodesic motion in space-time, where
time is absolute and space is Euclidean. Newtonian cosmology formulated by
Heckmann agrees implicitly with Cartan's formulation of Newtonian mechanics as
geodesic motion in space-time, but does not unfold the underlying geometric
picture. I present the transformation theory of Newtonian mechanics and gravity
developed by Cartan and Heckmann, and show via coordinate transformations that
Heckmann's Newtonian cosmological model has a center, so that the cosmological
principle cannot hold globally.
  It is possible to confuse the relativity principle with a position of
relativism. Mach's principle has much to do with the latter and nothing to do
with the former. Both general relativity and nonlinear dynamics inform us that
most coordinate systems ae defined locally by differential equations that are
globally nonintegrable: global extensions of local coordinates usually do not
exist. I explain how defining inertial frames locally by free fall
short-circuits Mach's philosophic objectios to Newtonian dynamics.


title: Protein Folding Simulations in a Deformed Energy Landscape

abstract:
  A modified version of stochastic tunneling, a recently introduced global
optimization technique, is introduced as a new generalized-ensemble technique
and tested for a benchmark peptide, Met-enkephalin. It is demonstrated that the
new technique allows to evaluate folding properties of this peptide


title: The New Science of Complexity

abstract:
  Deterministic chaos, and even maximum computational complexity, have been
discovered within Newtonian dynamics. Economists assume that prices and price
changes can also obey abstract mathematical laws of motion. Sociologists and
other postmodernists advertise that physics and chemistry have outgrown their
former limitations, that chaos and complexity provide new holistic paradigms
for science, and that the boundaries between the hard and soft sciences, once
impenetrable, have disappeared like the Berlin Wall. Three hundred years after
the deaths of Galileo, Descartes, and Kepler, and the birth of Newton,
reductionism appears to be on the decline, with holistic approaches to science
on the upswing. We therefore examine the evidence that dynamical laws of motion
may be discovered from empirical studies of chaotic or complex phenomena, and
also review the foundation of reductionism in invariance principle.


title: Simple quantum systems in the momentum representation

abstract:
  The momentum representation is seldom used in quantum mechanics courses. Some
students are thence surprised by the change in viewpoint when, in doing
advanced work, they have to use the momentum rather than the coordinate
representation. In this work, we give an introduction to quantum mechanics in
momentum space, where the Schr\"odinger equation becomes an integral equation.
To this end we discuss standard problems, namely, the free particle, the
quantum motion under a constant potential, a particle interacting with a
potential step, and the motion of a particle under a harmonic potential. What
is not so standard is that they are all conceived from momentum space and hence
they, with the exception of the free particle, are not equivalent to the
coordinate space ones with the same names. All the problems are solved within
the momentum representation making no reference to the systems they correspond
to in the coordinate representation.


title:
Application of Conditioning to the Gaussian-with-Boundary Problem in the
  Unified Approach to Confidence Intervals

abstract:
  Roe and Woodroofe (RW) have suggested that certain conditional probabilities
be incorporated into the ``unified approach'' for constructing confidence
intervals, previously described by Feldman and Cousins (FC). RW illustrated
this conditioning technique using one of the two prototype problems in the FC
paper, that of Poisson processes with background. The main effect was on the
upper curve in the confidence belt. In this paper, we attempt to apply this
style of conditioning to the other prototype problem, that of Gaussian errors
with a bounded physical region. We find that the lower curve on the confidence
belt is also moved significantly, in an undesirable manner.


title:
Decay channels and appearance sizes of doubly anionic gold and silver
  clusters

abstract:
  Second electron affinities of Au_N and Ag_N clusters and the dissociation
energies for fission of the Au_N^{2-} and Ag_N^{2-} dianions are calculated
using the finite-temperature shell-correction method and allowing for triaxial
deformations. Dianionic clusters with N > 2 are found to be energetically
stable against fission, leaving electron autodetachment as the dominant decay
process. The second electron affinities exhibit pronounced shell effects in
excellent agreement with measured abundance spectra for Au_N^{2-} (N < 30),
with appearance sizes N=12 for gold dianionic clusters and N=24 for silver
dianionic clusters.


title: Dream of a Christmas lecture

abstract:
  We recall the origins of differential calculus from a modern perspective.
This lecture should be a victory song, but the pain makes it to sound more as
an oath for vendetta, coming from Syracuse two milenia before.


title: Speed of Gravity and Gravitational Horizon

abstract:
  Pioneer-10 unexpected anomalous deceleration hurtling through the solar
system might have revealed a secret of nature that gravitational information
propagating at very high but finite speed rushing to gravitational horizon
opens a window to Universe neighborhood.
  Dark energy may be owing to interactive gravitational horizons of cousin
universes. The necessary condition for the conjecture to be true is that the
speed of gravity must be faster than the speed of light.The sufficient
condition is that the dark energy content would be increasing with the age of
our Universe, while more and more gravitational horizons of cousin universes
might reach the gravitational horizon of ours in the neighborhood that may be
boundless in space-time flow without beginning or end.
  Keys: Inseparability Principle, Scale Conversion, Speed of Gravity,
Gravitational Horizon, Neighborhood of universes, Dark Energy.