303 research outputs found
Structure and cluster formation in size asymmetric soft electrolyte systems
We examine the structure and thermodynamic properties of systems composed ions with rigid Gaussian charge distributions of differing widths that only interact electrostatically. These ultrasoft electrolytes [1,2] provide insight into the role of electrostatics in colloidal systems and have been observed to exhibit a liquid-vapor phase transition, as well as aggregation. We perform molecular dynamics and Monte Carlo simulations over a broad range of ion densities and electrostatic coupling strengths for systems containing ions with different width charge distributions. Under certain conditions, these systems are observed to form large, finite sized clusters in an isotropic phase. The structure of these clusters, their charge and electrostatic potential distribution, and energetics of formation are analyzed in detail. We compare and interpret the simulation results with a splitting field theory [3] framework that focuses on fluctuations in the electrostatic potential. Within this approach, the short wavelength and long wavelength fluctuations are treated within different approximation schemes. This theory can accurately describe the counterion mediated attractive interactions between like-charged plates [3,4] and the one-component plasma (OCP) [5] from the weak, intermediate, and strong coupling regimes. As the charge distribution of one of the ion species in the ultrasoft electrolyte broadens, the system more closely resembles the OCP, where the splitting theory is known to work well. We carefully examine the evolution of ultrasoft electrolyte as the width of one of the ions changes from being infinitely broad to smaller sizes. In particular, we present spatial correlations in the fluctuations of the electrostatic potential, decomposing them into short and long wavelength contributions. This information is used to extend the splitting theory to capture the region of cluster formation
Multiple Front Propagation Into Unstable States
The dynamics of transient patterns formed by front propagation in extended
nonequilibrium systems is considered. Under certain circumstances, the state
left behind a front propagating into an unstable homogeneous state can be an
unstable periodic pattern. It is found by a numerical solution of a model of
the Fr\'eedericksz transition in nematic liquid crystals that the mechanism of
decay of such periodic unstable states is the propagation of a second front
which replaces the unstable pattern by a another unstable periodic state with
larger wavelength. The speed of this second front and the periodicity of the
new state are analytically calculated with a generalization of the marginal
stability formalism suited to the study of front propagation into periodic
unstable states. PACS: 47.20.Ky, 03.40.Kf, 47.54.+rComment: 12 page
Spatiotemporal communication with synchronized optical chaos
We propose a model system that allows communication of spatiotemporal
information using an optical chaotic carrier waveform. The system is based on
broad-area nonlinear optical ring cavities, which exhibit spatiotemporal chaos
in a wide parameter range. Message recovery is possible through chaotic
synchronization between transmitter and receiver. Numerical simulations
demonstrate the feasibility of the proposed scheme, and the benefit of the
parallelism of information transfer with optical wavefronts.Comment: 4 pages, 5 figure
Acoustic Emission from crumpling paper
From magnetic systems to the crust of the earth, many physical systems that
exibit a multiplicty of metastable states emit pulses with a broad power law
distribution in energy. Digital audio recordings reveal that paper being
crumpled, a system that can be easily held in hand, is such a system. Crumpling
paper both using the traditional hand method and a novel cylindrical geometry
uncovered a power law distribution of pulse energies spanning at least two
decades: (exponent 1.3 - 1.6) Crumpling initally flat sheets into a compact
ball (strong crumpling), we found little or no evidence that the energy
distribution varied systematically over time or the size of the sheet. When we
applied repetitive small deformations (weak crumpling) to sheets which had been
previously folded along a regular grid, we found no systematic dependence on
the grid spacing. Our results suggest that the pulse energy depends only weakly
on the size of the paper regions responsible for sound production.Comment: 12 pages of text, 9 figures, submitted to Phys. Rev. E, additional
information availible at http://www.msc.cornell.edu/~houle/crumpling
Hysteresis and hierarchies: dynamics of disorder-driven first-order phase transformations
We use the zero-temperature random-field Ising model to study hysteretic
behavior at first-order phase transitions. Sweeping the external field through
zero, the model exhibits hysteresis, the return-point memory effect, and
avalanche fluctuations. There is a critical value of disorder at which a jump
in the magnetization (corresponding to an infinite avalanche) first occurs. We
study the universal behavior at this critical point using mean-field theory,
and also present preliminary results of numerical simulations in three
dimensions.Comment: 12 pages plus 2 appended figures, plain TeX, CU-MSC-747
Synchronization of Coupled Systems with Spatiotemporal Chaos
We argue that the synchronization transition of stochastically coupled
cellular automata, discovered recently by L.G. Morelli {\it et al.} (Phys. Rev.
{\bf 58 E}, R8 (1998)), is generically in the directed percolation universality
class. In particular, this holds numerically for the specific example studied
by these authors, in contrast to their claim. For real-valued systems with
spatiotemporal chaos such as coupled map lattices, we claim that the
synchronization transition is generically in the universality class of the
Kardar-Parisi-Zhang equation with a nonlinear growth limiting term.Comment: 4 pages, including 3 figures; submitted to Phys. Rev.
Dynamics of localized structures in vector waves
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.Comment: 4 pages, 5 figures included in the text. To appear in Phys. Rev.
Lett. (2000). Related material at http://www.imedea.uib.es/Nonlinear and
http://www.imedea.uib.es/Photonics . In this new version, Fig. 3 has been
replaced by a better on
Ordering and finite-size effects in the dynamics of one-dimensional transient patterns
We introduce and analyze a general one-dimensional model for the description
of transient patterns which occur in the evolution between two spatially
homogeneous states. This phenomenon occurs, for example, during the
Freedericksz transition in nematic liquid crystals.The dynamics leads to the
emergence of finite domains which are locally periodic and independent of each
other. This picture is substantiated by a finite-size scaling law for the
structure factor. The mechanism of evolution towards the final homogeneous
state is by local roll destruction and associated reduction of local
wavenumber. The scaling law breaks down for systems of size comparable to the
size of the locally periodic domains. For systems of this size or smaller, an
apparent nonlinear selection of a global wavelength holds, giving rise to long
lived periodic configurations which do not occur for large systems. We also
make explicit the unsuitability of a description of transient pattern dynamics
in terms of a few Fourier mode amplitudes, even for small systems with a few
linearly unstable modes.Comment: 18 pages (REVTEX) + 10 postscript figures appende
Wound-up phase turbulence in the Complex Ginzburg-Landau equation
We consider phase turbulent regimes with nonzero winding number in the
one-dimensional Complex Ginzburg-Landau equation. We find that phase turbulent
states with winding number larger than a critical one are only transients and
decay to states within a range of allowed winding numbers. The analogy with the
Eckhaus instability for non-turbulent waves is stressed. The transition from
phase to defect turbulence is interpreted as an ergodicity breaking transition
which occurs when the range of allowed winding numbers vanishes. We explain the
states reached at long times in terms of three basic states, namely
quasiperiodic states, frozen turbulence states, and riding turbulence states.
Justification and some insight into them is obtained from an analysis of a
phase equation for nonzero winding number: rigidly moving solutions of this
equation, which correspond to quasiperiodic and frozen turbulence states, are
understood in terms of periodic and chaotic solutions of an associated system
of ordinary differential equations. A short report of some of our results has
been published in [Montagne et al., Phys. Rev. Lett. 77, 267 (1996)].Comment: 22 pages, 15 figures included. Uses subfigure.sty (included) and
epsf.tex (not included). Related research in
http://www.imedea.uib.es/Nonlinea
Noise induced transition from an absorbing phase to a regime of stochastic spatiotemporal intermittency
We introduce a stochastic partial differential equation capable of
reproducing the main features of spatiotemporal intermittency (STI).
Additionally the model displays a noise induced transition from laminarity to
the STI regime. We show by numerical simulations and a mean-field analysis that
for high noise intensities the system globally evolves to a uniform absorbing
phase, while for noise intensities below a critical value spatiotemporal
intermittence dominates. A quantitative computation of the loci of this
transition in the relevant parameter space is presented.Comment: 4 pages, 6 eps figures. Submitted to Phys. Rev. Lett. See for
additional information http://imedea.uib.es
- …