1,178 research outputs found
Free energy landscapes, dynamics and the edge of chaos in mean-field models of spin glasses
Metastable states in Ising spin-glass models are studied by finding iterative
solutions of mean-field equations for the local magnetizations. Two different
equations are studied: the TAP equations which are exact for the SK model, and
the simpler `naive-mean-field' (NMF) equations. The free-energy landscapes that
emerge are very different. For the TAP equations, the numerical studies confirm
the analytical results of Aspelmeier et al., which predict that TAP states
consist of close pairs of minima and index-one (one unstable direction) saddle
points, while for the NMF equations saddle points with large indices are found.
For TAP the barrier height between a minimum and its nearby saddle point scales
as (f-f_0)^{-1/3} where f is the free energy per spin of the solution and f_0
is the equilibrium free energy per spin. This means that for `pure states', for
which f-f_0 is of order 1/N, the barriers scale as N^{1/3}, but between states
for which f-f_0 is of order one the barriers are finite and also small so such
metastable states will be of limited physical significance. For the NMF
equations there are saddles of index K and we can demonstrate that their
complexity Sigma_K scales as a function of K/N. We have also employed an
iterative scheme with a free parameter that can be adjusted to bring the system
of equations close to the `edge of chaos'. Both for the TAP and NME equations
it is possible with this approach to find metastable states whose free energy
per spin is close to f_0. As N increases, it becomes harder and harder to find
solutions near the edge of chaos, but nevertheless the results which can be
obtained are competitive with those achieved by more time-consuming computing
methods and suggest that this method may be of general utility.Comment: 13 page
Geometry-induced asymmetric diffusion
Past work has shown that ions can pass through a membrane more readily in one
direction than the other. We demonstrate here in a model and an experiment that
for a mixture of small and large particles such asymmetric diffusion can arise
solely from an asymmetry in the geometry of the pores of the membrane. Our
deterministic simulation considers a two-dimensional gas of elastic disks of
two sizes diffusing through a membrane, and our laboratory experiment examines
the diffusion of glass beads of two sizes through a metal membrane. In both
experiment and simulation, the membrane is permeable only to the smaller
particles, and the asymmetric pores lead to an asymmetry in the diffusion rates
of these particles. The presence of even a small percentage of large particles
can clog a membrane, preventing passage of the small particles in one direction
while permitting free flow of the small particles in the other direction. The
purely geometric kinetic constraints may play a role in common biological
contexts such as membrane ion channels.Comment: published with minuscule change
Critical Networks Exhibit Maximal Information Diversity in Structure-Dynamics Relationships
Network structure strongly constrains the range of dynamic behaviors
available to a complex system. These system dynamics can be classified based on
their response to perturbations over time into two distinct regimes, ordered or
chaotic, separated by a critical phase transition. Numerous studies have shown
that the most complex dynamics arise near the critical regime. Here we use an
information theoretic approach to study structure-dynamics relationships within
a unified framework and how that these relationships are most diverse in the
critical regime
Topology and Evolution of Technology Innovation Networks
The web of relations linking technological innovation can be fairly described
in terms of patent citations. The resulting patent citation network provides a
picture of the large-scale organization of innovations and its time evolution.
Here we study the patterns of change of patents registered by the US Patent and
Trademark Office (USPTO). We show that the scaling behavior exhibited by this
network is consistent with a preferential attachment mechanism together with a
Weibull-shaped aging term. Such attachment kernel is shared by scientific
citation networks, thus indicating an universal type of mechanism linking ideas
and designs and their evolution. The implications for evolutionary theory of
innovation are discussed.Comment: 6 pages, 5 figures, submitted to Physical Review
Parametric ordering of complex systems
Cellular automata (CA) dynamics are ordered in terms of two global
parameters, computable {\sl a priori} from the description of rules. While one
of them (activity) has been used before, the second one is new; it estimates
the average sensitivity of rules to small configurational changes. For two
well-known families of rules, the Wolfram complexity Classes cluster
satisfactorily. The observed simultaneous occurrence of sharp and smooth
transitions from ordered to disordered dynamics in CA can be explained with the
two-parameter diagram
Manufacture, observation, and test of membranes with locatable single pores
A method for generating single pores down to 0.1 ÎŒm diameter in the center of a large circular foil is described, based on nuclear tracks. The foil is framed by a tension ring which enables one to handle the foils in a wellâdefined precise way. The single pore has a lateral displacement of ±0.1 mm with respect to the tension ring center. The foils used are polycarbonate of the type Makrofol and have thicknesses between 2 and 10 ÎŒm. For calibration of the single pore diameters, multiple nuclear tracks between 0.1 and 3.5 ÎŒm diameter are etched and observed by microscopy. The microscopic observations are compared with gasâflow measurements, using two alternative methods: multiple holes are tested under viscous flow conditions of N2 gas at normal temperature and pressure; single holes are tested under collisionless flow conditions of 4He gas at liquidânitrogen temperature, using a capacitance method.Peer reviewe
Asymptotically stable phase synchronization revealed by autoregressive circle maps
A new type of nonlinear time series analysis is introduced, based on phases,
which are defined as polar angles in spaces spanned by a finite number of
delayed coordinates. A canonical choice of the polar axis and a related
implicit estimation scheme for the potentially underlying auto-regressive
circle map (next phase map) guarantee the invertibility of reconstructed phase
space trajectories to the original coordinates. The resulting Fourier
approximated, Invertibility enforcing Phase Space map (FIPS map) is well suited
to detect conditional asymptotic stability of coupled phases. This rather
general synchronization criterion unites two existing generalisations of the
old concept and can successfully be applied e.g. to phases obtained from ECG
and airflow recordings characterizing cardio-respiratory interaction.Comment: PDF file, 232 KB, 24 pages, 3 figures; cheduled for Phys. Rev. E
(Nov) 200
Normal Modes of a Vortex in a Trapped Bose-Einstein Condensate
A hydrodynamic description is used to study the normal modes of a vortex in a
zero-temperature Bose-Einstein condensate. In the Thomas-Fermi (TF) limit, the
circulating superfluid velocity far from the vortex core provides a small
perturbation that splits the originally degenerate normal modes of a
vortex-free condensate. The relative frequency shifts are small in all cases
considered (they vanish for the lowest dipole mode with |m|=1), suggesting that
the vortex is stable. The Bogoliubov equations serve to verify the existence of
helical waves, similar to those of a vortex line in an unbounded weakly
interacting Bose gas. In the large-condensate (small-core) limit, the
condensate wave function reduces to that of a straight vortex in an unbounded
condensate; the corresponding Bogoliubov equations have no bound-state
solutions that are uniform along the symmetry axis and decay exponentially far
from the vortex core.Comment: 15 pages, REVTEX, 2 Postscript figures, to appear in Phys. Rev. A. We
have altered the material in Secs. 3B and 4 in connection with the normal
modes that have |m|=1. Our present treatment satisfies the condition that the
fundamental dipole mode of a condensate with (or without) a vortex should
have the bare frequency $\omega_\perp
Dimension of interaction dynamics
A method allowing to distinguish interacting from non-interacting systems
based on available time series is proposed and investigated. Some facts
concerning generalized Renyi dimensions that form the basis of our method are
proved. We show that one can find the dimension of the part of the attractor of
the system connected with interaction between its parts. We use our method to
distinguish interacting from non-interacting systems on the examples of
logistic and H\'enon maps. A classification of all possible interaction schemes
is given.Comment: 15 pages, 14 (36) figures, submitted to PR
Effect of Chaotic Noise on Multistable Systems
In a recent letter [Phys.Rev.Lett. {\bf 30}, 3269 (1995), chao-dyn/9510011],
we reported that a macroscopic chaotic determinism emerges in a multistable
system: the unidirectional motion of a dissipative particle subject to an
apparently symmetric chaotic noise occurs even if the particle is in a
spatially symmetric potential. In this paper, we study the global dynamics of a
dissipative particle by investigating the barrier crossing probability of the
particle between two basins of the multistable potential. We derive
analytically an expression of the barrier crossing probability of the particle
subject to a chaotic noise generated by a general piecewise linear map. We also
show that the obtained analytical barrier crossing probability is applicable to
a chaotic noise generated not only by a piecewise linear map with a uniform
invariant density but also by a non-piecewise linear map with non-uniform
invariant density. We claim, from the viewpoint of the noise induced motion in
a multistable system, that chaotic noise is a first realization of the effect
of {\em dynamical asymmetry} of general noise which induces the symmetry
breaking dynamics.Comment: 14 pages, 9 figures, to appear in Phys.Rev.
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