1,230 research outputs found
Interface Fluctuations, Burgers Equations, and Coarsening under Shear
We consider the interplay of thermal fluctuations and shear on the surface of
the domains in various systems coarsening under an imposed shear flow. These
include systems with nonconserved and conserved dynamics, and a conserved order
parameter advected by a fluid whose velocity field satisfies the Navier-Stokes
equation. In each case the equation of motion for the interface height reduces
to an anisotropic Burgers equation. The scaling exponents that describe the
growth and coarsening of the interface are calculated exactly in any dimension
in the case of conserved and nonconserved dynamics. For a fluid-advected
conserved order parameter we determine the exponents, but we are unable to
build a consistent perturbative expansion to support their validity.Comment: 10 RevTeX pages, 2 eps figure
Coarsening Dynamics of a Nonconserved Field Advected by a Uniform Shear Flow
We consider the ordering kinetics of a nonconserved scalar field advected by
a uniform shear flow. Using the Ohta-Jasnow-Kawasaki approximation, modified to
allow for shear-induced anisotropy, we calculate the asymptotic time dependence
of the characteristic length scales, L_parallel and L_perp, that describe the
growth of order parallel and perpendicular to the mean domain orientation. In
space dimension d=3 we find, up to constants, L_parallel = gamma t^{3/2},
L_perp = t^{1/2}, where gamma is the shear rate, while for d = 2 we find
L_parallel = gamma^{1/2} t (ln t)^{1/4}, L_perp = gamma^{-1/2}(ln t)^{-1/4} .
Our predictions for d=2 can be tested by experiments on twisted nematic liquid
crystals.Comment: RevTex, 4 page
Continuum time limit and stationary states of the Minority Game
We discuss in detail the derivation of stochastic differential equations for
the continuum time limit of the Minority Game. We show that all properties of
the Minority Game can be understood by a careful theoretical analysis of such
equations. In particular, i) we confirm that the stationary state properties
are given by the ground state configurations of a disordered (soft) spin
system; ii) we derive the full stationary state distribution; iii) we
characterize the dependence on initial conditions in the symmetric phase and
iv) we clarify the behavior of the system as a function of the learning rate.
This leaves us with a complete and coherent picture of the collective behavior
of the Minority Game. Strikingly we find that the temperature like parameter
which is introduced in the choice behavior of individual agents turns out to
play the role, at the collective level, of the inverse of a thermodynamic
temperature.Comment: Revised version (several new results added). 12 pages, 5 figure
Recommended from our members
Alterations in T1 of normal and reperfused infarcted myocardium after Gd-BOPTA versus GD-DTPA on inversion recovery EPI.
This study tested whether Gd-BOPTA/Dimeg or Gd-DTPA exerts greater relaxation enhancement for blood and reperfused infarcted myocardium. Relaxivity of Gd-BOPTA is increased by weak binding to serum albumin. Thirty-six rats were subjected to reperfused infarction before contrast (doses = 0.05, 0.1, and 0.2 mmol/kg). delta R1 was repeatedly measured over 30 min. Gd-BOPTA caused greater delta R1 for blood and myocardium than did Gd-DTPA; clearance of both agents from normal- and infarcted myocardium was similar to blood clearance; plots of delta R1 myocardium/delta R1 blood showed equilibrium phase contrast distribution. Fractional contrast agent distribution volumes were approximately 0.24 for both agents in normal myocardium, 0.98 and 1.6 for Gd-DTPA and Gd-BOPTA, respectively, in reperfused infarction. The high value for Gd-BOPTPA was ascribed to greater relaxivity in infarction versus blood. It was concluded that Gd-BOPTA/Dimeg causes a greater delta R1 than Gd-DTPA in regions which contain serum albumin
Generalized strategies in the Minority Game
We show analytically how the fluctuations (i.e. standard deviation) in the
Minority Game (MG) can be made to decrease below the random coin-toss limit if
the agents use more general behavioral strategies. This suppression of the
standard deviation results from a cancellation between the actions of a crowd,
in which agents act collectively and make the same decision, and an anticrowd
in which agents act collectively by making the opposite decision to the crowd.Comment: Revised manuscript: a few minor typos corrected. Results unaffecte
Reply to Comment on ``Thermal Model for Adaptive Competition in a Market''
We reply to the Comment of Challet et al. [cond-mat/0004308] on our paper
[Phys. Rev. Lett. 83, 4429 (1999)]. We show that the claim of the Comment that
the effects of the temperature in the Thermal Minority Game ``can be eliminated
by time rescaling'' and consequently the behaviour is ``independent of T'' has
no general validity.Comment: 1 page, 1 figur
Glassy dynamics, metastability limit and crystal growth in a lattice spin model
We introduce a lattice spin model where frustration is due to multibody
interactions rather than quenched disorder in the Hamiltonian. The system has a
crystalline ground state and below the melting temperature displays a dynamic
behaviour typical of fragile glasses. However, the supercooled phase loses
stability at an effective spinodal temperature, and thanks to this the Kauzmann
paradox is resolved. Below the spinodal the system enters an off-equilibrium
regime corresponding to fast crystal nucleation followed by slow activated
crystal growth. In this phase and in a time region which is longer the lower
the temperature we observe a violation of the fluctuation-dissipation theorem
analogous to structural glasses. Moreover, we show that in this system there is
no qualitative difference between a locally stable glassy configuration and a
highly disordered polycrystal
Statistical mechanics of systems with heterogeneous agents: Minority Games
We study analytically a simple game theoretical model of heterogeneous
interacting agents. We show that the stationary state of the system is
described by the ground state of a disordered spin model which is exactly
solvable within the simple replica symmetric ansatz. Such a stationary state
differs from the Nash equilibrium where each agent maximizes her own utility.
The latter turns out to be characterized by a replica symmetry broken
structure. Numerical results fully agree with our analytic findings.Comment: 4 pages, 1 Postscript figure. Revised versio
Geometric approach to the dynamic glass transition
We numerically study the potential energy landscape of a fragile glassy
system and find that the dynamic crossover corresponding to the glass
transition is actually the effect of an underlying geometric transition caused
by a qualitative change in the topological properties of the landscape.
Furthermore, we show that the potential energy barriers connecting local glassy
minima increase with decreasing energy of the minima, and we relate this
behaviour to the fragility of the system. Finally, we analyze the real space
structure of activated processes by studying the distribution of particle
displacements for local minima connected by simple saddles
On the stationary points of the TAP free energy
In the context of the p-spin spherical model, we introduce a method for the
computation of the number of stationary points of any nature (minima, saddles,
etc.) of the TAP free energy. In doing this we clarify the ambiguities related
to the approximations usually adopted in the standard calculations of the
number of states in mean field spin glass models.Comment: 11 pages, 1 Postscript figure, plain Te
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