279 research outputs found
Grain boundary motion in layered phases
We study the motion of a grain boundary that separates two sets of mutually
perpendicular rolls in Rayleigh-B\'enard convection above onset. The problem is
treated either analytically from the corresponding amplitude equations, or
numerically by solving the Swift-Hohenberg equation. We find that if the rolls
are curved by a slow transversal modulation, a net translation of the boundary
follows. We show analytically that although this motion is a nonlinear effect,
it occurs in a time scale much shorter than that of the linear relaxation of
the curved rolls. The total distance traveled by the boundary scales as
, where is the reduced Rayleigh number. We obtain
analytical expressions for the relaxation rate of the modulation and for the
time dependent traveling velocity of the boundary, and especially their
dependence on wavenumber. The results agree well with direct numerical
solutions of the Swift-Hohenberg equation. We finally discuss the implications
of our results on the coarsening rate of an ensemble of differently oriented
domains in which grain boundary motion through curved rolls is the dominant
coarsening mechanism.Comment: 16 pages, 5 figure
Penta-Hepta Defect Motion in Hexagonal Patterns
Structure and dynamics of penta-hepta defects in hexagonal patterns is
studied in the framework of coupled amplitude equations for underlying plane
waves. Analytical solution for phase field of moving PHD is found in the far
field, which generalizes the static solution due to Pismen and Nepomnyashchy
(1993). The mobility tensor of PHD is calculated using combined analytical and
numerical approach. The results for the velocity of PHD climbing in slightly
non-optimal hexagonal patterns are compared with numerical simulations of
amplitude equations. Interaction of penta-hepta defects in optimal hexagonal
patterns is also considered.Comment: 4 pages, Postscript (submitted to PRL
Learning from Monte Carlo Rollouts with Opponent Models for Playing Tron
This paper describes a novel reinforcement learning system for learning to play the game of Tron. The system combines Q-learning, multi-layer perceptrons, vision grids, opponent modelling, and Monte Carlo rollouts in a novel way. By learning an opponent model, Monte Carlo rollouts can be effectively applied to generate state trajectories for all possible actions from which improved action estimates can be computed. This allows to extend experience replay by making it possible to update the state-action values of all actions in a given game state simultaneously. The results show that the use of experience replay that updates the Q-values of all actions simultaneously strongly outperforms the conventional experience replay that only updates the Q-value of the performed action. The results also show that using short or long rollout horizons during training lead to similar good performances against two fixed opponents
Defect Dynamics for Spiral Chaos in Rayleigh-Benard Convection
A theory of the novel spiral chaos state recently observed in Rayleigh-Benard
convection is proposed in terms of the importance of invasive defects i.e
defects that through their intrinsic dynamics expand to take over the system.
The motion of the spiral defects is shown to be dominated by wave vector
frustration, rather than a rotational motion driven by a vertical vorticity
field. This leads to a continuum of spiral frequencies, and a spiral may rotate
in either sense depending on the wave vector of its local environment. Results
of extensive numerical work on equations modelling the convection system
provide some confirmation of these ideas.Comment: Revtex (15 pages) with 4 encoded Postscript figures appende
Dynamics and Selection of Giant Spirals in Rayleigh-Benard Convection
For Rayleigh-Benard convection of a fluid with Prandtl number \sigma \approx
1, we report experimental and theoretical results on a pattern selection
mechanism for cell-filling, giant, rotating spirals. We show that the pattern
selection in a certain limit can be explained quantitatively by a
phase-diffusion mechanism. This mechanism for pattern selection is very
different from that for spirals in excitable media
Renormalization Group Theory And Variational Calculations For Propagating Fronts
We study the propagation of uniformly translating fronts into a linearly
unstable state, both analytically and numerically. We introduce a perturbative
renormalization group (RG) approach to compute the change in the propagation
speed when the fronts are perturbed by structural modification of their
governing equations. This approach is successful when the fronts are
structurally stable, and allows us to select uniquely the (numerical)
experimentally observable propagation speed. For convenience and completeness,
the structural stability argument is also briefly described. We point out that
the solvability condition widely used in studying dynamics of nonequilibrium
systems is equivalent to the assumption of physical renormalizability. We also
implement a variational principle, due to Hadeler and Rothe, which provides a
very good upper bound and, in some cases, even exact results on the propagation
speeds, and which identifies the transition from ` linear'- to `
nonlinear-marginal-stability' as parameters in the governing equation are
varied.Comment: 34 pages, plain tex with uiucmac.tex. Also available by anonymous ftp
to gijoe.mrl.uiuc.edu (128.174.119.153), file /pub/front_RG.tex (or .ps.Z
Neural Networks for State Evaluation in General Game Playing
Abstract. Unlike traditional game playing, General Game Playing is concerned with agents capable of playing classes of games. Given the rules of an unknown game, the agent is supposed to play well without human intervention. For this purpose, agent systems that use deterministic game tree search need to automatically construct a state value function to guide search. Successful systems of this type use evaluation functions derived solely from the game rules, thus neglecting further improvements by experience. In addition, these functions are fixed in their form and do not necessarily capture the game’s real state value function. In this work we present an approach for obtaining evaluation functions on the basis of neural networks that overcomes the aforementioned problems. A network initialization extracted from the game rules ensures reasonable behavior without the need for prior training. Later training, however, can lead to significant improvements in evaluation quality, as our results indicate.
Dynamical Properties of Multi-Armed Global Spirals in Rayleigh-Benard Convection
Explicit formulas for the rotation frequency and the long-wavenumber
diffusion coefficients of global spirals with arms in Rayleigh-Benard
convection are obtained. Global spirals and parallel rolls share exactly the
same Eckhaus, zigzag and skewed-varicose instability boundaries. Global spirals
seem not to have a characteristic frequency or a typical size ,
but their product is a constant under given experimental
conditions. The ratio of the radii of any two dislocations (,
) inside a multi-armed spiral is also predicted to be constant. Some of
these results have been tested by our numerical work.Comment: To appear in Phys. Rev. E as Rapid Communication
Grain boundary pinning and glassy dynamics in stripe phases
We study numerically and analytically the coarsening of stripe phases in two
spatial dimensions, and show that transient configurations do not achieve long
ranged orientational order but rather evolve into glassy configurations with
very slow dynamics. In the absence of thermal fluctuations, defects such as
grain boundaries become pinned in an effective periodic potential that is
induced by the underlying periodicity of the stripe pattern itself. Pinning
arises without quenched disorder from the non-adiabatic coupling between the
slowly varying envelope of the order parameter around a defect, and its fast
variation over the stripe wavelength. The characteristic size of ordered
domains asymptotes to a finite value $R_g \sim \lambda_0\
\epsilon^{-1/2}\exp(|a|/\sqrt{\epsilon})\epsilon\ll 1\lambda_0a$ a constant of order unity. Random fluctuations allow defect motion to
resume until a new characteristic scale is reached, function of the intensity
of the fluctuations. We finally discuss the relationship between defect pinning
and the coarsening laws obtained in the intermediate time regime.Comment: 17 pages, 8 figures. Corrected version with one new figur
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