29,355 research outputs found
Isochronal synchronization of delay-coupled systems
We consider small network models for mutually delay-coupled systems which
typically do not exhibit stable isochronally synchronized solutions. We show
that for certain coupling architectures which involve delayed self feedback to
the nodes, the oscillators become isochronally synchronized. Applications are
shown for both incoherent pump coupled lasers and spatio-temporal coupled fiber
ring lasers.Comment: 5 pages, accepted for publication in Physical Review
Random field Ising systems on a general hierarchical lattice: Rigorous inequalities
Random Ising systems on a general hierarchical lattice with both, random
fields and random bonds, are considered. Rigorous inequalities between
eigenvalues of the Jacobian renormalization matrix at the pure fixed point are
obtained. These inequalities lead to upper bounds on the crossover exponents
.Comment: LaTeX, 13 pages, figs. 1a,1b,2. To be published in PR
Modeling urban street patterns
Urban streets patterns form planar networks whose empirical properties cannot
be accounted for by simple models such as regular grids or Voronoi
tesselations. Striking statistical regularities across different cities have
been recently empirically found, suggesting that a general and
details-independent mechanism may be in action. We propose a simple model based
on a local optimization process combined with ideas previously proposed in
studies of leaf pattern formation. The statistical properties of this model are
in good agreement with the observed empirical patterns. Our results thus
suggests that in the absence of a global design strategy, the evolution of many
different transportation networks indeed follow a simple universal mechanism.Comment: 4 pages, 5 figures, final version published in PR
Complete chaotic synchronization in mutually coupled time-delay systems
Complete chaotic synchronization of end lasers has been observed in a line of
mutually coupled, time-delayed system of three lasers, with no direct
communication between the end lasers. The present paper uses ideas from
generalized synchronization to explain the complete synchronization in the
presence of long coupling delays, applied to a model of mutually coupled
semiconductor lasers in a line. These ideas significantly simplify the analysis
by casting the stability in terms of the local dynamics of each laser. The
variational equations near the synchronization manifold are analyzed, and used
to derive the synchronization condition that is a function of the parameters.
The results explain and predict the dependence of synchronization on various
parameters, such as time-delays, strength of coupling and dissipation. The
ideas can be applied to understand complete synchronization in other chaotic
systems with coupling delays and no direct communication between synchronized
sub-systems.Comment: 22 pages, 6 figure
End to end distance on contour loops of random gaussian surfaces
A self consistent field theory that describes a part of a contour loop of a
random Gaussian surface as a trajectory interacting with itself is constructed.
The exponent \nu characterizing the end to end distance is obtained by a Flory
argument. The result is compared with different previuos derivations and is
found to agree with that of Kondev and Henley over most of the range of the
roughening exponent of the random surface.Comment: 7 page
Computations in Large N Matrix Mechanics
The algebraic formulation of Large N matrix mechanics recently developed by
Halpern and Schwartz leads to a practical method of numerical computation for
both action and Hamiltonian problems. The new technique posits a boundary
condition on the planar connected parts X_w, namely that they should decrease
rapidly with increasing order. This leads to algebraic/variational schemes of
computation which show remarkably rapid convergence in numerical tests on some
many- matrix models. The method allows the calculation of all moments of the
ground state, in a sequence of approximations, and excited states can be
determined as well. There are two unexpected findings: a large d expansion and
a new selection rule for certain types of interaction.Comment: 27 page
The Induced Magnetic Field of the Moon: Conductivity Profiles and Inferred Temperature
Electromagnetic induction in the moon driven by fluctuations of the interplanetary magnetic field is used to determine the lunar bulk electrical conductivity. The present data clearly show the north-south and east-west transfer function difference as well as high frequency rollover. The difference is shown to be compatible over the mid-frequency range with a noise source associated with the compression of the local remanent field by solar wind dynamic pressure fluctuations. Models for two, three, and four layer; current layer, double current layer, and core plus current layer moons are generated by inversion of the data using a theory which incorporates higher order multipoles. Core radii conductivities generally are in the range 1200 to 1300 km and 0.001 to 0.003 mhos/m; and for the conducting shell 1500 to 1700 km with 0.0001 to 0.0007 mhos/m with an outer layer taken as nonconducting. Core temperature based on available olivine data is 700 to 1000 C
Efficient Multi-Robot Motion Planning for Unlabeled Discs in Simple Polygons
We consider the following motion-planning problem: we are given unit
discs in a simple polygon with vertices, each at their own start position,
and we want to move the discs to a given set of target positions. Contrary
to the standard (labeled) version of the problem, each disc is allowed to be
moved to any target position, as long as in the end every target position is
occupied. We show that this unlabeled version of the problem can be solved in
time, assuming that the start and target positions are at
least some minimal distance from each other. This is in sharp contrast to the
standard (labeled) and more general multi-robot motion-planning problem for
discs moving in a simple polygon, which is known to be strongly NP-hard
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