157 research outputs found
Sporadicity and synchronization in one-dimensional asymmetrically coupled maps
A one-dimensional chain of sporadic maps with asymmetric nearest neighbour
couplings is numerically studied. It is shown that in the region of strong
asymmetry the system becomes spatially fully synchronized, even in the
thermodinamic limit, while the Lyapunov exponent is zero. For weak asymmetry
the synchronization is no more complete, and the Lyapunov exponent becomes
positive. In addition one has a clear relation between temporal and spatial
chaos, {\it i.e.}: a positive effective Lyapunov exponent corresponds to a lack
of synchronization and {\it vice versa}Comment: 9 pages + 3 figures (postscript appended uuencoded tar), IOP style
(appended uuencoded compress
Existence and Stability of Steady Fronts in Bistable CML
We prove the existence and we study the stability of the kink-like fixed
points in a simple Coupled Map Lattice for which the local dynamics has two
stable fixed points. The condition for the existence allows us to define a
critical value of the coupling parameter where a (multi) generalized
saddle-node bifurcation occurs and destroys these solutions. An extension of
the results to other CML's in the same class is also displayed. Finally, we
emphasize the property of spatial chaos for small coupling.Comment: 18 pages, uuencoded PostScript file, J. Stat. Phys. (In press
Two Skyrmion Dynamics with Omega Mesons
We present our first results of numerical simulations of two skyrmion
dynamics using an -meson stabilized effective Lagrangian. We consider
skyrmion-skyrmion scattering with a fixed initial velocity of , for
various impact parameters and groomings. The physical picture that emerges is
surprisingly rich, while consistent with previous results and general
conservation laws. We find meson radiation, skyrmion scattering out of the
scattering plane, orbiting and capture to bound states.Comment: 19 pages, 22 figure
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An adaptive projection method for the modeling of unsteady, low-Mach number combustion
In this paper the authors present an adaptive projection method for modeling unsteady, low-Mach reacting flow in an unconfined region. The equations they solve are based on a model for low-Mach number combustion that consists of the evolution equations for density, species concentrations, enthalpy, and momentum coupled with a constraint on the divergence of the flow. The algorithm is based on a projection methodology in which they first advance the evolution equations and then solve an elliptic equation to enforce the divergence constraint. The adaptive mesh refinement (AMR) scheme uses a time-varying, hierarchical grid structure composed of uniform rectangular grids of varying resolution. The integration scheme on the grid hierarchy is a recursive procedure in which a coarse grid is advanced, fine grids are advanced multiple steps to reach the same time as the coarse grid, and the coarse and the fine grids are synchronized. The method is valid for multiple grids on each level and multiple levels of refinement. The method is currently implemented for laminar, axisymmetric flames with a reduced kinetics mechanism and a Lewis number of unity. Two methane-air flames, one steady and the other flickering, are presented as numerical examples
BARYON-BARYON INTERACTIONS IN LARGE N_C CHIRAL PERTURBATION THEORY
Interactions of two baryons are considered in large chiral perturbation
theory and compared to the interactions derived from the Skyrme model. Special
attention is given to a torus-like configuration known to be present in the
Skyrme model.Comment: 18 pages, REVTEX, 8 uuencoded PS figures appende
Bifurcations in Globally Coupled Map Lattices
The dynamics of globally coupled map lattices can be described in terms of a
nonlinear Frobenius--Perron equation in the limit of large system size. This
approach allows for an analytical computation of stationary states and their
stability. The complete bifurcation behaviour of coupled tent maps near the
chaotic band merging point is presented. Furthermore the time independent
states of coupled logistic equations are analyzed. The bifurcation diagram of
the uncoupled map carries over to the map lattice. The analytical results are
supplemented with numerical simulations.Comment: 19 pages, .dvi and postscrip
Collision-Induced Decay of Metastable Baby Skyrmions
Many extensions of the standard model predict heavy metastable particles
which may be modeled as solitons (skyrmions of the Higgs field), relating their
particle number to a winding number. Previous work has shown that the
electroweak interactions admit processes in which these solitons decay,
violating standard model baryon number. We motivate the hypothesis that
baryon-number-violating decay is a generic outcome of collisions between these
heavy particles. We do so by exploring a 2+1 dimensional theory which also
possesses metastable skyrmions. We use relaxation techniques to determine the
size, shape and energy of static solitons in their ground state. These solitons
could decay by quantum mechanical tunneling. Classically, they are metastable:
only a finite excitation energy is required to induce their decay. We attempt
to induce soliton decay in a classical simulation by colliding pairs of
solitons. We analyze the collision of solitons with varying inherent
stabilities and varying incident velocities and orientations. Our results
suggest that winding-number violating decay is a generic outcome of collisions.
All that is required is sufficient (not necessarily very large) incident
velocity; no fine-tuning of initial conditions is required.Comment: 24 pages, 7 figures, latex. Very small changes onl
Synchronisation in Coupled Sine Circle Maps
We study the spatially synchronized and temporally periodic solutions of a
1-d lattice of coupled sine circle maps. We carry out an analytic stability
analysis of this spatially synchronized and temporally periodic case and obtain
the stability matrix in a neat block diagonal form. We find spatially
synchronized behaviour over a substantial range of parameter space. We have
also extended the analysis to higher spatial periods with similar results.
Numerical simulations for various temporal periods of the synchronized
solution, reveal that the entire structure of the Arnold tongues and the
devil's staircase seen in the case of the single circle map can also be
observed for the synchronized coupled sine circle map lattice. Our formalism
should be useful in the study of spatially periodic behaviour in other coupled
map lattices.Comment: uuencoded, 1 rextex file 14 pages, 3 postscript figure
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