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 $\omega$-meson stabilized effective Lagrangian. We consider skyrmion-skyrmion scattering with a fixed initial velocity of $\beta=0.5$, 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

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 $N_C$ 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

Understanding Microbialite Morphology Using a Comprehensive Suite of Three-Dimensional Analysis Tools

Abstract Microbialites can have complex morphologies that preserve clues to ancient microbial ecology. However, extracting and interpreting these clues is challenging due to both the complexity of microbial structures and the difficulties of connecting morphology to microbial processes. Fenestrate microbialites from the 2521 -3 Ma Gamohaan Formation, South Africa, have intricate structures composed of three distinct microbial structures: steeply dipping supports (surfaces defined by organic inclusions), more shallowly dipping supports with diffuse organic inclusions below them, and draping laminae. In polished slabs, shallowly dipping supports with diffuse organic inclusions show apparent dips from 27°to 60°, and supports without associated zones of diffuse inclusions dip 75°to 88°, which suggests a distinction between support types based on orientation. However, dips exposed in polished slabs are apparent dips, and three-dimensional analysis is required for analysis of true dips. Through the Keck Center for Active Visualization in Earth Sciences (KeckCAVES), we used locally developed software that controls a three-dimensional environment with head and hand tracking (an ''immersive environment'') to visualize and interpret virtual microbialite data sets. Immersive environments have not penetrated into standard scientific work processes (''workflows'') due to their high costs, steep learning curves, and low productivity for users. By contrast, our suite of software tools allowed us to develop a personalized scientific workflow that provides a complete path from initial ideas to characterization of fenestrate microbialites' features. Results of three-dimensional analysis of fenestrate microbialites show that supports with inclusions dip 65°to 75°, whereas supports without inclusions dip 85°to 90°. These results demonstrate that all supports have very steep dips, and a 10°dip gap exists between supports with and without inclusions, which suggests they grew in fundamentally different ways. Results also emphasize how valuable three-dimensional analysis is when combined with a comprehensive workflow for understanding intricate structures such as fenestrate microbialites