Hierarchy and Polysynchrony in an adaptive network

We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be non-trivial. The structure of the network shows interesting hierarchical properties and in certain parameter regions the dynamics is polysynchronous: nodes can be divided in differently synchronized classes but contrary to cluster synchronization, nodes in the same class need not be connected to each other. These complicated synchrony patterns have been conjectured to play roles in systems biology and circuits. The adaptive system we study describes ways whereby this behaviour can evolve from undifferentiated nodes.Comment: 13 pages, 17 figure

The flow field in the slender combustion chambers of solid propellant rockets

We analyse the near inviscid flow field generated in a slender non-axisymmetric cylindrical cavity by the gasification and combustion reactions of a surrounding solid propellant grain. These reactions are confined to a thin layer adjacent to the surface of the solid propellant, so that the flow is non-reacting in most of the cavity, and of the same form as the flow in slender ducts due to fluid injection through lateral porous walls. The non-reacting flow can be described in terms of self-similar solutions of the Navier -Stokes equations that we calculate numerically for star-shaped grain configurations, with Reynolds numbers only moderately large for the flow to remain laminar and steady. The self-similar flows for non-axisymmetric configurations show strong axial vortices that we analyze using the Euler simplified form of the flow equations for large Reynolds numbers, and the general solution of the Burgers equation for strained vortices that describes their viscous cores; a logarithmic singularity could then be encountered at their center line

Bifurcations in the Lozi map

We study the presence in the Lozi map of a type of abrupt order-to-order and order-to-chaos transitions which are mediated by an attractor made of a continuum of neutrally stable limit cycles, all with the same period.Comment: 17 pages, 12 figure

Coexistence of periods in a bisecting bifurcation

The inner structure of the attractor appearing when the Varley-Gradwell-Hassell population model bifurcates from regular to chaotic behaviour is studied. By algebraic and geometric arguments the coexistence of a continuum of neutrally stable limit cycles with different periods in the attractor is explained.Comment: 13 pages, 5 figure

Density functional simulation of small Fe nanoparticles

We calculate from first principles the electronic structure, relaxation and magnetic moments in small Fe particles, applying the numerical local orbitals method in combination with norm-conserving pseudopotentials. The accuracy of the method in describing elastic properties and magnetic phase diagrams is tested by comparing benchmark results for different phases of crystalline iron to those obtained by an all-electron method. Our calculations for the bipyramidal Fe_5 cluster qualitatively and quantitatively confirm previous plane-wave results that predicted a non-collinear magnetic structure. For larger bcc-related (Fe_35) and fcc-related (Fe_38, Fe_43, Fe_62) particles, a larger inward relaxation of outer shells has been found in all cases, accompanied by an increase of local magnetic moments on the surface to beyond 3 mu_B.Comment: 15 pages with 6 embedded postscript figures, updated version, submitted to Eur.Phys.J.

Torsional Alfv\'en waves in solar partially ionized plasma: effects of neutral helium and stratification

Ion-neutral collisions may lead to the damping of Alfven waves in chromospheric and prominence plasmas. Neutral helium atoms enhance the damping in certain temperature interval, where the ratio of neutral helium and neutral hydrogen atoms is increased. Therefore, the height-dependence of ionization degrees of hydrogen and helium may influence the damping rate of Alfven waves. We aim to study the effect of neutral helium in the damping of Alfven waves in stratified partially ionized plasma of the solar chromosphere. We consider a magnetic flux tube, which is expanded up to 1000 km height and then becomes vertical due to merging with neighboring tubes, and study the dynamics of linear torsional Alfven waves in the presence of neutral hydrogen and neutral helium atoms. We start with three-fluid description of plasma and consequently derive single-fluid magnetohydrodynamic (MHD) equations for torsional Alfven waves. Thin flux tube approximation allows to obtain the dispersion relation of the waves in the lower part of tubes, while the spatial dependence of steady-state Alfven waves is governed by Bessel type equation in the upper part of tubes. Consecutive derivation of single-fluid MHD equations results in a new Cowling diffusion coefficient in the presence of neutral helium which is different from previously used one. We found that shorter-period (< 5 s) torsional Alfven waves damp quickly in the chromospheric network due to ion-neutral collision. On the other hand, longer-period (> 5 s) waves do not reach the transition region as they become evanescent at lower heights in the network cores. Propagation of torsional Alfven waves through the chromosphere into the solar corona should be considered with caution: low-frequency waves are evanescent due to the stratification, while high-frequency waves are damped due to ion neutral collisions.Comment: 9 pages, 7 figures (accepted in A&A

Families of piecewise linear maps with constant Lyapunov exponent

We consider families of piecewise linear maps in which the moduli of the two slopes take different values. In some parameter regions, despite the variations in the dynamics, the Lyapunov exponent and the topological entropy remain constant. We provide numerical evidence of this fact and we prove it analytically for some special cases. The mechanism is very different from that of the logistic map and we conjecture that the Lyapunov plateaus reflect arithmetic relations between the slopes.Comment: 26 pages, 13 figure

Emergence of hierarchical networks and polysynchronous behaviour in simple adaptive systems

We describe the dynamics of a simple adaptive network. The network architecture evolves to a number of disconnected components on which the dynamics is characterized by the possibility of differently synchronized nodes within the same network (polysynchronous states). These systems may have implications for the evolutionary emergence of polysynchrony and hierarchical networks in physical or biological systems modeled by adaptive networks.Comment: 4 pages, 4 figure