Piecewise Linear Models for the Quasiperiodic Transition to Chaos

We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking and the quasi-periodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps. Our main results describe (1) the sets of maps in these families having some prescribed rotation interval; (2) the boundaries between zero and positive topological entropy and between zero length and non-zero length rotation interval; and (3) the structure and bifurcations of the attractors in one of these families. We discuss the interpretation of these maps as low-order spline approximations to the classic ``sine-circle'' map and examine more generally the implications of our results for the case of smooth circle maps. We also mention a possible connection to recent experiments on models of a driven Josephson junction.Comment: 75 pages, plain TeX, 47 figures (available on request

Critical and Near-Critical Branching Processes

Scale-free dynamics in physical and biological systems can arise from a variety of causes. Here, we explore a branching process which leads to such dynamics. We find conditions for the appearance of power laws and study quantitatively what happens to these power laws when such conditions are violated. From a branching process model, we predict the behavior of two systems which seem to exhibit near scale-free behavior--rank-frequency distributions of number of subtaxa in biology, and abundance distributions of genotypes in an artificial life system. In the light of these, we discuss distributions of avalanche sizes in the Bak-Tang-Wiesenfeld sandpile model.Comment: 9 pages LaTex with 10 PS figures. v.1 of this paper contains results from non-critical sandpile simulations that were excised from the published versio

Possible interference effect in the Stern-Gerlach phenomenon

We show that if it is possible to manufacture a beam of spin-1/2 heavy atoms corresponding to a quantum-mechanical pure state, then the dark lines of the Stern-Gerlach effect should display a fine structure. The two lips of the open-mouth pattern will each be a doublet; the lighter area between the two lines of the doublet arises from an interference between silver atoms on opposite sides of the incoming beam. We obtain a simple classical model giving exactly the same angular distribution around the open mouth. However, this classical model does not give the fine structure

Multifractal Behaviour of n-Simplex Lattice

We study the asymptotic behaviour of resistance scaling and fluctuation of resistance that give rise to flicker noise in an {\em n}-simplex lattice. We propose a simple method to calculate the resistance scaling and give a closed-form formula to calculate the exponent, $\beta_L$, associated with resistance scaling, for any n. Using current cumulant method we calculate the exact noise exponent for n-simplex lattices.Comment: Latex, 9 pages including one figur

A Bethe lattice representation for sandpiles

Avalanches in sandpiles are represented throughout a process of percolation in a Bethe lattice with a feedback mechanism. The results indicate that the frequency spectrum and probability distribution of avalanches resemble more to experimental results than other models using cellular automata simulations. Apparent discrepancies between experiments are reconciled. Critical behavior is here expressed troughout the critical properties of percolation phenomena.Comment: 5 pages, 4 figures, submitted for publicatio

Mode-Locking in Driven Disordered Systems as a Boundary-Value Problem

We study mode-locking in disordered media as a boundary-value problem. Focusing on the simplest class of mode-locking models which consists of a single driven overdamped degree-of-freedom, we develop an analytical method to obtain the shape of the Arnol'd tongues in the regime of low ac-driving amplitude or high ac-driving frequency. The method is exact for a scalloped pinning potential and easily adapted to other pinning potentials. It is complementary to the analysis based on the well-known Shapiro's argument that holds in the perturbative regime of large driving amplitudes or low driving frequency, where the effect of pinning is weak.Comment: 6 pages, 7 figures, RevTeX, Submitte

External and Turbomachinery Flow Control Working Group

Broad Flow Control Issues: a) Understanding flow physics. b) Specific control objective(s). c) Actuation. d) Sensors. e) Integrated active flow control system. f) Development of design tools (CFD, reduced order models, controller design, understanding and utilizing instabilities and other mechanisms, e.g., streamwise vorticity)

On species delimitation: Yet another lemur species or just genetic variation?

<p>Abstract</p> <p>Background</p> <p>Although most taxonomists agree that species are independently evolving metapopulation lineages that should be delimited with several kinds of data, the taxonomic practice in Malagasy primates (Lemuriformes) looks quite different. Several recently described lemur species are based solely on evidence of genetic distance and diagnostic characters of mitochondrial DNA sequences sampled from a few individuals per location. Here we explore the validity of this procedure for species delimitation in lemurs using published sequence data.</p> <p>Results</p> <p>We show that genetic distance estimates and <it>Population Aggregation Analysis </it>(PAA) are inappropriate for species delimitation in this group of primates. Intra- and interspecific genetic distances overlapped in 14 of 17 cases independent of the genetic marker used. A simulation of a fictive taxonomic study indicated that for the mitochondrial D-loop the minimum required number of individuals sampled per location is 10 in order to avoid false positives via PAA.</p> <p>Conclusions</p> <p>Genetic distances estimates and PAA alone should not be used for species delimitation in lemurs. Instead, several nuclear and sex-specific loci should be considered and combined with other data sets from morphology, ecology or behavior. Independent of the data source, sampling should be done in a way to ensure a quantitative comparison of intra- and interspecific variation of the taxa in question. The results of our study also indicate that several of the recently described lemur species should be reevaluated with additional data and that the number of good species among the currently known taxa is probably lower than currently assumed.</p