Hydrodynamic synchronization of flagellar oscillators

We survey the theory synchronization in collections of noisy oscillators. This framework is applied to flagellar synchronization by hydrodynamic interactions. The time-reversibility of hydrodynamics at low Reynolds numbers prompts swimming strokes that break symmetry to facilitate hydrodynamic synchronization. We discuss different physical mechanisms for flagellar synchronization, which break this symmetry in different ways.Comment: 15 pages, 3 figures; accepted for publication in EPJ Special Topics Issue,Lecture Notes of the Summer School "Microswimmers -- From Single Particle Motion to Collective Behaviour'', organised by the DFG Priority Programme SPP 1726 (Forschungszentrum J\"ulich, J\"ulich, 2015

Competition and the Evolution of Market Structure in the E-conomy : A Simulation Analysis

In this paper an evolutionary simulation model, based on replicator dynamics, is developed. The purpose is to identify changes in the patterns of evolution of the market structure caused by Information and Communication Technologies (ICT) in the E-conomy in comparison to the Old Economy (without ICT). The relationship between the two economy concepts can be summed up from an industrial organization point of view with the help of stylized facts about the evolution of the market structure as phases in an industrial life cycle. The simulation results show that economic development progresses from the E-conomy to the (next) Old Economy. --Industrial life cycle,ICT,Evolution of market structure,Replicator dynamics,Simulation analysis

Rearrangements and Tunneling Splittings in Small Water Clusters

Recent far-infrared vibration-rotation tunneling (FIR-VRT) experiments pose new challenges to theory because the interpretation and prediction of such spectra requires a detailed understanding of the potential energy surface (PES) away from minima. In particular we need a global description of the PES in terms of a complete reaction graph. Hence all the transition states and associated mechanisms which might give rise to observable tunneling splittings must be characterized. It may be possible to guess the detailed permutations of atoms from the transition state alone, but experience suggests this is unwise. In this contribution a brief overview of the issues involved in treating the large amplitude motions of such systems will be given, with references to more detailed discussions and some specific examples. In particular we will consider the effective molecular symmetry group, the classification of rearrangement mechanisms, the location of minima and transition states and the calculation of reaction pathways. The application of these theories to small water clusters ranging from water dimer to water hexamer will then be considered. More details can be found in recent reviews.Comment: 15 pages, 5 figures. This paper was prepared in August 1997 for the proceedings volume of the NATO-ASI meeting on "Recent Theoretical and Experimental Advances in Hydrogen Bonded Clusters" edited by Sotiris Xantheas, which has so far not appeare

Enhancing Ionic Conductivity of Bulk Single Crystal Yttria-Stabilized Zirconia by Tailoring Dopant Distribution

We present an ab-initio based kinetic Monte Carlo model for ionic conductivity in single crystal yttria-stabilized zirconia. Ionic interactions are taken into account by combining density functional theory calculations and the cluster expansion method and are found to be essential in reproducing the effective activation energy observed in experiments. The model predicts that the effective energy barrier can be reduced by 0.15-0.25 eV by arranging the dopant ions into a super-lattice.Comment: Submitted to Phys. Rev. Lett. on 8/3/2010 (in review

Hilbert spaces and the pair correlation of zeros of the Riemann zeta-function

Montgomery's pair correlation conjecture predicts the asymptotic behavior of the function $N(T,\beta)$ defined to be the number of pairs $\gamma$ and $\gamma'$ of ordinates of nontrivial zeros of the Riemann zeta-function satisfying $0<\gamma,\gamma'\leq T$ and $0 < \gamma'-\gamma \leq 2\pi \beta/\log T$ as $T\to \infty$. In this paper, assuming the Riemann hypothesis, we prove upper and lower bounds for $N(T,\beta)$, for all $\beta >0$, using Montgomery's formula and some extremal functions of exponential type. These functions are optimal in the sense that they majorize and minorize the characteristic function of the interval $[-\beta, \beta]$ in a way to minimize the $L^1\big(\mathbb{R}, \big\{1 - \big(\frac{\sin \pi x}{\pi x}\big)^2 \big\}\,dx\big)$-error. We give a complete solution for this extremal problem using the framework of reproducing kernel Hilbert spaces of entire functions. This extends previous work by P. X. Gallagher in 1985, where the case $\beta \in \frac12 \mathbb{N}$ was considered using non-extremal majorants and minorants.Comment: to appear in J. Reine Angew. Mat

Bifurcations and Complete Chaos for the Diamagnetic Kepler Problem

We describe the structure of bifurcations in the unbounded classical Diamagnetic Kepler problem. We conjecture that this system does not have any stable orbits and that the non-wandering set is described by a complete trinary symbolic dynamics for scaled energies larger then $\epsilon_c=0.328782\ldots$.Comment: 15 pages PostScript uuencoded with figure