Dynamic Modeling and Simulation of a Real World Billiard

Gravitational billiards provide an experimentally accessible arena for testing formulations of nonlinear dynamics. We present a mathematical model that captures the essential dynamics required for describing the motion of a realistic billiard for arbitrary boundaries. Simulations of the model are applied to parabolic, wedge and hyperbolic billiards that are driven sinusoidally. Direct comparisons are made between the model's predictions and previously published experimental data. It is shown that the data can be successfully modeled with a simple set of parameters without an assumption of exotic energy dependence.Comment: 10 pages, 3 figure

General-Relativistic Curvature of Pulsar Vortex Structure

The motion of a neutron superfluid condensate in a pulsar is studied. Several theorems of general-relativistic hydrodynamics are proved for a superfluid. The average density distribution of vortex lines in pulsars and their general-relativistic curvature are derived.Comment: 18 pages, 1 figure

Temporal and dimensional effects in evolutionary graph theory

The spread in time of a mutation through a population is studied analytically and computationally in fully-connected networks and on spatial lattices. The time, t_*, for a favourable mutation to dominate scales with population size N as N^{(D+1)/D} in D-dimensional hypercubic lattices and as N ln N in fully-connected graphs. It is shown that the surface of the interface between mutants and non-mutants is crucial in predicting the dynamics of the system. Network topology has a significant effect on the equilibrium fitness of a simple population model incorporating multiple mutations and sexual reproduction. Includes supplementary information.Comment: 6 pages, 4 figures Replaced after final round of peer revie

On a Conjecture of Rapoport and Zink

In their book Rapoport and Zink constructed rigid analytic period spaces $F^{wa}$ for Fontaine's filtered isocrystals, and period morphisms from PEL moduli spaces of $p$-divisible groups to some of these period spaces. They conjectured the existence of an \'etale bijective morphism $F^a \to F^{wa}$ of rigid analytic spaces and of a universal local system of $Q_p$-vector spaces on $F^a$. For Hodge-Tate weights $n-1$ and $n$ we construct in this article an intrinsic Berkovich open subspace $F^0$ of $F^{wa}$ and the universal local system on $F^0$. We conjecture that the rigid-analytic space associated with $F^0$ is the maximal possible $F^a$, and that $F^0$ is connected. We give evidence for these conjectures and we show that for those period spaces possessing PEL period morphisms, $F^0$ equals the image of the period morphism. Then our local system is the rational Tate module of the universal $p$-divisible group and enjoys additional functoriality properties. We show that only in exceptional cases $F^0$ equals all of $F^{wa}$ and when the Shimura group is $GL_n$ we determine all these cases.Comment: v2: 48 pages; many new results added, v3: final version that will appear in Inventiones Mathematica

EHL traction analysis of perfluoropolyether fluids based on bulk modulus

Using three kinds of commercial perfluoropolyether (PFPE) fluids, the authors carried out high pressure density test at the pressure up to 1.2 GPa. Tangent bulk modulus and secant bulk modulus of the PFPE fluids were calculated by using the test results. Relationships of these moduli with pressure and temperature were examined. High pressure viscosity of each PFPE fluid was measured and the pressure viscosity coefficients of the PFPE fluids were obtained. In addition, the maximum traction coefficient and the limiting shear stress of each fluid were evaluated from the traction test employing a ball-on-disk testing machine. As a result, it was found that the maximum traction coefficient and the limiting shear stress are closely related to the tangent bulk modulus and the secant bulk modulus, respectively. The significant relationship of the maximum traction coefficient with the molecular packing parameter represented by the product of the pressure viscosity coefficient and the mean Hertzian pressure was also confirmed

Structural Plasticity and Noncovalent Substrate Binding in the GroEL Apical Domain. A study using electrospray ionization mass spectrometry and fluorescence binding studies

Advances in understanding how GroEL binds to non-native proteins are reported. Conformational flexibility in the GroEL apical domain, which could account for the variety of substrates that GroEL binds, is illustrated by comparison of several independent crystallographic structures of apical domain constructs that show conformational plasticity in helices H and I. Additionally, ESI-MS indicates that apical domain constructs have co-populated conformations at neutral pH. To assess the ability of different apical domain conformers to bind co-chaperone and substrate, model peptides corresponding to the mobile loop of GroES and to helix D from rhodanese were studied. Analysis of apical domain-peptide complexes by ESI-MS indicates that only the folded or partially folded apical domain conformations form complexes that survive gas phase conditions. Fluorescence binding studies show that the apical domain can fully bind both peptides independently. No competition for binding was observed, suggesting the peptides have distinct apical domain-binding sites. Blocking the GroES-apical domain-binding site in GroEL rendered the chaperonin inactive in binding GroES and in assisting the folding of denatured rhodanese, but still capable of binding non-native proteins, supporting the conclusion that GroES and substrate proteins have, at least partially, distinct binding sites even in the intact GroEL tetradecamer