Ricci flow of conformally compact metrics

In this paper we prove that given a smoothly conformally compact metric there is a short-time solution to the Ricci flow that remains smoothly conformally compact. We adapt recent results of Schn\"urer, Schulze and Simon to prove a stability result for conformally compact Einstein metrics sufficiently close to the hyperbolic metric.Comment: 26 pages, 2 figures. Version 2 includes stronger stability result and fixes several typo

Notes on a post-Dderridean applied linguistics

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A simulation technique for many spheres in quasi-static motion under frame-invariant pair drag and Brownian forces

We report on details of a simulation technique for particles under quasi-static motion determined by a balance of conservative and dissipative interactions acting at the pair level. We develop frame-invariant and linear viscous interactions between pairs of translating and rotating spheres in a form suitable for computation. We report an o(N) method for generating Brownian forces correlated with a pair resistance tensor and show how explicit finite difference schemes lead naturally to an algorithm with Brownian motion and an estimate of the Brownian stress. We justify the algorithm by appeal to the second-order Langevin equation. We discuss the choice of time step and imposition of boundary conditions. We assess a model of this kind as an approximation for colloid spheres concentrated in a fluid medium under shear flow. It is noted that the algorithm is also that required for simulation, in the diffusive limit, of a technique known as dissipative particle dynamics. We report on structural effects in Brownian sphere colloids and their sensitivity to the model details. We argue that the approximation has heuristic value in the study of the rheology in concentrated colloid systems. Its predictions for the rheology of suspensions are in semi-quantitative agreement with experiment

Continuous shear thickening transitions in model concentrated colloids - the role of interparticle forces

The role of interactions between close particles in the shear thickening of concentrated colloids is examined by using a Stokesian dynamics simulation of model systems. The interactions are repulsive thermodynamic forces and lubrication forces. Three different models are contrasted in their thickening behavior: Brownian spheres, polymer coated spheres, and Hookian spheres. Respectively, they show: a "mild" continuous thickening, a "strong" continuous thickening, and a strain thickening with loss of steady state. The relationship of order-disorder transitions and thickening is examined. Depending on the volume fraction and range of repulsive forces, thickening can be observed with or without an order-disorder transition at its onset. The different thickening responses arise from the dependence of the relaxation time of close particle contacts on interparticle gap. A time-scale based criterion for strong thickening is proposed and supported by the simulations. A simple theoretical model based the motion of a pair of particles leads to this criterion, but also predicts the mild thickening of Brownian spheres. It gives a simple fitting of flow curves which includes the details of the interparticle interactions. (C) 2004 The Society of Rheology

"Contact networks" in continuously shear thickening colloids

Many body effects that occur in continuous shear thickening of concentrated colloid suspensions are examined by using a Stokesian dynamics simulation of model systems of polymer coated particles. The shear thickening state is probed in a number of ways: computed scattering intensities, imaging of density variation using Voronoi constructions, examination of the distribution of interparticle forces, and computation of the fabric of contacts. The shear thickening transition in these systems is found to be associated with the growth of a network of close particle contacts and shear induced density variations. This paper focuses on the network of contacts. The distributions of force magnitude are found to be exponential. The network directly relates to the normal stress differences. Both the data and simple physical argument suggest that thickening can be viewed as an approach to "jamming." (C) 2004 The Society of Rheology

Kinetic theory of jamming in hard-sphere startup flows

We consider the problem of hard spheres shearing from rest with hydrodynamic lubrication, but no Brownian forces. A theoretical model is presented, in terms of the aggregation of elongated clusters of particles, and predicts a jamming transition, where stress and average cluster size tend to infinity after a finite amount of strain. The model is compared with simulation data [Europhys. Lett. 32, 535 (1995)], and predicts a critical volume fraction above which jamming will occur in macroscopic systems

Metastable states and the kinetics of colloid phase separation

We report on the results of extensive Brownian dynamics simulations of colloid phase separation due to depletion flocculation. We study in detail the effect of potential variation at fixed volume fraction of colloid and fixed range of interaction. We find a variety of nonequilibrium behaviors for quenches into the colloid fluid+crystal phase coexistence regime. We present clear evidence of metastability, of homogeneous nucleation, and of a kinetically arrested gel state. We also find evidence that suggests a density instability in the metastable colloid fluid preceding crystal nucleation. Our findings are consistent with a previous proposal that nonequilibrium behavior is determined by a metastable vapor+liquid binodal hidden in the fluid+crystal phase coexistence regim