Linear viscoelasticity of entangled wormlike micelles bridged by telechelic polymers : an experimental model for a double transient network

We survey the linear viscoelasticity of a new type of transient network: bridged wormlike micelles, whose structure has been characterized recently [Ramos and Ligoure, (2007)]. This composite material is obtained by adding telechelic copolymers (water-soluble chains with hydrophobic stickers at each extremity) to a solution of entangled wormlike micelles (WM). For comparison, naked WM and WM decorated by amphiphilic copolymers are also investigated. While these latter systems exhibit almost a same single ideal Maxwell behavior, solutions of bridged WM can be described as two Maxwell fluids components blends, characterized by two markedly different characteristic times, t_fast and t_slow, and two elastic moduli, G_fast and G_slow, with G_fast >> G_slow. We show that the slow mode is related to the viscoelasticity of the transient network of entangled WM, and the fast mode to the network of telechelic active chains (i.e. chains that do not form loops but bridge two micelles). The dependence of the viscoelasticity with the surfactant concentration, phi, and the sticker-to-surfactant molar ratio, beta, is discussed. In particular, we show that G_fast is proportional to the number of active chains in the material, phi beta. Simple theoretical expectations allow then to evaluate the bridges/loops ratio for the telechelic polymers

Spatial birth-and-death processes in random environment

We consider birth-and-death processes of objects (animals) defined in ${\bf Z}^d$ having unit death rates and random birth rates. For animals with uniformly bounded diameter we establish conditions on the rate distribution under which the following holds for almost all realizations of the birth rates: (i) the process is ergodic with at worst power-law time mixing; (ii) the unique invariant measure has exponential decay of (spatial) correlations; (iii) there exists a perfect-simulation algorithm for the invariant measure. The results are obtained by first dominating the process by a backwards oriented percolation model, and then using a multiscale analysis due to Klein to establish conditions for the absence of percolation.Comment: 48 page

Dimension Estimation Using Random Connection Models

Information about intrinsic dimension is crucial to perform dimensionality reduction, compress information, design efficient algorithms, and do statistical adaptation. In this paper we propose an estimator for the intrinsic dimension of a data set. The estimator is based on binary neighbourhood information about the observations in the form of two adjacency matrices, and does not require any explicit distance information. The underlying graph is modelled according to a subset of a specific random connection model, sometimes referred to as the Poisson blob model. Computationally the estimator scales like n log n, and we specify its asymptotic distribution and rate of convergence. A simulation study on both real and simulated data shows that our approach compares favourably with some competing methods from the literature, including approaches that rely on distance information

The random geometry of equilibrium phases

This is a (long) survey about applications of percolation theory in equilibrium statistical mechanics. The chapters are as follows: 1. Introduction 2. Equilibrium phases 3. Some models 4. Coupling and stochastic domination 5. Percolation 6. Random-cluster representations 7. Uniqueness and exponential mixing from non-percolation 8. Phase transition and percolation 9. Random interactions 10. Continuum modelsComment: 118 pages. Addresses: [email protected] http://www.mathematik.uni-muenchen.de/~georgii.html [email protected] http://www.math.chalmers.se/~olleh [email protected]

Application of Discrete Element Method and Computational Fluid Dynamics to Selected Dispersed Phase Flow Problems

A parallel discrete particle modelling framework (PAR_DPM3D) is applied to study three fundamental multiphase flow problems: The sedimentation of a cluster of particles in a viscous ambient fluid, multiphase flow in a bench-scale fluidized bed and granular segregation and mixing dynamics in a rotating drum. Various phenomena including torus formation and particle cluster breakup are reproduced. We provide new insights into the volume fraction dependence of the dynamic characteristics of a settling particle cluster and find a similar dependence in the simulations as in the theoretical predictions of Nitsche and Batchelor 1. Similarities in the interaction between a system of two particle clouds and a system of two immiscible droplets was established with an observed increase in the velocity of the trailing cloud due to drag reduction in the wake of the leading cloud. Second, we show how existing drag models may be inadequate to predicting the macroscale properties of a gas-solid fluidized bed. Using an energy and force balance approach we provide new closures that account for some inhomogeneous flow structures and implement these closures within the PAR_DPM3D framework to predicting the axial pressure drop and transverse particle velocity profiles Finally, we present results from particle dynamics simulation of “S+D” granular systems (where size and density drive segregation simultaneously) in various irregular shaped tumblers in the rolling regime (10-4 \u3c Fr \u3c 10-2). We develop a new way of quantifying the state of mixing or segregation has been developed. Using this new measure of segregation (or entropy of mixing) we compare segregation dynamics for different shapes of tumblers

Lace Expansion and Mean-Field Behavior for the Random Connection Model

We consider the random connection model for three versions of the connection function $\varphi$: A finite-variance version (including the Boolean model), a spread-out version, and a long-range version. We adapt the lace expansion to fit the framework of the underlying continuum-space Poisson point process to derive the triangle condition in sufficiently high dimension and furthermore to establish the infra-red bound. From this, mean-field behavior of the model can be deduced. As an example, we show that the critical exponent $\gamma$ takes its mean-field value $\gamma=1$ and that the percolation function is continuous.Comment: 62 page

Strong disorder RG approach of random systems

There is a large variety of quantum and classical systems in which the quenched disorder plays a dominant r\^ole over quantum, thermal, or stochastic fluctuations : these systems display strong spatial heterogeneities, and many averaged observables are actually governed by rare regions. A unifying approach to treat the dynamical and/or static singularities of these systems has emerged recently, following the pioneering RG idea by Ma and Dasgupta and the detailed analysis by Fisher who showed that the Ma-Dasgupta RG rules yield asymptotic exact results if the broadness of the disorder grows indefinitely at large scales. Here we report these new developments by starting with an introduction of the main ingredients of the strong disorder RG method. We describe the basic properties of infinite disorder fixed points, which are realized at critical points, and of strong disorder fixed points, which control the singular behaviors in the Griffiths-phases. We then review in detail applications of the RG method to various disordered models, either (i) quantum models, such as random spin chains, ladders and higher dimensional spin systems, or (ii) classical models, such as diffusion in a random potential, equilibrium at low temperature and coarsening dynamics of classical random spin chains, trap models, delocalization transition of a random polymer from an interface, driven lattice gases and reaction diffusion models in the presence of quenched disorder. For several one-dimensional systems, the Ma-Dasgupta RG rules yields very detailed analytical results, whereas for other, mainly higher dimensional problems, the RG rules have to be implemented numerically. If available, the strong disorder RG results are compared with another, exact or numerical calculations.Comment: review article, 195 pages, 36 figures; final version to be published in Physics Report

Topological defects in lattice models and affine Temperley-Lieb algebra

This paper is the first in a series where we attempt to define defects in critical lattice models that give rise to conformal field theory topological defects in the continuum limit. We focus mostly on models based on the Temperley-Lieb algebra, with future applications to restricted solid-on-solid (also called anyonic chains) models, as well as non-unitary models like percolation or self-avoiding walks. Our approach is essentially algebraic and focusses on the defects from two points of view: the "crossed channel" where the defect is seen as an operator acting on the Hilbert space of the models, and the "direct channel" where it corresponds to a modification of the basic Hamiltonian with some sort of impurity. Algebraic characterizations and constructions are proposed in both points of view. In the crossed channel, this leads us to new results about the center of the affine Temperley-Lieb algebra; in particular we find there a special subalgebra with non-negative integer structure constants that are interpreted as fusion rules of defects. In the direct channel, meanwhile, this leads to the introduction of fusion products and fusion quotients, with interesting mathematical properties that allow to describe representations content of the lattice model with a defect, and to describe its spectrum.Comment: 41