In highly concentrated surfactant solutions the surfactant molecules self-assemble into long flexible "wormy" structures. Properties of these wormlike micellar solutions make them ideal for use in oil recovery and in body care products (shampoo). These properties depend strongly on temperature and concentration conditions. In solution the "worms" entangle, forming a network, but also continuously break and reform, thus earning the name ‘living polymers’. In flow these fluids exhibit spatial inhomogeneities, shear-banding, and dynamic elastic recoil. In this talk a rheological equation of state that is capable of describing these fluids is described The resultant governing macroscale equations consist of a coupled nonlinear partial differential equation system. Model predictions are presented, contrasted with experimental results, and contrasted with predictions of other existing models. Generalizations of the model to allow the capturing of behaviors under changing concentration or temperature conditions, namely power law and stretched exponential relaxation as opposed to exponential relaxation, will be discussed and particularly a mesoscale stochastic simulation network model will be presented.
The entire history of mathematics in one hour, as illustrated by around 300 postage stamps featuring mathematics and mathematicians from across the world.
From Euclid to Euler, from Pythagoras to Poincaré, and from Fibonacci to the Fields Medals, all are featured in attractive, charming and sometimes bizarre stamps. No knowledge of mathematics or philately required.
Quantum Mechanics presents a radically different perspective on physical reality compared with the world of classical physics. In particular, results such as the Bell and Kochen-Specker theorems highlight the essentially non-local and contextual nature of quantum mechanics. The rapidly developing field of quantum information seeks to exploit these non-classical features of quantum physics to transcend classical bounds on information processing tasks.
In this talk, we shall explore the rich mathematical structures underlying these results. The study of non-locality and contextuality can be expressed in a unified and generalised form in the language of sheaves or bundles, in terms of obstructions to global sections. These obstructions can, in many cases, be witnessed by cohomology invariants. There are also strong connections with logic. For example, Bell inequalities, one of the major tools of quantum information and foundations, arise systematically from logical consistency conditions.
These general mathematical characterisations of non-locality and contextuality also allow precise connections to be made with a number of seemingly unrelated topics, in classical computation, logic, and natural language semantics. By varying the semiring in which distributions are valued, the same structures and results can be recognised in databases and constraint satisfaction as in probability models arising from quantum mechanics. A rich field of contextual semantics, applicable to many of the situations where the pervasive phenomenon of contextuality arises, promises to emerge.
Dynamics of small particles in fluids have fascinated scientists for centuries. Phenomena such as Brownian motion, sedimentation, and electrophoresis continue to inspire cutting-edge research and innovations. The fluid in which the particles move is typically isotropic, such as water or a polymer solution. Recently, we started to explore what would happen if particles are placed in an anisotropic fluid: a liquid crystal. The study reveals that the liquid crystal changes dramatically both the statics and dynamics, leading to levitation of the particles, their anomalous Brownian motion and new mechanisms of electrokinetics. The new phenomena are rooted in anisotropy of the liquid crystal properties, such as different electric conductivity in the directions parallel and perpendicular to the average molecular orientation.