Strathclyde

Controlling film flows has long been a central target for fluid dynamicists due to its numerous applications, in fields from heat exchangers to biochemical recovery, to semiconductor manufacture. However, despite its significance in the literature, most analyses have focussed on the “forward” problem: what effect a given control has on the flow. Often these problems are already complex, incorporating the - generally multiphysical - interplay of hydrodynamic phenomena with the mechanism of control. Indeed, many systems still defy meaningful agreement between models and experiments.
 
The inverse problem - determining a suitable control scheme for producing a specified flow - is considerably harder, and much more computationally expensive (often involving thousands of calculations of the forward problem). Performing such calculations for the full Navier-Stokes problem is generally prohibitive.

We examine the use of electric fields as a control mechanism. Solving the forward problem involves deriving a low-order model that turns out to be accurate even deep into the shortwave regime. We show that the weakly-nonlinear problem is Kuramoto-Sivashinsky-like, allowing for greater analytical traction. The fully nonlinear problem can be solved numerically via the use of a rapid solver, enabling solution of both the forward and adjoint problems on sub-second timescales, allowing for both terminal and regulation optimal control studies to be implemented. Finally, we examine the feasibility of controlling direct numerical simulations using these techniques.

Although not all complex networks are embedded into physical spaces, it is possible to find an abstract Euclidean space in which they are embedded. This Euclidean space naturally arises from the use of the concept of network communicability. In this talk I will introduce the basic concepts of communicability, communicability distance and communicability angles. Both, analytic and computational evidences will be provided that shows that the average communicability angle represents a measure of the spatial efficiency of a network. We will see how this abstract spatial efficiency is related to the real-world efficiency with which networks uses the available physical space for classes of networks embedded into physical spaces. More interesting, we will show how this abstract concept give important insights about properties of networks not embedded in physical spaces.

We discuss how various types of orientational and

translational ordering in different liquid crystal phases are

described by macroscopic tensor order parameters. In

particular, we consider a mean-field molecular-statistical

theory of the transition from the orthogonal uniaxial smectic

phase and the tilted biaxial phase composed of biaxial

molecules. The relationship between macroscopic order

parameters, molecular invariant tensors and the symmetry of

biaxial molecules is discussed in detail. Finally we use

microscopic and macroscopic symmetry arguments to consider the

mechanisms of the ferroelectric ordering in tilted smectic

phases determined by molecular chirality.

Mike Giles recently came up with a very general technique that improves the fundamental complexity of Monte Carlo simulation in the context where stochastic differential equations are simulated numerically. I will discuss some work with Mike Giles and Xuerong Mao that extends the theoretical support for this approach to the case of financial options without globally Lipschitz payoff functions. I will also suggest other application areas where this multi-level approach might prove valuable, including stochastic computation in cell biology.