Past

According to Witten a gauge theory with a mass gap contains a possibly trivial Topological Field Theory  (TFT) in the infrared.  We show that in SU(N) YM it there exists a trivial TFT defined by   twistor Wilson loops whose v.e.v. is 1 in the large-N limit for any shape of the loops supported on certain Lagrangian submanifolds of space-time that lift to Lagrangian submanifolds of twistor space.

We derive a new version of the Makeenko-Migdal loop equation for the topological twistor Wilson loops, the holomorphic loop equation, that involves the change of variables in the YM functional integral from the connection to the anti-selfdual part of the curvature and the choice of a holomorphic gauge.

Employing the holomorphic loop equation and viewing Floer homology the other way around,
we associate to arcs asymptotic in both directions to the cusps of the Lagrangian submanifolds the critical points of an effective action implied by the holomorphic loop equation. The critical points of the effective action, being associated to the homology of the punctured Lagrangian submanifolds, consist of surface operators of the YM theory, supported on the punctures.  The correlators of surface operators in the TFT satisfy for large momentum the constraint that follows by the renormalization group and by the asymptotic freedom and they are saturated by an infinite sum of pure poles of scalar and pseudoscalar glueballs, whose joint spectrum is exactly linear in the mass squared.

For several physical purposes we outline  a related construction of a twistorial Topological String Theory dual to the TFT, that involves the Chern-Simons action on Lagrangian submanifolds of  
twistor space.

Relative entropy weighted optimization is convex optimization problem over the space of probability measures. Many convex optimization problems can be rephrased as such a problem. This is particularly useful since this problem type admits a quasi-explicit solution (i.e. as the expectation over a random variable), which immediately provides a Monte-Carlo method for numerically computing the solution of the optimization problem.

In this talk we discuss the background and application of this approach to stochastic optimal control problems, which may be considered as relative entropy weighted problems with Wiener space as probability space, and its connection with the theory of large deviations for Brownian functionals. As a particular application we discuss the minimization of the local time in a given point of Brownian motion with drift.

Recent years have seen rapid expansion of the capabilities 
to recreate in vivo conditions using in vitro microfluidic assays.  
A wide range of single cell and cell population behaviors can now 
be replicated, controlled and imaged for detailed studies to gain 
new insights.  Such experiments also provide useful fodder for 
computational models, both in terms of estimating model parameters 
and for testing model-generated hypotheses.  Our experiments have 
focused in several different areas.  
1) Single cell migration experiments in 3D collagen gels have 
revealed that interstitial flow can lead to biased cell migration 
in the upstream direction, with important implications to cancer 
invasion.  We show this phenomenon to be a consequence of 
integrin-mediated mechanotransduction.  
2) Endothelial cells seeded in fibrin gels form perfusable 
vascular networks within 2-3 days through a process termed 
“vasculogenesis”.  The process by which cells sense their 
neighbours, extend projections and form anastomoses, and 
generate interconnected lumens can be observed through time-lapse 
microscopy.  
3) These vascular networks, once formed, can be perfused with 
medium containing cancer cells that become lodged in the 
smaller vessels and proceed to transmigrate across the endothelial 
barrier and invade into the surrounding matrix.  High resolution 
imaging of this process reveals a fascinating sequence of events 
involving interactions between a tumour cell, endothelial cells, 
and underlying matrix.  These three examples will be presented 
with a view toward gaining new insights through computational 
modelling of the associated phenomena.

We will present in this lecture the global existence of weak solutions and the local existence and uniqueness of strong-in-time solutions for the fully-coupled Navier-Stokes/Q-tensor system on a bounded domain $\O\subset\mathbb{R}^d$ ($d=2,3$) with inhomogenerous Dirichlet and Neumann or mixed boundary conditions. Our result is valid for any physical parameter $\xi$ and we consider the Navier-Stokes equations with a general (but smooth) viscosity coefficient.

The good use of condiments is one of the secrets of a tasty quiche. If you want to delight your guests, add a pinch of ground pepper or cinnamon to the yellow liquid formed by the mix of the eggs and the crème fraiche. Here, is a surprise : even if the liquid is at rest, the pinch of milled pepper spreads by itself at the surface of the mixture. It expands in a circular way, and within a few seconds, it covers an area equal to several times its initial one. Why does it spread like that ? What factors influence this dispersion ? I will present some experiments and mathematical models of this process.

*****     PLEASE NOTE THIS SEMINAR TAKES PLACE ON TUESDAY     *****

Reduced ODE models describing coarsening dynamics of droplets in nanometric polymer film interacting on solid substrate in the presence of large slippage at the liquid/solid interface are derived from one-dimensional lubrication equations. In the limiting case of the infinite slip length corresponding to the free suspended films a collision/absorption model then arises and is solved explicitly. The exact collision law is derived. Existence of a threshold at which the collision rates switch from algebraic to exponential ones is shown.

*****     PLEASE NOTE THIS SEMINAR TAKES PLACE ON TUESDAY     *****

*****     PLEASE NOTE THIS SEMINAR TAKES PLACE ON MONDAY     *****

Ultralow interfacial tension mixtures have interfacial tensions that are 1,000 times, or more, lower than typical oil-water systems. Despite the recent utility of ultralow interfacial tension mixtures in industry and research, quantifying the interfacial tension remains challenging. Here I describe a technique that measures ultralow interfacial tensions by magnetically deflecting paramagnetic spheres in a co-flow microfluidic device. This method involves the tuning of the distance between the co-flowing interface and the magnetic field source, and observing the behavior of the magnetic particles as they approach the liquid-liquid interface--the particles either pass through or are trapped. I demonstrate the effectiveness of this technique for measuring very low interfacial tensions by testing solutions of different surfactant concentrations, and show that the results are comparable with measurements made using a spinning drop tensiometer.

*****     PLEASE NOTE THIS SEMINAR TAKES PLACE ON MONDAY     *****

*****     PLEASE NOTE THIS SEMINAR WILL TAKE PLACE ON MONDAY 24TH JUNE 2013     *****

Energy equations describing magnetic and inertial confinement functions (ICF) are strongly coupled, time dependent non-linear PDEs. The huge disparity of the coefficients in the coupled non-linear equations brings tremendous numerical difficulties to get high resolution solutions. It results in highly ill-conditioned linear systems in each non-linear iteration. Solving the resulted non-linear systems is time-consuming which takes up to 90% in the total simulation time. Many customized numerical techniques have to be employed to get a robust and accurate solution.This talk will present an inexact Newton-Krylov-Schwarz framework to solve the problem, demonstrating how to integrate preconditioning, partial Jacobian matrix forming techniques, parallel computing techniques with the Newton-Krylov solvers to solve the challenging problem. The numerical results will be shown and other numerical problems will be mentioned.

*****     If anyone is planning to take the 11.36 train after the seminar to the NA conference in Glasgow a taxi from the Gibson building is being arranged. Please contact Jude, @email, to book a place in the taxi.     *****

The Bayesian approach to inverse problems is of paramount importance in quantifying uncertainty about the input to and the state of a system of interest given noisy observations. Herein we consider the forward problem of the forced 2D Navier Stokes equation. The inverse problem is inference of the forcing, and possibly the initial condition, given noisy observations of the velocity field. We place a prior on the forcing which is in the form of a spatially correlated temporally white Gaussian process, and formulate the inverse problem for the posterior distribution. Given appropriate spatial regularity conditions, we show that the solution is a continuous function of the forcing. Hence, for appropriately chosen spatial regularity in the prior, the posterior distribution on the forcing is absolutely continuous with respect to the prior and is hence well-defined. Furthermore, the posterior distribution is a continuous function of the data.

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This is a joint work with Andrew Stuart and Kody Law (Warwick)

*****     PLEASE NOTE THIS SEMINAR WILL COMMENCE AT 12.00     *****

I will present experimental work on collective dynamics in two different systems: (i) a collection of self propelled droplets and (ii) coupled mechanical oscillators.  

In the first part, I will talk about microswimmers made from water-in-oil emulsion droplets. Following a brief description of the swimming mechanism, I will discuss some of the collective effects that emerge in quasi 1 and 2 dimensional confinements of swimming droplets. Specifically, I dwell on hydrodynamic and volume exclusion interactions, only through which these droplets can couple their motions. 

In the second part, I will present recent results about an intriguing dynamic known as a chimera state. In the world of coupled oscillators, a chimera state is the co-existence of synchrony and asynchrony in a population of identical oscillators, which are coupled nonlocally. Following nearly 10 years of intense theoretical research, it has been an imminent question whether these chimera states exist in real systems. Recently, we built an experiment with of springs, swings and metronomes and realised, for the first time, these symmetry breaking states in a purely physical system.

*****     PLEASE NOTE THIS SEMINAR WILL COMMENCE AT 12.00     *****