Past Industrial and Applied Mathematics Seminar

22 November 2012
16:00
Abstract
We propose a model to reproduce qualitatively and quantitatively the experimental behavior obtained by the AFM techniques for the titin. Via an energetic based minimization approach we are able to deduce a simple analytical formulations for the description of the mechanical behavior of multidomain proteins, giving a physically base description of the unfolding mechanism. We also point out that our model can be inscribed in the led of the pseudo-elastic variational damage model with internal variable and fracture energy criteria of the continuum mechanics. The proposed model permits simple analytical calculations and to reproduce hard-device experimental AFM procedures. The proposed model also permits the continuum limit approximation which maybe useful to the development of a three-dimensional multiscale constitutive model for biological tissues.
• Industrial and Applied Mathematics Seminar
15 November 2012
16:00
Abstract
Ultracold atomic gases have recently proven to be enormously rich systems from the perspective of a condensed matter physicist. With the advent of optical lattices, such systems can now realise idealised model Hamiltonians used to investigate strongly correlated materials. Conversely, ultracold atomic gases can exhibit quantum phases and dynamics with no counterpart in the solid state due to their extra degrees of freedom and unique environments virtually free of dissipation. In this talk, I will discuss examples of such behaviour arising from spinor degrees of freedom on which my recent research has focused. Examples will include bosons with artificially induced spin-orbit coupling and the non-equilibrium dynamics of spinor condensates.
• Industrial and Applied Mathematics Seminar
8 November 2012
16:00
Stephen Wilson
Abstract
In this talk I shall describe two rather different, but not entirely unrelated, problems involving thin-film flow of a viscous fluid which I have found of interest and which may have some application to a number of practical situations, including condensation in heat exchangers and microfluidics. The first problem, which is joint work with Adam Leslie and Brian Duffy at the University of Strathclyde, concerns the steady three-dimensional flow of a thin, slowly varying ring of fluid on either the outside or the inside of a uniformly rotating large horizontal cylinder. Specifically, we study full-ring'' solutions, corresponding to a ring of continuous, finite and non-zero thickness that extends all the way around the cylinder. These full-ring solutions may be thought of as a three-dimensional generalisation of the full-film'' solutions described by Moffatt (1977) for the corresponding two-dimensional problem. We describe the behaviour of both the critical and non-critical full-ring solutions. In particular, we show that, while for most values of the rotation speed and the load the azimuthal velocity is in the same direction as the rotation of the cylinder, there is a region of parameter space close to the critical solution for sufficiently small rotation speed in which backflow occurs in a small region on the upward-moving side of the cylinder. The second problem, which is joint work with Phil Trinh and Howard Stone at Princeton University, concerns a rigid plate moving steadily on the free surface of a thin film of fluid. Specifically, we study two problems involving a rigid flat (but not, in general, horizontal) plate: the pinned problem, in which the upstream end of plate is pinned at a fixed position, the fluid pressure at the upstream end of the plate takes a prescribed value and there is a free surface downstream of the plate, and the free problem, in which the plate is freely floating and there are free surfaces both upstream and downstream of the plate. For both problems, the motion of the fluid and the position of the plate (and, in particular, its angle of tilt to the horizontal) depend in a non-trivial manner on the competing effects of the relative motion of the plate and the substrate, the surface tension of the free surface, and of the viscosity of the fluid, together with the value of the prescribed pressure in the pinned case. Specifically, for the pinned problem we show that, depending on the value of an appropriately defined capillary number and on the value of the prescribed fluid pressure, there can be either none, one, two or three equilibrium solutions with non-zero tilt angle. Furthermore, for the free problem we show that the solutions with a horizontal plate (i.e.\ zero tilt angle) conjectured by Moriarty and Terrill (1996) do not, in general, exist, and in fact there is a unique equilibrium solution with, in general, a non-zero tilt angle for all values of the capillary number. Finally, if time permits some preliminary results for an elastic plate will be presented. Part of this work was undertaken while I was a Visiting Fellow in the Department of Mechanical and Aerospace Engineering in the School of Engineering and Applied Science at Princeton University, Princeton, USA. Another part of this work was undertaken while I was a Visiting Fellow in the Oxford Centre for Collaborative Applied Mathematics (OCCAM), University of Oxford, United Kingdom. This publication was based on work supported in part by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
• Industrial and Applied Mathematics Seminar
1 November 2012
16:00
Peter Kramer
Abstract
Recent years have seen increasing attention to the subtle effects on intracellular transport caused when multiple molecular motors bind to a common cargo. We develop and examine a coarse-grained model which resolves the spatial configuration as well as the thermal fluctuations of the molecular motors and the cargo. This intermediate model can accept as inputs either common experimental quantities or the effective single-motor transport characterizations obtained through systematic analysis of detailed molecular motor models. Through stochastic asymptotic reductions, we derive the effective transport properties of the multiple-motor-cargo complex, and provide analytical explanations for why a cargo bound to two molecular motors moves more slowly at low applied forces but more rapidly at high applied forces than a cargo bound to a single molecular motor. We also discuss how our theoretical framework can help connect in vitro data with in vivo behavior.
• Industrial and Applied Mathematics Seminar
25 October 2012
16:00
John Hinch
Abstract
We study a thin liquid film on a vertical fibre. Without gravity, there is a Rayleigh-Plateau instability in which surface tension reduces the surface area of the initially cylindrical film. Spherical drops cannot form because of the fibre, and instead, the film forms bulges of roughly twice the initial thickness. Large bulges then grow very slowly through a ripening mechanism. A small non-dimensional gravity moves the bulges. They leave behind a thinner film than that in front of them, and so grow. As they grow into large drops, they move faster and grow faster. When gravity is stronger, the bulges grow only to finite amplitude solitary waves, with equal film thickness behind and in front. We study these solitary waves, and the effect of shear-thinning and shear-thickening of the fluid. In particular, we will be interested in solitary waves of large amplitudes, which occur near the boundary between large and small gravity. Frustratingly, the speed is only determined at the third term in an asymptotic expansion. The case of Newtonian fluids requires four terms.
• Industrial and Applied Mathematics Seminar
18 October 2012
16:00
Richard Craster
Abstract
Some striking, and potentially useful, effects in electrokinetics occur for bipolar membranes: applications are in medical diagnostics amongst other areas. The purpose of this talk is to describe the experiments, the dominant features observed and then model the phenomena: This uncovers the physics that control this process. Time-periodic reverse voltage bias across a bipolar membrane is shown to exhibit transient hysteresis. This is due to the incomplete depletion of mobile ions, at the junction between the membranes, within two adjoining polarized layers; the layer thickness depends on the applied voltage and the surface charge densities. Experiments show that the hysteresis consists of an Ohmic linear rise in the total current with respect to the voltage, followed by a decay of the current. A limiting current is established for a long period when all the mobile ions are depleted from the polarized layer. If the resulting high field within the two polarized layers is sufficiently large, water dissociation occurs to produce proton and hydroxyl travelling wave fronts which contribute to another large jump in the current. We use numerical simulation and asymptotic analysis to interpret the experimental results and to estimate the amplitude of the transient hysteresis and the water-dissociation current.
• Industrial and Applied Mathematics Seminar
11 October 2012
16:00
Martin Everett
Abstract
The use of formal mathematical models in sociology started in the 1940s and attracted mathematicians such as Frank Harary in the 1950s. The idea is to take the rather intuitive ideas described in social theory and express these in formal mathematical terms. Social network analysis is probably the best known of these and it is the area which has caught the imagination of a wider audience and has been the subject of a number of popular books. We shall give a brief over view of the field of social networks and will then look at three examples which have thrown up problems of interest to the mathematical community. We first look at positional analysis techniques and give a formulation that tries to capture the notion of social role by using graph coloration. We look at algebraic structures, properties, characterizations, algorithms and applications including food webs. Our second and related example looks at core-periphery structures in social networks. Our final example relates to what the network community refer to as two-mode data and a general approach to analyzing networks of this form. In all cases we shall look at the mathematics involved and discuss some open problems and areas of research that could benefit from new approaches and insights.
• Industrial and Applied Mathematics Seminar
14 June 2012
16:00
Abstract
The computational analysis of a mathematical model describing a complex system is often based on the following roadmap: first, an experiment is conceived, in which the measured data are (either directly or indirectly) related to the input data of the model equations; second, such equations are computationally solved to provide iconographic reconstructions of the unknown physical or physiological parameters of the system; third, the reconstructed images are utilized to validate the model or to inspire appropriate improvements. This talk will adopt such framework to investigate three applied problems, respectively in solar physics, neuroscience and physiology. The solar physics problem is concerned with the exploitation of hard X-ray data for the comprehension of energy transport mechanisms in solar flares. The neuroscientific problem is the one to model visual recognition in humans with the help of a magnetocencephalography experiment. Finally, the physiological problem investigates the kinetics of the kidney-bladder system by means of nuclear data.
• Industrial and Applied Mathematics Seminar
7 June 2012
16:00
Luciano da F. Costa
Abstract
Complex networks have been used to model almost any real-world complex systems. An especially important issue regards how to related their structure and dynamics, which contributes not only for the better understanding of such systems, but also to the prediction of important dynamical properties from specific topological features. In this talk I revise related research developed recently in my group. Particularly attention is given to the concept of accessibility, a new measurement integrating topology and dynamics, and the relationship between frequency of visits and node degree in directed modular complex networks. Analytical results are provided that allow accurate prediction of correlations between structure and dynamics in systems underlain by directed diffusion. The methodology is illustrated with respect to the macaque cortical network.
• Industrial and Applied Mathematics Seminar
31 May 2012
16:00
Ingenuin Gasser
Abstract
In this seminar we discuss the gas dynamics of chimneys, solar updraft towers and energy towers. The main issue is to discuss simple fluid dynamic models which still describe the main features of the mentioned applications. We focus first on one dimensional compressible models. Then we apply a small Mach number asymptotics to reduce to complexity and to avoid the known problems of fully compressible models in the small Mach number regime. In case of the energy tower in addition we have to model the evaporation process. Finally we obtain a much simpler fluid dynamic model which allows robust and very fast numerical simulations. We discuss the qualitative behaviour and the good agreement with expermental data (in cases such data are available).
• Industrial and Applied Mathematics Seminar