Past Seminars › Seminar Series

Industrial and Applied Mathematics Seminar (past)

Thu, 16/05
16:00 		Ed Tarleton (Material Science Oxford) Industrial and Applied Mathematics Seminar Add to calendar DH 1st floor SR
Modelling size effects in microcantilevers
Focused ion beam milling allows small scale single crystal cantilevers to be produced with cross-sectional dimensions on the order of microns which are then tested using a nanoindenter allowing both elastic and plastic materials properties to be measured. EBSD allows these cantilevers to be milled from any desired crystal orientation. Micro-cantilever bending experiments suggest that sufficiently smaller cantilevers are stronger, and the observation is believed to be related to the effect of the neutral axis on the evolution of the dislocation structure. A planar model of discrete dislocation plasticity was used to simulate end-loaded cantilevers to interpret the behaviour observed in the experiments. The model allowed correlation of the simulated dislocation structure to the experimental load displacement curve and GND density obtained from EBSD. The planar model is sufficient for identifying the roles of the neutral axis and source spacing in the observed size effect, and is particularly appropriate for comparisons to experiments conducted on crystals orientated for plane strain deformation. The effect of sample dimensions and dislocation source density are investigated and compared to small scale mechanical tests conducted on Titanium and Zirconium.
Thu, 09/05
16:00 		Chiara Daraio (ETH, Zurich) Industrial and Applied Mathematics Seminar Add to calendar DH 1st floor SR
Discrete nonlinear dynamics and the design of new materials
We develop a physical understanding of how stress waves propagate in uniform, heterogeneous, ordered and disordered media composed of discrete granular particles. We exploit this understanding to create experimentally novel materials and devices at different scales, (for example, for application in energy absorption, acoustic imaging and energy harvesting). We control the constitutive behavior of the new materials selecting the particles’ geometry, their arrangement and materials properties. One-dimensional chains of particles exhibit a highly nonlinear dynamic response, allowing a completely new type of wave propagation that has opened the door to exciting fundamental physical observations (i.e., compact solitary waves, energy trapping phenomena, and acoustic rectification). This talk will focus on energy localization and redirection in one-, two- and three-dimensional systems. (For an extended abstract please contact Ruth preston@maths.ox.ac.uk).
Thu, 02/05
16:00 		Richard Katz (Oxford) Industrial and Applied Mathematics Seminar Add to calendar DH 1st floor SR
Consequences of Viscous Anisotropy in Partially Molten Rocks
In partially molten regions of Earth, rock and magma coexist as a two-phase aggregate in which the solid grains of rock form a viscously deformable matrix. Liquid magma resides within the permeable network of pores between grains. Deviatoric stress causes the distribution of contact area between solid grains to become anisotropic; this causes anisotropy of the matrix viscosity. The anisotropic viscosity tensor couples shear and volumetric components of stress/strain rate. This coupling, acting over a gradient in shear stress, causes segregation of liquid and solid. Liquid typically migrates toward higher shear stress, but under specific conditions, the opposite can occur. Furthermore, in a two-phase aggregate with a porosity-weakening viscosity, matrix shear causes porosity perturbations to grow into a banded structure. We show that viscous anisotropy reduces the angle between these emergent high-porosity features and the shear plane. This is consistent with lab experiments.
Thu, 25/04
16:00 		Angel Ramos (Universidad Complutense de Madrid) Industrial and Applied Mathematics Seminar Add to calendar Gibson Grd floor SR
A mathematical approach to the mathematical modelling of Lithium-ion batteries
In this talk we will discuss the mathematical modelling of the performance of Lithium-ion batteries. A mathematical model based on a macro-homogeneous approach developed by John Neuman will be presented. The uniqueness and existence of solution of the corresponding problem will be also discussed.
Thu, 07/03
16:00 		Gert Van Der Heijden (UCL London) Industrial and Applied Mathematics Seminar Add to calendar DH 1st floor SR
Theory of equilibria of elastic braids with applications to DNA supercoiling
We formulate a new theory for equilibria of 2-braids, i.e., structures formed by two elastic rods winding around each other in continuous contact and subject to a local interstrand interaction. Unlike in previous work no assumption is made on the shape of the contact curve. The theory is developed in terms of a moving frame of directors attached to one of the strands with one of the directors pointing to the position of the other strand. The constant-distance constraint is automatically satisfied by the introduction of what we call braid strains. The price we pay is that the potential energy involves arclength derivatives of these strains, thus giving rise to a second-order variational problem. The Euler-Lagrange equations for this problem (in Euler-Poincare form) give balance equations for the overall braid force and moment referred to the moving frame as well as differential equations that can be interpreted as effective constitutive relations encoding the effect that the second strand has on the first as the braid deforms under the action of end loads. Hard contact models are used to obtain the normal contact pressure between strands that has to be non-negative for a physically realisable solution without the need for external devices such as clamps or glue to keep the strands together. The theory is first illustrated by a few simple examples and then applied to several problems that require the numerical solution of boundary-value problems. Both open braids and closed braids (links and knots) are considered and current applications to DNA supercoiling are discussed.
Thu, 28/02
16:00 		Emmanuel Villermaux (IRPHE France) Industrial and Applied Mathematics Seminar Add to calendar DH 1st floor SR
Breaking Threads and Fragmenting Necklaces
Abstract available upon request - Ruth Preston preston@maths.ox.ac.uk
Thu, 21/02
16:00 		Ben MacArthur (Southampton) Industrial and Applied Mathematics Seminar Add to calendar DH 1st floor SR
Feedback and embryonic stem cell fate commitment
Self-renewal and pluripotency of mouse embryonic stem (ES) cells are controlled by a complex transcriptional regulatory network (TRN) which is rich in positive feedback loops. A number of key components of this TRN, including Nanog, show strong temporal expression fluctuations at the single cell level, although the precise molecular basis for this variability remains unknown. In this talk I will discuss recent work which uses a genetic complementation strategy to investigate genome-wide mRNA expression changes during transient periods of Nanog down-regulation. Nanog removal triggers widespread changes in gene expression in ES cells. However, we found that significant early changes in gene expression were reversible upon re-induction of Nanog, indicating that ES cells initially adopt a flexible “primed” state. Nevertheless, these changes rapidly become consolidated irreversible fate decisions in the continued absence of Nanog. Using high-throughput single cell transcriptional profiling we observed that the early molecular changes are both stochastic and reversible at the single cell level. Since positive feedback commonly gives rise to phenotypic variability, we also sought to determine the role of feedback in regulating ES cell heterogeneity and commitment. Analysis of the structure of the ES cell TRN revealed that Nanog acts as a feedback “linchpin”: in its presence positive feedback loops are active and the extended TRN is self-sustaining; while in its absence feedback loops are weakened, the extended TRN is no longer self-sustaining and pluripotency is gradually lost until a critical “point-of-no-return” is reached. Consequently, fluctuations in Nanog expression levels transiently activate different sub-networks in the ES cell TRN, driving transitions between a (Nanog expressing) feedback-rich, robust, self-perpetuating pluripotent state and a (Nanog-diminished), feedback-depleted, differentiation-sensitive state. Taken together, our results indicate that Nanog- dependent feedback loops play a central role in controlling both early fate decisions at the single cell level and cell-cell variability in ES cell populations.
Thu, 14/02
16:00 		David Abrahams (Manchester) Industrial and Applied Mathematics Seminar Add to calendar DH 1st floor SR
Effective material properties of complex composite materials with application to wave propagation
Motivated by industrial and biological applications, the Waves Group at Manchester has in recent years been interested in developing methods for obtaining the effective properties of complex composite materials. As time allows we shall discuss a number of issues, such as differences between composites with periodic and aperiodic distributions of inclusions, and modelling of nonlinear composites.
Thu, 07/02
16:00 		Ian Hewitt (Oxford) Industrial and Applied Mathematics Seminar Add to calendar DH 1st floor SR
Fluid injection beneath an elastic lid : sixth-order thin-film problems
I discuss models for the planar spreading of a viscous fluid between an elastic lid and an underlying rigid plane. These have application to the growth of magmatic intrusions, as well as to other industrial and biological processes; simple experiments of an inflated blister will be used for motivation. The height of the fluid layer is described by a sixth order non-linear diffusion equation, analogous to the fourth order equation that describes surface tension driven spreading. The dynamics depend sensitively on the conditions at the contact line, where the sheet is lifted from the substrate and where some form of regularization must be applied to the model. I will explore solutions with a pre-wetted film or a constant-pressure fluid lag, for flat and inclined planes, and compare with the analogous surface tension problems.
Thu, 31/01
16:00 		Yi Bin Fu (Keele, UK) Industrial and Applied Mathematics Seminar Add to calendar DH 1st floor SR
Provisional (A mathematical theory for aneurysm initiation)
When a rubber membrane tube is inflated, a localized bulge will initiate when the internal pressure reaches a certain value known as the initiation pressure. As inflation continues, the bulge will grow in diameter until it reaches a maximum size, after which the bulge will spread in both directions. This simple phenomenon has previously been studied both experimentally, numerically, and analytically, but surprisingly it is only recently that the character of the initiation pressure has been fully understood. In this talk, I shall first show how the entire inflation process can be described analytically, and then apply the ideas to the mathematical modelling of aneurysm initiation in human arteries.
Thu, 24/01
16:00 		Elie Raphael (ESPCI) Industrial and Applied Mathematics Seminar Add to calendar DH 1st floor SR
Moving at the air-water interface
It is generally believed that in order to generate waves, a small object (like an insect) moving at the air-water surface must exceed the minimum wave speed (about 23 centimeters per second). We show that this result is only valid for a rectilinear uniform motion, an assumption often overlooked in the literature. In the case of a steady circular motion (a situation of particular importance for the study of whirligig beetles), we demonstrate that no such velocity threshold exists and that even at small velocities a finite wave drag is experienced by the object. This wave drag originates from the emission of a spiral-like wave pattern. The results presented should be important for a better understanding of the propulsion of water-walking insects. For example, it would be very interesting to know if whirligig beetles can take advantage of such spirals for echolocation purposes.
Thu, 17/01
16:00 		Jared Tanner (Oxford University) Industrial and Applied Mathematics Seminar Add to calendar DH 1st floor SR
Compressed sensing and matrix completion: exploiting simplicity in data
The essential information contained in most large data sets is small when compared to the size of the data set. That is, the data can be well approximated using relatively few terms in a suitable transformation. Compressed sensing and matrix completion show that this simplicity in the data can be exploited to reduce the number of measurements. For instance, if a vector of length $ N $ can be represented exactly using $ k $ terms of a known basis then $ 2k\log(N/k) $ measurements is typically sufficient to recover the vector exactly. This can result in dramatic time savings when k << N, which is typical in many applications such as medical imaging. As another example consider an $ m \times n $ matrix of rank $ r $. This class of matrices has $ r(m+n-r) $ degrees of freedom. Computationally simple and efficient algorithms are able to recover random rank $ r $ matrices from only about 10 measurements than the number of degrees of freedom.
Thu, 29/11/2012
16:00 		Jesús San Martin (Universidad Politécnica de Madrid) Industrial and Applied Mathematics Seminar Add to calendar Gibson Grd floor SR
Composition law of periodic orbits in discrete dynamical systems
The periodic orbits of a discrete dynamical system can be described as permutations. We derive the composition law for such permutations. When the composition law is given in matrix form the composition of different periodic orbits becomes remarkably simple. Composition of orbits in bifurcation diagrams and decomposition law of composed orbits follow directly from that matrix representation.
Thu, 22/11/2012
16:00 		Giuseppe Saccomandi (Universita' degli Studi Perugia) Industrial and Applied Mathematics Seminar Add to calendar DH 1st floor SR
An Energy model for the mechanically driven unfolding of titin macromolecules
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.
Thu, 15/11/2012
16:00 		Ryan Barnett (Imperial College London) Industrial and Applied Mathematics Seminar Add to calendar DH 1st floor SR
Multi-Component Ultracold Quantum Gases: Themes from Condensed Matter Physics and Beyond
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.
Thu, 08/11/2012
16:00 		Stephen Wilson (University of Strathclyde) Industrial and Applied Mathematics Seminar Add to calendar DH 1st floor SR
Fluid Rings and Floating Plates
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).
Thu, 01/11/2012
16:00 		Peter Kramer (RPI) Industrial and Applied Mathematics Seminar Add to calendar DH 1st floor SR
Bridging Scales in Molecular Motor Models: From Single to Multiple Motor Systems
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.
Thu, 25/10/2012
16:00 		John Hinch (Cambridge DAMTP) Industrial and Applied Mathematics Seminar Add to calendar DH 1st floor SR
Large drops of a power-law fluid in a thin film on a vertical fibre
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.
Thu, 18/10/2012
16:00 		Richard Craster (Imperial College London) Industrial and Applied Mathematics Seminar Add to calendar DH 1st floor SR
Ion transport and non-equilibrium hysteresis in bipolar membranes - by Richard Craster (joint work with O. Matar, D. Conroy from Imperial College, Chemical Engineering and L. Cheng, H-C Chang from Notre-Dame, Chemical Engineering and Microfluidics Lab)
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.
Thu, 11/10/2012
16:00 		Martin Everett (University of Manchester) Industrial and Applied Mathematics Seminar Add to calendar DH 1st floor SR
Mathematical sociology is not an oxymoron
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.

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

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