Past Industrial and Applied Mathematics Seminar

12 June 2014
16:00
Frank Smith
Abstract
The talk is on impacts, penetrations and lift-offs involving bodies and fluids, with applications that range from aircraft and ship safety and our tiny everyday scales of splashing and washing, up to surface movements on Mars. Several studies over recent years have addressed different aspects of air-water effects and fluid-body interplay theoretically. Nonlinear interactions and evolutions are key here and these are to be considered in the presentation. Connections with experiments will also be described.
  • Industrial and Applied Mathematics Seminar
5 June 2014
16:00
Abstract
The synthesis of complex-shaped colloids and nanoparticles has recently undergone unprecedented advancements. It is now possible to manufacture particles shaped as dumbbells, cubes, stars, triangles, and cylinders, with exquisite control over the particle shape. How can particle geometry be exploited in the context of capillarity and surface-tension phenomena? This talk examines this question by exploring the case of complex-shaped particles adsorbed at the interface between two immiscible fluids, in the small Bond number limit in which gravity is not important. In this limit, the "Cheerio's effect" is unimportant, but interface deformations do emerge. This drives configuration dependent capillary forces that can be exploited in a variety of contexts, from emulsion stabilisation to the manufacturing of new materials. It is an opportunity for the mathematics community to get involved in this field, which offers ample opportunities for careful mathematical analysis. For instance, we find that the mathematical toolbox provided by 2D potential theory lead to remarkably good predictions of the forces and torques measured experimentally by tracking particle pairs of cylinders and ellipsoids. New research directions will also be mentioned during the talk, including elasto-capillary interactions and the simulation of multiphase composites.
  • Industrial and Applied Mathematics Seminar
29 May 2014
16:00
Ben Leimkuhler
Abstract
Molecular modelling has become a valuable tool and is increasingly part of the standard methodology of chemistry, physics, engineering and biology. The power of molecular modelling lies in its versatility: as potential energy functions improve, a broader range of more complex phenomena become accessible to simulation, but much of the underlying methodology can be re-used. For example, the Verlet method is still the most popular molecular dynamics scheme for constant energy molecular dynamics simulations despite it being one of the first to be proposed for the purpose. One of the most important challenges in molecular modelling remains the computation of averages with respect to the canonical Gibbs (constant temperature) distribution, for which the Verlet method is not appropriate. Whereas constant energy molecular dynamics prescribes a set of equations (Newton's equations), there are many alternatives for canonical sampling with quite different properties. The challenge is therefore to identify formulations and numerical methods that are robust and maximally efficient in the computational setting. One of the simplest and most effective methods for sampling is based on Langevin dynamics which mimics coupling to a heat bath by the incorporation of random forces and an associated dissipative term. Schemes for Langevin dynamics simulation may be developed based on the familiar principle of splitting. I will show that the invariant measure ('long term') approximation may be strongly affected by a simple re-ordering of the terms of the splitting. I will describe a transition in weak numerical order of accuracy that occurs (in one case) in the t->infty limit. I will also entertain some more radical suggestions for canonical sampling, including stochastic isokinetic methods that enable the use of greatly enlarged timesteps for expensive but slowly-varying force field components.
  • Industrial and Applied Mathematics Seminar
22 May 2014
16:00
Davide Bigoni
Abstract
A perturbative method is introduced to analyze shear bands formation and development in ductile solids subject to large strain. Experiments on discrete systems made up of highly-deformable elements [1] confirm the validity of the method and suggest that an elastic structure can be realized buckling for dead, tensile loads. This structure has been calculated, realized and tested and provides the first example of an elastic structure buckling without elements subject to compression [2]. The perturbative method introduced for the analysis of shear bands can be successfuly employed to investigate other material instabilities, such as for instance flutter in a frictional, continuum medium [3]. In this context, an experiment on an elastic structure subject to a frictional contact shows for the first time that a follower load can be generated using dry friction and that this load can induce flutter instability [4]. The perturbative approach may be used to investigate the strain state near a dislocation nucleated in a metal subject to a high stress level [5]. Eshelby forces, similar to those driving dislocations in solids, are analyzed on elastic structures designed to produce an energy release and therefore to evidence configurational forces. These structures have been realized and they have shown unexpected behaviours, which opens new perspectives in the design of flexible mechanisms, like for instance, the realization of an elastic deformable scale [6]. [1] D. Bigoni, Nonlinear Solid Mechanics Bifurcation Theory and Material Instability. Cambridge Univ. Press, 2012, ISBN:9781107025417. [2] D. Zaccaria, D. Bigoni, G. Noselli and D. Misseroni Structures buckling under tensile dead load. Proc. Roy. Soc. A, 2011, 467, 1686. [3] A. Piccolroaz, D. Bigoni, and J.R. Willis, A dynamical interpretation of flutter instability in a continuous medium. J. Mech. Phys. Solids, 2006, 54, 2391. [4] D. Bigoni and G. Noselli Experimental evidence of flutter and divergence instabilities induced by dry friction. J. Mech. Phys. Solids,2011,59,2208. [5] L. Argani, D. Bigoni, G. Mishuris Dislocations and inclusions in prestressed metals. Proc. Roy. Soc. A, 2013, 469, 2154 20120752. [6] D. Bigoni, F. Bosi, F. Dal Corso and D. Misseroni, Instability of a penetrating blade. J. Mech. Phys. Solids, 2014, in press.
  • Industrial and Applied Mathematics Seminar
15 May 2014
16:00
Ramon Grima
Abstract
Several experimental studies have shown that the abundance distributions of proteins in a population of isogenic cells may display multiple distinct maxima. Each of these maxima may be associated with a subpopulation of a particular phenotype, the quantification of which is important for understanding cellular decision-making. I will present a novel methodology which allows us to quantify multi-modal gene expression distributions and single cell power spectra in gene regulatory networks. The method is based on an extension of the linear noise approximation; in particular we rigorously show that, in the limit of slow promoter dynamics, these distributions can be systematically approximated as a mixture of Gaussian components. The resulting closed-form approximation provides a practical tool for studying complex nonlinear gene regulatory networks that have thus far been amenable only to stochastic simulation. I will demonstrate the applicability of our approach to several examples and discuss some new dynamical characteristics e.g., how the interplay of transcriptional and translational regulation can be exploited to control the multimodality of gene expression distributions in two-promoter networks and how genetic oscillators can display concerted noise-induced bimodality and noise-induced oscillations.
  • Industrial and Applied Mathematics Seminar
8 May 2014
16:00
Jonathan Ward
Abstract
Adaptive network models, in which node states and network topology coevolve, arise naturally in models of social dynamics that incorporate homophily and social influence. Homophily relates the similarity between pairs of agents' states to their network coupling strength, whilst social influence causes the convergence of coupled agents' states. In this talk, I will describe a deterministic adaptive network model of attitude formation in social groups that incorporates these effects, and in which the attitudinal dynamics are represented by an activator-inhibitor process. I will show that consensus, corresponding to all nodes adopting the same attitudinal state and being fully connected, may destabilise via Turing instability, giving rise to chaotic dynamics. For the case where there are just two agents, I will illustrate, using numerical continuation, how such chaotic dynamics arise.
  • Industrial and Applied Mathematics Seminar
1 May 2014
16:00
Mary Lou Zeeman
Abstract
One of the things sustainability applications have in common with industrial applications is their close connection with decision-making and policy. We will discuss how a decision-support viewpoint may inspire new mathematical questions. For example, the concept of resilience (of ecosystems, food systems, communities, economies, etc) is often described as the capacity of a system to withstand disturbance and retain its functional characteristics. This has several familiar mathematical interpretations, probing the interaction between transient dynamics and noise. How does a focus on resilience change the modeling, dynamical and policy questions we ask? I look forward to your ideas and discussion.
  • Industrial and Applied Mathematics Seminar
13 March 2014
16:00
Marcus Roper
Abstract
Familiar species; humans, mammals, fish, reptiles and plants represent only a razor’s edge of the Earth’s immense biodiversity. Most of the Earth’s multicellular species lie buried in soil, inside of plants, and in the undergrowth, and include millions of unknown species, almost half of which are thought to be fungi. Part of the amazing success of fungi may be the elegant solutions that they have evolved to the problems of dispersing, growing and adapting to changing environments. I will describe how we using both math modeling and experiments to discover some of these solutions. I will focus on (i) how cytoplasmic mixing enables some species to tolerate internal genetic diversity, making them better pathogens and more adaptable, and (ii) how self-organization of these flows into phases of transport and stasis enables cells to function both as transport conduits, and to perform other functions like growth and secretion.
  • Industrial and Applied Mathematics Seminar
6 March 2014
16:00
Beatrice Pelloni
Abstract
In this talk, I will discuss the effect of boundary conditions on the solvability of PDEs that have formally an integrable structure, in the sense of possessing a Lax pair. Many of these PDEs arise in wave propagation phenomena, and boundary value problems for these models are very important in applications. I will discuss the extent to which general approaches that are successful for solving the initial value problem extend to the solution of boundary value problem. I will survey the solution of specific examples of integrable PDE, linear and nonlinear. The linear theory is joint work with David Smith. For the nonlinear case, I will discuss boundary conditions that yield boundary value problems that are fully integrable, in particular recent joint results with Thanasis Fokas and Jonatan Lenells on the solution of boundary value problems for the elliptic sine-Gordon equation.
  • Industrial and Applied Mathematics Seminar
27 February 2014
16:00
Michael Dallaston
Abstract
Two-dimensional viscous fluid flow problems come about either because of a thin gap geometry (Hele-Shaw flow) or plane symmetry (Stokes flow). Such problems can also involve free boundaries between different fluids, and much has been achieved in this area, including by many at Oxford. In this seminar I will discuss some new results in this field. Firstly I will talk about some of the results of my PhD on contracting inviscid bubbles in Hele-Shaw flow, in particular regarding the effects of surface tension and kinetic undercooling on the free boundary. When a bubble contracts to a point, these effects are dominant, and lead to a menagerie of possible extinction shapes. This limiting problem is a generalisation of the curve shortening flow equation from the study of geometric PDEs. We are currently exploring properties of this generalised flow rule. Secondly I will discuss current work on applying a free boundary Stokes flow model to the evolution of subglacial water channels. These channels are maintained by the balance between inward creep of ice and melting due to the flow of water. While these channels are normally modelled as circular or semicircular in cross-section, the inward creep of a viscous fluid is unstable. We look at some simplistic viscous dissipation models and the effect they have on the stability of the channel shape. Ultimately, a more realistic turbulent flow model is needed to understand the morphology of the channel walls.
  • Industrial and Applied Mathematics Seminar

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