Past Industrial and Applied Mathematics Seminar

6 November 2014
16:00
Matthew Wright
Abstract
Persistent homology is a tool for identifying topological features of (often high-dimensional) data. Typically, the data is indexed by a one-dimensional parameter space, and persistent homology is easily visualized via a persistence diagram or "barcode." Multi-dimensional persistent homology identifies topological features for data that is indexed by a multi-dimensional index space, and visualization is challenging for both practical and algebraic reasons. In this talk, I will give an introduction to persistent homology in both the single- and multi-dimensional settings. I will then describe an approach to visualizing multi-dimensional persistence, and the algebraic and computational challenges involved. Lastly, I will demonstrate an interactive visualization tool, the result of recent work to efficiently compute and visualize multi-dimensional persistent homology. This work is in collaboration with Michael Lesnick of the Institute for Mathematics and its Applications.
  • Industrial and Applied Mathematics Seminar
30 October 2014
16:00
Steven Dargaville
Abstract
LiFePO4 is a commercially available battery material with good theoretical discharge capacity, excellent cycle life and increased safety compared with competing Li-ion chemistries. During discharge, LiFePO4 material can undergo phase separation, between a highly and lowly lithiated form. Discharge of LiFePO4 crystals has traditionally been modelled by one-phase Stefan problems, which assume that phase separation occurs. Recent work has been using phase-field models based on the Cahn-Hilliard equation, which only phase-separates when thermodynamically favourable. In the past year or two, this work has been having considerable impact in both theoretical and experimental electrochemistry. Unfortunately, these models are very difficult to solve numerically and involve large, coupled systems of nonlinear PDEs across several different size scales that include a range of different physics and cannot be homogenised effectively. This talk will give an overview of recent developments in modelling LiFePO4 and the sort of strategies used to solve these systems numerically.
  • Industrial and Applied Mathematics Seminar
16 October 2014
16:00
Garegin Papoian
Abstract
Acto-myosin network growth and remodeling in vivo is based on a large number of chemical and mechanical processes, which are mutually coupled and spatially and temporally resolved. To investigate the fundamental principles behind the self-organization of these networks, we have developed detailed physico-chemical, stochastic models of actin filament growth dynamics, where the mechanical rigidity of filaments and their corresponding deformations under internally and externally generated forces are taken into account. Our work sheds light on the interplay between the chemical and mechanical processes, and also will highlights the importance of diffusional and active transport phenomena. For example, we showed that molecular transport plays an important role in determining the shapes of the commonly observed force-velocity curves. We also investigated the nonlinear mechano-chemical couplings between an acto-myosin network and an external deformable substrate.
  • Industrial and Applied Mathematics Seminar
19 June 2014
16:00
Pierre Degond
Abstract
We are interested in large systems of agents collectively looking for a consensus (about e.g. their direction of motion, like in bird flocks). In spite of the local character of the interactions (only a few neighbours are involved), these systems often exhibit large scale coordinated structures. The understanding of how this self-organization emerges at the large scale is still poorly understood and offer fascinating challenges to the modelling science. We will discuss a few of these issues on a selection of specific examples.
  • 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

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