Past Industrial and Applied Mathematics Seminar

26 April 2012
16:00
Mario di Bernardo
Abstract
In a variety of problems in engineering and applied science, the goal is to design or control a network of dynamical agents so as to achieve some desired asymptotic behaviour. Examples include consensus and rendez-vous problems in robotics, synchronization of generator angles in power grids or coordination of oscillations in bacterial populations. A pressing challenge in all of these problems is to derive appropriate analytical tools to prove convergence towards the target behaviour. Such tools are not only invaluable to guarantee the desired performance, but can also provide important guidelines for the design of decentralized control strategies to steer the collective behaviour of the network of interest in a desired manner. During this talk, a methodology for analysis and design of convergence in networks will be presented which is based on the use of a classical, yet not fully exploited, tool for convergence analysis: contraction theory. As opposed to classical methods for stability analysis, the idea is to look at convergence between trajectories of a system of interest rather that at their asymptotic convergence towards some solution of interest. After introducing the problem, a methodology will be derived based on the use of matrix measures induced by non-Euclidean norms that will be exploited to design strategies to control the collective behaviour of networks of dynamical agents. Representative examples will be used to illustrate the theoretical results.
  • Industrial and Applied Mathematics Seminar
13 April 2012
15:00
SPECIAL EVENT OCIAM joint with The Oxford Internet Institute Jure Leskovec
Abstract
TALK 1 -- social media for OII: TITLE: Computational Perspectives on the Structure and Information Flows in On-Line Networks ABSTRACT: With an increasing amount of social interaction taking place in on-line settings, we are accumulating massive amounts of data about phenomena that were once essentially invisible to us: the collective behavior and social interactions of hundreds of millions of people Analyzing this massive data computationally offers enormous potential both to address long-standing scientific questions, and also to harness and inform the design of future social computing applications: What are emerging ideas and trends? How is information being created, how it flows and mutates as it is passed from a node to node like an epidemic? We discuss how computational perspective can be applied to questions involving structure of online networks and the dynamics of information flows through such networks, including analysis of massive data as well as mathematical models that seek to abstract some of the underlying phenomena. TALK 2 -- Community detection: TITLE: Networks, Communities and the Ground-Truth ABSTRACT: Nodes in complex networks organize into communities of nodes that share a common property, role or function, such as social communities, functionally related proteins, or topically related webpages. Identifying such communities is crucial to the understanding of the structural and functional roles of networks.Current work on overlapping community detection (often implicitly) assumes that community overlaps are less densely connected than non-overlapping parts of communities. This is unnatural as it means that the more communities nodes share, the less likely it is they are linked. We validate this assumption on a diverse set of large networks and find an increasing relationship between the number of shared communities of a pair of nodes and the probability of them being connected by an edge, which means that parts of the network where communities overlap tend to be more densely connected than the non-overlapping parts of communities. Existing community detection methods fail to detect communities with such overlaps. We propose a model-based community detection method that builds on bipartite node-community affiliation networks. Our method successfully detects overlapping, non-overlapping and hierarchically nested communities. We accurately identify relevant communities in networks ranging from biological protein-protein interaction networks to social, collaboration and information networks. Our results show that while networks organize into overlapping communities, globally networks also exhibit a nested core-periphery structure, which arises as a consequence of overlapping parts of communities being more densely connected.
  • Industrial and Applied Mathematics Seminar
1 March 2012
16:00
Jamal Uddin
Abstract
The industrial prilling process is amongst the most favourite technique employed in generating monodisperse droplets. In such a process long curved jets are generated from a rotating drum which in turn breakup and from droplets. In this talk we describe the experimental set-up and the theory to model this process. We will consider the effects of changing the rheology of the fluid as well as the addition of surface agents to modify breakup characterstics. Both temporal and spatial instability will be considered as well as nonlinear numerical simulations with comparisons between experiments.
  • Industrial and Applied Mathematics Seminar
23 February 2012
16:00
Brian Sleeman
Abstract
The inverse acoustic obstacle scattering problem, in its most general form, seeks to determine the nature of an unknown scatterer from knowl- edge of its far eld or radiation pattern. The problem which is the main concern here is: If the scattering cross section, i.e the absolute value of the radiation pattern, of an unknown scatterer is known determine its shape. In this talk we explore the problem from a number of points of view. These include questions of uniqueness, methods of solution including it- erative methods, the Minkowski problem and level set methods. We con- clude by looking at the problem of acoustically invisible gateways and its connections with cloaking
  • Industrial and Applied Mathematics Seminar
16 February 2012
16:00
Thilo Gross
Abstract
A central challenge in socio-physics is understanding how groups of self-interested agents make collective decisions. For humans many insights in the underlying opinion formation process have been gained from network models, which represent agents as nodes and social contacts as links. Over the past decade these models have been expanded to include the feedback of the opinions held by agents on the structure of the network. While a verification of these adaptive models in humans is still difficult, evidence is now starting to appear in opinion formation experiments with animals, where the choice that is being made concerns the direction of movement. In this talk I show how analytical insights can be gained from adaptive networks models and how predictions from these models can be verified in experiments with swarming animals. The results of this work point to a similarity between swarming and human opinion formation and reveal insights in the dynamics of the opinion formation process. In particular I show that in a population that is under control of a strongly opinionated minority a democratic consensus can be restored by the addition of uninformed individuals.
  • Industrial and Applied Mathematics Seminar
9 February 2012
16:00
Abstract
Brittle failure through multiple cracks occurs in a wide variety of contexts, from microscopic failures in dental enamel and cleaved silicon to geological faults and planetary ice crusts. In each of these situations, with complicated stress geometries and different microscopic mechanisms, pairwise interactions between approaching cracks nonetheless produce characteristically curved fracture paths. We investigate the origins of this widely observed "en passant" crack pattern by fracturing a rectangular slab which is notched on each long side and then subjected to quasistatic uniaxial strain from the short side. The two cracks propagate along approximately straight paths until they pass each other, after which they curve and release a lens-shaped fragment. We find that, for materials with diverse mechanical properties, each curve has an approximately square-root shape, and that the length of each fragment is twice its width. We are able to explain the origins of this universal shape with a simple geometrical model.
  • Industrial and Applied Mathematics Seminar
2 February 2012
16:00
Eugene Benilov
Abstract
This work builds on the foundation laid by Benney & Timson (1980), who examined the flow near a contact line and showed that, if the contact angle is 180 degrees, the usual contact-line singularity does not arise. Their local analysis, however, does not allow one to determine the velocity of the contact line and their expression for the shape of the free boundary involves undetermined constants - for which they have been severely criticised by Ngan & Dussan V. (1984). As a result, the ideas of Benny & Timson (1980) have been largely forgotten. The present work shows that the criticism of Ngan & Dussan V. (1984) was, in fact, unjust. We consider a two-dimensional steady Couette flow with a free boundary, for which the local analysis of Benney & Timson (1980) can be complemented by an analysis of the global flow (provided the slope of the free boundary is small, so the lubrication approximation can be used). We show that the undetermined constants in the solution of Benney & Timson (1980) can all be fixed by matching their local solution to the global one. The latter also determines the contact line's velocity, which we compute among other characteristics of the global flow.
  • Industrial and Applied Mathematics Seminar
26 January 2012
16:00
Yichao Zhu
Abstract
Understanding the fatigue of metals under cyclic loads is crucial for some fields in mechanical engineering, such as the design of wheels of high speed trains and aero-plane engines. Experimentally it has been found that metal fatigue induced by cyclic loads is closely related to a ladder shape pattern of dislocations known as a persistent slip band (PSB). In this talk, a quantitative description for the formation of PSBs is proposed from two angles: 1. the motion of a single dislocation analised by using asymptotic expansions and numerical simulations; 2. the collective behaviour of a large number of dislocations analised by using a method of multiple scales.
  • Industrial and Applied Mathematics Seminar
19 January 2012
16:00
Russell Davies
Abstract
It is an inherent premise in Boltzmann's formulation of linear viscoelasticity, that for shear deformations at constant pressure and constant temperature, every material has a unique continuous relaxation spectrum. This spectrum defines the memory kernel of the material. Only a few models for representing the continuous spectrum have been proposed, and these are entirely empirical in nature. Extensive laboratory time is spent worldwide in collecting dynamic data from which the relaxation spectra of different materials may be inferred. In general the process involves the solution of one or more exponentially ill-posed inverse problems. In this talk I shall present rigorous models for the continuous relaxation spectrum. These arise naturally from the theory of continuous wavelet transforms. In solving the inverse problem I shall discuss the role of sparsity as one means of regularization, but there is also a secondary regularization parameter which is linked, as always, to resolution. The topic of model-induced super-resolution is discussed, and I shall give numerical results for both synthetic and real experimental data. The talk is based on joint work with Neil Goulding (Cardiff University).
  • Industrial and Applied Mathematics Seminar

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