Past Industrial and Applied Mathematics Seminar

25 April 2013
16:00
Abstract
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.
  • Industrial and Applied Mathematics Seminar
7 March 2013
16:00
Gert Van Der Heijden
Abstract
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.
  • Industrial and Applied Mathematics Seminar
21 February 2013
16:00
Ben MacArthur
Abstract
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.
  • Industrial and Applied Mathematics Seminar
14 February 2013
16:00
David Abrahams
Abstract
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.
  • Industrial and Applied Mathematics Seminar
7 February 2013
16:00
Ian Hewitt
Abstract
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.
  • Industrial and Applied Mathematics Seminar
31 January 2013
16:00
Yi Bin Fu
Abstract
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.
  • Industrial and Applied Mathematics Seminar
24 January 2013
16:00
Elie Raphael
Abstract
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.
  • Industrial and Applied Mathematics Seminar
17 January 2013
16:00
Jared Tanner
Abstract
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% more measurements than the number of degrees of freedom.
  • Industrial and Applied Mathematics Seminar
29 November 2012
16:00
Abstract
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.
  • Industrial and Applied Mathematics Seminar

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