Past Industrial and Applied Mathematics Seminar

14 June 2018
16:00
to
17:30
Antonio Desimone
Abstract

Locomotion strategies employed by unicellular organism are a rich source of inspiration for studying mechanisms for shape control. They are particularly interesting because they are invisible to the naked eye, and offer surprising new solutions to the question of how shape can be controlled.

In recent years, we have studied locomotion and shape control in Euglena gracilis. This unicellular protist is particularly intriguing because it can adopt different motility strategies: swimming by flagellar propulsion, or crawling thanks to large amplitude shape changes of the whole body (a behavior known as metaboly). We will survey our most recent findings within this stream of research.

  • Industrial and Applied Mathematics Seminar
7 June 2018
16:00
to
17:30
David Fairhurst
Abstract

In laboratories around the world, scientists use magnetic stirrers to mix solutions and dissolve powders. It is well known that at high drive rates the stir bar jumps around erratically with poor mixing, leading to its nick-name 'flea'. Investigating this behaviour, we discovered a state in which the flea levitates stably above the base of the vessel, supported by magnetic repulsion between flea and drive magnet. The vertical motion is oscillatory and the angular motion a superposition of rotation and oscillation. By solving the coupled vertical and angular equations of motion, we characterised the flea’s behaviour in terms of two dimensionless quantities: (i) the normalized drive speed and (ii) the ratio of magnetic to viscous forces. However, Earnshaw’s theorem states that levitation via any arrangement of static magnets is only possible with additional stabilising forces. In our system, we find that these forces arise from the flea’s oscillations which pump fluid radially outwards, and are only present for a narrow range of Reynold's numbers. At slower, creeping flow speeds, only viscous forces are present, whereas at higher speeds, the flow reverses direction and the flea is no longer stable. We also use both the levitating and non-levitating states to measure rheological properties of the system.

  • Industrial and Applied Mathematics Seminar
31 May 2018
16:00
to
17:30
Herbert Huppert
Abstract

There are a huge number of nonlinear partial differential equations that do not have analytic solutions.   Often one can find similarity solutions, which reduce the number of independent variables, but still leads, generally, to a nonlinear equation.  This can, only sometimes, be solved analytically.  But always the solution is independent of the initial conditions.   What role do they play?   It is generally stated that the similarity  solution agrees with the (not determined) exact solution when (for some variable say t) obeys t >> t_1.   But what is  t_1?   How does it depend on the initial conditions?  How large must  t be for the similarity solution to be within 15, 10, 5, 1, 0.1, ….. percent of the real solution?   And how does this depend on the parameters and initial conditions of the problem?   I will explain how two such typical, but somewhat different, fundamental problems can be solved, both analytically and numerically,  and compare some of the results with small scale laboratory experiments, performed during the talk.  It will be suggested that many members of the audience could take away the ideas and apply them in their own special areas.

  • Industrial and Applied Mathematics Seminar
24 May 2018
16:00
to
17:30
Frederic Dias
Abstract

Statements in media about record wave heights being measured are more and more common, the latest being about a record wave of almost 24m in the Southern Ocean on 9 May 2018. We will review some of these wave measurements and the various techniques to measure waves. Then we will explain the various mechanisms that can produce extreme waves both in wave tanks and in the ocean. We will conclude by providing the mechanism that, we believe, explains some of the famous extreme waves. Note that extreme waves are not necessarily rogue waves and that rogue waves are not necessarily extreme waves.

  • Industrial and Applied Mathematics Seminar
17 May 2018
16:00
to
17:30
Professor John Lister
Abstract

The peeling of an elastic sheet away from thin layer of viscous fluid is a simply-stated and generic problem, that involves complex interactions between flow and elastic deformation on a range of length scales. 

I will illustrate the possibilities by considering theoretically and experimentally the injection and spread of viscous fluid beneath a flexible elastic lid; the injected fluid forms a blister, which spreads by peeling the lid away at the  perimeter of the blister. Among the many questions to be considered are the mechanisms for relieving the elastic analogue of the contact-line problem, whether peeling is "by bending" or "by pulling", the stability of the peeling front, and the effects of a capillary meniscus when peeling is by air injection. The result is a plethora of dynamical regimes and asymptotic scaling laws.

  • Industrial and Applied Mathematics Seminar
10 May 2018
16:00
to
17:30
Ehud Yariv
Abstract

Superhydrophobic surfaces, formed by air entrapment within the cavities of a hydrophobic solid substrate, offer a promising potential for drag reduction in small-scale flows. It turns out that low-drag configurations are associated with singular limits, which to date have typically been addressed using numerical schemes. I will discuss the application of singular perturbations to several of the canonical problems in the field. 


 

  • Industrial and Applied Mathematics Seminar
3 May 2018
16:00
to
17:30
Pedro Reis
Abstract

Elastic gridshells arise from the buckling of an initially planar grid of rods. Architectural elastic gridshells first appeared in the 1970’s. However, to date, only a limited number of examples have been constructed around the world, primarily due to the challenges involved in their structural design. Yet, elastic gridshells are highly appealing: they can cover wide spans with low self-weight, they allow for aesthetically pleasing shapes and their construction is typically simple and rapid. A more mundane example is the classic pasta strainer, which, with its remarkably simple design, is a must-have in every kitchen.

This talk will focus on the geometry-driven nature of elastic gridshells. We use a geometric model based on the theory of discrete Chebyshev nets (originally developed for woven fabric) to rationalize their actuated shapes. Validation is provided by precision experiments and rod-based simulations. We also investigate the linear mechanical response (rigidity) and the non-local behavior of these discrete shells under point-load indentation. Combining experiments, simulations, and scaling analysis leads to a master curve that relates the structural rigidity to the underlying geometric and material properties. Our results indicate that the mechanical response of elastic gridshells, and their underlying characteristic forces, are dictated by Euler's elastica rather than by shell-related quantities. The prominence of geometry that we identify in elastic gridshells should allow for our results to transfer across length scales: from architectural structures to micro/nano–1-df mechanical actuators and self-assembly systems.

  • Industrial and Applied Mathematics Seminar
26 April 2018
16:00
to
17:30
José Bico
Abstract

Tubing issues: 

- Moving a sphere in a narrow pipe

What is the force required to move an object inside a narrow elastic pipe? The constriction by the tube induces a normal force on the sphere. In the case of solid friction, the pulling force may  be simply deduced from Coulomb’s law. How does is such force modified by the addition of a lubricant? This coupled problem between elasticity and viscous flow results in a non-linear dependence of the force with the traction speed.

- Baromorphs

When a bicycle tyre is inflated the cross section of the pipe increases much more than its circumference. Can we use this effect to induce non-isotropic growth in a plate?  We developed, through standard casting techniques, flat plates imbedded with a network of channels of controlled geometry. How are such plates deformed as pressure is applied to this network? Using a simplified mechanical model, 3D complex shapes can be programmed and dynamically actuated. 

  • Industrial and Applied Mathematics Seminar
8 March 2018
16:00
to
17:30
Massimiliano Gei
Abstract

The talk originates from two studies on the dynamic properties of one-dimensional elastic quasicrystalline solids. The first one refers to a detailed investigation of scaling and self-similarity of the spectrum of an axial waveguide composed of repeated elementary cells designed by adopting the family of generalised Fibonacci substitution rules corresponding to the so-called precious means. For those, an invariant function of the circular frequency, the Kohmoto's invariant, governs self-similarity and scaling of the stop/pass band layout within defined ranges of frequencies at increasing generation index. The Kohmoto's invariant also explains the existence of particular frequencies, named canonical frequencies, associated with closed orbits on the geometrical three-dimensional representation of the invariant. The second part shows the negative refraction properties of a Fibonacci-generated quasicrystalline laminate and how the tuning of this phenomenon can be controlled by selecting the generation index of the sequence.

  • Industrial and Applied Mathematics Seminar
1 March 2018
16:00
to
17:30
Abstract

Most motile bacteria are equipped with multiple helical flagella, slender appendages whose rotation in viscous fluids allow the cells to self-propel. We highlight in this talk two consequences of hydrodynamics for bacteria. We first show how the swimming of cells with multiple flagella is enabled by an elastohydrodynamic instability. We next demonstrate how interactions between flagellar filaments mediated by the fluid govern the ability of the cells to reorient. 

  • Industrial and Applied Mathematics Seminar

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