Past 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
22 February 2018
16:00
to
17:30
Abstract

What if one desires to have a World perfectly slippery to water? What are the strategies that can be adopted? And how can smart slippery surfaces be created? In this seminar, I will outline approaches to creating slippery surfaces, which all involve reducing or removing droplet contact with the solid, whilst still supporting the droplet. The first concept is to decorate the droplet surface with particles, thus creating liquid marbles and converting the droplet-solid contact into a solid-solid contact. The second concept is to use the Leidenfrost effect to instantly vaporize a layer of water, thus creating a film of vapor and converting the droplet-solid contact into vapor-solid contact. The third concept is to infuse oil into the surface, thus creating a layer of oil and converting the droplet-solid contact into a lubricant-solid contact. I will also explain how we design such to have smart functionality whilst retaining and using the mobility of contact lines and droplets. I will show how Leidenfrost levitation can lead to new types of heat engines [1], how a microsystems approach to the Leidenfrost effect can reduce energy input and lead to a new type of droplet microfluidics [2] (Fig. 1a) and how liquid diodes can be created [3]. I will explain how lubricant impregnated surfaces lead to apparent contact angles [4] and how the large retained footprint of the droplet allows droplet transport and microfluidics using energy coupled via a surface acoustic wave (SAW) [5]. I will argue that droplets confined between reconfigurable slippery boundaries can be continuously translated in an energy invariant manner [6] (Fig. 1b). I will show that a droplet Cheerios effect induced by the menisci arising from structuring the underlying lubricated surface or by droplets in close proximity to each other can be used to guide and position droplets [7] (Fig. 1c). Finally, I will show that active control of droplet spreading by electric field induced control of droplet spreading, via electrowetting or dielectrowetting, can be achieved with little hysteresis [8] and can be a new method to investigate the dewetting of surfaces [9].

Figure 1 Transportation and positioning of droplets using slippery surfaces: (a) Localized Leidenfrost effect, (b) Reconfigurable boundaries, and (c) Droplet Cheerio’s effect.

Acknowledgements The financial support of the UK Engineering & Physical Sciences Research Council (EPSRC) and Reece Innovation ltd is gratefully acknowledged. Many collaborators at Durham, Edinburgh, Nottingham Trent and Northumbria Universities were instrumental in the work described.

[1] G.G. Wells, R. Ledesma-Aguilar, G. McHale and K.A. Sefiane, Nature Communications, 2015, 6, 6390.

[2] L.E. Dodd, D. Wood, N.R. Geraldi, G.G. Wells, et al., ACS Applied & Materials Interfaces, 2016, 8, 22658.

[3] J. Li, X. Zhou , J. Li, L. Che, J. Yao, G. McHale, et al., Science Advances, 2017, 3, eaao3530.

[4] C. Semprebon, G. McHale, and H. Kusumaatmaja, Soft Matter, 2017, 13, 101.

[5] J.T. Luo, N.R. Geraldi, J.H. Guan, G. McHale, et al., Physical Review Applied, 2017, 7, 014017.

[6] É. Ruiz-Gutiérrez, J.H. Guan, B.B. Xu, G. McHale, et al., Physical Review Letters, 2017, 118, 218003.

[7] J.H. Guan, É. Ruiz-Gutiérrez, B.B. Xu, D. Wood, G. McHale, et al., Soft Matter, 2017, 13, 3404.

[8] Z. Brabcová, G. McHale, G.G. Wells, et al., Applied Physics Letters, 2017, 110, 121603.

[9] A.M.J. Edwards, R. Ledesma-Aguilar, et al., Science Advances, 2016, 2, e1600183

  • Industrial and Applied Mathematics Seminar
15 February 2018
16:00
to
17:30
Abstract

A polymer, or microscopic elastic filament, is often modelled as a linear chain of rigid bodies interacting both with themselves and a heat bath. Then the classic notions of persistence length are related to how certain correlations decay with separation along the chain. I will introduce these standard notions in mathematical terms suitable for non specialists, and describe the standard results that apply in the simplest cases of wormlike chain models that have a straight, minimum energy (or ground or intrinsic) shape. Then I will introduce an appropriate  splitting of a matrix recursion in the group SE(3) which deconvolves the distinct effects of stiffness and intrinsic shape in the more complicated behaviours of correlations that arise when the polymer is not intrinsically straight. The new theory will be illustrated by fully implementing it within a simple sequence-dependent rigid base pair model of DNA. In that particular context, the persistence matrix factorisation generalises and justifies the prior scalar notions of static and dynamic persistence lengths.

  • Industrial and Applied Mathematics Seminar
8 February 2018
16:00
to
17:30
Nicolas Vandewalle
Abstract

When soft ferromagnetic particles are suspended at air-water interfaces in the presence of a vertical magnetic field, dipole-dipole repulsion competes with capillary attraction such that 2d structures self-assemble. The complex arrangements of such floating bodies are emphasized. The equilibrium distance between particles exhibits hysteresis when the applied magnetic field is modified. Irreversible processes are evidenced. By adding a horizontal and oscillating magnetic field, periodic deformations of the assembly are induced. We show herein that collective particle motions induce locomotion at low Reynolds number. The physical mechanisms and geometrical ingredients behind this cooperative locomotion are identified. These physical mechanisms can be exploited to much smaller scales, offering the possibility to create artificial and versatile microscopic swimmers.

Moreover, we show that it is possible to generate complex structures that are able to capture particles, perform cargo transport, fluid mixing, etc.

  • Industrial and Applied Mathematics Seminar
1 February 2018
16:00
to
17:30
Renaud Lambiotte
Abstract

In this talk, I will present some recent results exploring the connections between dynamical systems and network science. I will particularly focus on large-scale structures and their dynamical interpretation. Those may correspond to communities/clusters or classes of dynamically equivalent nodes. If time allows, I will also present results where the underlying network structure is unknown and where communities are directly inferred from time series observed on the nodes.

 

  • Industrial and Applied Mathematics Seminar
25 January 2018
16:00
to
17:30
Abstract

How do organisms cope with cellular variability to achieve well-defined morphologies and architectures? We are addressing this question by combining experiments with live plants and analyses of (stochastic) models that integrate cell-cell communication and tissue mechanics. During the talk, I will survey our results concerning plant architecture (phyllotaxis) and organ morphogenesis.

  • Industrial and Applied Mathematics Seminar
18 January 2018
16:00
to
17:30
James Gleeson
Abstract

Network models may be applied to describe many complex systems, and in the era of online social networks the study of dynamics on networks is an important branch of computational social science.  Cascade dynamics can occur when the state of a node is affected by the states of its neighbours in the network, for example when a Twitter user is inspired to retweet a message that she received from a user she follows, with one event (the retweet) potentially causing further events (retweets by followers of followers) in a chain reaction. In this talk I will review some simple models that can help us understand how social contagion (the spread of cultural fads and the viral diffusion of information) depends upon the structure of the social network and on the dynamics of human behaviour. Although the models are simple enough to allow for mathematical analysis, I will show examples where they can also provide good matches to empirical observations of cascades on social networks.

  • Industrial and Applied Mathematics Seminar
6 December 2017
11:30
to
13:00
Yuli Chashechkin
Abstract

Using synchronized high-speed video camera, hydrophone and microphone we investigated flow patterns, the impact and secondary sound pulses emitted by oscillating bubbles. On the submerging  drop found short capillary waves produced by small secondary impact droplets. Picturesque filament and grid structures produced by colour drop of mixing fluid registered on the surface of the cavity and crown. Physical model includes discussion of the potential surface energy effects.

  • Industrial and Applied Mathematics Seminar
30 November 2017
16:00
to
17:30
Giuseppe Zurlo
Abstract

Inelastic surface growth associated with continuous creation of incompatibility on the boundary of an evolving body is behind a variety of both natural processes (embryonic development,  tree growth) and technological processes (dam construction, 3D printing). Despite the ubiquity of such processes, the mechanical aspects of surface growth are still not fully understood. In this talk we present  a new approach to surface growth that allows one to address inelastic effects,  path dependence of the growth process and the resulting geometric frustration. In particular, we show that incompatibility developed during deposition can be fine-tuned to ensure a particular behaviour of the system in physiological (or working) conditions. As an illustration, we compute an explicit deposition protocol aimed at "printing" arteries, that guarantees the attainment of desired stress distributions in physiological conditions. Another illustration is the growth starategy for explosive plants, allowing a complete release of residual elastic energy with a single cut.

  • Industrial and Applied Mathematics Seminar

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