Past 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
23 November 2017
16:30
Alexander Bradley
Abstract

It is thought that the hairy legs of water walking arthropods are able to remain clean and dry because the flexibility of the hairs spontaneously moves drops off the hairs. We present a mathematical model of this bending-induced motion, or bendotaxis, and study how it performs for wetting and non-wetting drops. Crucially, we show that both wetting and non-wetting droplets move in the same direction (using physical arguments and numerical solutions). This suggests that a surface covered in elastic filaments (such as the hairy leg of insects) may be able to universally self-clean. To quantify the efficiency of this effect, we explore the conditions under which drops leave the structure by ‘spreading’ rather than translating and also how long it takes to do so.

  • Industrial and Applied Mathematics Seminar
23 November 2017
16:00
Matthew Butler
Abstract

Many species of insects adhere to vertical and inverted surfaces using footpads that secrete thin films of a mediating fluid. The fluid bridges the gap between the foot and the target surface. The precise role of this liquid is still subject to debate, but it is thought that the contribution of surface tension to the adhesive force may be significant. It is also known that the footpad is soft, suggesting that capillary forces might deform its surface. Inspired by these physical ingredients, we study a model problem in which a thin, deformable membrane under tension is adhered to a flat, rigid surface by a liquid droplet. We find that there can be multiple possible equilibrium states, with the number depending on the applied tension and aspect ratio of the system. The presence of elastic deformation  ignificantly enhances the adhesion force compared to a rigid footpad. A mathematical model shows that the equilibria of the system can be controlled via two key parameters depending on the imposed separation of the foot and target surface, and the tension applied to the membrane. We confirm this finding experimentally and show that the system may transition rapidly between two states as the two parameters are varied. This suggests that different strategies may be used to adhere strongly and then detach quickly.

  • Industrial and Applied Mathematics Seminar
16 November 2017
16:00
to
17:30
Giovanni Samaey
Abstract

We present a framework for the design, analysis and application of computational multiscale methods for slow-fast high-dimensional stochastic processes. We call these processes "microscopic'', and assume existence of an approximate "macroscopic'' model that captures the slow behaviour of a selected set of macroscopic state variables. The methodology combines short bursts of microscopic simulation with extrapolation at the macroscopic level. The methodology requires the careful study of a few key algorithmic ingredients. First, we need to properly initialise the microscopic system, based on a given macroscopic state and (possibly) a prior microscopic state that contains additional information about the system. Second, we need to control the variance of the noise that originates from the microscopic Monte Carlo simulation. Third, we need to analyse stability of the extrapolation step. We will discuss these aspects on two types of model problems -- scale-separated SDEs and kinetic equations -- and show the efficacity of the resulting methods in diverse applications, ranging from tumor growth to fusion energy.

  • Industrial and Applied Mathematics Seminar
9 November 2017
16:00
to
17:30
Stephen Watson
Abstract

The statistical physics governing phase-ordering dynamics following a symmetry breaking rst-order phase transition is an area of active research. The Coarsening/Ageing of the ensemble of phase domains, wherein irreversible annihilation or joining of domains yields a growing characteristic domain length, is an omniprescent feature whose universal characteristics one would wish to understand. Driven kinetic Ising models and growing nano-faceted crystals are theoretically important examples of such Coarsening (Ageing) Dynamical Systems (CDS), since they additionally break thermodynamic uctuation-dissipation relations. Power-laws for the growth in time of the characteristic size of domains, and a concomitant scale-invariance of associated length distributions, have so frequently been empirically observed that their presence has acquired the status of a principle; the so-called Dynamic-Scaling Hypothesis. But the dynamical symmetries of a given CDS- its Coarsening Group G - may include more than the global spatio-temporal scalings underlying the Dynamic Scaling Hypothesis. In this talk, I will present a recently developed theoretical framework (Ref.[1]) that shows how the symmetry group G of a Coarsening (ageing) Dynamical System necessarily yields G-equivariance (covariance) of its universal statistical observables. We exhibit this theory for a variety of model systems, of both thermodynamic and driven type, with symmetries that may also be Emergent (Ref. [2,3]) and/or Hidden. We will close with a magical theoretical coarsening law that combines Lorentzian and Parabolic symmetries!

References
[1] Lorentzian symmetry predicts universality beyond scaling laws, SJ Watson, EPL 118 (5), 56001, (Aug.2, 2017) Editor's Choice
[2] Emergent parabolic scaling of nano-faceting crystal growth Stephen J. Watson, Proc. R. Soc. A 471: 20140560 (2015)
[3] Scaling Theory and Morphometrics for a Coarsening Multiscale Surface, via a Principle of Maximal Dissipation", Stephen

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

Phytoplankton moving in the ocean, spermatozoa making their way  through the female reproductive tract and harmful bacteria that form biofilms on implanted medical devices interact with a surrounding fluid. Their length scales are small enough so that viscous effects dominate inertial effects allowing the resulting fluid dynamics to be described by the linear Stokes equations. However,  nonlinear behavior can occur because these structures are flexible and their form evolves with the flow. In addition, the fluid environment may also  be complex because of embedded microstructures that further complicate the dynamics.  We will discuss recent successes and challenges in describing these elastohydrodynamic systems.

  • Industrial and Applied Mathematics Seminar
26 October 2017
16:00
to
17:30
Abstract

Brain convolutions are specificity of mammals. Varying in intensity according to the animal species, it is measured by an index called the gyrification index, ratio between the effective surface of the cortex compared to its apparent surface. Its value is closed to 1 for rodents (smooth brain), 2.6 for new-borns and 5 for dolphins.  For humans, any significant deviation is a signature of a pathology occurring in fetal life, which can be detected now by magnetic resonance imaging (MRI). We propose a simple model of growth for a bilayer made of the grey and white matter, the grey matter being in cortical position. We analytically solved the Neo-Hookean approximation in the short and large wavelength limits. When the upper layer is softer than the bottom layer (possibly, the case of the human brain), the selection mechanism is dominated by the physical properties of the upper layer. When the anisotropy favours the growth tangentially as for the human brain, it decreases the threshold value for gyri formation. The gyrification index is predicted by a post-buckling analysis and compared with experimental data. We also discuss some pathologies in the model framework.

  • Industrial and Applied Mathematics Seminar
19 October 2017
16:00
to
17:30
Pasquale Ciarletta
Abstract

Discontinuous solutions, such as cracks or cavities, can suddenly appear in elastic solids when a limiting condition is reached. Similarly, self-contacting folds can nucleate at a free surface of a soft material subjected to a critical compression. Unlike other elastic instabilities, such as buckling and wrinkling, creasing is still poorly understood. Being invisible to linearization techniques, crease nucleation is a problem of high mathematical complexity.

In this talk, I will discuss some recent theoretical insights solving the quest for both the nucleation threshold and the emerging crease morphology.  The analytic predictions are in  agreement with experimental and numerical data. They prove a fundamental insight either for understanding the creasing onset in living matter, e.g. brain convolutions, or for guiding engineering applications, e.g. morphable meta-materials.

  • Industrial and Applied Mathematics Seminar
12 October 2017
16:00
Maria Bruna
Abstract

In this talk we consider a system of interacting Brownian particles. When diffusing particles interact with each other their motions are correlated, and the configuration space is of very high dimension. Often an equation for the one-particle density function (the concentration) is sought by integrating out the positions of all the others. This leads to the classic problem of closure, since the equation for the concentration so derived depends on the two-particle correlation function. We discuss two  common closures, the mean-field (MFA) and the Kirkwood-superposition approximations, as well as an alternative approach, which is entirely systematic, using matched asymptotic expansions (MAE). We compare the resulting (nonlinear) diffusion models with Monte Carlo simulations of the stochastic particle system, and discuss for which types of interactions (short- or long-range) each model works best. 

  • Industrial and Applied Mathematics Seminar

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