Tendons are vital connective tissues that anchor muscle to bone to allow the transfer of forces to the skeleton. They exhibit highly non-linear viscoelastic mechanical behaviour that arises due to their complex, hierarchical microstructure, which consists of fibrous subunits made of the protein collagen. Collagen molecules aggregate to form fibrils with diameters of tens to hundreds of nanometres, which in turn assemble into larger fibres called fascicles with diameters of tens to hundreds of microns. In this talk, I will discuss the relationship between the three-dimensional organisation of the fibrils and fascicles and the macroscale mechanical behaviour of the tendon. In particular, I will show that very simple constitutive behaviour at the microscale can give rise to highly non-linear behaviour at the macroscale when combined with geometrical effects.

When solving stochastic partial differential equations (SPDEs) driven by additive spatial white noise the efficient sampling of white noise realizations can be challenging. In this talk we present a novel sampling technique that can be used to efficiently compute white noise samples in a finite element and multilevel Monte Carlo (MLMC) setting.
After discretization, the action of white noise on a test function yields a Gaussian vector with the FEM mass matrix as covariance. Sampling such a vector requires an expensive Cholesky factorization and for this reason P0 representations, for which the mass matrix is diagonal, are generally preferred in the literature. This however has other disadvantages. In this talk we introduce an alternative factorization that is naturally parallelizable and has linear cost and memory complexity (in the number of mesh elements).
Moreover, in a MLMC framework the white noise samples must be coupled between subsequent levels so as to respect the telescoping sum. We show how our technique can be used to enforce this coupling even in the case in which the hierarchy is non-nested via a supermesh construction. We conclude the talk with numerical experiments that demonstrate the efficacy of our method. We observe optimal convergence rates for the finite element solution of the elliptic SPDEs of interest. In a MLMC setting, a good coupling is enforced and the telescoping sum is respected.
 

The next generation emissive displays including quantum dot LED(QLED) and organic LED(OLED) could be efficiently manufactured by inkjet printing, where nano-scale droplets are injected in banked substrate and after evaporation they leave layers of thin film that forms pixels of a display. This novel manufacturing method would greatly reduce cost and improve reliability. However, it is observed in practice that the deposit becomes much thicker near the bank edge and emission is faint there. This motivated the project and in this talk, we will mathematically model the phenomeno, understand its origin and investigate ways of making more uniform deposit by means of simulation.

Blisters form when a thin surface layer of a solid body separates/delaminates from the underlying bulk material over a finite, bounded region. It is ubiquitous in a range of industrial applications, e.g. blister test is applied to assess the strength of adhesion between thin elastic films and their solid substrates, and during natural processes, such as formation and spreading of laccoliths or retinal detachment.

We study a special case of blistering, in which a thin elastic membrane is adhered to the substrate by a thin layer of viscous fluid. In this scenario, the expansion of the newly formed blister by fluid injection occurs via a displacement flow, which peels apart the adhered surfaces through a two-way interaction between flow and deformation. If the injected fluid is less viscous than the fluid already occupying the gap, patterns of short and stubby fingers form on the propagating fluid interface in a radial geometry. This process is regulated by membrane compliance, which if increased delays the onset of fingering to higher flow rates and reduces finger amplitude. We find that the morphological features of the fingers are selected in a simple way by the local geometry of the compliant cell. In contrast, the local geometry itself is determined from a complex fluid–solid interaction, particularly in the case of rectangular blisters. Furthermore, changes to the geometry of the channel cross-section in the latter case lead to a rich variety of possible interfacial patterns. Our experiments provide a link between studies of airway reopening, Saffman-Taylor fingering and printer’s instability.   

There is a mismatch between levels of crime and its fear and often, cities might see an increase or a decrease in crime over time while the fear of crime remains unchanged. A model that considers fear of crime as an opinion shared by simulated individuals on a network will be presented, and the impact that different distributions of crime have on the fear experienced by the population will be explored. Results show that the dynamics of the fear is sensitive to the distribution of crime and that there is a phase transition for high levels of concentration of crime.

If G is a topological group, a G-flow X is a non-empty, compact, Hausdorff space on which G acts continuously; it is minimal if all G-orbits are dense. By a theorem of Ellis, there is a (unique) minimal G-flow M(G) which is universal: there is a continuous G-map to every other G-flow. 

Here, we will be interested in the case where G = Aut(K) for some structure K, usually omega-categorical. Work of Kechris, Pestov and Todorcevic and others gives conditions on K under which structural Ramsey Theory (due to Nesetril - Rodl and others) can be used to compute M(G). 

In the first part of the talk I will give a description of the above theory and when it applies (the 'tame case'). In the second part, I will describe joint work with J. Hubicka and J. Nesetril which shows that the omega-categorical structures constructed in the late 1980's by Hrushovski as counterexamples to Lachlan's conjecture are not tame and moreover, minimal flows of their automorphism groups have rather different properties to those in the tame case.