Spring 2013

The following is a list of applied maths seminar dates for the forthcoming semester. The seminars usually take place on Monday afternoons at 2pm.

Pattern formation in exciton-polariton condensates

Date: Monday 4th February (3pm, S3.05)
Speaker: Natalia Berloff (Cambridge) [HS]
Abstract: I will discuss the phenomena observed in, and properties of, microcavity exciton-polariton condensates. These are condensates of mixed light and matter, consisting of superpositions of photons in semiconductor microcavities and excitons in quantum wells. Because of the imperfect confinement of the photon component, exciton-polaritons have a finite lifetime, and have to be continuously re-populated. Therefore, exciton-polariton condensates lie somewhere between equilibrium Bose-Einstein condensates and lasers. I review in particular the evidence for condensation, the coherence properties studied experimentally, and the wide variety of spatial structures either observed or predicted to exist in exciton-polariton condensates, including quantised vortices and other coherent structures.

Solidification of molten metallic foams

Date: Monday 11th February
Speaker: Peter Stewart (Oxford) [RJW]
Abstract: High-porosity metallic solids can be formed by solidification of the corresponding molten gas-liquid foam. However, molten metallic foams are thermally and dynamically unstable, so in the absence of solidification the thin liquid films drain rapidly toward the bubble vertices and eventually
become unstable to interfacial instabilities, leading to film rupture and bubble coalescence. To explore the competition between coarsening and freezing we have constructed a large-scale network model to describe the dynamics and stability of a planar foam with low liquid fraction, incorporating a coupling between pressure and volume in the gas bubbles, surface tension forces on the gas- liquid interfaces, draining flow in the films, a criterion for film rupture, temperature variations and a solidification front. Initially, the foam is arranged in a regular array of approximately polygonal bubbles, held at a uniform temperature above the melting point of the material. The walls of the container are then cooled to a temperature well below the melting point, driving a solidification front
inwards; numerical simulations of the model predict the structure of the resulting porous metal solid.

tba

Date: Monday 18th February
Speaker: Davide Proment (UEA)
Abstract:

Localised Three-Dimensional Capillary-Gravity waves: Solitons and Breathers

Date: Monday 25th February
Speaker: Paul Milewski (Bath) [MGB,EP]
Abstract: The capillary gravity wave problem exhibits a large variety of phenomena, one of which is the combination of geometric and nonlinear self-interaction focussing of localised disturbances. While in the small amplitude limit this focussing leads to an instability with  finite-time blowup of model equations, we show that in the full fluid equations, the focussing is arrested, and, instead, fully localised breathers are generated.

tba

Date: Monday 4th March
Speaker: Peter Mason (Durham) [HS]
Abstract:

Theoretical Models of Blood Flow in Vascular Networks: Discrete and Continuum Approaches

Date: Monday 11th March
Speaker: Rebecca Shipley (UCL) [RJW]
Abstract: The vasculature comprises a hierarchy of vessels that is frequently categorized according to vessel size. Although the geometry and topology of the vasculature is organ-specific, blood flows into an organ from a feeding artery, through the arterioles into the microcirculation, and exits through the venules then veins. Gas exchange occurs primarily in the microcirculation and, indeed, the function of the vasculature is to provide oxygen for cellular metabolism. Understanding and predicting the flow of blood through these networks will play a crucial role in, for example, promoting angiogenesis and vascular remodelling to treat myocardial ischaemia, and in analyzing perfusion maps extracted using medical imaging techniques. Traditional modelling approaches employ a discrete approach by solving equations for blood flow in each vessel of a network. However, recent advancements in imaging methods have led to a wealth of data that describe vascular structure in a highly detailed way, and it is becoming too computationally intensive to simulate flow and mass transport in the complete vascular tree using a discrete approach. Continuum models must be developed that can be used alongside a discrete approach to capture the key functional properties of blood flow. Continuum multiscale models that describe blood flow in the microcirculation, derived using the mathematical process of asymptotic homogenization, will be discussed. A strategy for combining discrete and continuum models to simulate blood flow in large networks will be presented, and results of testing this strategy for explicit examples of rat mesentary networks will be demonstrated.

Student BAMC Practice Talks

Date: Monday 18th March
Speaker:
Abstract:

 

For further details about the seminars, or to join our mailing list, please contact Robert Whittaker.