BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:2nd year PhD student talks - James Cummins\, Tom Daggitt\, William Oxley\, Alistair Hales\, Jenny Dingwall\, Matt Davison\, Elvinas Ribinska s\, James Mason\, Joseph Webber DTSTART:20220527T134500Z DTEND:20220527T160100Z UID:TALK173495@talks.cam.ac.uk CONTACT:Prof. Jerome Neufeld DESCRIPTION:* 1445 - 1458 James Mason\n* 1458 - 1511 Tom Daggitt\n* 1511 - 1524 William Oxley\n* 1524 - 1537 Alistair Hales\n* 1537 - 1550 Jenny Din gwall\n\n* 1550 - 1610 coffee\n\n* 1610 - 1623 Matt Davison\n* 1623 - 1636 Elvinas Ribinskas\n* 1636 - 1649 James Cummins \n* 1649 - 1701 Joseph Web ber\n\n------------------------------------------\n\n*James Mason*\n\nMacr oscopic behaviour in a two-species exclusion process via the method of mat ched asymptotics\n\nWe consider a two-species simple exclusion process on a periodic lattice. We use the method of matched asymptotics to derive evo lution equations for the two population densities in the dilute regime\, n amely a cross-diffusion system of partial differential equations for the t wo species densities. First\, our result captures non-trivial interaction terms neglected in the mean-field approach\, including a non-diagonal mobi lity matrix with explicit density dependence. Second\, it generalises the rigorous hydrodynamic limit of Quastel [Commun. Pure Appl. Math. 45(6)\, 6 23--679 (1992)]\, valid for species with equal jump rates and given in ter ms of a non-explicit self-diffusion coefficient\, to the case of unequal r ates in the dilute regime. In the equal-rates case\, by combining matched asymptotic approximations in the low- and high-density limits\, we obtain a cubic polynomial approximation of the self-diffusion coefficient that is numerically accurate for all densities. This cubic approximation agrees e xtremely well with numerical simulations. It also coincides with the Tayl or expansion up to the second order in the density of the self-diffusion c oefficient obtained using a rigorous recursive method. \n\n\n*Tom Daggitt* \n\nVariations in Observations of Geosynchronous Magnetopause and Last Clo sed Drift Shell Crossings with Magnetic Local Time\n \nWe present an analy sis of events in which the number of electrons trapped in Earth's outer ra diation belts drops rapidly due to inward movement of the outer edge of Ea rth's magnetic field. These observations are compared to models of the lar gest trapped electron orbits derived from models of Earth's magnetic field and particle tracing models. These models of the largest trapped orbits a gree well with the losses seen over the timescale of hours\, but fail to r eproduce more rapid decreases in the number of electrons measured on the t imescale of minutes. We show that different satellites in geostationary or bit observe different trends in the trapped electron population on timesca les of less than a day during geomagnetic storms due to their separation i n longitude. These differences demonstrate that data from at least three s atellites in geostationary orbit\, ideally more\, may be required for accu rate\, high time resolution forecasting and reconstruction of Earth's radi ation belts during geomagnetic storms.\n\n*William Oxley*\n\nAmplitude Thr esholds for Zombie Vortex Instability\n \nRotating\, stratified and shear ed flows\, where the shear is in a direction perpendicular to the (stable) vertical stratification\, are found in a wide range of settings that incl ude the atmosphere and oceans\, as well as protoplanetary disks. The addit ion of stable stratification to rotating shear flows is of interest as it can have a destabilising effect. A number of studies of these types of flo ws\, through numerical experiments\, show vortices appearing in lattice li ke structures\, after spreading across the domain due to an initial locali sed perturbation. This finite amplitude instability was first identified b y Marcus et. al. 2013\, who gave it the name ‘Zombie Vortex Instability ’ (ZVI) due to its formation mechanism. The individual vortices result f rom the excitation of baroclinic critical layers\, and each vortex then ac ts as a source for a new initial perturbation\, which allows the process t o repeat. Baroclinic critical layers are similar to their classical namesa ke\, and take the form of sharp changes in perturbation variables around l ocations which are singular in the linear inviscid theory. In contrast to classical critical layers\, which form where the perturbation phase speed matches the speed of the mean flow\, baroclinic critical layers form at th e locations where the phase speed of a perturbation (relative to the backg round shear) matches the characteristic gravity wave speed. This instabili ty has been suggested by Marcus et. al. (2013) as a candidate to destabili ze dead zones in protoplanetary discs\, although that suggestion has been questions by other authors (e.g. Lesur & Latter 2016). Building on previou s analytical and numerical studies\, I have been investigating ZVI numeric ally to try and gain more insight into the formation mechanism\, and in pa rticular what are the conditions we must impose on the initial perturbatio n in order to produce ZVI. One of the key challenges to overcome is how to actually identify ZVI\, and how to focus on one individual occurrence of the replication process. To do this\, a carefully chosen initial condition is used and the problem is simulated using various different parameters.\ n\n*Alistair Hales*\n\nReduction of Leading-Edge Noise Using Tailored Turb ulence Anisotropy\n\nIn this talk I give an outline of a new mathematical model to approximate the leading edge noise from the scattering of anisotr opic flow off a rigid aerofoil. Thin aerofoil theory is used to model an a erofoil as a semi-infinite plate and the scattering of incoming turbulence is solved via the application of the Wiener-Hopf technique. This theoreti cal is integrated over a wavenumber-frequency spectrum to account for gene ral incoming turbulence which is obtained using the method of Gaussian dec omposition\, accounting for and modelling anisotropy in the incoming turbu lence.\n\n*Jenny Dingwall*\n\nModelling the accumulation of buoyant partic les under wind-driven and convective turbulence using large-eddy simulatio ns\n \nBuoyant material such as microplastics tend to accumulate near the ocean surface in regions with convergent surface currents where they can b e harmful to marine life. We investigate the accumulation of buoyant trace rs and Lagrangian surface particles by small-scale turbulence in the ocean mixed layer under combined wind and convective forcing using large-eddy s imulations. Surface cooling drives convection\, and under this regime pers istent convective vortices form which trap buoyant material\, leading to l arge concentrations. For sufficiently weak winds\, convective vortices sur vive but become less effective at clustering material as the wind stress i ncreases. Under strong wind forcing\, convective vortices are no longer vi sible\, but some particle clustering occurs in downwelling regions associa ted with longitudinal wind rolls.\n\n*Matt Davison*\n\nReaction-Diffusion Dynamics of the Tropical Atmosphere\n \nThe Madden-Julian Oscillation (MJ O) is a precipitating disturbance that propagates eastward across the Indi an and Pacific oceans every 30-60 days. There is no single accepted theore tical explanation for the MJO and in climate models the MJO is often poorl y represented. It has been suggested that there is a relation between the MJO and the phenomenon of convective aggregation observed in 'convection-r esolving' numerical simulations. I will describe an extension of a previou s theoretical model of convective aggregation\, based solely on reaction-d iffusion\, to include large scale dynamics. The new model consists of the shallow water equations and a moisture equation coupled through the effect s of moisture on radiation and latent heat release. When the latter are ch osen such that there are two stable states alongside the initial unstable radiative-convective equilibrium\, convective aggregation is observed. Sin ce this model has dynamics we can include rotation\, and on an equatorial beta-plane the dynamical model exhibits coherent\, moist\, eastward propag ating disturbances\, and therefore appears to represent the mechanism behi nd the MJO.\n\n*Elvinas Ribinskas*\n\nReduced modelling of ice sheet respo nse to climate perturbations\n\nIce sheet melting associated to climate ch ange poses the risk of significantly increasing the sea level. Modelling h ow ice sheets respond to climate perturbations allows us predict this chan ge. Reduced models in particular can be used to also infer how the underly ing physical processes influence ice sheet response to external forcings. I will present a reduced model of a land-terminating ice sheet that is for ced by a prescribed ablation-accumulation law. The model consists of a sim plified ice flow law\, basic meltwater network and a basal boundary condit ion that couples ice flow to the basal meltwater pressure. The steady-stat e solutions of the model are found to be non-unique. Also\, we learn that longitudinal stresses have to be included into the model for it to represe nt a realistic ice sheet. In the end\, I will present preliminary results of the improved model and possible directions for future work.\n\n*James C ummins*\n\nUnconventional computing & the n-queens problem\n\nTraditional computers can not keep up with the increasing speed and power expected of them. Unconventional computing architectures overcome this by using gain-d issipative systems to improve computational performance. These platforms m ay comprise of lasers\, superconducting qubits\, polariton condensates\, o r photon condensates. In this talk we explore how such systems can solve o ne of the oldest problems in mathematics: the n-queens problem.\n\n*Joseph Webber*\n\nDynamics of super-absorbent hydrogels\n\nHydrogels are soft ma terials formed from a hydrophilic polymer scaffold surrounded by adsorbed water molecules\, and may comprise over 99% water by volume in their fully -swollen state. As such\, when allowed to swell and dry\, their volumes ma y change to an extreme degree\, rendering linear poroelastic models invali d owing to the large magnitudes of the strains involved. Models proposed i n the literature to describe this extreme swelling and drying often rely o n a complex molecular-scale understanding of polymer-water interactions an d formulate gel dynamics in terms of a free energy density. In this talk\, I will summarise a new formulation for the dynamics of hydrogels which tr eats them as instantaneously incompressible linear-elastic materials\, whi lst allowing for nonlinearities in the isotropic strains corresponding to swelling and drying. Key features of this model include a complete descrip tion of any gel using only three material parameters\, a nonlinear diffusi on equation governing swelling and drying\, and an associated equation to describe the displacement field\, from which the shape of the hydrogel can be deduced. Applications of this model to a number of different problems will then be discussed briefly. LOCATION:MR2\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr idge END:VEVENT END:VCALENDAR