Postgraduate Seminars Autumn 2024
These seminars (unless otherwise stated) will take place on Thursdays at 2pm-3pm on an almost weekly basis.
Talks are being given by 2nd and 3rd year Mathematics PhD students for PhD students.
26 September 2024 in 25 Gordon Street - Room 416
Speaker: Luke Debono
TITLE: an introduction to molecular modelling of complex fluids in rheology
Abstract:
In this seminar, I will introduce the field of rheology with some fundamental concepts supported by real world examples of complex fluids. We will then consider molecular simulation as a tool for conducting microscale experiments on different molecular models of complex fluids. Finally, I will introduce my own modelling approach followed by some results from the past year.
03 October 2024 in 25 Gordon Street - Room 416
Speaker: Xinyu Yao
TITLE: free surface flow past a high-speed submerged hydrofoil
Abstract:
In this seminar, I will introduce, in the limit of large Froude number, a closed-form, numerical solution of spectral method for steady, two-dimensional, inviscid, free-surface attached flow over a submerged planar hydrofoil for arbitrary angles of attack and depths of submergence. The doubly connected flow domain is conformally mapped to a concentric annulus in an auxiliary plane. The complex flow potential and its derivative, the complex velocity, are obtained in the auxiliary plane by considering their form at known special points in the flow, and the required conformal mapping is determined by explicit integration. Finally, three real solution parameters of the conformal mapping will be determined as the simultaneous roots of three nonlinear algebraic equations arising from the flow normalization through Newton’s iteration. The numerical solution format enables precise evaluation of various flow quantities, including the lift on the foil, in relation to physical parameters.
10 October 2024 in 25 Gordon Street - Room 416
Speaker: Courteney Hirst
TITLE: Erosion of surfaces by trapped vortices
Abstract:
Two two-dimensional free boundary problems describing the erosion of solid surfaces by the flow of inviscid fluid in the presence of trapped vortices are considered. The first problem tackles an initially flat, infinite fluid-solid interface with uniform flow at infinity and a vortex in equilibrium above the surface. The second involves flow around a finite body with a trailing Föppl-type vortex pair. The conformal invariance of the complex potential permits both problems to be formulated as a Polubarinova-Galin (PG) type equation in which the time-dependent eroding surface in the physical plane is mapped to the fixed boundary of the unit disk. The Hamiltonian governing the equilibrium position of the vortex (or vortex pair in the second problem) is also found from the same map. In each problem the PG equation giving the conformal map is found numerically and the time-dependent evolution of the interface and vortex location determined. Different models governing the erosion of the interface are investigated in which the normal velocity of the boundary depends on some given function of the fluid flow velocity at the boundary. Typically, in the infinite surface case, erosion leads to the formation of a symmetric valley beneath the vortex which, in turn, moves downward toward the interface. A finite body undergoes erosion which is asymmetric in the flow direction leading to a flattening of the lee surface of the body so displaying some similarity to experiments and associated viscous theory.
17 October 2024 in 25 Gordon Street - Room 416
Speaker: Dhruva Pamulaparthy
TITLE: Do elephants dream of electric sheep? - large deviations in nonequilibrium systems with memory
Abstract:
This talk is an introduction (with minimum maths!) to the type of problems that I currently work on. We will examine memory-dependence in nonequilibrium systems through simple toy examples, building to processes that never forget such as “elephant” random walks. Systems with memory are routinely encountered in physics (spin-glasses), biology (active-matter), engineering (transportation) and mathematics (probability theory). We are particularly interested in statistical properties of quantities such as currents which in general are characterized by large deviations describing rare-events and fluctuations. However, we will find that memory complicates large-deviation calculations and advanced computational methods such as machine learning become necessary.
24 October 2024 in 25 Gordon Street - Room 416
Speaker: Devi Prasad Panigrahi
TITLE: can biological cells exhibit emergent material properties during collective migration?
Abstract:
In this talk we will look at collective migration of biological cells as a generalized N-body problem. In particular, we will be using Agent-Based simulations to formulate pair-wise interaction rules that can explain some experimental observations seen in chemotaxis of Dictyostelium aggregates. We want to understand migrating cell collectives as an ‘active’ fluid, which shares some common features with traditional fluids such as water. While such phenomenological models already exist in the literature, it is not clear how these macroscale properties arise from cell-cell interactions. The aim of this project is to bridge this gap between single cell experimental literature and observations on collective migration, using agent-based simulations.
31 October 2024 in 25 Gordon Street - Room 416
Speaker: Thomas Caussade
TITLE: high-frequency scattering and oscillatory integrals
Abstract:
Scattering is the interaction between waves and materials and is fundamental in electromagnetics, acoustics, and many other areas. Wave scattering problems can be modelled by boundary integral equations and solved accurately using the boundary element method (BEM). However, the computational cost quickly grows as the wave’s frequency increases, becoming unsuitable for practical purposes.
In this talk, I will first present the main ideas behind the Hybrid Numerical-Asymptotic (HNA) method, which combines conventional BEM techniques with high-frequency asymptotics to produce good approximations with a virtually frequency-independent number of degrees of freedom. While there is much evidence demonstrating the potential power of the HNA methods, there does not (yet) exist a freely available implementation which realises the premise of frequency-independent computational times. A major issue is the lack of robust and reliable quadrature rules to tackle the challenging oscillatory integrals that arise in this formulation. Oscillatory quadrature rules, such as the numerical steepest descent (NSD) method, are a promising way to evaluate these. In the second part of this talk, I will present the NSD method applied to a simple but illustrative case and introduce some recent theoretical results regarding the rigorous convergence analysis of this method.
07 November 2024 - Reading Week - No Seminar
14 November 2024 in 25 Gordon Street - Room 416
Speaker: Yumin Lu
TITLE: portfolio selection in contests
Abstract:
In an investment contest with incomplete information, a finite number of agents dynamically trade assets with idiosyncratic risk and are rewarded based on the relative ranking of their terminal portfolio values. We explicitly characterize a symmetric Nash equilibrium of the contest and rigorously verify its uniqueness. The connection between the reward structure and the agents’ portfolio strategies is examined. A top-heavy payout rule results in an equilibrium portfolio return distribution with high positive skewness, which suffers from a large likelihood of poor performance. Risky asset holding increases when competition intensifies in a winner-takes-all contest.
21 November 2024 in 25 Gordon Street - Room 416
Speaker: Anushka Herale
TITLE: a minimal continuum model of clogging in spatio-temporally varying channels
Abstract:
Particle suspensions in confined geometries exhibit rich dynamics, including flowing, jamming, and clogging. It has been observed that jamming and clogging in particular are promoted by variations in channel geometry or fluid material properties - such variations are often present in industrial systems (e.g. local confinements) and biological systems (e.g. stiffening of red blood cells in deoxygenated conditions in sickle cell disease). The aim of this talk is to shed light on the macroscopic dynamics of particulate suspensions in these conditions. To this end, we present a continuum two-phase model of particle suspensions that accounts for spatio-temporally varying material properties or channel geometries. The model comprises a continuous particle phase which advects with flow and has material properties dependent on the particle volume fraction, and a suspending fluid which flows through the particle phase obeying Darcy’s law. We are able to show the emergence of high and low particle density regions and complete clogging of the particle phase in both pressure-driven flows. These results clarify how spatial variation in material and channel properties can contribute to clogging of particle suspensions.
28 November 2024 in 25 Gordon Street - Room 416
Speaker: Maria Chivers
TITLE: geometries of black hole horizons
Abstract:
The geometry of every black hole is very different and complicated. The aim of this talk is to introduce three black holes in order to compare their symmetries, horizons and other important features. I will try to show the importance of studying the near horizon geometry of black holes, where Killing vectors will be used to generate the symmetries of their horizons. For each black hole, Killing vector fields will be found in order to find the symmetries and isometries of their individual metric. Using this, special type of horizons called the Killing horizon will be derived.
05 December 2024 in 25 Gordon Street - Room 416
Speaker: Giovanni Bracchi
TITLE: the hyperbolic propagator of the operator curl
Abstract:
In this talk, I will describe an algorithm for analysing the spectral asymptotics of curl on a connected oriented closed Riemannian 3-manifold. This approach hinges on careful examination of the kernel of the propagator of curl, represented as an oscillatory integral modulo smooth contributions, in the small-time limit. This is part of a broader project devoted to the study of spectral asymmetry of first-order systems on manifolds. In the end, I will provide formulae for the first three positive and negative mollified Weyl coefficients of curl.
12 December 2024 in 25 Gordon Street - Room 416
Speaker: Claudia De Sousa Miranda Perez
TITLE: minimal kinetic modelling unravels heterogeneity and variability in sickle cell disease
Abstract:
Sickle-cell disease (SCD) is a genetic blood disorder induced by the polymerisation of sickle haemoglobin (HbS) inside red blood cells (RBCs) in reduced oxygen tension. HbS polymerisation causes RBCs to become stiffer, contributing to occlusion of blood vessels. Despite decades of intensive investigation of HbS aggregation mechanisms, single-cell measurements of haemoglobin polymerisation in heterogeneous cell populations are only recently starting to be made. These experiments reveal that SCD saturation distributions at intermediate oxygen tensions are bimodal, suggesting the existence of two subpopulations of RBCs within the same patient — one with a significant amount of polymer, and the other with barely any polymers present. New theoretical frameworks are needed to explain the mechanisms leading to this bimodality, as well as the connection between RBC properties and patient-specific clinical outcomes. In this talk, we present approximate analytical expressions both for the probability density function of the saturation and the time delays of an RBC population at constant oxygen tension and explore critical HbS concentration and saturation as potential biomarkers for SCD.