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Presenting a poster pitch and a poster
Presenting a poster pitch and a poster
Ashleigh Ratcliffe (University of Leicester) - On the equation x^4-y^4=D
Ashleigh Ratcliffe (University of Leicester) - On the equation x^4-y^4=D
This poster summarises a list of integers expressible as a difference of two rational fourth powers and the known methods used prove which integers are not representable as a difference of two rational fourth powers.
Mingjia Yan (University of Cambridge) - Geometric Field Theory for Elastohydrodynamics of Cosserat Rods
Mingjia Yan (University of Cambridge) - Geometric Field Theory for Elastohydrodynamics of Cosserat Rods
The Cosserat rod provides a mathematical framework for slender bodies that can stretch, shear, twist and bend, in viscous fluids. We demonstrate that the resulting elastohydrodynamic equations of motion, formulated using Cartan's method of moving frames, fits into a geometric field theory where the configuration field takes values in SE(3), the Lie group of rigid motions. This geometric formulation yields coordinate-free equations that are invariant under spatial symmetries. We also build structure-preserving numerical schemes to simulate the rod motions .
Karla Bonic-Babic (University of Oxford) - A comparison of three methods for estimating the probability of a major outbreak
Karla Bonic-Babic (University of Oxford) - A comparison of three methods for estimating the probability of a major outbreak
Early in an infectious disease outbreak, it is often unclear whether transmission will fade out or take off. We compare three methods for estimating the probability of a major outbreak (PMO) from early incidence data: i) an analytic approach; ii) simulation-based trajectory matching; and iii) a machine-learning classifier trained on simulated outbreaks. All three yield consistent PMO estimates but differ in mechanistic transparency and flexibility. We highlight when each approach is most useful. These tools apply whenever a pathogen invades a new location, not just at the start of an epidemic.
Presenting a a poster
Presenting a a poster
Michelle Simons (University of Edinburgh) - Understanding Gell-Mann's Quark Model through SU(3)-described Oscillators
Michelle Simons (University of Edinburgh) - Understanding Gell-Mann's Quark Model through SU(3)-described Oscillators
The primary objective of this project involved working out the Lie algebra of the SU(3) group in terms of the algebra of three independent harmonic oscillators, following Schwinger’s oscillator method of angular momentum. Describing the SU(3) Lie algebra in this manner allows for an interpretation of the up, down, and strange quarks in the Gell-Mann quark model as independent harmonic oscillators. This method also explains the v-spin and u-spin analogues of isospin.
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