Thu, 04 Jun 2026
12:00 -
13:00
L3
DPhil Talks
Georgina Ryan + Yunhao Ding + William Gillow + Callum Marsh
(OCIAM)
Abstract
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Title: (Georgina) Modelling intermediate-current transitions in asymmetric-valence binary electrolytes
Abstract: The valences of ions in a binary electrolyte impact the performance of electrochemical devices, but most electrochemical modelling focuses on symmetric š§ :š§ binary electrolytes. We study the impact of asymmetric ion valences on the spatial distribution of the positive and negative ion concentrations and electric potential inside a simple electrochemical device. We consider a one-dimensional steady-state PoissonāNernstāPlanck model with imposed constant ionic fluxes. Numerical simulations reveal a smooth valence-dependent transition point at an intermediate current where the classical boundary layers vanish. We fully characterise this transition using asymptotic analysis. In addition, we produce implicit analytic expressions for general asymmetric binary electrolytes alongside explicit solutions for 2ā¢š§ :š§, š§ :2ā¢š§, and symmetric š§ :š§ electrolytes. Our results collapse onto a suitably scaled phase diagram to predict the observed transition in terms of ion valences and fluxes.
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Title: (Yunhao) How Routing Shapes Robustness in Path Percolation
Abstract: Traffic-induced failures arise when repeated flows progressively exhaust the network resources they traverse, from packet loss in communication systems to congestion breakdown in transportation networks. Path percolation models this process by removing edges along sampled originādestination paths.
In this talk, I introduce a generalised path-percolation framework in which both the routing protocol and the demand ensemble can be varied. Paths are sampled from a temperature-controlled routing ensemble interpolating between shortest-path and noisy transport. I show that finite routing horizons preserve mean-field critical behaviour, while routing details strongly affect the percolation threshold through the localisation of network load. Comparing pair-uniform and source-uniform demand ensembles further reveals how finite connected components can accommodate local demand and alter fragmentation dynamics.
Finally, when the routing horizon scales as š¶= š^1/3, the system enters a distinct crossover regime with nontrivial scaling and a characteristic growth of path length before giant-component collapse. These results highlight how microscopic routing organisation shapes macroscopic network robustness.
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Title: (William) Modelling Confined Surfactant Systems Out of Thermodynamic Equilibrium
Abstract: Surfactants are chemicals that adsorb to interfaces, thereby reducing the surface energy. Non-uniform adsorption results in a gradient in surface energy, which induces a Marangoni flow in the fluid. To model this, we utilise a thermodynamically self-consistent approach, in which the constitutive laws for the surface energy and the adsorption rate are fundamentally connected. We make use of these constitutive laws in the modelling of surfactant dynamics in a confined geometry, with various initial conditions, and determine when non-equilibrium effects play a significant role in these dynamics.
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Title: (Callum) Extended Pseudo-spectral Physics-informed Neural Networks for Phase-field Models
Abstract: Phase-field models provide a fundamental continuum framework for describing phase separation and pattern formation in many physical and biological systems. Their predictive capability depends critically on constitutive quantities such as the bulk free-energy density and interfacial thickness parameter, which are often unknown and must be inferred from limited observations. In this work, we introduce an extended pseudo-spectral physics-informed neural network (ESPINN) framework for the inverse identification of phase-field models from transient snapshot data. The proposed method simultaneously reconstructs the bulk chemical potential and unknown gradient coefficients directly from dynamically evolving structures.
Numerical experiments show that ESPINN accurately recovers both the functional form of the free energy and the interfacial thickness parameter. Remarkably, substantial constitutive information can be extracted even from a single snapshot pair, while additional snapshots improve robustness and reduce variance across training runs. The framework remains stable in the presence of noise, with reconstruction accuracy improving as more observations are incorporated. These results highlight ESPINN as a data-efficient and physically consistent approach for learning constitutive structure in continuum models of phase separation.
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