[08/07/23] The role of exponential asymptotics and complex singularities in self-similarity, transitions, and branch merging of nonlinear dynamics. We study a prototypical example in nonlinear dynamics where transition to self-similarity in a singular limit is fundamentally changed as a parameter is varied. Here, we focus on the complicated dynamics that occur in a generalised unstable thin-film equation that yields finite-time rupture. A parameter, n, is introduced to model more general disjoining pressures. For the standard case of van der Waals intermolecular forces, n = 3, it was previously established that a countably infinite number of self-similar solutions exist leading to rupture. Each solution can be indexed by a parameter, ϵ = ϵ1 < ϵ2 < . . . < 0, and the prediction of the discrete set of solutions requires examination of terms beyond-all-orders in ϵ. However, recent numerical results have demonstrated the surprising complexity that exists for general values of n. In particular, the bifurcation structure of self-similar solutions now exhibits branch merging as n is varied. In this work, we shall present key ideas of how branch merging can be interpreted via exponential asymptotics.

Our study has been published in the Physica D: Nonlinear Phenomena journal, special issue on Applied and Computational Complex Analysis in the Study of Nonlinear Phenomena.

[04/07/23] Prof. Serafim Kalliadasis together with Prof. Pierre Degond from Institut de Mathématiques de Toulouse, CNRS & Université Paul Sabatier, Toulouse, France and Prof. Grigorios Pavliotis from the Department of Mathematics, Imperial College London, UK co-organised the CNRS-ICL workshop "Mean field limits for interacting particle systems: uniform propagation of chaos, phase transitions and applications" July 4, 2023 - July 6, 2023. Details are given here.

[23/06/23] Antonio Malpica-Morales gave a talk and presented a poster about our latest research work on "Physics-informed Bayesian inference of external potentials in classical density-functional theory" at the Imperial President's PhD Scholars Research Symposium 2023. You can check the details of this research work in the Projects section.

 [10/03/23] Prof. Serafim Kalliadasis together with Jim Lutsko from Université Libre de Bruxelles and Erik Santiso from North Carolina State University co-organised the CECAM flagship workshop "Metastability and multiscale effects in interfacial phenomena" March 13, 2023 - March 15, 2023. Details are given here.

[10/03/23] We are pleased that Dr. Peter Yatsyshin has been offered a Turing Research Fellowship with The Alan Turing Institute.

[07/02/23] Unconditional bound-preserving and energy-dissipating finite-volume schemes for the Cahn-Hilliard equation.  We propose finite-volume schemes for the Cahn-Hilliard equation which unconditionally and discretely preserve the boundedness of the phase field and the dissipation of the free energy. Our numerical framework is applicable to a variety of free-energy potentials, including Ginzburg-Landau and Flory-Huggins, to general wetting boundary conditions, and to degenerate mobilities. Its central thrust is the upwind methodology, which we combine with a semi-implicit formulation for the free-energy terms based on the classical convex-splitting approach. The extension of the schemes to an arbitrary number of dimensions is straightforward thanks to their dimensionally split nature, which allows to efficiently solve higher-dimensional problems with a simple parallelization. The numerical schemes are validated and tested through a variety of examples, in different dimensions, and with various contact angles between droplets and substrates.

Our work has been submitted in the journal Communications in Computational Physics. You can see the simulations in the following link.