Applied Mathematics Seminars Autumn 2024
See below for information regarding the Applied Seminars in Autumn 2024.
Seminars take place online on Tuesdays at 3.00pm on Zoom via the link https://ucl.zoom.us/j/99614222402. Many of the seminars will be ‘hybrid’ (i.e. in person +zoom). If you require any more information on the Applied seminars please contact Prof Jean-Marc Vanden-Broeck (e-mail: j.vanden-broeck AT ucl.ac.uk or tel: 020-7679-2835) or Prof Ilia Kamotski (e-mail: i.kamotski AT ucl.ac.uk or tel: 020-7679-3937).
Tuesday 8 October 2024 in Engineering Front Building, Executive Suite 103
Speaker: Gunnar Peng (UCL)
Title: Singularity and instability in drop electrohydrodynamics
Abstract:
Electrical manipulation of microscale flows has applications in e.g. printing, coating, microfabrication and microfluidics. Due to the nonlinear coupling between electrical and flow fields, even the simple case of a drop in an electric field can exhibit complex phenomena such as streaming from the poles or equator, and symmetry-breaking Quincke rotation or equatorial vortices. We consider a two-dimensional circular drop, neglecting deformation, and show that the Taylor-Melcher leaky-dielectric model reduces to a nonlinear integro-differential equation for the time evolution of the surface-charge density, which we simulate using a finite-difference scheme and analyse using asymptotic methods. We identify and charactarise a steady-state singularity in which the surface-charge density blows up as x^(-1/3), a finite-time singularity in which it blows up as (t0-t)^(-1/2), and a symmetry-breaking instability to Quincke rotation which can be subcritical, resulting in multi-stability.
Tuesday 15 October 2024 in Engineering Front Building, Executive Suite 103
Speaker: Dmitri Tseluiko (Loughborough)
Title: Singularity formation in inverted film flow and transition to dripping
Abstract:
The gravity-driven flow of a liquid film under an inclined plate is investigated at zero Reynolds number. Travelling-wave solutions are analysed assuming either a fixed fluid volume or a fixed flow rate for two thin-film models with either linearised or full curvature (the LCM and FCM, respectively) and the full equations of Stokes flow. Of particular interest is the breakdown of travelling-wave solutions as the plate inclination angle is increased, which is associated with the onset of dripping and which is analysed by asymptotic analysis and by constructing bifurcation diagrams for a wide range of parameters. It is found that the thin-film models either provide an accurate prediction for dripping onset or else supply an upper bound on the critical inclination angle [1]. The predictions from the asymptotic analysis and bifurcation diagrams are corroborated by direct numerical simulations for the Navier-Stokes equations using the open-source volume-of-fluid Gerris software.
Tuesday 23 October 2024 - no seminar
Tuesday 29 October 2024 in Engineering Front Building, Executive Suite 103
Speaker: Edwina Yeo (UCL)
Title: clumping and clotting: multiscale modelling of responsive species in fluid flows
Abstract:
A wide range of biological and therapeutic species change their behaviour, geometry or propensity to adhere in response to external stimuli. For instance, bacteria modify their swimming behaviour close to fluid boundaries and proteins unfold differently depending on local flow structure. Predicting the behaviour of these species in macroscale fluid flows is vital to mitigate and understand effects such as aggregation or surface adhesion.
In this talk, I will present examples of incorporating discrete microscale behaviour into continuum models via mean-field modelling. These applications include microscale protein unfolding to predict blood clot initiation, microscale magnetic interactions to predict the transport of magnetic nanoparticles and the dynamics of bacteria as they initiate biofilms. I will discuss the benefits of upscaling for model parameterisation and prediction as well as the limitations of the resulting macroscale models to reproduce discrete dynamics.
Tuesday 5 November 2024 - no seminar (Reading Week)
Tuesday 12 November 2024 on Zoom
Speaker: Anna-Lisa Varri (University of Edinburgh)
Title: rotating stellar systems and their black holes
Abstract:
The study of self-gravitating spheroidal rotating bodies is a classical fluid dynamics problem with a distinguished history, yet its kinetic counterpart has rarely been explored. As an example, I will present a family of self-consistent kinetic equilibria describing uniformly rotating, axisymmetric quasi-isothermal stellar systems. Such equilibria define a singular perturbation Vlasov-Poisson problem with a free boundary which can be approached using an asymptotic expansion based on the rotation strength parameter. I will then illustrate an extension to the case of self-consistent equilibria with a central black hole. Explicit asymptotic results are obtained over three nested regimes surrounding the sharp transition between equilibria dominated by the mass of the host stellar system or by the mass of the central black hole. I will conclude by discussing the astrophysical relevance of these results in the current era of black hole images and gravitational wave detections.
Tuesday 19 November 2024 on Zoom
Speaker: Lois Baker (University of Edinburgh)
Title: lagrangian filtering for wave-mean flow decomposition
Abstract:
In geophysical and astrophysical flows, we are often interested in understanding the impact of internal waves on the non-wavelike flow. For example, oceanic internal waves generated at the surface and the seafloor transfer energy from the large scale flow to dissipative scales, thereby influencing the global ocean state. A primary challenge in the study of wave-flow interactions is how to separate these processes – since waves and non-wavelike flows can vary on similar spatial and temporal scales in the Eulerian frame. However, in a Lagrangian flow-following frame, temporal filtering offers a convenient way to isolate waves. In this talk I’ll present and discuss some recently developed methods for evolving Lagrangian mean fields alongside the governing equations in a numerical simulation, allowing effective filtering of waves from non-wavelike processes.
Tuesday 26 November 2024 in Engineering Front Building, Executive Suite 103 & on Zoom
Speaker: Carina Dunlop (UCL)
Title: what do cells and tissues feel? integration of cell contractility, adhesion and ecm stiffness in mechanosensing
Abstract:
The role of tissue stiffness in controlling cell behaviour is well established. This has been shown across cell types and includes behaviours such as cell differentiation and drug susceptibility, with clear implications for health and disease. In experimental investigation of mechanosensing, bioengineered gels with defined mechanical properties are used to mimic varying tissue microenvironments. I will here discuss active matter models for cell and tissue mechanobiology, which incorporates observed sub-cellular spatial variations in mechanical activity and adhesion into continuum level descriptions of tissue response. Applications to epithelial sheets and organoids will be discussed including recent results showing that cells change active contractility in response to changes in adhesion patterning.
Tuesday 3 December 2024 in Engineering Front Building, Executive Suite 103 & on Zoom
Speaker: Catherine Kamal (UCL)
Title: ultra-thin particles under viscous shear
Abstract:
The classical no-slip condition occurs when a flowing liquid adheres to the surface of a particle. However, for ultra-thin particles with atomically smooth surfaces, such as disk-like graphene or rod-like carbon nanotubes, the liquid has been shown to slip over the surface instead. We investigate theoretically and computationally the effect of such hydrodynamic slip on the motion of isolated axisymmetric ellipsoidal particles in a viscous shear flow field when subject to a Navier-slip boundary condition. Under no-slip and neglectable Brownian fluctuations, the particles classically follow a complex periodic orbit known as a ‘Jeffery orbit’. We show analytically and computationally that, surprisingly, these periodic orbits vanish at a threshold value for the Navier-slip length for all geometric aspect ratios other than unity, which corresponds to a sphere. When the slip length exceeds this threshold, the particles align indefinitely in the flow. This result is due to slip reducing the tangential traction distribution over the planer surface of the particle when the surface is aligned in the flow direction. We then show that this change in orientational microstructure can bring remarkable changes to the macroscale variables of the suspension. For example, we predict that the effective viscosity can be smaller than the base fluid under certain flow conditions for typical slip length values, giving rise to new strategies to reduce friction in flow.
Tuesday 10 December 2024 in Engineering Front Building, Executive Suite 103 & on Zoom
Speaker: Mike Nieves (Keele University)
Title: resonances responses in structured elastic strips
Abstract:
We consider waves propagating through elastic triangular lattice strips formed from periodically placed masses interconnected by elastic rods. Of particular interest is the behaviour of the strips near resonance regimes, which we investigate for (i) a semi-infinite strip and (ii) a strip with gyroscopes attached to its junctions.
In the first part of the talk, we discuss the semi-infinite lattice strip and investigate the phenomenon of edge resonance for Lamb waves [1]. For real frequencies the edge resonance phenomenon is characterised by localised vibrations at the free edge of the strip. We show that resonance can be excited through the edge’s interaction with an incident zero order symmetric Lamb wave [2] and that the phenomenon occurs when only such modes can propagate. In particular, we verify the existence of a complex resonance frequency for the strip, associated with an eigenmode of the homogenous problem without an incident wave, that is responsible for the appearance of the edge resonance. We demonstrate how the solution to the scattering problem is derived via the Z-transform. This is then exploited to trace the appearance of the complex edge resonance frequency through the identification of quasi-resonance frequencies, at which amplitudes of evanescent waves reflected by the edge become large and the amplitude of the propagating reflected wave can fluctuate. For lattice strips of a fixed width, we also investigate the dependency of the complex edge resonance frequency on the lattice spacing.
In the second part of the talk, we consider the gyroscopic elastic strip. The presence of the gyroscopes makes the system non-reciprocal. Near resonance, this allows the medium to support uni-directional Lamb waves when subjected to forcing [3]. We discuss the solution to this problem and demonstrate how information related to this can lead to designs of novel waveguides. Namely, we illustrate how we can create networks of structured strips that can channel waves that propagate from one point in the system, along any predefined controllable path in the network, to any other point in the system.
All analytical results are accompanied by numerical simulations illustrating the approaches and their effectiveness when benchmarked against independent calculations based on the finite element method.
References:
[1] G. Carta, M. Nieves, M. Brun, V. Pagneux (2024): Edge resonance in triangular lattices strips and continuum approximation, (in preparation).
[2] G. Carta, M. Nieves, M. Brun (2023): Lamb waves in discrete homogeneous and heterogeneous systems: Dispersion properties, asymptotics and non-symmetric wave propagation, Eur. J, Mech. A-Solid 100, 104695.
[3] G. Carta, M.J., Nieves, M. Brun, (2023): Forcing the Silence of the Lamb waves: Uni-directional propagation in structured gyro-elastic strips and networks, Eur. J. Mec. A-Solid 101, 105070