Thu, 09 Jun 2022

12:00 - 13:00
L1

The ever-growing blob of fluid

Graham.Benham@maths.ox.ac.uk
(Mathematical Institute)
Abstract

Consider the injection of a fluid onto an impermeable surface for an infinite length of time... Does the injected fluid reach a finite height, or does it keep on growing forever? The classical theory of gravity currents suggests that the height remains finite, causing the radius to grow outwards like the square root of time. When the fluid resides within a porous medium, the same is thought to be true. However, recently I used some small scale experiments and numerical simulations, spanning 12 orders of magnitude in dimensionless time, to demonstrate that the height actually grows very slowly, at a rate ~t^(1/7)*(log(t))^(1/2). This strange behaviour can be explained by analysing the flow in a narrow "inner region" close to the source, in which there are significant vertical velocities and non-hydrostatic pressures. Analytical scalings are derived which match closely with both numerics and experiments, suggesting that the blob of fluid is in fact ever-growing, and therefore becomes unbounded with time.

Thu, 17 Nov 2022

12:00 - 13:00
L1

OCIAM TBC

Professor John Maddocks
(École Polytechnique Fédérale de Lausanne (EPFL))

The join button will be published 30 minutes before the seminar starts (login required).

Further Information

Born in Scotland and a former member of the British Olympic sailing team, the mathematician obtained his doctorate in Oxford. After several years as professor of mathematics in Maryland, USA, he returned to Europe to the École Polytechnique Fédérale de Lausanne (EPFL), where he has worked for nearly 20 years.

John Maddocks is a prominent expert in the multiscale modeling of DNA, the nucleic acid-based biological molecule that carries genetic information. He is interested above all in the nanomechanical properties of DNA molecules. These properties determine how DNA is "packed" and stored in our cells.

Text adapted from TU Berlin

Thu, 13 Oct 2022

12:00 - 13:00
L1

OCIAM TBC

Steven Strogatz
(Cornell University)
Further Information

Steven is Jacob Gould Schurman Professor of Applied Mathematics. He is known for his work on nonlinear systems, including contributions to the study of synchronization in dynamical systems, and for his research in a variety of areas of applied mathematics, including mathematical biology and complex network theory.

Thu, 27 Oct 2022

12:00 - 13:00
L1

OCIAM TBC

Saverio Spagnolie
(Univeresity of Wisconsin-Madison)

The join button will be published 30 minutes before the seminar starts (login required).

Further Information

Saverio E. Spagnolie is Associate Professor of Mathematics and (by courtesy) Chemical & Biological Engineering. His research areas include Fluid Mechanics, Soft Matter, Biophysics, Applied Mathematics, Numerical Methods.

 
Thu, 20 Oct 2022

12:00 - 13:00
L1

OCIAM TBC

Prof Halim Kusumaatmaja
(Durham University)

The join button will be published 30 minutes before the seminar starts (login required).

Abstract

Prof Halim Kusumaatmaja's group is interested in theoretical and computational soft matter and biophysics. Their work is interdisciplinary, lying at the interface between Physics, Chemistry, Engineering and Biology. They are also part of the Durham Centre for Soft Matter, the Biophysical Sciences Institute, and the SOFI CDT. See here for more detailed descriptions.

Thu, 02 Jun 2022

12:00 - 13:00
L1

Hybrid modeling for the stochastic simulation of spatial and non-spatial multi-scale chemical kinetics

Konstantinos Zygalakis
(School of Mathematical Sciences University of Edinburgh)
Abstract

It is well known that stochasticity can play a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be adequately modeled by Markov processes and, for such systems, methods such as Gillespie’s algorithm are typically employed. While such schemes are easy to implement and are exact, the computational cost of simulating such systems can become prohibitive as the frequency of the reaction events increases. This has motivated numerous coarse-grained schemes, where the “fast” reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation for systems where all reactants are present in large concentrations, the approximation breaks down when the fast chemical species exist in small concentrations, giving rise to significant errors in the simulation. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as computing observables of cell cycle models. In this talk, we present a hybrid scheme for simulating well-mixed stochastic kinetics, using Gillespie–type dynamics to simulate the network in regions of low reactant concentration, and chemical Langevin dynamics when the concentrations of all species are large. These two regimes are coupled via an intermediate region in which a “blended” jump-diffusion model is introduced. Examples of gene regulatory networks involving reactions occurring at multiple scales, as well as a cell-cycle model are simulated, using the exact and hybrid scheme, and compared, both in terms of weak error, as well as computational cost. If there is time, we will also discuss the extension of these methods for simulating spatial reaction kinetics models, blending together partial differential equation with compartment based approaches, as well as compartment based approaches with individual particle models.

This is joint work with Andrew Duncan (Imperial), Radek Erban (Oxford), Kit Yates (Bath), Adam George (Bath), Cameron Smith (Bath), Armand Jordana (New York )

Thu, 12 May 2022

12:00 - 13:00
L1

Averaged interface conditions: evaporation fronts in porous media (Ellen Luckins) & Macroscopic Transport in Heterogeneous Porous Materials (Lucy Auton)

Lucy Auton & Ellen Luckins
(Mathematical Institute, University of Oxford)
Abstract

Macroscopic Transport in Heterogeneous Porous Materials

Lucy Auton

Solute transport in porous materials is a key physical process in a wide variety of situations, including contaminant transport, filtration, lithium-ion batteries, hydrogeological systems, biofilms, bones and soils. Despite the prevalence of solute transport in porous materials, the effect of microstructure on flow and transport remains poorly understood and improving our understanding of this remains a major challenge.  In this presentation, I consider a two-dimensional microstructure comprising an array of obstacles of smooth but arbitrary shape, the size and spacing of which can vary along the length of the porous medium, allowing for anisotropy.  I use a nontrivial extension to classical homogenisation theory via the method of multiple scales to rigorously upscale the novel problem involving cells of varying area. This results in simple effective continuum equations for macroscale flow and transport where the effect of the microscale geometry on the macroscopic transport and removal is encoded within these simple macroscale equations via effective parameters such as an effective local anisotropic diffusivity and an effective local adsorption rate.  For a simple example geometry I exploit the two degrees of microstructural freedom in this problem, obstacle size and obstacle spacing, to investigate scenarios of uniform porosity but heterogenous microstructure, noting the impact this heterogeneity has on filter efficiency. 

This model constitutes the development of the core framework required to consider other crucial problems such as solute transport within soft porous materials for which there does not currently exist a simple macroscale model where the effective diffusivity and removal depend on the microstructure. Further, via this methodology I will  derive a  bespoke model for fluoride and arsenic removal filters. With this model I will be able to optimise the design of fluoride-removal filters which are being deployed across rural India. The design optimisation will both increase filter lifespan and reduce filter cost, enabling more people to access safe drinking water

 

Averaged interface conditions: evaporation fronts in porous media

Ellen Luckins

Homogenisation methods are powerful tools for deriving effective PDE models for processes incorporating multiple length-scales. For physical systems in which interface processes are crucial to the overall system, we might ask how the microstructure impacts the effective interface conditions, in addition to the PDEs in the bulk. In this talk we derive an effective model for the motion of an evaporation front through porous media, combining homogenisation and boundary layer analysis to derive averaged interface conditions at the evaporation front. Our analysis results in a new effective parameter in the boundary conditions, which encodes how the shape and speed of the porescale evaporating interfaces impact the overall drying process.

Mon, 10 Oct 2022

12:45 - 13:45
L1

Timelike Liouville gravity on the sphere and the disk

Teresa Bautista
(King's College London)
Abstract

Liouville conformal field theory models two-dimensional gravity with a cosmological constant and conformal matter. In its timelike regime, it reproduces the characteristic negative kinetic term of the conformal factor of the metric in the Einstein-Hilbert action, the sign which infamously makes the gravity path integral ill-defined. In this talk, I will first discuss the perturbative computation of the timelike Liouville partition function around the sphere saddle and propose an all-orders result. I will then turn to the disk and present the bulk 1-point functions of this CFT, and discuss possible interpretations in terms of boundary conditions.

Thu, 28 Apr 2022

12:00 - 13:00
L1

Modeling and Design Optimization for Pleated Membrane Filters

Yixuan Sun & Zhaohe Dai
(Mathematical Institute (University of Oxford))
Abstract

Statics and dynamics of droplets on lubricated surfaces

Zhaohe Dai

The abstract is "Slippery liquid infused porous surfaces are formed by coating surface with a thin layer of oil lubricant. This thin layer prevents other droplets from reaching the solid surface and allows such deposited droplets to move with ultra-low friction, leading to a range of applications. In this talk, we will discuss the static and dynamic behaviour of droplets placed on lubricated surfaces. We will show that the layer thickness and the size of the substrate are key parameters in determining the final equilibrium. However, the evolution towards the equilibrium is extremely slow (on the order of days for typical experimental parameter values). As a result, we suggest that most previous experiments with oil films lubricating smooth substrates are likely to have been in an evolving, albeit slowly evolving, transient state.

 

Modeling and Design Optimization for Pleated Membrane Filters

Yixuan Sun

Membrane filtration is widely used in many applications, ranging from industrial processes to everyday living activities. With growing interest from both industrial and academic sectors in understanding the various types of filtration processes in use, and in improving filter performance, the past few decades have seen significant research activity in this area. Experimental studies can be very valuable, but are expensive and time-consuming, therefore theoretical studies offer potential as a cost-effective and predictive way to improve on current filter designs. In this work, mathematical models, derived from first principles and simplified using asymptotic analysis, are proposed for pleated membrane filters, where the macroscale flow problem of Darcy flow through a pleated porous medium is coupled to the microscale fouling problem of particle transport and deposition within individual pores of the membrane. Asymptotically-simplified models are used to describe and evaluate the membrane performance numerically and filter design optimization problems are formulated and solved for industrially-relevant scenarios. This study demonstrates the potential of such modeling to guide industrial membrane filter design for a range of applications involving purification and separation.

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