Forthcoming events in this series


Thu, 18 Feb 2021

12:00 - 13:00
Virtual

Identifiability and inference for models in mathematical biology.

Professor Ruth Baker
(University of Oxford)
Further Information

We continue this term with our flagship seminars given by notable scientists on topics that are relevant to Industrial and Applied Mathematics. 

Note the new time of 12:00-13:00 on Thursdays.

This will give an opportunity for the entire community to attend and for speakers with childcare responsibilities to present.

Abstract

Simple mathematical models have had remarkable successes in biology, framing how we understand a host of mechanisms and processes. However, with the advent of a host of new experimental technologies, the last ten years has seen an explosion in the amount and types of quantitative data now being generated. This sets a new challenge for the field – to develop, calibrate and analyse new, biologically realistic models to interpret these data. In this talk I will showcase how quantitative comparisons between models and data can help tease apart subtle details of biological mechanisms, as well as present some steps we have taken to tackle the mathematical challenges in developing models that are both identifiable and can be efficiently calibrated to quantitative data.

Thu, 11 Feb 2021

12:00 - 13:00
Virtual

Peristalsis, beading and hexagons: three short stories about elastic instabilities in soft solids

John Biggins
(Cambridge)
Further Information

We continue this term with our flagship seminars given by notable scientists on topics that are relevant to Industrial and Applied Mathematics. 

Note the new time of 12:00-13:00 on Thursdays.

This will give an opportunity for the entire community to attend and for speakers with childcare responsibilities to present.

Abstract

This talk will be three short stories on the general theme of elastic
instabilities in soft solids. First I will discuss the inflation of a
cylindrical cavity through a bulk soft solid, and show that such a
channel ultimately becomes unstable to a finite wavelength peristaltic
undulation. Secondly, I will introduce the elastic Rayleigh Plateau
instability, and explain that it is simply 1-D phase separation, much
like the inflationary instability of a cylindrical party balloon. I will
then construct a universal near-critical analytic solution for such 1-D
elastic instabilities, that is strongly reminiscent of the
Ginzberg-Landau theory of magnetism. Thirdly, and finally, I will
discuss pattern formation in layer-substrate buckling under equi-biaxial
compression, and argue, on symmetry grounds, that such buckling will
inevitably produce patterns of hexagonal dents near threshold.

Thu, 04 Feb 2021

12:00 - 13:00
Virtual

From Fast Cars to Breathing Aids: the UCL Ventura Non-Invasive Ventilator for COVID-19

Rebecca Shipley
(UCL)
Further Information

We continue this term with our flagship seminars given by notable scientists on topics that are relevant to Industrial and Applied Mathematics. 

Note the new time of 12:00-13:00 on Thursdays.

This will give an opportunity for the entire community to attend and for speakers with childcare responsibilities to present.

Abstract

In March 2020, as COVID-19 cases started to surge for the first time in the UK, a team spanning UCL engineers, University College London Hospital (UCLH) intensivists and Mercedes Formula 1 came together to design, manufacture and deploy non-invasive breathing aids for COVID-19 patients. We reverse engineered and an off-patent CPAP (continuous positive airways pressure) device, the Philips WhisperFlow, and changed its design to minimise its oxygen utilisation (given that hospital oxygen supplies are under extreme demand). The UCL-Ventura received regulatory approvals from the MHRA within 10 days, and Mercedes HPP manufactured 10,000 devices by mid-April. UCL-Ventura CPAPs are now in use in over 120 NHS hospitals.


In response to international need, the team released all blueprints open source to enable local manufacture in other countries, alongside a support package spanning technical, manufacturing, clinical and regulatory components. The designs have been downloaded 1900 times across 105 countries, and around 20 teams are now manufacturing at scale and deploying in local hospitals. We have also worked closely with NGOs, on a non-profit basis, to deliver devices directly to countries with urgent need, including Palestine, Uganda and South Africa.

Thu, 28 Jan 2021

12:00 - 13:00
Virtual

Rheology of dense granular suspensions

Elisabeth Guazzelli
(MSC CNRS Université de Paris)
Further Information

We continue this term with our flagship seminars given by notable scientists on topics that are relevant to Industrial and Applied Mathematics. 

Note the new time of 12:00-13:00 on Thursdays.

This will give an opportunity for the entire community to attend and for speakers with childcare responsibilities to present.

Abstract

Suspensions are composed of mixtures of particles and fluid and are
ubiquitous in industrial processes (e.g. waste disposal, concrete,
drilling muds, metalworking chip transport, and food processing) and in
natural phenomena (e.g. flows of slurries, debris, and lava). The
present talk focusses on the rheology of concentrated suspensions of
non-colloidal particles. It addresses the classical shear viscosity of
suspensions but also non-Newtonian behaviour such as normal-stress
differences and shear-induced migration. The rheology of dense
suspensions can be tackled via a diversity of approaches that are
introduced. In particular, the rheometry of suspensions can be
undertaken at an imposed volume fraction but also at imposed values of
particle normal stress, which is particularly well suited to yield
examination of the rheology close to the jamming transition. The
influences of particle roughness and shape are discussed.

Thu, 21 Jan 2021

12:00 - 13:30
Virtual

Node-based approximation of contagion dynamics on networks

Cameron Hall
(University of Bristol)
Abstract

Contagion models on networks can be used to describe the spread of information, rumours, opinions, and (more topically) diseases through a population. In the simplest contagion models, each node represents an individual that can be in one of a number of states (e.g. Susceptible, Infected, or Recovered), and the states of the nodes evolve according to specified rules. Even with simple Markovian models of transmission and recovery, it can be difficult to compute the dynamics of contagion on large networks: running simulations can be slow, and the system of master equations is typically too large to be tractable.

 One approach to approximating contagion dynamics is to assume that each node state is independent of the neighbouring node states; this leads to a system of ODEs for the node state probabilities (the “first-order approximation”) that always overestimates the speed of infection spread. This approach can be made more sophisticated by introducing pair approximations or higher-order moment closures, but this dramatically increases the size of the system and slows computations. In this talk, I will present some alternative node-based approximations for contagion dynamics. The first of these is exact on trees but will always underestimate the speed of infection spread on a network with loops. I will show how this can be combined with the classic first-order node-based approximation to obtain a node-based approximation that has similar accuracy to the pair approximation, but which is considerably faster to solve.

Thu, 03 Dec 2020

16:00 - 17:30
Virtual

Kirigami

Lakshminarayanan Mahadevan
(Harvard)
Further Information

We return this term to our usual flagship seminars given by notable scientists on topics that are relevant to Industrial and Applied Mathematics. 

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

Abstract

Kirigami, the relatively unheralded cousin of origami, is the art of cutting paper to articulate and deploy it as a whole. By varying the number, size, orientation and coordination of the cuts, artists have used their imagination and intuition to create remarkable sculptures in 2 and 3 dimensions. I will describe some of our attempts to quantify the inverse problem that artists routinely solve, combining elementary mathematical ideas, with computations and physical models. 

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Thu, 26 Nov 2020

16:00 - 17:00
Virtual

Convective instabilities in ternary alloy solidification

Daniel M. Anderson
(George Mason University)
Further Information

We return this term to our usual flagship seminars given by notable scientists on topics that are relevant to Industrial and Applied Mathematics. 

Abstract

Daniel M. Anderson

Department of Mathematical Sciences, George Mason University

Applied and Computational Mathematics Division, NIST

Binary and multicomponent alloy solidification occurs in many industrial materials science applications as well as in geophysical systems such as sea ice. These processes involve heat and mass transfer coupled with phase transformation dynamics and can involve the formation of mixed phase regions known as mushy layers.  The understanding of transport mechanisms within mushy layers has important consequences for how these regions interact with the surrounding liquid and solid regions.  Through linear stability analyses and numerical calculations of mathematical models, convective instabilities that occur in solidifying ternary alloys will be explored.  Novel fluid dynamical phenomena that are predicted for these systems will be discussed.

Thu, 19 Nov 2020

16:00 - 17:00
Virtual

OCIAM DPhils present their research

Amy Kent, Michael Negus, Edwina Yeo and Helen Zha
(University of Oxford)
Abstract

Amy Kent

Multiscale Mathematical Models for Tendon Tissue Engineering

 

Tendon tissue engineering aims to grow functional tendon in vitro. In bioreactor chambers, cells growing on a solid scaffold are fed with nutrient-rich media and stimulated by mechanical loads. The Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences is developing a Humanoid Robotic Bioreactor, where cells grow on a flexible fibrous scaffold actuated by a robotic shoulder. Tendon cells modulate their behaviour in response to shear stresses - experimentally, it is desirable to design robotic loading regimes that mimic physiological loads. The shear stresses are generated by flowing cell media; this flow induces deformation of the scaffold which in turn modulates the flow. Here, we capture this fluid-structure interaction using a homogenised model of fluid flow and scaffold deformation in a simplified bioreactor geometry. The homogenised model admits analytical solutions for a broad class of forces representing robotic loading. Given the solution to the microscale problem, we can determine microscale shear stresses at any point in the domain. In this presentation, we will outline the model derivation and discuss the experimental implications of model predictions.

=======================

Michael Negus

High-Speed Droplet Impact Onto Deformable Substrates: Analysis And Simulations

 

The impact of a high-speed droplet onto a substrate is a highly non-linear, multiscale phenomenon and poses a formidable challenge to model. In addition, when the substrate is deformable, such as a spring-suspended plate or an elastic sheet, the fluid-structure interaction introduces an additional layer of complexity. We present two modeling approaches for droplet impact onto deformable substrates: matched asymptotics and direct numerical simulations. In the former, we use Wagner's theory of impact to derive analytical expressions which approximate the behaviour during the early stages of the impact. In the latter, we use the open source volume-of-fluid code Basilisk to conduct direct numerical simulations designed to both validate the analytical framework and provide insight into the later times of impact. Through both methods, we are able to observe how the properties of the substrate, such as elasticity, affect the behaviour of the flow. We conclude by showing how these methods are complementary, as a combination of both can lead to a thorough understanding of the droplet impact across timescales.

=======================

Edwina Yeo

Modelling of Magnetically Targeted Stem Cell Delivery

 

Targeting delivery of stem cells to the site of an injury is a key challenge in regenerative medicine. One possible approach is to inject cells implanted withmagnetic nanoparticles into the blood stream. Cells can then be targeted to the delivery site by an external magnetic field. At the injury site, it is of criticalimportance that the cells do not form an aggregate which could significantly occlude the vessel.We develop a model for the transport of magnetically tagged cells in blood under the action of an external magnetic field. We consider a system of blood and stem cells in a single vessel.  We exploit the small aspect ratio of the vessel to examine the system asymptotically. We consider the system for a range of magnetic field strengths and varying strengths of the diffusion coefficient of the stem cells. We explore the different regimes of the model and determine the optimal conditions for the effective delivery of stem cells while minimising vessel occlusion.


=======================

Helen Zha

Mathematical model of a valve-controlled, gravity driven bioreactor for platelet production

Hospitals sometimes experience shortages of donor blood platelet supplies, motivating research into~\textit{in vitro}~production of platelets. We model a novel platelet bioreactor described in Shepherd et al [1]. The bioreactor consists of an upper channel, a lower channel, and a cell-seeded porous collagen scaffold situated between the two. Flow is driven by gravity, and controlled by valves on the four inlets and outlets. The bioreactor is long relative to its width, a feature which we exploit to derive a lubrication reduction of unsteady Stokes flow coupled to Darcy. As the shear stress experienced by cells influences platelet production, we use our model to quantify the effect of varying pressure head and valve dynamics on shear stress.

 

[1] Shepherd, J.H., Howard, D., Waller, A.K., Foster, H.R., Mueller, A., Moreau, T., Evans, A.L., Arumugam, M., Chalon, G.B., Vriend, E. and Davidenko, N., 2018. Structurally graduated collagen scaffolds applied to the ex vivo generation of platelets from human pluripotent stem cell-derived megakaryocytes: enhancing production and purity. Biomaterials.

Thu, 12 Nov 2020

16:00 - 17:00
Virtual

The fluid mechanics of suspensions

Helen Wilson
(University College London)
Further Information
Abstract

Materials made from a mixture of liquid and solid are, instinctively, very obviously complex. From dilatancy (the reason wet sand becomes dry when you step on it) to extreme shear-thinning (quicksand) or shear-thickening (cornflour oobleck) there is a wide range of behaviours to explain and predict. I'll discuss the seemingly simple case of solid spheres suspended in a Newtonian fluid matrix, which still has plenty of surprises up its sleeve.

Thu, 05 Nov 2020

16:00 - 17:30
Virtual

Stupid, but smart: chemotactic and autochemotactic effects in self-propelling droplets

Corinna Maass
(MPI Dynamics & Self-Organization)
Further Information

We return this term to our usual flagship seminars given by notable scientists on topics that are relevant to Industrial and Applied Mathematics. 

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

Abstract

Artificial microswimmers are an emerging field of research, attracting
interest as testing beds for physical theories of complex biological
entities, as inspiration for the design of smart materials, and for the
sheer elegance, and often quite counterintuitive phenomena of
experimental nonlinear dynamics.

Self-propelling droplets are among the most simplified swimmer models
imaginable, requiring just three components (oil, water, surfactant). In
this talk, I will show how these inherently stupid objects can make
surprisingly smart decisions based on interactions with microfluidic
structures and self-generated and external chemical fields.

Thu, 29 Oct 2020

16:00 - 17:00
Virtual

A Theory for Undercompressive Shocks in Tears of Wine

Andrea Bertozzi
(University of California Los Angeles)
Further Information

We return this term to our usual flagship seminars given by notable scientists on topics that are relevant to Industrial and Applied Mathematics. 

 

Abstract

We revisit the tears of wine problem for thin films in
water-ethanol mixtures and present a new model for the climbing
dynamics. The new formulation includes a Marangoni stress balanced by
both the normal and tangential components of gravity as well as surface
tension which lead to distinctly different behavior. The combined
physics can be modeled mathematically by a scalar conservation law with
a nonconvex flux and a fourth order regularization due to the bulk
surface tension. Without the fourth order term, shock solutions must
satisfy an entropy condition - in which characteristics impinge on the
shock from both sides. However, in the case of a nonconvex flux, the
fourth order term is a singular perturbation that allows for the
possibility of undercompressive shocks in which characteristics travel
through the shock. We present computational and experimental evidence
that such shocks can happen in the tears of wine problem, with a
protocol for how to observe this in a real life setting.

Thu, 22 Oct 2020

16:00 - 17:00
Virtual

Thin Film Flows on a Substrate of Finite Width: A Novel Similarity Solution

Howard Stone
(Princeton)
Further Information

We return this term to our usual flagship seminars given by notable scientists on topics that are relevant to Industrial and Applied Mathematics. 

 

Abstract

There are many examples of thin-film flows in fluid dynamics, and in many cases similarity solutions are possible. In the typical, well-known case the thin-film shape is described by a nonlinear partial differential equation in two independent variables (say x and t), which upon recognition of a similarity variable, reduces the problem to a nonlinear ODE. In this talk I describe work we have done on 1) Marangoni-driven spreading on pre-wetted films, where the thickness of the pre-wetted film affects the dynamics, and 2) the drainage of a film on a vertical substrate of finite width. In the latter case we find experimentally a structure to the film shape near the edge, which is a function of time and two space variables. Analysis of the corresponding thin-film equation shows that there is a similarity solution, collapsing three independent variables to one similarity variable, so that the PDE becomes an ODE. The solution is in excellent agreement with the experimental measurements.

Thu, 15 Oct 2020

16:00 - 17:00
Virtual

Inversion in Volvox: Forces and Fluctuations of Cell Sheet Folding

Pierre Haas
(University of Oxford)
Abstract

Tissue folding during animal development involves an intricate interplay
of cell shape changes, cell division, cell migration, cell
intercalation, and cell differentiation that obfuscates the underlying
mechanical principles. However, a simpler instance of tissue folding
arises in the green alga Volvox: its spherical embryos turn themselves
inside out at the close of their development. This inversion arises from
cell shape changes only.

In this talk, I will present a model of tissue folding in which these
cell shape changes appear as variations of the intrinsic stretches and
curvatures of an elastic shell. I will show how this model reproduces
Volvox inversion quantitatively, explains mechanically the arrest of
inversion observed in mutants, and reveals the spatio-temporal
regulation of different biological driving processes. I will close with
two examples illustrating the challenges of nonlinearity in tissue
folding: (i) constitutive nonlinearity leading to nonlocal elasticity in
the continuum limit of discrete cell sheet models; (ii) geometric
nonlinearity in large bending deformations of morphoelastic shells.
 

Thu, 18 Jun 2020

16:00 - 16:45
Virtual

OCIAM learns ... about wrinkling.

Professor Dominic Vella
(Mathematical Institute)
Further Information

This term's IAM seminar, a bi-weekly series entitled, 'OCIAM learns about ...' will involve internal speakers giving a general introduction to a topic on which they are experts.

Join the seminar in Zoom

https://zoom.us/j/91733296449?pwd=c29vMDluR0RCRHJia2JEcW1LUVZjUT09 
 Meeting ID: 917 3329 6449Password: 329856One 

Abstract


This week Professor Dominic Vella will talk about wrinkling  

In this talk I will provide an overview of recent work on the wrinkling of thin elastic objects. In particular, the focus of the talk will be on answering questions that arise in recent applications that seek not to avoid, but rather, exploit wrinkling. Such applications usually take place far beyond the threshold of instability and so key themes will be the limitations of “standard” instability analysis, as well as what analysis should be performed instead. I will discuss the essential ingredients of this ‘Far-from-Threshold’ analysis, as well as outlining some open questions.  

Thu, 04 Jun 2020

16:00 - 16:45

OCIAM learns...about modelling ice sheets

Professor Ian Hewitt
(Mathematical Institute)
Further Information

A new bi-weekly seminar series, 'OCIAM learns ..."

Internal speakers give a general introduction to a topic on which they are experts.

Abstract

Abstract

This talk will provide an overview of mathematical modelling applied to the behaviour of ice sheets and their role in the climate system.  I’ll provide some motivation and background, describe simple approaches to modelling the evolution of the ice sheets as a fluid-flow problem, and discuss some particular aspects of the problem that are active areas of current research.  The talk will involve a variety of interesting continuum-mechanical models and approximations that have analogues in other areas of applied mathematics.


You can join the meeting by clicking on the link below.
Join Zoom Meeting
https://zoom.us/j/91733296449?pwd=c29vMDluR0RCRHJia2JEcW1LUVZjUT09
Meeting ID: 917 3329 6449
Password: 329856

Thu, 28 May 2020

16:00 - 16:45

OCIAM learns ... about the many facets of community detection on networks 

Professor Renaud Lambiotte
(Mathematical Institute)
Further Information

A new bi-weekly seminar series, 'OCIAM learns...."

Internal speakers give a general introduction to a topic on which they are experts.

Abstract

The many facets of community detection on networks 

Community detection, the decomposition of a graph into essential building blocks, has been a core research topic in network science over the past years. Since a precise notion of what consti- tutes a community has remained evasive, community detection algorithms have often been com- pared on benchmark graphs with a particular form of assortative community structure and classified based on the mathematical techniques they employ. However, this comparison can be misleading because apparent similarities in their mathematical machinery can disguise different goals and rea- sons for why we want to employ community detection in the first place. Here we provide a focused review of these different motivations that underpin community detection. This problem-driven classification is useful in applied network science, where it is important to select an appropriate algorithm for the given purpose. Moreover, highlighting the different facets of community detection also delineates the many lines of research and points out open directions and avenues for future research.

Thu, 07 May 2020

16:00 - 16:45
Virtual

OCIAM learns ... about exponential asymptotics

Professor Jon Chapman
(Mathematical Institute)
Further Information

A new bi-weekly seminar series, 'OCIAM learns...."

Internal speakers give a general introduction to a topic on which they are experts.

Thu, 12 Mar 2020

16:00 - 17:30
L3

Modelling Dementia

Professor Alain Goriely
(Mathematical Institute)
Abstract

Neurodegenerative diseases such as Alzheimer’s or Parkinson’s are devastating conditions with poorly understood mechanisms and no known cure. Yet a striking feature of these conditions is the characteristic pattern of invasion throughout the brain, leading to well-codified disease stages visible to neuropathology and associated with various cognitive deficits and pathologies. In this talk, I will show that by linking new mathematical theories to recent progress in imaging, we can unravel some of the universal features associated with dementia and, more generally, brain functions. In particular, I will outline interesting mathematical problems and ideas that naturally appear in the process.

Thu, 05 Mar 2020

16:00 - 17:30
L3

IAM Seminar TBC

Jessica Williams and Andrew Krause
(Mathematical Institute (University of Oxford))
Abstract


Heterogeneity in Space and Time: Novel Dispersion Relations in Morphogenesis

Dr. Andrew Krause

Motivated by recent work with biologists, I will showcase some results on Turing instabilities in complex domains. This is scientifically related to understanding developmental tuning in the whiskers of mice, and in synthetic quorum-sensing patterning of bacteria. Such phenomena are typically modelled using reaction-diffusion systems of morphogens, and one is often interested in emergent spatial and spatiotemporal patterns resulting from instabilities of a homogeneous equilibrium. In comparison to the well-known effects of how advection or manifold structure impacts the modes which may become unstable in such systems, I will present results on instabilities in heterogeneous systems, reaction-diffusion systems on evolving manifolds, as well as layered reaction-diffusion systems. These contexts require novel formulations of classical dispersion relations, and may have applications beyond developmental biology, such as in understanding niche formation for populations of animals in heterogeneous environments. These approaches also help close the vast gap between the simplistic theory of instability-driven pattern formation, and the messy reality of biological development, though there is still much work to be done in concretely demonstrating such a theory's applicability in real biological systems.
 

Cavity flow characteristics and applications to kidney stone removal

Dr. Jessica Williams


Ureteroscopy is a minimally invasive surgical procedure for the removal of kidney stones. A ureteroscope, containing a hollow, cylindrical working channel, is inserted into the patient's kidney. The renal space proximal to the scope tip is irrigated, to clear stone particles and debris, with a saline solution that flows in through the working channel. We consider the fluid dynamics of irrigation fluid within the renal pelvis, resulting from the emerging jet through the working channel and return flow through an access sheath . Representing the renal pelvis as a two-dimensional rectangular cavity, we investigate the effects of flow rate and cavity size on flow structure and subsequent clearance time of debris. Fluid flow is modelled with the steady incompressible Navier-Stokes equations, with an imposed Poiseuille profile at the inlet boundary to model the jet of saline, and zero-stress conditions on the outlets. The resulting flow patterns in the cavity contain multiple vortical structures. We demonstrate the existence of multiple solutions dependent on the Reynolds number of the flow and the aspect ratio of the cavity using complementary numerical simulations and PIV experiments. The clearance of an initial debris cloud is simulated via solutions to an advection-diffusion equation and we characterise the effects of the initial position of the debris cloud within the vortical flow and the Péclet number on clearance time. With only weak diffusion, debris that initiates within closed streamlines can become trapped. We discuss a flow manipulation strategy to extract debris from vortices and decrease washout time.

 

Thu, 20 Feb 2020

16:00 - 17:30
L3

The brain's waterscape

Marie Elisabeth Rognes
(Simula Research Laboratory)
Further Information

Short bio:

Marie E. Rognes is Chief Research Scientist and Research Professor in Scientific Computing and Numerical Analysis at Simula Research Laboratory, Oslo, Norway. She received her Ph.D from the University of Oslo in 2009 with an extended stay at the University of Minneapolis, Twin Cities, Minneapolis, US. She has been at Simula Research Laboratory since 2009, led its Department for Biomedical Computing from 2012-2016 and currently leads a number of research projects focusing on mathematical modelling and numerical methods for brain mechanics including an ERC Starting Grant in Mathematics. She won the 2015 Wilkinson Prize for Numerical Software, the 2018 Royal Norwegian Society of Sciences and Letters Prize for Young Researchers within the Natural Sciences, and was a Founding Member of the Young Academy of Norway.

Abstract

Your brain has its own waterscape: whether you are reading or sleeping, fluid flows around or through the brain tissue and clears waste in the process. These physiological processes are crucial for the well-being of the brain. In spite of their importance we understand them but little. Mathematics and numerics could play a crucial role in gaining new insight. Indeed, medical doctors express an urgent need for modeling of water transport through the brain, to overcome limitations in traditional techniques. Surprisingly little attention has been paid to the numerics of the brain’s waterscape however, and fundamental knowledge is missing. In this talk, I will discuss mathematical models and numerical methods for the brain's waterscape across scales - from viewing the brain as a poroelastic medium at the macroscale and zooming in to studying electrical, chemical and mechanical interactions between brain cells at the microscale.
 

Thu, 13 Feb 2020

16:00 - 17:30
L3

Nonlinear Schrödinger PDEs and Some Applications in Atomic and Optical Physics

Professor Panos Kevrekidis
(University of Massachusetts)
Abstract

Nonlinear generalizations of the Schrödinger equation are of wide applicability to a range of areas including atomic and optical systems, 
plasma physics and water waves.  In this  talk we revisit some principal excitations in atomic and optical systems (such as Bose-Einstein condensates and photo-refractive crystals), namely dark solitonic fronts in single-component systems, and dark-bright waves in multi-component systems. Upon introducing them and explaining their existence and stability properties in one spatial dimension, we will extend them both in the form of stripes and in that rings in two-dimensions, presenting an alternative (adiabatic-invariant based) formulation of their stability and excitations. We will explore their filamentary dynamics, as well as the states that emerge from their transverse (snaking) instability. Then, we will consider these structures even in three dimensions, in the form of planar, as well as spherical shell wave patterns and generalize our adiabatic invariant formulation there. Finally, time permitting, we will give some glimpses of how some of these dynamical features in 1d and 2d generalize in a multi-orbital, time-dependent quantum setting.

Thu, 06 Feb 2020

18:00 - 19:00
NAPL

Multicellular Calculus

Professor Oliver Jensen
(University of Manchester)
Further Information

The lecture will take place in the Michael Dummett Lecture Theatre (Blue Boar quad, Christ Church).

Thu, 30 Jan 2020

16:00 - 17:30
L3

Feedback control of falling liquid films

Susana Gomes
(University of Warwick)
Abstract

The flow of a thin film down an inclined plane is an important physical phenomenon appearing in many industrial applications, such as coating (where it is desirable to maintain the fluid interface flat) or heat transfer (where a larger interfacial area is beneficial). These applications lead to the need of reliably manipulating the flow in order to obtain a desired interfacial shape. The interface of such thin films can be described by a number of models, each of them exhibiting instabilities for certain parameter regimes. In this talk, I will propose a feedback control methodology based on same-fluid blowing and suction. I use the Kuramoto–Sivashinsky (KS) equation to model interface perturbations and to derive the controls. I will show that one can use a finite number of point-actuated controls based on observations of the interface to stabilise both the flat solution and any chosen nontrivial solution of the KS equation. Furthermore, I will investigate the robustness of the designed controls to uncertain observations and parameter values, and study the effect of the controls across a hierarchy of models for the interface, which include the KS equation, (nonlinear) long-wave models and the full Navier–Stokes equations.

Thu, 23 Jan 2020

16:00 - 17:30
L3

Thermal Fluctuations in Free Surface Nanoflows

James Sprittles
(University of Warwick)
Abstract

The Navier-Stokes paradigm does not capture thermal fluctuations that drive familiar effects such as Brownian motion and are seen to be key to understanding counter-intuitive phenomena in nanoscale interfacial flows.  On the other hand, molecular simulations naturally account for these fluctuations but are limited to exceptionally short time scales. A framework that incorporates thermal noise is provided by fluctuating hydrodynamics, based on the so-called Landau-Lifshitz-Navier-Stokes equations, and in this talk we shall exploit these equations to gain insight into nanoscale free surface flows.  Particular attention will be given to flows with topological changes, such as the coalescence of drops, breakup of jets and rupture of thin liquid films for which both analytic linear stability results and numerical simulations will be presented and compared to the results of molecular dynamics.

Thu, 12 Dec 2019

12:00 - 13:30
L3

Analysis and computations of a nonlocal thin film model for two-fluid shear driven flows

Professor Saleh Tanveer
(Ohio State University)
Abstract


We present analysis and computations of a non-local thin film model developed by Kalogirou et al (2016) for a perturbed two-layer Couette flow when the thickness of the more viscous fluid layer next to the stationary wall is small compared to the thickness of the less viscous fluid. Travelling wave solutions and their stability are determined numerically, and secondary bifurcation points identified in the process. We also determine regions in parameter space where bistability is observed with two branches being linearly stable at the same time. The travelling wave solutions are mathematically justified through a quasi-solution analysis in a neighbourhood of an empirically constructed approximate solution. This relies in part on precise asymptotics of integrals of Airy functions for large wave numbers. The primary bifurcation about the trivial state is shown rigorously to be supercritical, and the dependence of bifurcation points, as a function of Reynolds number R and the primary wavelength 2πν−1/2 of the disturbance, is determined analytically. We also present recent results on time periodic solutions arising from Hoof-Bifurcation of the primary solution branch.


(This work is in collaboration with D. Papageorgiou & E. Oliveira )