AIMS seminars typically take place on Tuesdays from 1:15pm - 2:05pm in the Wolfson Lecture Theatre (Level 1 of the 4 West building)

Date                       Speaker (Affiliation)                                          Title and Abstract                                                                              Host           Away
1st October

Cameron  Hall

Engineering Mathematics, Bristol

Decontamination of neat agents using an immiscible cleanser

Following a spill of a hazardous chemical, it is important to remove the contaminating agent as quickly and completely as possible. This is often achieved by applying a cleanser, such as bleach, that will react with the agent to produce less harmful products. In many cases, a variety of different cleansers could be applied to deal with the same agent, and these different cleansers may react with the agent by different mechanisms to form different reaction products. This then leads to the central question: what properties of a cleanser (and, by association, what properties of the reaction mechanisms and reaction products) will promote fast and effective removal of an agent? This is, in essence, a problem that was presented at ESGI100 in Oxford in 2014, and has been the source of ongoing research by myself and others who participated in the study group.

In many cases of concern, contaminating agents are oily substances, while the cleansers that are effective against them are water-based. This means that the agent and cleanser are immiscible and the decontamination reaction takes place at the interface between the two phases. Since contaminating agents are often neat, this creates a moving boundary problem where the interface between the cleanser phase and the agent phase moves as the agent is consumed. In this talk, I will present and analyse a 1D mathematical model of decontamination that accounts for the moving boundary between the phases. This model includes a partition coefficient in order to represent the fact that the reaction product can be soluble in both phases, and leads to an unusual variety of Stefan problem. I will present work in which we use asymptotic and numerical methods to analyse the speed of the reaction and the movement of the interface, and we find that the time taken to total removal of the agent depends strongly on the concentration of the cleanser and on the partition coefficient, and less strongly on the reaction rate constant.

CJB

Students: Yyanis Johnson-Llambias

Lunch: CJB, Bernardo Casto Dominguez bcd28@bath.ac.uk, Tim Rogers

Coffee: PT

8th October

Phillipe Blondel

(Physics, Bath)

Checking climate change and saving the whales: mathematics and marine acoustics

Climate change is arguably the most important challenge facing humanity now, and we need to have reasonable facts before taking reasoned action. Oceans cover most of our planet, and acoustics is the only tool to map, monitor and understand physical and biological processes.

After a brief synthesis of acoustic instruments and the state of the planet, this talk will present some of the research done at Bath to monitor climate change, the effects of human activities and the health of marine ecosystems. Examples will include seafloor stability, from submarine landslides to tsunamis around Europe; Arctic environments and melting glaciers; the increases in shipping in warmer oceans, and impacts of energy extraction on protected species like whales. Local surveys and long-term datasets provide very large amounts of data, and mathematics are an essential tool to support acoustics. This will be illustrated with some current collaborations with mathematicians at Bath and further afield, including new projects starting in 2020.

PT

Students: Rosa, Peter

Lunch: Hook? PAM?

Coffee: PT

CJB

15th October

Ke Chen

Liverpool

Optimization Methods for Inverse Problems from Imaging

Optimization is often viewed as an active and yet mature research field. However the recent and rapid development in the emerging field of Imaging Sciences has provided a very rich source of new problems as well as big challenges for optimization. Such problems having typically non-smooth and non-convex functionals demand urgent and major improvements on traditional solution methods suitable for convex and differentiable functionals.

This talk presents a limited review of a set of Imaging Models which are investigated by the Liverpool group as well as other groups, out of the huge literature of related works. We start with image restoration models regularised by the total variation and high order regularizers. We then show some results from image registration to align a pair of images which may be in single-modality or multimodality with the latter very much non-trivial. Next we review the variational models for image segmentation. Finally we show some recent attempts to extend our image registration models from more traditional optimization to the Deep Learning framework.

Joint work with recent and current collaborators including D P Zhang, A Theljani, M Roberts, J P Zhang, A Jumaat, T Thompson.

ME

Students: Margaret Duff, Rosa Kowalewski

Lunch: ME, Silvia Gazzola

Coffee: ME, PT

CJB
22nd Oct

Matt Thorpe

Cambridge

How Many Labels Do You Need For Semi-Supervised Learning?

Given a data set of which a small subset are labelled, the goal of semi-supervised learning is to find the unknown labels. A popular method is to minimise a discrete p-Dirichlet energy defined on a graph constructed from the data. As the size of the data set increases one hopes that solutions of the discrete problem converge to a continuum variational problem with the continuum p-Dirichlet energy. It follows from Sobolev regularity that one cannot impose constraints if p is less than the dimension of the data hence, in this regime, one must also increase the number of labels in order to avoid labels "disappearing" in the limit. In this talk I will address the question of what is the minimal number of labels needed for an asymptotically well-posed problem. To compare labelling functions on different domains we use a metric based on optimal transport which then allows for the application of methods from the calculus of variation, in particular Gamma-convergence, and methods from PDE's, such as constructing barrier functions in order to apply the maximum principle. We can further show rates of convergence.

This is joint work with Jeff Calder (Minnesota) and Dejan Slepcev (CMU).

Main host: ME

Students: Eric Baruch, Adwaye Rambojun, Margaret Duff

Lunch: ME, CJB

Coffee: ME, PT

29th Oct

Martin Richter

Nottingham

Dynamical Energy Analysis - Describing vibrational energy distributions using ray-tracing and transfer operators

Dynamical Energy Analysis is a ray-based method to describe the high-frequency vibrational behaviour of complex mechanical systems ranging from gear boxes over car bodies to whole ship hulls. After a short introduction of the method and some of its recent applications we will address the convergence properties using simple example geometries, a proof for the latter and investigate the role of coexisting integrable and chaotic ray dynamics.

Main host: Hayley Wragg

Students: Shaerdan, Tina, Yyanis, Aaron Pimm

Lunch: CJB, Haley,

Coffee: PT

5th Nov

Takashi Sakajo

Kyoto

(visiting INI)

Topological Flow Data Analysis - Theory and Applications

We have investigated a mathematical theory classifying the topological structures of streamline patterns for 2D incompressible (Hamiltonian) vector fields on surfaces such as a plane and a spherical surface, in which a unique combinatorial structure, called partially Cyclically Ordered rooted Tree (COT), associated with a symbolic expression (COT representation) is assigned to every streamline topology. With the COT representations, one can identify the topological streamline structures without ambiguity and predict the possible transition of streamline patterns with a mathematical rigor. In addition, we have recently developed a software converting the values of stream function on structured/non-structured grid points in the plane into the COT representation automatically. It enables us to conduct the classification of streamline topologies for a large amount of flow datasets and the snapshots of time-series of flow evolutions obtained by measurements and numerical simulations, which we call Topological Flow Data Analysis (TFDA). The combinatorial classification theory of flow topologies is now extended to the flow of finite type, which contains Morse-Smale vector fields, compressible flows and 2D slices of 3D vector fields. I will present an overview of basic theory and its applications to atmospheric data and engineering problem.

Main host: PT

Speaker will be there entire day. Dinner planned evening of 4 Nov.

Dinner Mon: Toland, YJ-L, PT

Lunch Tues: CJB, YJ-L, JS, Opmeer, Guiver, Eike, Juan

Lunch Wed: PT, YJ-K, JS,

12th Nov

Ines Aniceto

Southampton

Unraveling the analytic structure of observables: from local asymptotics to global properties

The perturbative expansions of many physical quantities are divergent, and defined only as asymptotic series. It is well known that this divergence reflects the existence of nonperturbative, exponentially damped contributions, which are not captured by a perturbative analysis. This connection between perturbative and non-perturbative contributions to a given physical observable can be systematically studied using the theory of resurgence, allowing us to construct a full non-perturbative solution from perturbative asymptotic data.

In this talk I will start by reviewing the essential role of resurgence theory, coupled to exponentially accurate numerical methods, in the description of the analytic solution behind an asymptotic series, and its relation to the so-called Stokes phenomena and phase transitions. I will then exemplify how these techniques can be applied to to the calculation of poles of solutions to the Painlevé I non-linear ODE, a subject of great interest in both mathematics and physics.

Main host: PT

Student meetings: Yyanis, Josh Shelton

Lunch host: PAM, Yyanis, Josh

Coffee: PT

CJB
19th Nov

John Billingham

Nottingham

Slow travelling wave solutions of the nonlocal Fisher-KPP equation

In this talk I will discuss travelling wave solutions, u = U(x-ct), of the nonlocal Fisher-KPP equation in one spatial dimension,

u_t = D u_xx + u(1-phi*u)

with D << 1 and c << 1, where phi*u is the spatial convolution of the population density, u(x,t), with a continuous, symmetric, strictly positive kernel, phi(x), which is decreasing for x>0 and has a finite derivative as x -> 0+.

The formal method of matched asymptotic expansions and numerical methods can be used to solve the travelling wave equation for various kernels, phi(x), when c << 1. The most interesting feature of the leading order solution behind the wavefront is a sequence of tall, narrow spikes with O(1) weight, separated by regions where U is exponentially small. The regularity of phi(x) at x=0 is a key factor in determining the number and spacing of the spikes, and the spatial extent of the region where spikes exist.

Main host: CJB

Student meetings: Matthias Klar??, CJB group?

26th Nov

Yury Korolev

Cambridge

Inverse problems with imperfect forward operators and applications in image deblurring

The goal of image reconstruction is obtaining an image of the object of interest from indirectly measured, and typically noisy, data. Mathematically this is formulated as an inverse problem, where the forward operator models data acquisition. In practice, not only the data are noisy, but also the forward operator is often not perfectly known as it may involve imperfect calibration measurements or simplified models. The approach that I am developing relies on partially ordered spaces. In the partial order based framework, errors in the forward operator are described using order intervals in a partial order for linear operators. I will discuss convergence rates of this method and show that they reduce to known ones for problems with exact operators if the operator error goes to zero. I will also present applications in image deblurring with errors in the blurring kernel.

Main host: ME

Lunch+meetings: Silvia G, Clarice P

CJB
3rd Dec

CJB
10th Dec

Danila Prikazchikov

Keele

On Lowest Vibration Spectra of High-Contrast Composite Elastic Structures

The lowest spectra of high-contrast elastic multi-component structures are discussed. Examples of such structures appear in various areas of modern engineering, including, in particular, layered structures, e.g. photovoltaic panels and laminated glass. Other prospective areas involve, in particular, energy harvesting, soft robotics etc.

The consideration starts from low-frequency analysis for a strongly inhomogeneous, multi-component elastic rod. The presence of contrast in material properties of the components causes the effect of the first non-zero eigenvalue tending to zero. The approach relies on the concept of  “almost rigid body motion”, performed by the stronger components subject to homogeneous Neumann type boundary conditions. A perturbation procedure provides both estimates for frequencies satisfying a polynomial equation, along with piecewise polynomial approximations for the eigenforms.  Then, the analysis is extended to scalar 2D, and vector problems in elasticity. Finally, the effect of high contrast in stiffness is discussed in the problem of surface wave propagation in an elastic half-space coated by a thin soft elastic layer.

KDC
17th Dec

Emmanuel Fort

ESPCI Paris

CANCELLED DUE TO STRIKES IN FRANCEPAM
7 Jan
Week 12 – no talks scheduled(?)
PT
14 Jan  Inter-term break

21Jan

-23 Jan

Mini study group on Geo-spatial problems

28 Jan

Inter-term break (ITT)

4 Feb

Clodoaldo Ragazzo

Institute for Mathematics and Statistics (IME)

University of São Paulo (USP), Brazil

Modelling of tidal  forces with  application to the librations of Enceladus.

I will present the basic elements of the theory of tidal deformations. I will show how different  visco-elastic models can be used to describe the rheology of a celestial body.  The results are presented by means of a concrete application: the analysis of the libration of Enceladus due to Saturn.

PAMCJB
11 Feb

Sabine Hauert

Engineering Mathematics,

University of Bristol

Swarm engineering across scales: From nanomedicine to robots

Swarm engineering allows us to make robots that work in large numbers (over 1000), and tiny sizes (under 1 cm). Swarm strategies are either inspired from nature (ant colonies, fish shoals, bird flocks, cellular systems) or are automatically discovered using machine learning and crowdsourcing. Demonstrated applications range from the deployment of swarms of flying robots to create outdoor communication networks, or the use of 1000 coin-sized robots to form structures and explore the environment, to the design of nanoparticles for cancer treatment.

AS CJB
18 Feb

Engineering Mathematics,

University of Bristol

Wiggly mathematical tales of a sperm tail and other fables

Breakthrough research into the mathematics of the sperm tail has profound implications for life itself, from human reproduction to the left-right symmetry of organs in our body, including vital, though finite, ramifications for Brexit, the universe and everything else. In this talk, I will attempt to brainwash the audience into thinking that fluid dynamics, elasticity and some exquisite Green’s functions will change your life (they won’t). After genius-level mathematical calculations, I will endeavour to show some predictive insights into the movement of this specialised microorganism, with little-to-no impact in real life. Connecting Alan Turing, Stokes, quantum theory and Olympic swimmer Michael Phelps, this talk will recount the never-ending mathematical fables of the sperm.

AS
25 Feb
INI/ICMS
3 Mar

Dwaipayan Chakrabarti

School of Chemistry, University of Birmingham

Colloids Get Creative: Key to Open Crystals

Open crystals are sparsely populated periodic structures [1], which, when composed of colloidal particles, are appealing for their variety of applications, for example, as photonic materials, phononic and mechanical metamaterials, as well as porous media [1-5]. Although colloidal particles are promising building blocks for bottom up routes to crystals, programming self-assembly of colloidal particles into open crystals has proved to be elusive. Building on our recent work [6-8], I will here talk about a hierarchical self-assembly scheme for triblock patchy particles to address the challenges met with programming self-assembly into colloidal open crystals [9-12]. The presentation will demonstrate in silico the hierarchical self-assembly of colloidal open crystals via what we call closed clusters, which stop to grow beyond a certain size in the first stage and are thus self-limiting. By employing a variety of computer simulation techniques, I will show that the design space supports different closed clusters (e.g. tetrahedra or octahedra with variable valences) en route to distinct open crystals. Our design rules thus open up the prospects of realising a number of colloidal open crystals from designer triblock patchy particles, including certain colloidal open crystals much sough-after for their attractive photonic applications.

References
[1] M. Cates, Nature Mater., 2013, 12, 179-180.
[2] J. D. Joannopoulos, P. R. Villeneuve and S. Fan, Nature, 1997, 386, 143.
[3] K. Aryana and M. B. Zanjani, J. Appl. Phys., 2018, 123, 185103.
[4] X. Mao and T. C. Lubensky, Annu. Rev. Condens. Matter Phys., 2018, 9, 413.
[5] X. Mao, Q. Chen and S. Granick, Nature Mater. 2013, 12, 217.
[6] D. Morphew and D. Chakrabarti, Nanoscale, 2015, 7, 8343.
[7] D. Morphew and D. Chakrabarti, Soft Matter, 2016, 12, 9633.
[8] D. Morphew and D. Chakrabarti, Nanoscale, 2018, 10, 13875.
[9] D. Morphew, J. Shaw, C. Avins and D. Chakrabarti, ACS Nano, 2018, 12, 2355.
[10] A. B. Rao et al., Manuscript in communication, 2019.
[11] A. Neophytou et al., Manuscript in preparation, 2020.
[12] J. Shaw et al., Manuscript in preparation, 2020.

AS
10 Mar

CJB
11 March

Kit Yates (Bath)

Bath Taps/IMI Popular  Lecture:  The maths of life and deathCJB
17 Mar

Lisa Kreusser (Cambridge)

An anisotropic interaction model for simulating fingerprints

The recent, rapid advances in modern biology and data science have opened up a whole range of challenging mathematical problems. In this talk I will discuss a class of interacting particle models with anisotropic repulsive-attractive interaction forces. These models are motivated by the simulation of fingerprint databases, which are required in forensic science and biometric applications. In existing models, the forces are isotropic and particle models lead to non-local aggregation PDEs with radially symmetric potentials. The central novelty in the models I consider is an anisotropy induced by an underlying tensor field. This innovation does not only lead to the ability to describe real-world phenomena more accurately, but also renders their analysis significantly harder compared to their isotropic counterparts. I will discuss the role of anisotropic interaction in these models, present a stability analysis of line patterns, and show numerical results for the simulation of fingerprints.

CJB

24 Mar

in

CB 5.1

Mike Fraser

Department of Computer Science,

University of Bath

Multi-Material Fabrication through Acoustic Patterning

Fabrication techniques often depend on specific materials, reducing designers' ability to play with and combine diverse forms. Acoustic technologies offer the opportunity to advance fabrication processes by applying ultrasound fields to actuate liquids and solids into defined patterns. Unlike existing multi-material prototyping, acoustic fields can pattern a broad scope of materials and a wide range of material scales. We demonstrate acoustic fabrication, establish forms and patterns that are created by typical standing waves, and show the ability to rapidly compose multi-material patterns with objects, particles and aerosols. Our approach emphasizes the playful nature of including everyday materials in design, and highlights opportunities for using more sustainable materials in rapid prototyping.

AS
31 MarBath graduate studentsPractice talks for BAMC
AS
7 Apr---BAMC in Glasgow — no talks scheduled

14 Apr---Easter break

21 Apr

Paul Shepherd

ACE Bath

CJBAS
28 Apr

Bert Wuyts

Exeter

CJB,AS
5 May

AS
12 May

Darren Crowdy (Imperial)

CJB
19 May

Daniel Harris

Engineering

Brown University

Hydrodynamic mechanisms for particle aggregation at fluid interfaces

Understanding the forces on small bodies at fluid interfaces has significant relevance to a range of natural and artificial systems. In this talk, I will discuss two recent investigations of fluid-mediated attraction mechanisms of non-Brownian particles, at free surfaces and within density stratified fluids.

In the first part, I will present direct measurements of the attractive force between centimetric disks floating at an air-water interface. It is well known that objects at a fluid interface may interact due to the mutual deformation they induce on the free surface, however few direct measurements of such forces have been reported. In the present work, we characterize how the attraction force depends on the disk radius, mass, and relative spacing. The measured forces are rationalized with scaling arguments and compared directly to numerical predictions.

In the second part, I will describe a novel attractive mechanism by which particles at isopycnals within a density stratified fluid may self-assemble and form large aggregates without need for short-range binding effects (adhesion). This phenomenon arises through a subtle interplay of effects involving solute diffusion, impermeable boundaries, and the geometry of the aggregate. Control experiments with two particles isolate the individual dynamics, which are quantitatively predicted through numerical integration of the underlying equations of motion.

Ongoing and future work in these areas will also be discussed.

PAM

Unassigned speakers

Sarah Waters, Annela Seddon (Bristol Physics)