Seminars (unless otherwise stated) will take place on **Tuesdays at 3.00pm in South Wing Garwood Lecture Theatre **- see the map for further details. There will be tea afterwards in **Maths Room 606** (6th Floor, 25 Gordon Street) - see map for further details. 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).

## 08 October 2019

### Speaker: Dr Marie-Therese Wolfram (Warwick University)

##### Title: On mean-field models for segregation dynamics

**Abstract: **

In this talk we derive and analyze different mean-field models for groups of individuals undergoing a random walk. We consider two situations - first an individual based approach for a single species, second a lattice based model for two interacting species. In the first case, individuals reduce their individual stochasticity in response to high densities in their neighbourhood. In the second each species has the tendency to stay within their own group and avoid the other. We formally derive the corresponding mean field models and study the formation of aggregated and segregated states. Furthermore we illustrate the dynamics of the respective models with computational experiments.

## 15 October 2019

### Speaker: Prof Scott McCue (Queensland University of Technology, Brisbane)

##### Title: Using time-frequency analysis to identify features of steady and unsteady ship wakes

**Abstract: **

The motivation here is to study how properties of a ship wake can be extracted from surface height data collected at a single point as the ship travels past. The tool we use is a spectrogram, which is a heat map that visualises the time-dependent frequency spectrum of the surface height signal. In this talk, the focus will be on presenting the theoretical framework which involves an idealised mathematical model with a pressure distribution applied to the surface. A geometric argument based on linear water wave theory provides encouraging results for a range of ship speeds. The effects of nonlinearity are also studied. We compare our theoretical predictions with experimental results from the field and from data collected at the Australian Maritime College. This type of work has the potential to inform ship design, the detection of irregular vessels, and how coastal damage is attributed to specific vessels in shipping channels.

## 22 October 2019

### Speaker: Dr David Hewett (UCL)

##### Title: Wave scattering by fractal screens

**Abstract: **

The mathematical analysis of acoustic and electromagnetic wave scattering by planar screens is a classical topic. The standard technique involves reformulating the problem as a boundary integral equation on the screen, which can be solved numerically using a boundary element method. Theory and computation are both well-developed for the case where the screen is an open subset of the plane with smooth (e.g. Lipschitz or smoother) boundary. In this talk I will explore the case where the screen is an arbitrary subset of the plane; in particular, the screen could have fractal boundary, or itself be a fractal. Such problems are of interest in the study of fractal antennas in electrical engineering, light scattering by snowflakes/ice crystals in atmospheric physics, and in certain diffraction problems in laser optics. The roughness of the screen presents challenging questions concerning how boundary conditions should be enforced, and the appropriate function space setting. But progress is possible and there is interesting behaviour to be discovered: for example, a sound-soft screen with zero area (planar measure zero) can scatter waves provided the fractal dimension of the set is large enough. Accurate computations are also challenging because of the need to adapt the mesh to the fine

structure of the fractal. As well as presenting numerical results, I will outline some of our recent results, and some outstanding open questions, from the point of view of numerical analysis of boundary element method approximations.

## 29 October 2019

### Speaker: Prof Anthony Mulholland (Bristol University)

##### Title: Fractal Ultrasonic Transducers

**Abstract: **This talk will present the mathematics that led to the manufacture of the world's first fractal ultrasonic transducer; the device is based on a particular fractal the Sierpinski Gasket. Ultrasonic transducers are probably best known for their use in foetal imaging; we have perhaps all stared at grainy images of a baby in the womb trying to convince ourselves about who the child most resembles! It is clear that there is much room for improvement and it turns out that fractal designs are one route that is now being pursued. The transmission and reception sensitivities of most piezoelectric ultrasonic transducers are dictated by their geometrical structures. This structure is normally a regular, periodic one with one principallength scale, which, due to the resonant nature of the devices, determines the central operating frequency. There is engineering interest in building wide-bandwidth devices, and so it follows that, in their design, resonators that have a range of length scales should be used. This talk describes a mathematical model of a fractal ultrasound transducer whose piezoelectric components span a range of length scales. There have been many previous studies of wave propagation in the Sierpinski gasket but this paper is the first to study its complement. This is a critically important mathematical development as the complement is formed from a broad distribution of triangle sizes, whereas the Sierpinski gasket is formed from triangles of equal size. Within this structure, the electrical and mechanical fields fluctuate in tune with the time-dependent displacement of these substructures. A new set of basis functions is developed that allow us to express this displacement. A renormalization approach is then used to develop a recursion scheme that analytically describes the key components from the discrete matrices that arise. Expressions for the transducer’s operational characteristics are then derived and analysed as a function of the driving frequency. It transpires that the fractal device has a significantly higher reception sensitivity (18 dB) and a significantly wider bandwidth (3 MHz) than an equivalent Euclidean (standard) device.

## 05 November 2019 in Maths Room 500

### Speaker: Dr Daniel Onofrei (University of Houston, USA)

##### Title: Field control in exterior regions through surface sources

**Abstract: **In this talk we will present our results concerning the problem of exterior field control through surface currents with applications to pattern synthesis, scattering cancellation and design of essentially non-radiating sources. We will first offer a brief review of our existent results concerning the control of scalar fields and then discuss how these controls can be used for Maxwell fields. We will then present current results for the control of acoustic and electromagnetic fields together with numerical simulations for various applied scenarios.

## 12 November 2019

##### See the Departmental Colloquium webpage

## 19 November 2019 - CANCELLED

## 26 November 2019 - CANCELLED

## 03 December 2019 - CANCELLED

**Special Seminar**

Thursday 05 December 2019 - 4pm in Room 416

### Speaker: Prof John Grue (University of Oslo, Norway)

##### Title: Mini-tsunami made by ship moving across a depth change

**Abstract: **

Ship moving across a shallow depth change, in water of small or narrow space, may create a small tsunami, 0.5-1 km long, observed as harbor wave on shore, where a wave height up to 1.4 m has been measured. We give an interpretation of the generation process of this new phenomenon. At a depth change, the ship-induced fluid velocity produces a reaction velocity of equal magnitude and opposite direction, orthogonal to the new bottom. This velocity appears as a vertical velocity at the water surface, making the waves. The waves propagate with the shallow water speed upstream of a ship moving at subcritical speed. Theory and numerical calculations for a real ship geometry are compared to a moving pressure distribution. Computations compare favourably to a few available wave height measurements. Recent observations will be discussed.

Reference: J. Grue, Ship generated mini-tsunamis. J. Fluid Mech. 2017, Vol. 816.

## 10 December 2019

### Speaker: Prof Adriana Dawes (The Ohio State University)

##### Title: Antagonistic motor protein dynamics in contractile ring structures

**Abstract: **

Ring-shaped contractile structures play important roles in biological processes including wound healing and cell division. Many of these contractile structures rely on motor proteins called myosins for constriction. We investigate force generation by the Type II myosins NMY-1 and NMY-2 using ring channels, contractile ring structures in the nematode worm C. elegans gonad that do not completely close, as our model system. By exploiting the ring channel's circular geometry, we derive a second order ODE to describe the evolution of the radius of the ring channel. By comparing our model predictions to experimental depletion of NMY-1 and NMY-2, we show that these myosins act antagonistically to each other, with NMY-1 exerting force orthogonally and NMY-2 exerting force tangentially to the ring channel opening. Stochastic simulations are currently being used to determine how NMY-1 and NMY-2 may be producing these antagonistic forces, with new tools from topological data analysis identifying persistent ring-like structures in the simulation data.