Past Junior Applied Mathematics Seminar

17 October 2017
12:45
Abstract

Many metallurgical processes involve the heat treatment of granular material due to large alternating currents. To understand how the current propagates through the material, one must understand the bulk resistivity, that is, the resistivity of the granular material as a whole. The literature suggests that the resistance due to contacts between particles contributes significantly to the bulk resistivity, therefore one must pay particular attention to these contacts. 

My work is focused on understanding the precise impact of small contacts on the current propagation. The scale of the contacts is several order of magnitude smaller than that of the furnace itself, therefore we apply matched asymptotics methods to study how the current varies with the size of the contact.

  • Junior Applied Mathematics Seminar
13 June 2017
12:45
Abstract

One of the greatest challenges in developing renewable energy sources is finding an efficient energy storage solution to smooth out the inherently fluctuating supply. One cheap solution is lead-acid batteries, which are used to provide off-grid solar energy in developing countries. However, modelling of this technology has fallen behind other types of battery; the state-of-the-art models are either overly simplistic, fitting black-box functions to current and voltage data, or overly complicated, requiring complex and time-consuming numerical simulations. Neither of these methods offers great insight into the chemical behaviour at the micro-scale.

In our research, we use asymptotic methods to explore the Newman porous-electrode model for a constant-current discharge at low current densities, a good estimate for real-life applications. In this limit, we obtain a simple yet accurate formula for the cell voltage as a function of current density and time. We also gain quantitative insight into the effect of various parameters on this voltage. Further, our model allows us to quantitatively investigate the effect of ohmic resistance and mass transport limitations, as a correction to the leading order cell voltage. Finally, we explore the effect on cell voltage of other secondary phenomena, such as growth of a discharge-product layer in the pores and reaction-induced volume changes in the electrolyte.

  • Junior Applied Mathematics Seminar
30 May 2017
12:45
Abstract

In this talk we consider the limiting behaviour of the strong solution of the Navier--Stokes equation as the viscosity goes to zero, on a three--dimensional region with curved boundary. Under the Navier and kinematic boundary conditions, we show that the solution converges to that of the Euler equation (in suitable topologies). The proof is based on energy estimates and differential--geometric considerations. This is a joint work with Profs. Gui-Qiang Chen and Zhongmin Qian, both at Oxford. 

  • Junior Applied Mathematics Seminar
16 May 2017
12:45
Markus Schmidtchen
Abstract

Multi-agent systems in nature oftentimes exhibit emergent behaviour, i.e. the formation of patterns in the absence of a leader or external stimuli such as light or food sources. We present a non-local two species crossinteraction model with cross-diffusion and explore its long-time behaviour. We observe a rich zoology of behaviours exhibiting phenomena such as mixing and/or segregation of both species and the formation of travelling pulses.

  • Junior Applied Mathematics Seminar
2 May 2017
12:45
Abstract

In this presentation, we give an overview of the numerical methods used in commercial oil and gas reservoir simulation. The models are described by flow through porous media and are solved using a series of nested numerical methods. Most of the computational effort resides in solving large linear systems resulting from Newton iterations. Therefore, we will go in greater detail about the iterative linear solvers and preconditioning techniques.

Note: This talk will cover similar topics to the InFoMM group meeting talks on Friday 28th April, but I will discuss more mathematical details for this JAMS talk.

  • Junior Applied Mathematics Seminar
24 January 2017
12:30
Fabian Ying
Abstract

In this talk, I will talk about my current approach to model customer movements and in particular congestion inside supermarkets using queuing networks. As the research question for my project is ‘How should one design supermarkets to minimize congestion?’, I will then talk about my current progress in understanding how the network structure can affect this dynamics.

  • Junior Applied Mathematics Seminar
29 November 2016
12:45
Roxana Pamfil
Abstract

A successful programme of personalised discounts and recommendations relies on identifying products that customers want, based both on items bought in the past and on relevant products that the customers have not yet purchased. Using basket-level grocery shopping data, we aim to use clustering ("community detection") techniques to identify groups of shoppers with similar preferences, along with the corresponding products that they purchase, in order to design better recommendation systems.


Stochastic block models (SBMs) are an increasingly popular class of methods for community detection. In this talk, I will expand on some work done by Newman and Clauset [1] that uses a modified SBM for community detection in annotated networks. In these networks, additional information in the form of node metadata is used to improve the quality of the inferred community structure. The method can be extended to bipartite networks, which contain two types of nodes and edges only between nodes of different types. I will show some results obtained from applying this method to a bipartite network of customers and products. Finally, I will discuss some desirable extensions to this method such as incorporating edge weights and assessing the relationship between metadata and network structure in a statistically robust way.


[1] Structure and inference in annotated networks, MEJ Newman and A Clauset, Nature Communications 7, 11863 (2016).


Note: This talk will cover similar topics to my presentation in the InFoMM group meeting on Friday, November 25 but it won't be exactly the same. I will focus more on the mathematical details for my JAMS talk.
 

  • Junior Applied Mathematics Seminar

Pages