{"id":31,"date":"2020-11-12T11:57:33","date_gmt":"2020-11-12T11:57:33","guid":{"rendered":"https:\/\/www.maths.nottingham.ac.uk\/personal\/etzjadw\/?page_id=31"},"modified":"2020-11-12T11:57:33","modified_gmt":"2020-11-12T11:57:33","slug":"research","status":"publish","type":"page","link":"https:\/\/www.maths.nottingham.ac.uk\/personal\/etzjadw\/research\/","title":{"rendered":"Research"},"content":{"rendered":"\n

My research interests fall into three broad categories: nonlinear waves, coagulation processes, and mathematical medicine and biology. Please contact me if you are interested in pursuing a PhD in any of these areas.<\/p>\n\n\n\n

Nonlinear Waves<\/strong><\/p>\n\n\n\n

– Travelling Kinks and Breathers in FPU-Klein-Gordon lattices:<\/strong> – I started working on solitons on lattices for my PhD thesis, and have continued, expanding to cover more complex modes and higher-dimensional lattices.<\/p>\n\n\n\n

– Breathing of DNA:<\/strong> – this is one application of breathers on lattices, but with Charlie Laughton, we have worked on parameterising stochastic differential equation models using AMBER.<\/p>\n\n\n\n

– Fluxons in Josephson Junctions:<\/strong> – collaborative work with Hadi Susanto is focused on understanding a range of nonlinear dynamics relevant to current and potential nanotechnological devices.<\/p>\n\n\n\n

– ICMS meeting on Nonlinear Waves and Solitons on Lattices<\/strong> – in April 2011, there was a meeting in honour of Chris Eilbeck on his retirement. Details of speakers, talk titles, abstracts are available here<\/a>.<\/p>\n\n\n\n

Coagulation-fragmentation problems<\/strong><\/p>\n\n\n\n

– Polymer nucleation:<\/strong> – collaborative work with Richard Graham focuses on the effects of flow, stretch, nuclei orientation, etc.<\/p>\n\n\n\n

– Origins of Life:<\/strong> – I am interested in modelling the chemical processes which occur during the formation of chiral polymers\/crystals, also the information storage of primitive DNA\/RNA sequences, and simple metabolic processes by which cell-like structures form.<\/p>\n\n\n\n

– Island growth during deposition:<\/strong> – for example in molecular beam epitaxy (MBE), the continuous deposition of atoms on a surface causes islands to form; the size distribution of these islands often follows a self-similar form. I am interested in analysing the large-time asymptotics of this process.<\/p>\n\n\n\n

– Generalised nucleation theory:<\/strong> I am interested in analysing a range of techniques, for example asymptotics of the Becker-Doring equations, as well as the Smoluchowski equations, and approximation techniques based on coarse-graining and continuum limits.<\/p>\n\n\n\n

Mathematical Medicine and Biology<\/strong><\/p>\n\n\n\n

– mRNA degradation:<\/strong> together with Dr Cornelia de Moor of the School of Pharmacy at Nottingham, I am working on the processes by which the poly-A-tails of mRNAs are eroded, leading to the destruction of mRNA.<\/p>\n\n\n\n

– Carbohydrate and Fat metabolism in humans:<\/strong> I am collaborating on the construction of computer simulations of human nutrition and the development of various metabolic conditions such as diabetes and fatty liver disease.<\/p>\n\n\n\n

– Carbon metabolism during seed germination:<\/strong> – I work with Mark Hooks (Bangor) on mathematical models of fluxes in and through the peroxysome\/glyoxysome.<\/p>\n\n\n\n

– Metabolic pathways in ovarian cells:<\/strong> – recent collaborative work with Kevin Sinclair (Biosciences, Nottingham) and Helen Byrne (Oxford) aims to model the methionine cycle.<\/p>\n\n\n\n

– Telomere dynamics, and the influence of cell cycle on drug treatment:<\/strong> – the evolution of telomere lengths is a process which can be modelled by discrete dynamical system that can be analysed using asymptotic techniques.<\/p>\n\n\n\n

– DNA condensation for gene therapy:<\/strong> – this reduces to a classic toy problem in physics, namely random sequential adsorption (RSA), also known as the parking problem. I am interested in deriving solutions to certain cases using asymptotic limits, and connections with MBE (see above), since both are described by coagulation-fragmentation processes. Earlier work in this area involved Snow Stolnik and Clive Roberts (Pharmaceutical Sciences, Nottingham) and Helen Byrne (Oxford).<\/p>\n","protected":false},"excerpt":{"rendered":"

My research interests fall into three broad categories: nonlinear waves, coagulation processes, and mathematical medicine and biology. Please contact me…<\/p>\n","protected":false},"author":14,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/www.maths.nottingham.ac.uk\/personal\/etzjadw\/wp-json\/wp\/v2\/pages\/31"}],"collection":[{"href":"https:\/\/www.maths.nottingham.ac.uk\/personal\/etzjadw\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.maths.nottingham.ac.uk\/personal\/etzjadw\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.maths.nottingham.ac.uk\/personal\/etzjadw\/wp-json\/wp\/v2\/users\/14"}],"replies":[{"embeddable":true,"href":"https:\/\/www.maths.nottingham.ac.uk\/personal\/etzjadw\/wp-json\/wp\/v2\/comments?post=31"}],"version-history":[{"count":2,"href":"https:\/\/www.maths.nottingham.ac.uk\/personal\/etzjadw\/wp-json\/wp\/v2\/pages\/31\/revisions"}],"predecessor-version":[{"id":35,"href":"https:\/\/www.maths.nottingham.ac.uk\/personal\/etzjadw\/wp-json\/wp\/v2\/pages\/31\/revisions\/35"}],"wp:attachment":[{"href":"https:\/\/www.maths.nottingham.ac.uk\/personal\/etzjadw\/wp-json\/wp\/v2\/media?parent=31"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}