The department of Mathematics and Statistics at the University of Limerick invites you to a seminar by Prof. Tim Myers (Centre de Recerca Matemàtica):

**Title:** Phase change at the nanoscale

**Abstract:** The basis of nanotechnology is the nanoparticle (NP), a unit of matter with a critical diameter between 1 and 100nm. Nanoparticles are currently used in a diverse range of applications, including: medicine (as synthetic skin, antioxidants, targeted delivery of drugs); manufacturing (flexible screens, packaging, fabrics); environment (breaking down oil, catalysts); energy (in fuel cells, batteries, solar cells) etc. In many of these applications the particles are exposed to high temperatures and so it is important to understand their response to a harsh thermal environment. The theory of phase change at the macroscale is well established, however, as the length-scale decreases the physical process starts to exhibit unusual behaviour. One reason for the change in behaviour is that nanoparticles have a very large ratio of surface to volume atoms and so surface properties rather than bulk properties dominate. This results in a mathematical description that differs significantly from that at the macroscale. In this talk we will discuss various issues that arise when modelling phase change at the nanoscale: 1) We present a novel formulation for the Stefan problem that reflects the fact material properties, such as latent heat and melt temperature, are size dependent. 2) A standard simplification is to study the one-phase problem, where one of the phases is set to the phase change temperature. When the phase change temperature varies this formulation loses energy. 3) Experiments at the nanoscale demonstrate that the well-known heat equation, based on Fourier's law no longer holds. More complex models, which exhibit heat waves must then be considered.

This seminar will take place on **Friday , April 21 ^{st} , at 4pm, in Room A2-002**.

If you have any questions regarding this seminar, please direct them to Iain Moyles (061 233726, iain.moyles@ul.ie).

A full list of upcoming seminars can be found at http://www.ulsites.ul.ie/macsi/node/48011

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Supported by Science Foundation Ireland funding, MACSI - the Mathematics Applications Consortium for Science and Industry (www.macsi.ul.ie), centred at the University of Limerick, is dedicated to the mathematical modelling and solution of problems which arise in science, engineering and industry in Ireland.

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