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STEFAN PROBLEMS FOR MELTING NANOSCALED PARTICLES

Part of: Miscellaneous topics - Partial differential equations Thermodynamics and heat transfer Partial differential equations, boundary value problems

Published online by Cambridge University Press:  04 September 2015

JULIAN M. BACK
JULIAN M. BACK*
Affiliation:
Mathematical Sciences, Queensland University of Technology, Brisbane QLD 4000, Australia email jvlianback@gmail.com
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Abstract

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Keywords

Stefan problemsGibbs–Thomson lawsurface tensionkinetic undercoolingblow-up

MSC classification

Primary: 80A22: Stefan problems, phase changes, etc.
Secondary: 35R37: Moving boundary problems 65N40: Method of lines
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 1 , February 2016 , pp. 173 - 176
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

Back, J. M., McCue, S. W., Hsieh, M.-N. and Moroney, T. J., ‘The effect of surface tension and kinetic undercooling on a radially-symmetric melting problem’, Appl. Math. Comput. 229 (2014), 41–52.Google Scholar
Back, J. M., McCue, S. W. and Moroney, T. J., ‘Numerical study of two ill-posed one phase Stefan problems’, ANZIAM J. 52 (2011), C430–C446.CrossRefGoogle Scholar
Back, J. M., McCue, S. W. and Moroney, T. J., ‘Including nonequilibrium interface kinetics in a continuum model for melting nano scaled particles’, Sci. Rep. 4 (2014), 7066.CrossRefGoogle Scholar
Dallaston, M. C. and McCue, S. W., ‘Bubble extinction in Hele-Shaw flow with surface tension and kinetic undercooling regularization’, Nonlinearity 26 (2013), 1639–1665.CrossRefGoogle Scholar
Font, F. and Myers, T. G., ‘Spherically symmetric nanoparticle melting with a variable phase change temperature’, J. Nanopart. Res. 15 (2013), 2086.CrossRefGoogle Scholar
Font, F., Myers, T. G. and Mitchell, S. L., ‘A mathematical model for nanoparticle melting with density change’, Microfluid. Nanofluid. 18 (2015), 233–243.CrossRefGoogle Scholar
King, J. R. and Evans, J. D., ‘Regularization by kinetic undercooling of blow-up in the ill-posed Stefan problem’, SIAM J. Appl. Math. 65 (2005), 1677–1707.CrossRefGoogle Scholar
Langer, J. S., Lectures in the Theory of Pattern Formation. Chance and Matter (Elsevier, Amsterdam, 1987).Google Scholar
McCue, S. W., Hsieh, M., Moroney, T. J. and Nelson, M. I., ‘Asymptotic and numerical results for a model of solvent-dependent drug diffusion through polymeric spheres’, SIAM J. Appl. Math. 71 (2011), 2287–2311.CrossRefGoogle Scholar
McCue, S. W., Wu, B. and Hill, J. M., ‘Micro/nanoparticle melting with spherical symmetry and surface tension’, IMA J. Appl. Math. 74 (2009), 439–457.CrossRefGoogle Scholar
Meirmanov, A. M., ‘The Stefan problem with surface tension in the three dimensional case with spherical symmetry: nonexistence of the classical solution’, European J. Appl. Math. 5 (1994), 1–19.CrossRefGoogle Scholar
Mitchell, S. L. and O’Brien, S. B. G., ‘Asymptotic, numerical and approximate techniques for a free boundary problem arising in the diffusion of glassy polymers’, Appl. Math. Comput. 219 (2012), 376–388.Google Scholar
Wu, B., McCue, S. W., Tillman, P. and Hill, J. M., ‘Single phase limit for melting nanoparticles’, Appl. Math. Model. 33 (2009), 2349–2367.CrossRefGoogle Scholar
Wu, B., Tillman, P., McCue, S. W. and Hill, J. M., ‘Nanoparticle melting as a Stefan moving boundary problem’, J. Nanosci. Nanotech. 9 (2009), 885–888.CrossRefGoogle ScholarPubMed