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Home > Faculties & Departments > applied mathematics

- Martin Meere
- Mícheál Ó Confhaola
- Pat O' Leary
- Petri T Piiroinen
- Tom Sherry
- Michael Tuite
- Matthew McCarthy Ph.D., D.Sc., M.R.I.A.: Professor - retired

The broad area of applied mathematics, with particular emphasis on the mathematics of diffusion. Most of the published research work to date has focused on the modelling and analysis of impurity diffusion mechanisms in semiconductors.

[1]
E. D. Allen, J. R. King & M. G. Meere, Impurity diffusion through strained semiconductors,
*The Quarterly Journal of Mechanics and Applied Mathematics
*
**58(4)**, 615-643 2005.

[2] M.G. Meere and J.R. King, The dissociative diffusion mechanism with charge effects II: two-dimensional in-diffusion,
*The Quarterly Journal of Mechanics and Applied Mathematics
*2004,
**57(1)**, 19-58 2004.

[3] J.R. King and M.G. Meere, A combined dissociative and kick-out diffusion model with charge effects, part I: in-diffusion,
*Mathematical Proceedings of the Royal Irish Academy*,
**102**A, 49-78 2002.

[4] J.R. King and M.G. Meere, A combined dissociative and kick-out diffusion model with charge effects, part II: out-diffusion,
*Mathematical Proceedings of the Royal Irish Academy*,
**102**A, 79-105 2002.

[5] M.G. Meere, B. Gleeson and J. Simmie, Modelling gas motion in a rapid compression machine,
*Journal of Engineering Mathematics*,
**44**, 57-82 2002.

[6] M.G. Meere and J.R. King, The dissociative diffusion mechanism with charge effects I: one-dimensional in-diffusion, The Quarterly Journal of Mechanics and Applied Mathematics
**54(3)**, 469-500 2001.

[7] J.R. King and M.G. Meere, The role of multiple charge states in zinc diffusion in gallium arsenide, Mathematical Proceedings of the Royal Irish Academy,
**101**A, 95-110 2001.

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Mícheál’s research interest is in Computational Atomic Physics. His contributions to Atomic Physics may be classified as belonging to two distinct but intimately related areas, namely Electron-Atom Collisions and Multiply Excited States of two and three-electron atomic systems. Excited states of an atomic system cause resonances in cross section for electron scattering off the corresponding ion. Furthermore, these highly-excited states are ideal systems for investigating the few-body Coulomb problem and for studying electron correlation.

[1] M.J. Conneely, L. Lipsky, K. Smith, P.G. Burke & R.J.W. Henry, A Computer Program for the Calculation of Electron Scattering and Photoionization Cross Sections of Atomic Systems with Configuration (np)q,
*Computer Physics Communications,
*
**1**, 306-324 1970.

[2] M.J. Conneely & L. Lipsky, Widths and Configuration Mixings of Two-Electron Systems

Below the N2 Threshold.
*Journal of Physics B: At. Mol. Phys.
*
**11**, 4135-4154 1978.

[3] M.J. Conneely & S. Geltman. Resonance Effects in Multichannel Free-Free Transitions

Near Electron Scattering Resonances of Hydrogen.
*Journal of Physics.
*B
**14**, 4847-4856 1981.

[4] M.J. Conneely, L. Lipsky & A. Russek. Three-Electron Systems with Inner Shell Vacancies.
*Phys. Rev.
*A
**46**, 7, 4012-4025 1992.

[5] M.J. Conneely, L. Lipsky, Hollow states of Lithium,
*Phys. Rev.
*A
**61**, 032506, 1-17 2000.

[6] M.J. Conneely & L. Lipsky, Energy Levels and Classifications of Triply Excited states of Li, Be,B2 and C3,
*Atomic Data and Nuclear Data Tables*.
**81**, No.1, 115-190 2002.

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Wave Propagation and the use of Symbolic Computation in Mechanics. He has published works on wave propagation in elastic and viscoelastic media.

[1] P.M. O’Leary & A.C. Eringen, Impact on Coaxial Circular Cylinders of Two Materials,
*J. Acous. Soc., Amer.
*
**56**, 469-476 1974.

[2] P.K. Curry, M.A. Hayes & P.M. O’Leary, Viscoelastic Rayleigh Waves,
*Quart. Appl. Mth*.
**35**, 35-53 1977.

[3] P.M. O’Leary & S.K. Datta, Dynamics of Buried Pipelines,
*Soil Dynamics and Earthquake Engineering*.
**4**, 151-159 1985.

[4] P.M. O’Leary, Surface Vibrations on a Semi-Infinite Viscoelastic Medium,
*Recent*
*Developments in acoustic waves
*(Springer), 291-298 1988.

[5] P.M. O’Leary, Response of a class of low-loss viscoelastic materials to an oscillating source,
*Proc. R.I.A. M.
*
**89**A, 219-224 1989.

[6] R. Esquivel & P.M. O’Leary, Symbolic computation applied to surface waves in layered elastic media,
*Proc. C.A.S.C.*, 95-103 2003.

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Multibody system dynamics, Numerical bifurcation analysis, Piecewise smooth dynamical systems

[1] Mason, J., Piiroinen, P.T., Wilson, R.E. and Homer, M.E., Basin of attraction in nonsmooth models of gear rattle, To appear in International Journal of Bifurcation and Chaos, 2008.

[2] Batako, A.D.L. and Piiroinen, P.T., Friction-Driven Vibro-Impact System for Percussive-Rotary Drilling - A Numerical Study of the System Dynamics, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 222(10), pp. 1925-1934, 2008.

[3] Budd, C., di Bernardo, M., Champneys, C., Nordmark, A.B., Olivar, G. and Piiroinen, P.T., Bifurcations in Piecewise Smooth Systems, SIAM Review 50(4), pp. 629-701, November 2008.

[4] Kowalczyk, P. and Piiroinen, P.T. Two-parameter sliding bifurcations of periodic solutions in a dry-friction oscillator, Physica D 237, pp. 1053-1073, 2008.

[5] Piiroinen, P.T. and Kuznetsov, Yu.A., An event-driven method to simulate Filippov systems with accurate computing of sliding motions, ACM Transactions on Mathematical Software 34(3), 2008.

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Tom has published widely in Theoretical High Energy Physics on areas such as unified gauge theories and renormalization, supersymmetry, regularization of quantum field theory models, classical solutions of quantum field theory models and B-physics phenomenology.

[1] Browne, S., O’Raifeartaigh, L. & Sherry, T.N., Asymptotic Freedom, Infrared Convergence and Supersymmetry,
*Nucl. Phys.
*B
**99**, 150-166 1975.

[2] Sherry, T.N., Higgs potential in the SU(5) model,
*J. Phys.
*A
**13**, 2205-2218 1980.

[3] Chakrabarti, A., Sherry, T.N. & Tchrakian, D.H., On axially symmetric self-dual gauge field configurations in 4p dimensions,
*Phys. Lett.
*
**162**B, 340-344 1985.

[4] McKeon, D.G.C. & Sherry, T.N., Operator regularization of Green’s functions,
*Phys. Rev. Lett.
*
**59**, 532-534 1987.

[5] McKeon, D.G.C. & Sherry, T.N., Radiative effects in a constant magnetic field using the quantum mechanical path integral,
*Mod. Phys. Lett.
*A
**9**, 2167-2178 1994.

[6] Brandt, F.T., McKeon, D.G.C. & Sherry, T.N., Supersymmetry in 22 dimensions,
*Mod.*
*Phys. Lett.
*A
**15**, 1349-1355 2000.

[7] Ahmady, M.R., Chistie, F.A., Elias, V., Fariborz, A.H.,Fattahi, N., McKeon, D.G.C., Sherry, T.N. & Steele, T.G., Closed form summation of RG-accessible logarithmic contributions to semi-leptonic B-decays and other perturbative processes.
*Phys. Rev.
*D
**66**, 014010, 1-25 2002.

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Interests both in theoretical physics (quantum field theory and conformal field theory) and pure mathematics (vertex operator algebras, the Monster group and modular groups). Most recently he has been working on Generalised Monstrous Moonshine using methods in conformal field theory with a Ph.D. student Rossen Ivanov and on genus two and higher conformal field theory and vertex operator algebras in collaboration with Geoff Mason of UC Santa Cruz.

[1] Tuite, M.P., The transverse hadronic energy distribution in deep inelastic scattering,
*Nucl.Phys.*B
**236**, 48-60 1984.

[2] Lautrup,B., Lavelle, M.J., Tuite,M.P. and Vladikas, A., Stochastic quantisation and gauge fixing in lattice gauge theories,
*Nucl.Phys.*B
**290**, 188-204 1987.

[3] Tuite, M.P., Monstrous Moonshine from orbifolds,
*Commun. Math. Phys.
*
**146**, 277-309 (1992).

[4] Tuite, M.P., On the relationship between the monstrous moonshine and the uniqueness of the moonshine module,
*Commun. Math. Phys.
*
**166**, 495-532 1995.

[5] Tuite, M.P., Genus two meromorphic conformal field theory,
*CRM Proceedings and*
*Lecture Notes
*
**30**, 231-251 2001.

[6] Ivanov, R. and Tuite, M.P., Rational Generalised Moonshine from Abelian Orbifoldings of the Moonshine Module,
*Nucl.Phys.*B
**635**, 435-472 2002.

[7] Mason, G. and Tuite, M.P., Torus chiral n-point functions for free boson and lattice vertex operator algebras,
*Commun. Math. Phys.
*
**235**, 47-68 2003.

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Mainly in the area of wave propagation in various media.

[1] M.F. McCarthy & H.F. Tiersten, A theory of Viscoelastic Composites Modelled as Interpenetrating Solid Continua with Memory,
*Archive for Rational Mechanics and Analysis,*
**81**, 21-51 1983.

[2] M.F. McCarthy G. Batra & A. Bedford, Acceleration Waves in a Particulate Suspension,
*International Journal of Engineering Science,
*
**24**, 1339-1349 1986.

[3] M.F. McCarthy & G.C. Gaunaurd, Resonances of Elastic Scatters in Fluid Half Spaces,
*LE.E.E. Journal of Ocean Engineering,
*
**12**, 395-403 1987.

[4] M.F. McCarthy, On One-dimensional Shock Waves in Composite Materials Modelled as Interpenetrating Solid Continua,
*Archives for Rational Mechanics and Analysis,
*
**103**, 169-191 1988.

[5] M.F. McCarthy & M.M. Carroll, Circularly polarised Waves of Finite Amplitude in Elastic Dielectrics,
*Nonlinear Effects in Fluids and Solids, Plenum New York and London*, 125-136 1997.

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Applied Mathematics

This page was last updated Tuesday, November 11, 2008

This page was last updated Tuesday, November 11, 2008