Dr Andrew Neate
Senior Lecturer
Mathematics
Telephone: (01792) 602092
Room: Office - 322
Third Floor
Computational Foundry
Bay Campus

I am a lecturer in the mathematics department and a member of the stochastic analysis research group.

I originally came to Swansea as an undergraduate and stayed to complete a Ph.D. in stochastic analysis under the supervision of Prof Aubrey Truman. After working in the insurance industry I returned to Swansea to take up my current post.

My research interests focus on probabilistic methods in mathematical physics particularly the relation between classical and quantum mechanics. Past topics include:

1. The semiclassical Coulomb/Kepler problem. This work began by considering the “atomic elliptic state”; a particular a stationary quantum state for the Coulomb problem which is concentrated on an ellipse. By considering the associated stochastic mechanics we have been able to provide a derivation of classical Keplerian motion in the semiclassical limit. This has lead to several papers investigating various aspects of semiclassical Coulomb problems.

2. Semiclassical asymptotics for heat and Burgers equations. This work has its origin in the Hamilton-Jacobi theory developed by A. Truman and D. Elworthy to investigate the semiclassical limit of heat and Schrodinger equations using classical mechanics. These ideas have been developed to include stochastic heat and Burgers equations and I initially worked on the analysis of the behaviour of singularities in the solution for the stochastic Burgers equation. More recently we have worked on extending these results to heat and Burgers equations including vector potentials.

Current research interests cover the above areas but also include stochastic analysis and graded algebras (joint with E. Beggs) and phase space path integrals (joint with A. Truman).

I am also involved in range of teaching and have taught courses including classical mechanics, Hamiltonian and Lagrangian mechanics, electro-magnetics, differential equations and mathematical modelling. I regularly supervise M.Sc. projects on mathematical finance.

Areas of Expertise

  • Stochastic analysis
  • Stochastic mechanics
  • Quantum mechanics
  • Mathematics Education

Publications

  1. Lyakhova, S., Neate, A. Further Mathematics and the transition between school and university mathematics Mathematics Education beyond 16: Pathways and Transitions
  2. Neate, A., Truman, A. Semiclassical stochastic mechanics for the Coulomb potential with applications to modelling dark matter Journal of Mathematical Physics 57 5 052103
  3. Tanner, H., Lyakhova, S., Neate, A. Choosing Further Mathematics Wales Journal of Education 18 2 23 40
  4. Neate, A., Truman, A. Semiclassical wave functions and semiclassical dynamics for the Kepler/Coulomb problem Journal of Physics A: Mathematical and Theoretical 47 22 225302
  5. Neate, A., Truman, A. A stochastic Burgers-Zeldovich model for the formation of planetary ring systems and the satellites of Jupiter and Saturn Journal of Mathematical Physics 54 3 033512

See more...

Teaching

  • MA-002 Fundamental Calculus

    This module introduces students to differential and integral calculus along with elementary applications.

  • MA-338 Analytical Dynamics

    An introduction to Lagrangian and Hamiltonian theories of dynamics. This course develops the mathematical theories of Lagrange and Hamilton which shed new light on the classical mechanics of Newton and provide the natural framework for the development of quantum mechanics.

  • MA-M38 Analytical Dynamics

    This module is an introduction to the Lagrangian and Hamiltonian formulations of mechanics.

Supervision

  • Large deviations and weak convergence for SFDEs/SPDEs with singular drifts«br /»«br /»«br /» and weak convergence of some kinds of stochastic differential equations with singular drifts. (current)

    Student name:
    PhD
    Other supervisor: Prof Chenggui Yuan
  • Topics on Transient Dirichlet Forms: Fundamental Solutions, Potentiial Kernels and Metric Measure Spaces (current)

    Student name:
    PhD
    Other supervisor: Prof Niels Jacob
  • Some Nonlinear Problems With Lack Of Compactness (awarded 2019)

    Student name:
    MSc
    Other supervisor: Dr Carlo Mercuri

Administrative Responsibilities

  • Year tutor - Department of Mathematics

    2009 - 2012

  • Outreach Officer - Department of Mathematics

    2012 - Present

Career History

Start Date End Date Position Held Location
2007 Present Lecturer Swansea University
2007 2007 Fixed Term Lecturer Swansea University
2005 2007 Pricing Analyst Admiral Insurance Group
2002 2005 Ph.D. University of Wales Swansea
1998 2002 M.Math (Hons) University of Wales Swansea

Research Groups

  • Stochastic Analysis Group

    Our group's research interests include: - Functional inequalities and applications - Stochastic partial differential equations and applications to fluid mechanics - Lévy-type processes - Non-commutative (quantum) probability - Stochastic modelling of fractal, multifractal and multiscale systems - Numerical simulation of stochastic processes - Infinite dimensional stochastic analysis