Teaching responsibilities:

Module Tutor

  • The Mathematician in Society (Level HE4)
  • Real Analysis (Level HE5)

Tutorial Support

  • Abstract Algebra (Level HE4)
  • Dynamics (Level HE5)
  • Vector Calculus (Level HE5)

Overview:

Tim obtained a first class MSci degree in Theoretical Physics with Applied Mathematics from Lancaster University in 2004 and continued at the University to gain his PhD in Mathematical Physics in 2008. His thesis involved the application of modern differential geometric methods to develop a relativistic version of elasticity in order to explore the dynamics of media in the presence of large gravitational tidal stresses (such as in rapidly rotating neutron stars) or when the motion of such media is comparable with that of light. By incorporating a description of classical electrodynamics, Tim was able to model the interaction of light with a deformable material and model the forces present in a laser-plasma accelerator. Tim further developed this work as part of his post-doctoral research positions at Lancaster University, The Cockcroft Institute  and as a member of the ALPHA-X collaboration (2007-2014), exploring the interactions of light with media at both a classical and quantum level. Tim has also explored nonlinear electrodynamics and, in particular, a generalization of classical electrodynamics introduced by Born and Infeld in order to ameliorate the singular self-energy of a point charge. Using work from his thesis, the effects of this nonlinear Born-Infeld electrodynamics was explored using plasmas. This work was acknowledged by the Institute of Physics as a “Highlight of 2011”.

Aside from research, Tim is a keen communicator of mathematics and science – having been a STEM Ambassador and involved with numerous outreach activities.

Tim is also an Associate Member of the HEA, a Member of the IoP and a Member of the LMS.

Current Research Interests

The application of modern differential geometric methods and analytic techniques to study:

  • Relativistic fluid models of beams of charged particles and plasmas
  • Classical and quantum electrodynamics
  • Quantum stresses in media induced by quantum electromagnetic vacuum fluctuations (Casimir effects)
  • Foundations of quantum theory
  • Quantum entanglement

Publications

"Towards a Model for Laser-induced Bi-qutrit States"
S. Goto, R. W. Tucker & T. J. Walton
(submitted to Physics Review Letters)

 

“Classical Dynamics of Free Electromagnetic Laser Pulses”
S. Goto, R. W. Tucker & T. J. Walton
(submitted to Nuclear Instruments and Methods B)


"Aspects of Quantum Energy and Stress in Inhomogeneous Unbounded Dielectric Continua"
S. Goto, R. W. Tucker & T. J. Walton
(submitted to Annals of Physics)


"On the Computation of Casimir Stresses in Open Media and Lifshitz Theory"
S. Goto, R. W. Tucker & T. J. Walton
J. Phys. A: Math. Theor., 46, 405301 (2013)

"Numerical Regularization of Electromagnetic Quantum Fluctuations in Inhomogeneous Dielectric Media"
S. Goto, A. C. Hale, R. W. Tucker & T. J. Walton
Phys. Rev. A, 85, 034103 (2012)

"Quantum Electromagnetic Vacuum Fluctuations in Inhomogeneous Dielectric Media"
S. Goto, R. W. Tucker & T. J. Walton
Proc. SPIE 8072, 80720O (2011) 

"Covariant Electromagnetic Constitutive Theory for Dispersive Continua"
S. Goto, J. Gratus, A. Hale, R. W. Tucker & T. J. Walton
Elasticity and Anelasticity, ed. I. A. Kiyko, G. L. Brovko & R. A. Vasin, Moscow: Moscow University Press, 264-271 (2011) 

"Exploring Born-Infeld Electrodynamics using Plasmas"
D. A. Burton, R. M. G. M. Trines, T. J. Walton & H. Wen
J. Phys. A: Math. Theor., 44 (095501) (2011)
(Selected as a "Highlight of 2011" by the journal) 

"The Electrodynamics of Inhomogeneous Rotating Media and the Abraham and Minkowski Tensors II: Applications"
S. Goto, R. W. Tucker & T. J. Walton
Proc. Roy. Soc. A, 467 (2125) 79-98 (2011) 

"The Electrodynamics of Inhomogeneous Rotating Media and the Abraham and Minkowski Tensors I: General Theory"
S. Goto, R. W. Tucker & T. J. Walton
Proc. Roy. Soc. A, 467 (2125) 59-78 (2011) 

"An Intrinsic Approach to Forces in Magnetoelectric Media"
R. W. Tucker & T. J. Walton
Il Nuovo Cimento C, 32(1) 205-229 (2009)