My research group is based in the School of Mathematics at the University of Edinburgh. We combine expertise in dynamics, classical, quantum and statistical mechanics with advanced scientific computing techniques to develop forefront simulation methodology for applications such as molecular dynamics.
On these pages you will find links to preprints and articles in journals, as well as some general information about the group. People interested in possibly joining the group, whether for upper division undergraduate, MSc, doctoral, or postdoctoral study are encouraged to use the email address below to find out about opportunities.
Contact Info:
email: b dot leimkuhler at-sign ed.ac.uk
mail: Ben Leimkuhler, School of Mathematics, James Clerk Maxwell Building, King's Buildings, University of Edinburgh, Edinburgh EH9 3JZ
My group's work is performed in collaboration with researchers in other areas of mathematics (numerical analysis, probability theory, analysis) and also with chemists, physicists, engineers and biomolecular modellers. This broad-based approach combines model development with simulation and rigorous numerical analysis. Our goal is to use the flexibility of our toolset to expand understanding of algorithms without much regard to whether or not the approach taken fits a particular formalism or mathematical school. We always appreciate the elegance that only a full mathematical theory can provide, but at the same time we are pragmatic: there are many problems which cannot be resolved in complete rigor using current theories. In these cases the boundaries of knowledge can usually still be explored using computational experiments on carefully chosen model problems. We use painstaking numerical testing to formulate conjectures which can later be subjects of in-depth mathematical study.
I am involved as an editor on several journals which reflect to some extent the breadth of my interests:
One of the most enjoyable aspects of my work is the ability to interact with others for whom mathematics is a real passion. My group has variety of close interactions with other research groups which helps to ensure that our work is well distributed to a broad community.
A few links to collaborators (former and future), ex-students/postdocs, other research colleagues and friends:
Book: Simulating Hamiltonian Dynamics, B. Leimkuhler and S. Reich, Cambridge University Press, 2005.
Weakly coupled heat bath models for Gibbs-like invariant states in nonlinear wave equations Rational construction of stochastic numerical methods for molecular sampling Comparing the efficiencies of stochastic isothermal molecular dynamics methods Adaptive stochastic methods for sampling driven molecular systems
J. Bajars, J. Frank and B. Leimkuhler, submitted, , 2012. PDF
B. Leimkuhler and C. Matthews, in press, , 2012. JOURNAL PDF
B. Leimkuhler, E. Noorizadeh and O. Penrose, Journal of Statistical Physics, 143: 921-942, 2011. JOURNAL PDF
A. Jones and B. Leimkuhler, Journal of Chemical Physics, 135: Preprint(2011) . JOURNAL
Dimensional reductions for the computation of time-dependent quantum expectations
B. Leimkuhler and G. Mazzi, SIAM Journal on Scientific Computing, 33: 2024-2038, 2011. JOURNAL
Stochastic-dynamical thermostats for constraints and stiff restraints
J. Bajars, J. Frank and B. Leimkuhler, The European Physical Journal, 200: 131-152, 2011. JOURNAL PDF
Simplified modelling of a thermal bath, with application to a fluid vortex system
S. Dubinkina, J. Frank, and B. Leimkuhler, SIAM Multiscale Modelling and Simulation, 8: 1882-1901, 2010. JOURNAL PDF
Generalized Bulgac-Kusnezov methods for sampling of the Gibbs-Boltzmann measure
B. Leimkuhler, Physical Review E, 81: Preprint(2010) . JOURNAL PDF
A gentle stochastic thermostat for molecular dynamics
B. Leimkuhler, E. Noorizadeh and F. Theil, Journal of Statistical Physics, 135: 261-277, 2009. JOURNAL PDF
A Metropolis-adjusted Nose-Hoover thermostat
B. Leimkuhler and S. Reich, ESAIM:Mathematical modelling and numerical analysis, 43: 743-755, 2009. JOURNAL PDF
A temperature control technique for nonequilibrium molecular simulation
B. Leimkuhler, F. Legoll and E. Noorizadeh, Journal of Chemical Physics, 128: Preprint(2008) . JOURNAL PDF
Molecular dynamics and the accuracy of numerically computed averages
S. Bond and B. Leimkuhler, Acta Numerica, 16: 1-65, 2007. JOURNAL PDF
Stabilized integration of Hamiltonian systems with hard-sphere inequality constraints
S. Bond and B. Leimkuhler, SIAM Journal on Scientific Computing, 30: 134-147, 2007. JOURNAL PDF
Molecular simulation in the canonical ensemble and beyond
Z. Jia and B. Leimkuhler, ESAIM:Mathematical modelling and numerical analysis, 41: 333-350, 2007. JOURNAL
Rapid thermal equilibration of coarse-grained molecular dynamics
S. Gill, Z. Jia, B. Leimkuhler and A. Cocks, Physical Review B, 73: Preprint(2006) . JOURNAL PDF
Geometric integrators for multiple timescale simulation
Z. Jia and B. Leimkuhler, Journal of Physics A, 39: 5379-5403, 2006. JOURNAL
Approach to thermal equilibrium in biomolecular simulation
E. Barth, B. Leimkuhler, and C. Sweet, New Algorithms for Macromolecular Simulation (Springer Lecture Notes in Computational Science and Engineering), 49: 125-140, 2006. JOURNAL PDF
A projective thermostatting technique
Z. Jia and B. Leimkuhler, SIAM Multiscale Modelling and Simulation, 4: 563-583, 2005. JOURNAL PDF
A Hamiltonian formulation for recursive multiple thermostats in a common timescale
B. Leimkuhler and C. Sweet, SIAM Journal on Applied Dynamical Systems, 4: 187-216, 2005. JOURNAL PDF
An efficient geometric integrator for thermostatted anti-/ferromagnetic Models
T. Arponen and B. Leimkuhler, BIT Numerical Mathematics, 44: 403-424, 2004. JOURNAL PDF
The canonical ensemble via symplectic integration using Nose and Nose-Poincare chains
B. Leimkuhler and C. Sweet, Journal of Chemical Physics, 121: 108-117, 2004. JOURNAL PDF
A parallel multiple time-scale reversible integrator for dynamics simulation
Z. Jia and B. Leimkuhler, Future Generation Computer Systems, 19: 415-424, 2003. JOURNAL PDF
Generating generalized distributions from dynamical simulation
E. Barth, B. Laird and B. Leimkuhler, Journal of Chemical Physics, 118: 5759-5769, 2003. JOURNAL PDF
Generalized dynamical thermostatting technique
B. Laird and B. Leimkuhler, Physical Review E 68, 016704 (2003), 68: Preprint(2003) . JOURNAL PDF
On the approximation of Feynman-Kac path integrals
S. Bond, B. Laird, and B. Leimkuhler, Journal of Computational Physics, 185: 472-483, 2003. JOURNAL PDF
An efficient multiple time-scale reversible integrator for the gravitational N-body problem
B. Leimkuhler, Applied Numerical Mathematics, 43: 175-190, 2002. JOURNAL PDF
A separated form of Nosé dynamics for constant temperature and pressure simulation
B. Leimkuhler, Computer Physics Communications, 148: 206-213, 2002. JOURNAL PDF
A test set for molecular dynamics
E. Barth, B. Leimkuhler, and S. Reich, Lecture Notes in Computational Science and Engineering, 24: 73-103, 2002. JOURNAL PDF
A reversible averaging integrator for multiple timescale dynamics
B. Leimkuhler and S. Reich, Journal of Computational Physics, 171: 95-114, 2001. JOURNAL PDF
Explicit, time-reversible and variable stepsize integration
T. Holder, B. Leimkuhler, and S. Reich, Applied Numerical Mathematics, 39: 367-377, 2001. JOURNAL PDF
Scaling invariance and adaptivity
C. Budd, B. Leimkuhler and M. Piggott, Applied Numerical Mathematics, 39: 261-288, 2001. JOURNAL PDF
Molecular dynamics algorithms for mixed hard-core/continuous potentials
Y. Houndonougbo, B. Laird, and B. Leimkuhler, Journal of Molecular Physics, 98: 309-316, 2000. JOURNAL PDF
A time-reversible, regularized, switching integrator for the N-body problem
A. Kvaerno and B. Leimkuhler, SIAM Journal on Scientific Computing, 22: 1016-1035, 2000. JOURNAL PDF
Geometric integrators based on scaling and switching A Semi-explicit, variable-stepsize integrator for constrained dynamics Reversible adaptive regularization: perturbed Kepler motion and classical atomic trajectories Reversible adaptive regularization methods for atomic N-body problems in applied fields Asymptotic error analysis of the Adaptive Verlet method The Nose-Poincare method for constant temperature molecular dynamics Timestep acceleration of waveform relaxation The Adaptive Verlet method Geometric integrators for classical spin systems Symplectic splitting methods for rigid body molecular dynamics A symplectic integrator for Riemannian manifolds Orthosymplectic integration of linear Hamiltonian systems Symplectic integration of constrained Hamiltonian systems Algorithms for constrained molecular dynamics Symplectic numerical integrators in constrained Hamiltonian systems Estimating waveform relaxation convergence Numerical solution of differential-algebraic equations for constrained mechanical motion Automatic integration of Euler-Lagrange equations with constraints
B. Leimkuhler, Proceedings of the Equadiff Conference (Berlin, 1999), World Scientific, 988-993, 2000. PDF
E. Barth, B. Leimkuhler, and S. Reich, SIAM Journal on Scientific Computing, 21: 1027-1044, 1999. JOURNAL PDF
B. Leimkuhler, Philosophical Transactions of the Royal Society of London A, 357: 1101-1134, 1999. JOURNAL PDF
B. Leimkuhler, Applied Numerical Mathematics, 29: 31-43, 1999. JOURNAL PDF
S. Cirilli, E. Hairer and B. Leimkuhler, BIT Numerical Mathematics, 39: 25-33, 1999. JOURNAL PDF
S. Bond, B. Leimkuhler and B. Laird, Journal of Computational Physics, 151: 114-134, 1999. JOURNAL PDF
B. Leimkuhler, SIAM Journal on Numerical Analysis, 35: 31-50, 1998. JOURNAL PDF
W. Huang and B. Leimkuhler, SIAM Journal on Scientific Computing, 18: 239-256, 1997. JOURNAL PDF
J. Frank, W. Huang and B. Leimkuhler, Journal of Computational Physics, 133: 160-172, 1997. JOURNAL PDF
A. Dullweber, B. Leimkuhler and R. McLachlan, Journal of Chemical Physics, 107: 5840-5851, 1997. JOURNAL PDF
B. Leimkuhler and G. Patrick, Journal of Nonlinear Science, 6: 367-384, 1996. JOURNAL PDF
B. Leimkuhler and E. Van Vleck, Numerische Mathematik, 77: 269-282, 1996. JOURNAL PDF
B. Leimkuhler and S. Reich, Mathematics of Computation, 63: 589-605, 1994. JOURNAL PDF
E. Barth, K. Kuczera, B. Leimkuhler and R. Skeel, Journal of Computational Chemistry, 16: 1192-1209, 1995. JOURNAL PDF
B. Leimkuhler and R. Skeel, Journal of Computational Physics, 112: 117-125, 1994. JOURNAL PDF
B. Leimkuhler, SIAM Journal on Scientific Computing, 14: 872-889, 1993. JOURNAL PDF
C. Fuehrer and B. Leimkuhler, Numerische Mathematik, 59: 55-69, 1991. JOURNAL PDF
C.W. Gear, B. Leimkuhler, G.K. Gupta, Journal of Computational and Applied Mathematics, 12-13: 77-90, 1985. JOURNAL PDF