Research interests
- Molecular dynamics simulations, rigid body systems
- Parallel programming techniques
- Accurate and stable integration methods
- Path Integral Monte Carlo and Molecular Dynamics of quantum systems
- Non-equilibrium systems (Brownian motion, fluctuation relations, nanoparticles, protein folding)
- Heterogeneous dynamics in fluids, glasses and undercooled liquids
- Dynamical systems theory
Molecular dynamics simulations of fluids
When a
problem cannot be tackled analytically, computer
simulation techniques can often still provide us with
information about the system. Our interest lies in
models with rigid molecules which interact through
discontinuous potentials. These can be simulated using
Discontinuous Molecular Dynamics, or DMD. DMD is a
powerful simulation technique for systems with
discontinous interactions, that we recently extended to
constrained systems [24, 25]. Rigid
bodies are a special case of constrained systems that
allow for a fast implementation of DMD by using the exact
solution of a torque-free rigid rotor[23].
The exact
solution of torque-free rigid rotors can also be used for
smoothly interacting rigid bodies by using so-called
symplectic integration schemes. These schemes allow one
to numerical simulate a many-particle system while
retaining time-reversibility, phase space conservation,
momentum conservation, and very good stability and energy
conservation. Such schemes are useful in simulations for
large systems at long time scales. Our implementation of
the free rigid rotor[23] means
that such schemes, which are typically developed for
point particle, can be extended to rigid, rotating
particles in a straightforward fashion [28].
With the exact
solutation of rigid rotating bodies, and given a smooth
potential, one can device a DMD simulatione of the system
by discretizing the potential energy surface to a
terraced landscape. This general construction can be done
automatically [31] so
that the technical difficulties in setting up a DMD
simulations only need to be resolved once.
Undercooled fluids and glasses
Heterogeneous dynamics in
(undercooled) fluids can be characterized using density
correlations at multiple times and positions in the
fluid. We have developed a mode coupling theory for these
correlations [8]
, which has been tested on a simple model, namely a
hard sphere fluid [9]. We are
currently working on extensions that can address the
problem of heterogeneities in supercooled liquids and
glasses [19,
8]. Other
work in this direction involves the (structural) glass
transition in stochastic systems [18].
Non-equilibrium physics on the mesoscale
In nano-scale systems, large statistical fluctuations of
work and heat take place, which are considerably larger
than for macroscopic objects. 
It turns out that fluctuations of work and of heat
production are very different. We have been able to show
that a well-known theorem (the Fluctuation
Theorem) for heat production is to be replaced in
these systems by a new theorem
[26,
20, 16,
17, 14, 13].
We found that this can be applied to small electric circuits as well, i.e., fluctuations in heat produced in certain circuits (containing a resistor and a conductor) also satisfy the new fluctuation theorem[15]. This has been experimentally verified [Garnier&Ciliberto, Phys. Rev. E 71, 060101(R), 2005].
A different aspect of this research is the description of small non-equilibrium systems at very short time scales, i.e., picoseconds and shorter. Since particles move only a distance on the order of nanometers or less in such short times, this is also relevant for nanophysics. We have developed a theory to describe the transport of particles of different kinds (mixtures) on these tiny scales, using so-called Green´s functions [27, 21, 22].
Chaos theory and transport processes
A subject that I have been interested in since my PhD thesis is the relation between dynamical systems and statistical physics. In collaboration with H. van Beijeren, J. R. Dorfman and D. Panja, quantities from the theory of dynamical systems, like Lyapunov exponents, were computed analytically for systems that are studied by statistical physics, e.g. a hard sphere gas. We also studied the relation of these with transport coefficients like the viscosity [12, 11, 10, 7, 6, 4].
Collaborators
| Jeremy Schofield (Toronto) | L. Hernández de la Peña (Urbana-Champaign) |
| E.G.D. Cohen (New York) | Sergio Ciliberto (Lyon) |
| S.S. Ashwin (Saskatoon) | Henk van Beijeren (Utrecht) |
| Debabrata Panja (Amsterdam) | J. Robert Dorfman (College Park, MD) |
| Christoph Dellago (Vienna) | Sheldon B. Opps (Charlottetown, PEI) |
| Theo W. Ruijgrok (Utrecht) | Igor P. Omelyan (Lviv, Ukraine) |
| Ray Kapral (Toronto) | Aaron Kelly (Toronto) |
| Gilles H. Peslherbe (Montreal) | Hanif Bayat (Toronto) |