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Assistant Research Professor.
Department of Computer
Science and Engineering,
University of Notre Dame,
325 Cushing Hall,
Notre Dame,
IN 46556.
tel: (574) 315 0842
fax: (574) 631 9260
e-mail:
chris.sweet@nd.edu |
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In July 2001 I obtained a first class honours degree in Mathematics
from the University of Leicester.
My Ph.D. thesis, entitled "Hamiltonian Thermostatting Techniques for
Molecular Dynamics Simulation", was submitted on 11th May 2004
at the University of Leicester, with the viva voce being held on 7th June 2004.
Collaboration between the Pande group (Folding at Home)
at Stanford and LCLS group at Notre Dame.
Currently I am investigating the use of Normal Mode Analysis (NMA) techniques
to facilitate the acceleration of numerical methods.
The aim is to approximate the kinetics or thermodynamics of a biomolecule
by a reduced model based on a normal mode decomposition of the dynamical
space. Our basis set uses the eigenvectors of a mass re-weighted Hessian
matrix calculated with a biomolecular force field. This particular choice has
the advantage of an ordering according to the eigenvalues, which has a
physical meaning (square-root of the mode frequency). Low frequency
eigenvalues correspond to more collective motions, whereas the highest
frequency eigenvalues are the limiting factor for the stability of the
integrator. The higher frequency modes are overdamped and relaxed near to
their energy minimum while respecting the subspace of low frequency dynamical
modes. The first paper 'Normal Mode Partitioning of Langevin Dynamics for Biomolecules' authored by
Christopher R. Sweet, Paula Petrone, Vijay S. Pande and Jesús A. Izaguirre
has completed the review process with the Journal of Chemical Physics. It should appear in March 2008.
An interactive website, www.normalmodes.info, illustrating
Normal Modes in Molecular Dynamics can be found here.
Supplementary information, code and scripts can be found here.
Earlier work can be found here.
Collaboration between LCLS group at Notre Dame and Robert D. Skeel at Purdue University.
Hybrid Monte Carlo (HMC) is a rigorous sampling method that uses molecular
dynamics as a global Monte Carlo move, but the acceptance rate of HMC decays
exponentially with system size. The Shadow Hybrid Monte Carlo (SHMC) was
previously introduced to overcome this performance degradation by sampling
instead from the shadow Hamiltonian defined for MD when using a symplectic
integrator. SHMC's performance is limited by the need to generate momenta for
the MD step from a non-separable shadow Hamiltonian.
To overcome this we have introduced the
Separable Shadow Hamiltonian Hybrid Monte Carlo (S2HMC) method, based on a
formulation of the leapfrog/Verlet integrator that corresponds to a more
separable shadow Hamiltonian, which allows efficient generation of momenta.
S2HMC gives the acceptance rate of a 4th order integrator at the cost of a
2nd order integrator.
Collaboration with Ben Leimkuhler at Edinburg University and Eric Barth at Kalamazoo College.
During the final two years I studied the thermostatting
of dynamical systems in order to generate simulations which sample
from the Gibbs, or canonical, ensemble. Molecular dynamics
trajectories that sample from this distribution can be generated
by introducing a modified Hamiltonian with additional degrees of
freedom as described by Nosé. To achieve the ergodicity
required for canonical sampling, a number of techniques have been
proposed based on incorporating additional thermostatting
variables, such as Nosé-Hoover chains. For Nosé
dynamics, it is often stated that the system is driven to
equilibrium through a resonant interaction between the
self-oscillation frequency of the thermostat variable and a
natural frequency of the underlying system. By pioneering the
introduction of multiple thermostat Hamiltonian formulations,
which are not restricted to chains, it has been possible to
clarify this perspective, using harmonic models, and exhibit
practical deficiencies of the standard Nosé-chain approach.
As a consequence of this it has been possible to propose a new
powerful "recursive thermostatting" procedure which obtains
canonical sampling without the stability problems encountered with
chains. This method also has the advantage that the choice of
Nosé mass is essentially independent of the system to be
thermostatted. In addition a Hamiltonian chains method,
Nosé-Poincaré chains, has been proposed where these
methods are appropriate. This research has yielded two papers,
"The Canonical Ensemble via Symplectic Integrators using
Nosé and Nosé-Poincaré chains" which has been
accepted for publication by the Journal of Chemical Physics, and
the more recent "A Hamiltonian Formulation for Recursive Multiple
Thermostats in a Common Timescale" which has been submitted for
publication. As an aid to understanding these methods I have
created a website where the methods can be compared which can be
accessed via the "
Recursive Thermostatting simulation
" link to
the left. This site uses a cgi script to integrate the simulation
for the specified time and return images of the resulting
thermostat variable phase-space, distributions and averaged local kinetic
energy.
This work continues, we are currently looking at the effect of
both statistical and dynamical thermostats on both the velocity auto-correlation
function and sampling for pentane in liquid and gas form.
I studied for my Ph.D under the supervision of Professor Benedict
Leimkuhler in the general area of Geometric Integrators. During my
research I developed an interest in software which provides a
visual interpretation of simulation data and have written several
programs using Trolltech Qt (as used for the Linux KDE interface)
and OpenGL. I have included movies of some of these simulations
on the left hand side "Links" section, and source code for a basic
gravitational model.
During the first year of my Ph.D. studies I looked at N-body systems,
such
as the Solar System, with particular reference to variable step-size
integrators. For fixed step-size integrators it is possible to
compose steps of different size to increase the order of the method
through the cancelation of error terms. When extending this to
variable step-size methods the expected increase in order is often
not obtained. Analysis of this problem led to a family of variable
step-size higher order methods detailed in the paper "Higher Order
Symmetric Variable Stepsize Methods" which has been submitted for
publication. A Solar System model has been integrated over one billion
years using these methods. As an aid to visualization I wrote an OpenGL
program to generate images from the simulation data for this model,
the Solar System movie/Gif from the left hand menu was generated
using this software. I also wrote a brief history of Solar System
simulations in an article for the Wrangler, a maths newsletter from
the University of Leicester which can be accessed from the left hand menu,
which included some of these graphics.
- C.R.Sweet, B.J.Leimkuhler.
The Canonical Ensemble via Symplectic
Integrators using Nose and Nose-Poincare chains.
J. Chem. Pys., 121, 108-126, 2004.
- C.R.Sweet, B.J.Leimkuhler.
A Hamiltonian Formulation for
Recursive Multiple Thermostats in a Common Timescale.
SIAM J. on
Applied Dynamical Systems, 4, 187-216, 2005.
- Paul Brenner, Christopher R. Sweet, Dustin VonHandorf, and Jesus A. Izaguirre.
Accelerating the replica exchange method through an efficient all-pairs exchange.
J. Chem. Phys., 126, 126-132, 2007.
- Christopher R. Sweet, Paula Petrone, Vijay S. Pande and Jesús A. Izaguirre.
Normal Mode Partitioning of Langevin Dynamics for Biomolecules.
J. Chem. Phys.
- E.Barth, B.J.Leimkuhler, C.R.Sweet.
Approach to Thermal
Equilibrium in Biomolecular Simulation.
New Algorithms for Macromolecular Simulation, Springer Berlin Heidelberg., 49, 125-140, 2006.
- T. Cickovski, C. Sweet and J. A. Izaguirre.
MDL, A Domain-Specific
Language for Molecular Dynamics.
In IEEE Proceedings of 40th Annual Simulation
Symposium, Norfolk, VA. 256-266, 2007.
- C.R.Sweet, B.J.Leimkuhler.
Higher Order Symmetric Variable Stepsize Methods.
Submitted to Numerische Mathematik.
- Christopher R. Sweet, Scott S. Hampton, Robert D. Skeel and Jesús A. Izaguirre.
Separable Shadow Hybrid Monte Carlo Method.
Submitted to J. Chem. Phys.
- Christopher R. Sweet, Scott S. Hampton, Jesús A. Izaguirre.
Optimal implementation of the Shadow hybrid Monte Carlo method.
Submitted to SIAM J. on Scientific Computing.
Java Molecular Viewer for use with Protomol,
the open-source molecular dynamics package from the LCLS
group at Notre Dame University. The code uses the JOGL
OpenGL bindings, and requires Java 1.6 or above. It adds real-time viewing capability to the simulation, by communicating
with the inbuilt Protomol sockets server. A number of molecular representations are provided, along with
querying of individual atom information. To run from the command line use "java -jar -Djava.library.lib=./ JMV.jar".
Example code for implementing a simple Gravitational model, where the orbiting
body can be wrapped in a bitmap can be downloaded here for either Microsoft
Windows or Linux. The code uses the Trolltech QT libraries,
the basis for the KDE desktop.
Examples of simulation movies.
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