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Christoph Dellago

Publications and source records attributed to Christoph Dellago.

10 recordsLinked to original sources
PubMed2006

Equilibrium free energies from fast-switching trajectories with large time steps.

Jarzynski's [Phys. Rev. Lett. 78, 2690 (1997)] identity for the free-energy difference between two equilibrium states can be viewed as a special case of a more general procedure based on phase-space mappings. Solving a system's equation of motion by approximate means generates a mapping that is perfectly valid for this purpose, regardless of how closely the solution mimics true time evolution. We exploit this fact, using crudely dynamical trajectories to compute free-energy differences that are in principle exact. Numerical simulations show that Newton's equation can be discretized to low order over very large time steps (limited only by the computer's ability to represent resulting values of dynamical variables) without sacrificing thermodynamic accuracy. For computing the reversible work required to move a particle through a dense liquid, these calculations are more efficient than conventional fast-switching simulations by more than an order of magnitude. We also explore consequences of the phase-space mapping perspective for systems at equilibrium, deriving an exact expression for the statistics of energy fluctuations in simulated conservative systems.

Journal Article↗
PubMed2005

Wang-Landau sampling with self-adaptive range.

We report a self-adapting version of the Wang-Landau algorithm that is ideally suited for application to systems with a complicated structure of the density of states. Applications include determination of two-dimensional densities of states and high-precision numerical integration of sharply peaked functions on multidimensional integration domains.

Journal Article↗
PubMed2005

Melting of icosahedral gold nanoclusters from molecular dynamics simulations.

Molecular dynamics simulations show that gold clusters with about 600-3000 atoms crystallize into a Mackay icosahedron upon cooling from the liquid. A detailed surface analysis shows that the facets on the surface of the Mackay icosahedral gold clusters soften but do not premelt below the bulk melting temperature. This softening is found to be due to the increasing mobility of vertex and edge atoms with temperature, which leads to inter-layer and intra-layer diffusion, and a shrinkage of the average facet size, so that the average shape of the cluster is nearly spherical at melting.

Journal Article↗
PubMed2005

Biased sampling of nonequilibrium trajectories: can fast switching simulations outperform conventional free energy calculation methods?

We have investigated the maximum computational efficiency of reversible work calculations that change control parameters in a finite amount of time. Because relevant nonequilibrium averages are slow to converge, a bias on the sampling of trajectories can be beneficial. Such a bias, however, can also be employed in conventional methods for computing reversible work, such as thermodynamic integration or umbrella sampling. We present numerical results for a simple one-dimensional model and for a Widom insertion in a soft sphere liquid, indicating that, with an appropriately chosen bias, conventional methods are in fact more efficient. We describe an analogy between nonequilibrium dynamics and mappings between equilibrium ensembles, which suggests that the practical inferiority of fast switching is quite general. Finally, we discuss the relevance of adiabatic invariants in slowly driven Hamiltonian systems for the application of Jarzynski's theorem.

Chemistry, Physical↗
PubMed2005

Surface-driven bulk reorganization of gold nanorods.

Molecular dynamic simulations are used to study the structural stability of gold nanorods upon heating. We show that the global stability of the rod is governed by the free energetics of its surface. In particular, an instability of surface facets nucleates a bulk instability that leads to both surface and bulk reorganization of the rod. The surface reorganizes to form new, more stable, {111} facets, while the underlying fcc lattice completely reorients to align with this new surface structure. Rods with predominantly {111} facets remain stable until melting.

Journal Article↗
PubMed2003

Simulation strategies and signatures of chaos in classical nonlinear response.

Algorithms are presented for overcoming the computational challenge of nonlinear response functions which describe the response of a classical system to a sequence of n pulses and depend on nth order multipoint stability matrices containing signatures of chaos. Simulations for the Lorentz gas demonstrate that finite field algorithms can be effectively used for the robust, long time calculation of nonlinear response functions. These offer the possibility to characterize chaos beyond the commonly used Lyapunov exponents and suggest new experimentally accessible measures of chaos.

Models, Statistical↗
PubMed2003

Proton transport through water-filled carbon nanotubes.

Proton transfer along 1D chains of water molecules inside carbon nanotubes is studied by simulations. Ab initio molecular dynamics and an empirical valence bond model yield similar structures and time scales. The proton mobility along 1D water chains exceeds that in bulk water by a factor of 40, but is reduced if orientational defects are present. Excess protons interact with hydrogen-bonding defects through long-range electrostatics, resulting in coupled motion of protons and defects.

Hydrogen↗
PubMed2002

Fluctuations, convergence times, correlation functions, and power laws from many-body Lyapunov spectra for soft and hard disks and spheres.

The dynamical instability of many-body systems is best characterized through the time-dependent local Lyapunov spectrum [lambda(j)], its associated comoving eigenvectors [delta(j)], and the "global" time-averaged spectrum [ ]. We study the fluctuations of the local spectra as well as the convergence rates and correlation functions associated with the delta vectors as functions of j and system size N. All the number dependences can be described by simple power laws. The various powers depend on the thermodynamic state and force law as well as system dimensionality.

Journal Article↗
PubMed2001

Transition path sampling: throwing ropes over rough mountain passes, in the dark.

This article reviews the concepts and methods of transition path sampling. These methods allow computational studies of rare events without requiring prior knowledge of mechanisms, reaction coordinates, and transition states. Based upon a statistical mechanics of trajectory space, they provide a perspective with which time dependent phenomena, even for systems driven far from equilibrium, can be examined with the same types of importance sampling tools that in the past have been applied so successfully to static equilibrium properties.

Journal Article↗