675 research outputs found
Paths of fluctuation induced switching
We demonstrate that the paths followed by a system in fluctuation-activated
switching form a narrow tube in phase space. A theory of the path distribution
is developed and its direct measurement is performed in a micromechanical
oscillator. The experimental and theoretical results are in excellent
agreement, with no adjustable parameters. We also demonstrate the lack of
time-reversal symmetry in switching of systems far from thermal equilibrium.Comment: Accepted to Phys. Rev. Let
A Doubly Nudged Elastic Band Method for Finding Transition States
A modification of the nudged elastic band (NEB) method is presented that
enables stable optimisations to be run using both the limited-memory
quasi-Newton (L-BFGS) and slow-response quenched velocity Verlet (SQVV)
minimisers. The performance of this new `doubly nudged' DNEB method is analysed
in conjunction with both minimisers and compared with previous NEB
formulations. We find that the fastest DNEB approach (DNEB/L-BFGS) can be
quicker by up to two orders of magnitude. Applications to permutational
rearrangements of the seven-atom Lennard-Jones cluster (LJ7) and highly
cooperative rearrangements of LJ38 and LJ75 are presented. We also outline an
updated algorithm for constructing complicated multi-step pathways using
successive DNEB runs.Comment: 13 pages, 8 figures, 2 table
Decoupling of diffusion from structural relaxation and spatial heterogeneity in a supercooled simple liquid
We report a molecular dynamics simulation of a supercooled simple monatomic
glass-forming liquid. It is found that the onset of the supercooled regime
results in formation of distinct domains of slow diffusion which are confined
to the long-lived icosahedrally structured clusters associated with deeper
minima in the energy landscape. As these domains, possessing a low-dimensional
geometry, grow with cooling and percolate below , the critical temperature
of the mode coupling theory, a sharp slowing down of the structural relaxation
relative to diffusion is observed. It is concluded that this latter anomaly
cannot be accounted for by the spatial variation in atomic mobility; instead,
we explain it as a direct result of the configuration-space constraints imposed
by the transient structural correlations. We also conjecture that the observed
tendency for low-dimensional clustering may be regarded as a possible mechanism
of fragility.Comment: To be published in PR
The network topology of a potential energy landscape: A static scale-free network
Here we analyze the topology of the network formed by the minima and
transition states on the potential energy landscape of small clusters. We find
that this network has both a small-world and scale-free character. In contrast
to other scale-free networks, where the topology results from the dynamics of
the network growth, the potential energy landscape is a static entity.
Therefore, a fundamentally different organizing principle underlies this
behaviour: The potential energy landscape is highly heterogeneous with the
low-energy minima having large basins of attraction and acting as the
highly-connected hubs in the network.Comment: 4 pages, 4 figures, revtex
Polytetrahedral Clusters
By studying the structures of clusters bound by a model potential that
favours polytetrahedral order, we find a previously unknown series of `magic
numbers' (i.e. sizes of special stability) whose polytetrahedral structures are
characterized by disclination networks that are analogous to hydrocarbons.Comment: 4 pages, 4 figure
Traveling through potential energy landscapes of disordered materials: the activation-relaxation technique
A detailed description of the activation-relaxation technique (ART) is
presented. This method defines events in the configurational energy landscape
of disordered materials, such as a-Si, glasses and polymers, in a two-step
process: first, a configuration is activated from a local minimum to a nearby
saddle-point; next, the configuration is relaxed to a new minimum; this allows
for jumps over energy barriers much higher than what can be reached with
standard techniques. Such events can serve as basic steps in equilibrium and
kinetic Monte Carlo schemes.Comment: 7 pages, 2 postscript figure
New Tetrahedral Global Minimum for the 98-atom Lennard-Jones Cluster
A new atomic cluster structure corresponding to the global minimum of the
98-atom Lennard-Jones cluster has been found using a variant of the
basin-hopping global optimization algorithm. The new structure has an unusual
tetrahedral symmetry with an energy of -543.665361, which is 0.022404 lower
than the previous putative global minimum. The new LJ_98 structure is of
particular interest because its tetrahedral symmetry establishes it as one of
only three types of exceptions to the general pattern of icosahedral structural
motifs for optimal LJ microclusters. Similar to the other exceptions the global
minimum is difficult to find because it is at the bottom of a narrow funnel
which only becomes thermodynamically most stable at low temperature.Comment: 3 pages, 2 figures, revte
Quasi-continuous Interpolation Scheme for Pathways between Distant Configurations
A quasi-continuous interpolation (QCI) scheme is introduced for characterizing physically realistic initial pathways from which to initiate transition state searches and construct kinetic transition networks. Applications are presented for peptides, proteins, and a morphological transformation in an atomic cluster. The first step in each case involves end point alignment, and we describe the use of a shortest augmenting path algorithm for optimizing permutational isomers. The QCI procedure then employs an interpolating potential, which preserves the covalent bonding framework for the biomolecules and includes repulsive terms between unconstrained atoms. This potential is used to identify an interpolating path by minimizing contributions from a connected set of images, including terms corresponding to minima in the interatomic distances between them. This procedure detects unphysical geometries in the line segments between images. The most difficult cases, where linear interpolation would involve chain crossings, are treated by growing the structure an atom at a time using the interpolating potential. To test the QCI procedure, we carry through a series of benchmark calculations where the initial interpolation is coupled to explicit transition state searches to produce complete pathways between specified local minima.This work was supported by the Engineering and Physical Sciences Research Council [grant number EP/H042660/1]This document is the unedited Author’s version of a Submitted Work that was subsequently accepted for publication in the Journal of Chemical Theory and Computation, copyright © American Chemical Society after peer review. To access the final edited and published work see http://dx.doi.org/10.1021/ct300483
Potential Energy Landscape Equation of State
Depth, number, and shape of the basins of the potential energy landscape are
the key ingredients of the inherent structure thermodynamic formalism
introduced by Stillinger and Weber [F. H. Stillinger and T. A. Weber, Phys.
Rev. A 25, 978 (1982)]. Within this formalism, an equation of state based only
on the volume dependence of these landscape properties is derived. Vibrational
and configurational contributions to pressure are sorted out in a transparent
way. Predictions are successfully compared with data from extensive molecular
dynamics simulations of a simple model for the fragile liquid orthoterphenyl.Comment: RevTeX4, 4 pages, 5 figure
Wigner's Dynamical Transition State Theory in Phase Space: Classical and Quantum
A quantum version of transition state theory based on a quantum normal form
(QNF) expansion about a saddle-centre-...-centre equilibrium point is
presented. A general algorithm is provided which allows one to explictly
compute QNF to any desired order. This leads to an efficient procedure to
compute quantum reaction rates and the associated Gamov-Siegert resonances. In
the classical limit the QNF reduces to the classical normal form which leads to
the recently developed phase space realisation of Wigner's transition state
theory. It is shown that the phase space structures that govern the classical
reaction d ynamicsform a skeleton for the quantum scattering and resonance
wavefunctions which can also be computed from the QNF. Several examples are
worked out explicitly to illustrate the efficiency of the procedure presented.Comment: 132 pages, 31 figures, corrected version, Nonlinearity, 21 (2008)
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