3,506 research outputs found
Saddle Points and Dynamics of Lennard-Jones Clusters, Solids and Supercooled Liquids
The properties of higher-index saddle points have been invoked in recent
theories of the dynamics of supercooled liquids. Here we examine in detail a
mapping of configurations to saddle points using minimization of , which has been used in previous work to support these theories. The
examples we consider are a two-dimensional model energy surface and binary
Lennard-Jones liquids and solids. A shortcoming of the mapping is its failure
to divide the potential energy surface into basins of attraction surrounding
saddle points, because there are many minima of that do not
correspond to stationary points of the potential energy. In fact, most liquid
configurations are mapped to such points for the system we consider. We
therefore develop an alternative route to investigate higher-index saddle
points and obtain near complete distributions of saddles for small
Lennard-Jones clusters. The distribution of the number of stationary points as
a function of the index is found to be Gaussian, and the average energy
increases linearly with saddle point index in agreement with previous results
for bulk systems.Comment: 14 pages, 7 figure
Kinetic Analysis of Discrete Path Sampling Stationary Point Databases
Analysing stationary point databases to extract phenomenological rate
constants can become time-consuming for systems with large potential energy
barriers. In the present contribution we analyse several different approaches
to this problem. First, we show how the original rate constant prescription
within the discrete path sampling approach can be rewritten in terms of
committor probabilities. Two alternative formulations are then derived in which
the steady-state assumption for intervening minima is removed, providing both a
more accurate kinetic analysis, and a measure of whether a two-state
description is appropriate. The first approach involves running additional
short kinetic Monte Carlo (KMC) trajectories, which are used to calculate
waiting times. Here we introduce `leapfrog' moves to second-neighbour minima,
which prevent the KMC trajectory oscillating between structures separated by
low barriers. In the second approach we successively remove minima from the
intervening set, renormalising the branching probabilities and waiting times to
preserve the mean first-passage times of interest. Regrouping the local minima
appropriately is also shown to speed up the kinetic analysis dramatically at
low temperatures. Applications are described where rates are extracted for
databases containing tens of thousands of stationary points, with effective
barriers that are several hundred times kT.Comment: 28 pages, 1 figure, 4 table
Quantum annealing of the Traveling Salesman Problem
We propose a path-integral Monte Carlo quantum annealing scheme for the
symmetric Traveling Salesman Problem, based on a highly constrained Ising-like
representation, and we compare its performance against standard thermal
Simulated Annealing. The Monte Carlo moves implemented are standard, and
consist in restructuring a tour by exchanging two links (2-opt moves). The
quantum annealing scheme, even with a drastically simple form of kinetic
energy, appears definitely superior to the classical one, when tested on a 1002
city instance of the standard TSPLIB.Comment: 5 pages, 2 figure
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Home accidents amongst elderly people: A locality study in Scotland
Aim
The aim of this locality study was to collect information on reported and unreported accidents amongst elderly people living in one locality in Scotland.
Method
Postal Survey- A postal questionnaire was sent to 3,757 men and women aged 65+ years living in one locality. The questionnaire asked respondents to indicate how many accidents they had experienced in the past twelve months, plus to indicate type and location. Information was gathered on living arrangements, ethnicity, gender, age and deprivation. Respondents were asked if they would be willing to take part in an interview study.
Interview Study - One hundred elders who had had at least one accident in the previous twelve months were interviewed.
Results
Postal Survey - Over a third of the respondents in the postal survey reported having had an accident in the previous twelve months. Bumps and drops and falls were the most common type of accident. Most accidents happened in the kitchen. Women reported more falls than men and those living alone reported more accidents than those living with others. Age was associated with the prevalence of accidents, but the association was somewhat curvilinear, with accidents decreasing with age and then increasing again.
Interview Study â Interviewees found it hard to differentiate one accident from another. Considerable reluctance to visit the GP after an accident was noted, with many not attending even for serious accidents. Almost forty percent were âveryâ distressed after their accident, and a quarter reported a loss of confidence. However, most did not worry about accidents. Few thought that their age, health or medications were a cause of their accidents
A Bell-Evans-Polanyi principle for molecular dynamics trajectories and its implications for global optimization
The Bell-Evans-Polanyi principle that is valid for a chemical reaction that
proceeds along the reaction coordinate over the transition state is extended to
molecular dynamics trajectories that in general do not cross the dividing
surface between the initial and the final local minima at the exact transition
state. Our molecular dynamics Bell-Evans-Polanyi principle states that low
energy molecular dynamics trajectories are more likely to lead into the basin
of attraction of a low energy local minimum than high energy trajectories. In
the context of global optimization schemes based on molecular dynamics our
molecular dynamics Bell-Evans-Polanyi principle implies that using low energy
trajectories one needs to visit a smaller number of distinguishable local
minima before finding the global minimum than when using high energy
trajectories
Energy Landscape and Global Optimization for a Frustrated Model Protein
The three-color (BLN) 69-residue model protein was designed to exhibit frustrated folding. We investigate the energy landscape of this protein using disconnectivity graphs and compare it to a Go model, which is designed to reduce the frustration by removing all non-native attractive interactions. Finding the global minimum on a frustrated energy landscape is a good test of global optimization techniques, and we present calculations evaluating the performance of basin-hopping and genetic algorithms for this system.Comparisons are made with the widely studied 46-residue BLN protein.We show that the energy landscape of the 69-residue BLN protein contains several deep funnels, each of which corresponds to a different ÎČ-barrel structure
NP-hardness of the cluster minimization problem revisited
The computational complexity of the "cluster minimization problem" is
revisited [L. T. Wille and J. Vennik, J. Phys. A 18, L419 (1985)]. It is argued
that the original NP-hardness proof does not apply to pairwise potentials of
physical interest, such as those that depend on the geometric distance between
the particles. A geometric analog of the original problem is formulated, and a
new proof for such potentials is provided by polynomial time transformation
from the independent set problem for unit disk graphs. Limitations of this
formulation are pointed out, and new subproblems that bear more direct
consequences to the numerical study of clusters are suggested.Comment: 8 pages, 2 figures, accepted to J. Phys. A: Math. and Ge
Topology change in commuting saddles of thermal N=4 SYM theory
We study the large N saddle points of weakly coupled N=4 super Yang-Mills
theory on S^1 x S^3 that are described by a commuting matrix model for the
seven scalar fields {A_0, \Phi_J}. We show that at temperatures below the
Hagedorn/`deconfinement' transition the joint eigenvalue distribution is S^1 x
S^5. At high temperatures T >> 1/R_{S^3}, the eigenvalues form an ellipsoid
with topology S^6. We show how the deconfinement transition realises the
topology change S^1 x S^5 --> S^6. Furthermore, we find compelling evidence
that when the temperature is increased to T = 1/(\sqrt\lambda R_{S^3}) the
saddle with S^6 topology changes continuously to one with S^5 topology in a new
second order quantum phase transition occurring in these saddles.Comment: 1+40 pages, 6 figures. v2: Title changed. Status of commuting saddles
clarified: New high T phase transition claimed in the commuting sector only,
not in the full theor
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