2,671 research outputs found
Some Further Results for the Stationary Points and Dynamics of Supercooled Liquids
We present some new theoretical and computational results for the stationary
points of bulk systems. First we demonstrate how the potential energy surface
can be partitioned into catchment basins associated with every stationary point
using a combination of Newton-Raphson and eigenvector-following techniques.
Numerical results are presented for a 256-atom supercell representation of a
binary Lennard-Jones system. We then derive analytical formulae for the number
of stationary points as a function of both system size and the Hessian index,
using a framework based upon weakly interacting subsystems. This analysis
reveals a simple relation between the total number of stationary points, the
number of local minima, and the number of transition states connected on
average to each minimum. Finally we calculate two measures of localisation for
the displacements corresponding to Hessian eigenvectors in samples of
stationary points obtained from the Newton-Raphson-based geometry optimisation
scheme. Systematic differences are found between the properties of eigenvectors
corresponding to positive and negative Hessian eigenvalues, and localised
character is most pronounced for stationary points with low values of the
Hessian index.Comment: 16 pages, 2 figure
Comment on ``Quasisaddles as relevant points of the potential energy surface in the dynamics of supercooled liquids'' [J. Chem. Phys. 116, 10297 (2002); cond-mat/0203301]
Recently, the properties of supercooled liquids have been studied by mapping
instaneous configurations onto minima of the gradient squared. It was
originally suggested that this mapping would probe higher-order saddle points
of the potential energy surface. However, it was subsequently shown that the
majority of the minima of this function are only local minima and so do not
correspond to saddles. In this comment, we provide a critique of the suggestion
made by Angelani et al. [J. Chem. Phys. 116, 10297 (2002); cond-mat/0203301]
that although these minima are not true saddles, they are almost saddles (hence
the term quasisaddles). This issue has important implications for the
interpretation of the results obtained by this approach.Comment: 2 page
Structural relaxation in Morse clusters: Energy landscapes
We perform a comprehensive survey of the potential energy landscapes of
13-atom Morse clusters, and describe how they can be characterized and
visualized. Our aim is to detail how the global features of the funnel-like
surface change with the range of the potential, and to relate these changes to
the dynamics of structural relaxation. We find that the landscape becomes
rougher and less steep as the range of the potential decreases, and that
relaxation paths to the global minimum become more complicated.Comment: 21 pages, 3 tables, 5 figure
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
Landscapes, dynamic heterogeneity and kinetic facilitation in a simple off-lattice model
We present a simple off-lattice hard-disc model that exhibits glassy
dynamics. The inherent structures are enumerated exactly, transitions between
metabasins are well understood, and the particle configurations that act to
facilitate dynamics are easily identified. The model readily maps to a coarse
grained dynamic facilitation description.Comment: 5 pages, 5 figures, submitted to PR
Coordination motifs and large-scale structural organization in atomic clusters
The structure of nanoclusters is complex to describe due to their
noncrystallinity, even though bonding and packing constraints limit the local
atomic arrangements to only a few types. A computational scheme is presented to
extract coordination motifs from sample atomic configurations. The method is
based on a clustering analysis of multipole moments for atoms in the first
coodination shell. Its power to capture large-scale structural properties is
demonstrated by scanning through the ground state of the Lennard-Jones and
C clusters collected at the Cambridge Cluster Database.Comment: 6 pages, 7 figure
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Improving double-ended transition state searches for soft-matter systems.
Transitions between different stable configurations of biomolecules are important in understanding disease mechanisms, structure-function relations, and novel molecular-scale engineering. The corresponding pathways can be characterized efficiently using geometry optimization schemes based on double-ended transition state searches. An interpolation is first constructed between the known states and then refined, yielding a band that contains transition state candidates. Here, we analyze an example where various interpolation schemes lead to bands with a single step transition, but the correct pathway actually proceeds via an intervening, low-energy minimum. We compare a number of different interpolation schemes for this problem. We systematically alter the number of discrete images in the interpolations and the spring constants used in the optimization and test two schemes for adjusting the spring constants and image distribution, resulting in a total of 2760 different connection attempts. Our results confirm that optimized bands are not necessarily a good description of the transition pathways in themselves, and further refinement to actually converge transition states and establish their connectivity is required. We see an improvement in the optimized bands if we employ the adjustment of spring constants with doubly-nudged elastic band and a smaller improvement from the image redistribution. The example we consider is representative of numerous cases we have encountered in a wide variety of molecular and condensed matter systems
Annoyance of helicopter-like sounds in urban background noise
Scenarios of urban air mobility see electric vertical take-off and landing aircraft (eVTOLs) operating within cities. Rotorcraft sounds are typically characterised by short bursts of noise, although eVTOLs offer more opportunities for a quieter sound design. We asked participants to compare the annoyance of a reference sequence of bursts of noise with a burst duration of 20 ms with that of a test sequence for which the burst duration was 1 or 5 ms. There were 20 bursts/s. A two-interval, two-alternative forced-choice task and a 1-up/1-down procedure was used. Both sequences were played in background noise that had either the same root-mean-square (RMS) level as the sequence of bursts or 10 dB less. The results were similar to those for loudness: On average, sequences with 1-ms bursts needed 6-8 dB less RMS level to sound equally annoying as the 20-ms bursts, and sequences with 5-ms bursts needed 2-4 dB less. This suggests that psychoacoustic annoyance is mainly explained by loudness and that the RMS level is an insufficient descriptor. Compared between the two background noise levels, the level difference for equal annoyance between short and 20-ms bursts was 1.5 dB larger in the louder background, which was statistically significant
Thermodynamics and the Global Optimization of Lennard-Jones clusters
Theoretical design of global optimization algorithms can profitably utilize
recent statistical mechanical treatments of potential energy surfaces (PES's).
Here we analyze the basin-hopping algorithm to explain its success in locating
the global minima of Lennard-Jones (LJ) clusters, even those such as \LJ{38}
for which the PES has a multiple-funnel topography, where trapping in local
minima with different morphologies is expected. We find that a key factor in
overcoming trapping is the transformation applied to the PES which broadens the
thermodynamic transitions. The global minimum then has a significant
probability of occupation at temperatures where the free energy barriers
between funnels are surmountable.Comment: 13 pages, 13 figures, revte
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