Mapping continuous potentials to discrete forms

Thomson, C Wyville; Lue, Leo; Bannerman, Marcus N.

doi:10.1063/1.4861669

Cited by 9 publications

(7 citation statements)

References 40 publications

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“…The second model is an equivalent square-shoulder potential where ε = +k B T . These potentials are the prototypes of more complex interaction models such as general stepped potentials [10]. Both simulations use N = 32 000 particles and a reduced number density of N σ 3 1 /V = 10 −3 .…”

Section: Validationmentioning

confidence: 99%

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Stable algorithm for event detection in event-driven particle dynamics: logical states

Strobl¹,

Bannerman²,

Pöschel³

2016

Comp. Part. Mech.

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Following the recent development of a stable event-detection algorithm for hard-sphere systems, the implications of more complex interaction models are examined. The relative location of particles leads to ambiguity when it is used to determine the interaction state of a particle in stepped potentials, such as the square-well model. To correctly predict the next event in these systems, the concept of an additional state that is tracked separately from the particle position is introduced and integrated into the stable algorithm for event detection.

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Section: Validationmentioning

confidence: 99%

“…As a particle pair cannot energetically occupy both states, only one region is valid at a particular point in their trajectory. Thus, for stepped or multi-state interactions such as the square-well or stepped Lennard-Jones potentials [10], the valid state dynamically changes with time.…”

Section: Introductionmentioning

confidence: 99%

Stable algorithm for event detection in event-driven particle dynamics: logical states

Strobl¹,

Bannerman²,

Pöschel³

2016

Comp. Part. Mech.

Self Cite

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“…We have performed event-driven simulations of N 108000 elastic smooth spheres carried out with the DynamO software package [34]. The spheres interact by a stepped parabolic-well type potential [35][36][37], a discretized version consisting of a sequence of 15 steps of widths 0.05σ, steps more than reasonable in most instances [37]. We have used σ, τ mσ 2 /ε √ , m, and T p as units of length, time, mass, and temperature, respectively.…”

Section: Thermodynamic Perturbation Theory and The Equation Of State mentioning

confidence: 99%

Thermodynamic Properties of the Parabolic-Well Fluid

Haro

Rodríguez‐Rivas

2021

Front. Phys.

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The thermodynamic properties of the parabolic-well fluid are considered. The intermolecular interaction potential of this model, which belongs to the class of the so-called van Hove potentials, shares with the square-well and the triangular well potentials the inclusion of a hard-core and an attractive well of relatively short range. The analytic second virial coefficient for this fluid is computed explicitly and an equation of state is derived with the aid of the second-order thermodynamic perturbation theory in the macroscopic compressibility approximation and taking the hard-sphere fluid as the reference system. For this latter, the fully analytical expression of the radial distribution function, consistent with the Carnahan-Starling equation of state as derived within the rational function approximation method, is employed. The results for the reduced pressure of the parabolic-well fluid as a function of the packing fraction and two values of the range of the parabolic-well potential at different temperatures are compared with Monte Carlo and Event‐driven molecular dynamics simulation data. Estimates of the values of the critical temperature are also provided.

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“…More details on APCA can be found in (Chakrabarti et al 2002). Approximating spectra by piecewise constant functions has also been used in other fields, taking into account the physical characteristics of the spectra to determine the location of the spectral segments (Thomson, Lue, and Bannerman 2014;Zehentbauer and Kiefer 2012). Konno and Kuno (1998) proposed a method that provides the best piecewise approximation (Konno and Kuno 1988).…”

Section: Spectral Representationmentioning

confidence: 99%

Unsupervised dimensionality reduction of hyperspectral images using representations of reflectance spectra

Aria

Menenti

Gorte

et al. 2020

International Journal of Remote Sensing

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Unsupervised feature selection (UFS) is a standard approach to reduce the dimensionality of hyperspectral images (HSIs). The main idea in UFS is to define a similarity metric, and select the features minimising the metric to reduce the data redundancy. In this paper, we proposed a novel criterion for unsupervised dimensionality reduction based on the representation of spectral reflectance to capture dominant reflectance variations. Since capturing all the spectral information from an entire hyperspectral dataset is a time-consuming process, we proposed a greedy search algorithm for spectral representation (GSSR). It divides the spectrum into spectral regions with less spectral variations and merges them. This algorithm, similar to FS techniques, preserves the original data from being distorted or compromised by a transformation. We compared the GSSR algorithm with well-known existing algorithms in different experiments using various datasets. Comparison with the best approximation to represent single spectra as well as entire hyperspectral scene revealed that spectral representation is almost the same. The difference between the best spectral representation and the ones provided by GSSR is less than 0.01%; while on average, GSSR is about 660 times faster to represent single spectra and 37 times faster for a complete hyperspectral scene. Five well-known unsupervised dimensionality reduction methods were also implemented and used for comparison analysis. Based on the image classification accuracy over two hyperspectral datasets, the spectral features identified by the proposed criterion improved the classification accuracy as well.

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Mapping continuous potentials to discrete forms

Cited by 9 publications

References 40 publications

Stable algorithm for event detection in event-driven particle dynamics: logical states

Stable algorithm for event detection in event-driven particle dynamics: logical states

Thermodynamic Properties of the Parabolic-Well Fluid

Unsupervised dimensionality reduction of hyperspectral images using representations of reflectance spectra

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