Characterizing the network topology of the energy landscapes of atomic clusters

Doye, Jonathan P. K.; Massen, Claire P.

doi:10.1063/1.1850468

Cited by 103 publications

(120 citation statements)

References 77 publications

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“…The number of links of each node (its degree) turns out to be strongly heterogeneous, possibly with scale-free degree distributions, which have been linked to scale-free distributions of the areas of the basins of attraction [25,26,27]. Complex network analysis tools have also been used to investigate the structure of energy landscapes of various systems of interest, such as Lennard-Jones atoms, proteins, or spin glasses, among others [21,22,23,27,28,29,30,31,32,33]. The energy of a minimum and its degree (i.e., the number of other minima which can be reached from this minimum) have been shown to be correlated, as well as the barriers to overcome to escape from a minimum.…”

Section: Introductionmentioning

confidence: 99%

Complex networks and glassy dynamics: walks in the energy landscape

Moretti¹,

Baronchelli²,

Barrat³

et al. 2011

J. Stat. Mech.

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Abstract. We present a simple mathematical framework for the description of the dynamics of glassy systems in terms of a random walk in a complex energy landscape pictured as a network of minima. We show how to use the tools developed for the study of dynamical processes on complex networks, in order to go beyond mean-field models that consider that all minima are connected to each other. We consider several possibilities for the transition rates between minima, and show that in all cases the existence of a glassy phase depends on a delicate interplay between the network's topology and the relationship between energy and degree of a minimum. Interestingly, the network's degree correlations and the details of the transition rates do not play any role in the existence (nor in the value) of the transition temperature, but have an impact only on more involved properties. For Glauber or Metropolis rates in particular, we find that the low-temperature phase can be further divided into two regions with different scaling properties of the average trapping time. Overall, our results rationalize and link the empirical findings about correlations between the energy of the minima and their degree, and should stimulate further investigations on this issue.

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Section: Introductionmentioning

confidence: 99%

Complex networks and glassy dynamics: walks in the energy landscape

Moretti¹,

Baronchelli²,

Barrat³

et al. 2011

J. Stat. Mech.

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show abstract

“…Zhang), sgzhou@fudan.edu.cn (S. G. Zhou) † Electronic address: llrong@dlut.edu.cn model et al [24,36,37,38]. Doye and Massen adopted an extension [25] of two-dimensional to investigate energy landscape networks [39,40]. Zhang et al proposed a minimal iterative algorithm for constructing high dimensional networks and studied their structural properties [41].…”

Section: Introductionmentioning

confidence: 99%

Evolving Apollonian networks with small-world scale-free topologies

Zhang¹,

Rong²,

Zhou³

2006

Phys. Rev. E

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We propose two types of evolving networks: evolutionary Apollonian networks (EAN) and general deterministic Apollonian networks (GDAN), established by simple iteration algorithms. We investigate the two networks by both simulation and theoretical prediction. Analytical results show that both networks follow power-law degree distributions, with distribution exponents continuously tuned from 2 to 3. The accurate expression of clustering coefficient is also given for both networks. Moreover, the investigation of the average path length of EAN and the diameter of GDAN reveals that these two types of networks possess small-world feature. In addition, we study the collective synchronization behavior on some limitations of the EAN.

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“…Low-energy structures tend to have large "basins of attraction" so that they occupy a large part of the structure space 80 and are therefore relatively easy to find in searches. Monte Carlo methods have been developed for measuring volumes of basins of attraction associated with minima in the potential energy surface.…”

Section: Importance Of Finding the Correct Structurementioning

confidence: 99%

Perspective: Role of structure prediction in materials discovery and design

Needs¹,

Pickard

2016

APL Materials

124

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Materials informatics owes much to bioinformatics and the Materials Genome Initiative has been inspired by the Human Genome Project. But there is more to bioinformatics than genomes, and the same is true for materials informatics. Here we describe the rapidly expanding role of searching for structures of materials using first-principles electronic-structure methods. Structure searching has played an important part in unraveling structures of dense hydrogen and in identifying the record-high-temperature superconducting component in hydrogen sulfide at high pressures. We suggest that first-principles structure searching has already demonstrated its ability to determine structures of a wide range of materials and that it will play a central and increasing part in materials discovery and design.

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Characterizing the network topology of the energy landscapes of atomic clusters

Cited by 103 publications

References 77 publications

Complex networks and glassy dynamics: walks in the energy landscape

Complex networks and glassy dynamics: walks in the energy landscape

Evolving Apollonian networks with small-world scale-free topologies

Perspective: Role of structure prediction in materials discovery and design

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