A generalization of the Carnahan–Starling approach with applications to four- and five-dimensional hard spheres

Ivanizki, Dmitry

doi:10.1016/j.physleta.2018.04.036

Cited by 3 publications

(2 citation statements)

References 35 publications

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“…This form captures numerical results quite well over the regime of interest, ϕ nf < ϕ < ϕ d . (Higher-order corrections would mostly account for deviations at lower ϕ [35], and hence are not considered.) As expected, we find that A → 0 as d → ∞ thus recovering Eq.…”

Section: A Equation Of Statementioning

confidence: 99%

The dimensional evolution of structure and dynamics in hard sphere liquids

Charbonneau,

Hu,

Kundu

et al. 2021

Preprint

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The formulation of the mean-field, infinite-dimensional solution of hard sphere glasses is a significant milestone for theoretical physics. How relevant this description might be for understanding low-dimensional glass-forming liquids, however, remains unclear. These liquids indeed exhibit a complex interplay between structure and dynamics, and the importance of this interplay might only slowly diminish as dimension d increases. A careful numerical assessment of the matter has long been hindered by the exponential increase of computational costs with d. By revisiting a once common simulation technique involving the use of periodic boundary conditions modeled on D d lattices, we here partly sidestep this difficulty, thus allowing the study of hard sphere liquids up to d = 13. Parallel efforts by Mangeat and Zamponi [Phys. Rev. E 93, 012609 (2016)] have expanded the mean-field description of glasses to finite d by leveraging standard liquid-state theory, and thus help bridge the gap from the other direction. The relatively smooth evolution of both structure and dynamics across the d gap allows us to relate the two approaches, and to identify some of the missing features that a finite-d theory of glasses might hope to include to achieve near quantitative agreement.

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Section: A Equation Of Statementioning

confidence: 99%

The dimensional evolution of structure and dynamics in hard sphere liquids

Charbonneau,

Hu,

Kundu

et al. 2021

Preprint

View full text Add to dashboard Cite

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“…While of course real experiments cannot be performed in these systems, they are amenable to computer simulations and theoretical developments. Many aspects concerning hard hyperspheres have been already dealt with, such as thermodynamic and structural properties [ 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , …”

Section: Introductionmentioning

confidence: 99%

Equation of State of Four- and Five-Dimensional Hard-Hypersphere Mixtures

Haro

Santos

Yuste

2020

Entropy

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New proposals for the equation of state of four-and five-dimensional hard-hypersphere mixtures in terms of the equation of state of the corresponding monocomponent hard-hypersphere fluid are introduced. Such proposals (which are constructed in such a way so as to yield the exact third virial coefficient) extend, on the one hand, recent similar formulations for hard-disk and (three-dimensional) hard-sphere mixtures and, on the other hand, two of our previous proposals also linking the mixture equation of state and the one of the monocomponent fluid but unable to reproduce the exact third virial coefficient. The old and new proposals are tested by comparison with published molecular dynamics and Monte Carlo simulation results and their relative merit is evaluated.

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The dimensional evolution of structure and dynamics in hard sphere liquids

Kundu

Morse

2022

The Journal of Chemical Physics

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The formulation of the mean-field infinite-dimensional solution of hard sphere glasses is a significant milestone for theoretical physics. How relevant this description might be for understanding low-dimensional glass-forming liquids, however, remains unclear. These liquids indeed exhibit a complex interplay between structure and dynamics, and the importance of this interplay might only slowly diminish as dimension d increases. A careful numerical assessment of the matter has long been hindered by the exponential increase in computational costs with d. By revisiting a once common simulation technique involving the use of periodic boundary conditions modeled on D d lattices, we here partly sidestep this difficulty, thus allowing the study of hard sphere liquids up to d = 13. Parallel efforts by Mangeat and Zamponi [Phys. Rev. E 93, 012609 (2016)] have expanded the mean-field description of glasses to finite d by leveraging the standard liquid–state theory and, thus, help bridge the gap from the other direction. The relatively smooth evolution of both the structure and dynamics across the d gap allows us to relate the two approaches and to identify some of the missing features that a finite- d theory of glasses might hope to include to achieve near quantitative agreement.

show abstract

A generalization of the Carnahan–Starling approach with applications to four- and five-dimensional hard spheres

Cited by 3 publications

References 35 publications

The dimensional evolution of structure and dynamics in hard sphere liquids

The dimensional evolution of structure and dynamics in hard sphere liquids

Equation of State of Four- and Five-Dimensional Hard-Hypersphere Mixtures

The dimensional evolution of structure and dynamics in hard sphere liquids

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