Geometrical frustration in two dimensions: idealizations and realizations of a hard-disk fluid in negative curvature.

Keywords

Frustration, Gaussian curvature, Curvature, Plane (geometry), Virial coefficient

References

• Is random close packing of spheres well defined?王素贞 — 2000
• XLV. On reciprocal figures and diagrams of forcesJames Clerk Maxwell — 1864
• Geometrical Frustration: FrontmatterJean‐François Sadoc, Rémy Mosseri — 1999
• Curvature and the Eigenvalues of the LaplacianH. P. McKean, I. M. Singer — 1967
• Hard disks on the hyperbolic plane.Carl D. Modes, Randall D. Kamien — 2007
• Course in Theoretical PhysicsL. Landau, E. M. Lifsic — 2013
• Smectic blue phases: layered systems with high intrinsic curvature.B. A. DiDonna, Randall D. Kamien — 2003
• Flatland: a Romance of Many DimensionsRobert C. Tucker — 1884
• Frustration and curvature - Glasses and the cholesteric blue phaseJames P. Sethna — 1983
• Three-dimensional periodic cubic membrane structure in the mitochondria of amoebaeChaos carolinensisYuru Deng, Mark Mieczkowski — 1998
• Cubic lipid-water phases: structures and biomembrane aspectsK. Larsson — 1989
• Minimal surfaces and multifunctionalityS. Torquato, A. Donev — 2004
• Analytic Calculation of B4 for Hard Spheres in Even DimensionsNathan Clisby, Barry M. McCoy — 2003
• Equation of state of a seven-dimensional hard-sphere fluid. Percus-Yevick theory and molecular-dynamics simulations.Miguel Robles, Mariano López de Haro, Andrés Santos — 2003
• Do cathedral glasses flowEdgar Dutra Zanotto — 1998
• Why is random close packing reproducible?Randall D. Kamien, Andrea J. Liu — 2007
• Das asymptotische verteilungsgesetz der eigenschwingungen eines beliebig gestalteten elastischen körpersHermann Weyl — 1915
• Spin glasses: Experimental facts, theoretical concepts, and open questionsKurt Binder, A. P. Young — 1986
• EMULSION GLASSES : A DYNAMIC LIGHT-SCATTERING STUDYGang Hu, A. H. Krall, H. Z. Cummins — 1999
• Equation of State of Classical Hard Spheres at High DensityZevi W. Salsburg, William W. Wood — 1962

Cited by

• Transition vitreuse et frustration géométriqueF. Sausset — 2008
• Viscous fluid fingering on a negatively curved surface.Rodolfo Brandão, José A. Miranda — 2015
• Structure and dynamics of topological defects in a glassy liquid on a negatively curved manifold.François Sausset, Gilles Tarjus, David R. Nelson — 2009
• Counterintuitive ground states in soft-core models.Henry Cohn, Abhinav Kumar — 2008
• Saddle-splay modulus of a particle-laden fluid interface for hard disksSergey V. Lishchuk — 2008
• A colloidal model system with tunable disorder: Solid-fluid transition and discontinuities in the limit of zero disorderChristoph Richter, Michael Schmiedeberg, Holger Stark — 2011
• Thermodynamics and structure of simple liquids in the hyperbolic planeFrançois Sausset, Gilles Tarjus, Pascal Viot — 2009
• Simple equation of state for hard disks on the hyperbolic plane.Mariano López de Haro, Andrés Santos, Santos B. Yuste — 2008
• Hard spheres on the gyroid surfaceTomonari Dotera, Masakiyo Kimoto, Jun-ichi Matsuzawa — 2012
• Droplet formation and scaling in dense suspensionsMarc Z. Miskin, Heinrich M. Jaeger — 2011
• Constraint percolation on hyperbolic lattices.Jorge H. Lopez, J. M. Schwarz — 2012
• Colloidal particles on quasicrystalline substratesMichael Schmiedeberg — 2008
• Hexagulation numbers: the magic numbers of equal spheres on triply periodic minimal surfacesTomonari Dotera, Hideaki Tanaka, Yusuke Takahashi — 2017
• Dynamics and thermodynamics of air-driven active spinners.Somayeh Farhadi, Sergio Machaca, Justin Aird — 2018
• Statistical Mechanics of Liquids and Fluids in Curved SpaceGilles Tarjus, François Sausset, Pascal Viot — 2010
• Droplet Formation and Scaling in Dense SuspensionsMarc Z. Miskin, Heinrich M. Jaeger — 2011
• Simple fluids, suspensions and selected random systemsP. Drygaś, S. Gluzman, V. Mityushev — 2020
• Applied Analysis of Composite Media: References2020
• Variations on the three-sphere: Laves' labyrinth loppedLauren Niu, Randall D. Kamien — 2026
• Thermodynamics and structure of simple liquids in the hyperbolic planeFrançois Sausset, Gilles Tarjus, Pascal Viot — 2012

Related papers

• On the Gaussian Curvature of Creased TubesKeith A. Seffen, C. R. Calladine — 2021
• Analysis of the effect of bending rigidity on Gaussian Curvature for clamped and simply supported thin circular platesPengfei Huang, Yanping Song, Guanlong Su — 2022
• Some Properties About Curvature QuantityA Lian — 1997
• Fracture prediction using Gaussian curvature analysisRichard J. Lisle, Julian M. Robinson — 1996
• Shape programming lines of concentrated Gaussian curvatureDaniel Duffy, Luka Cmok, John S. Biggins — 2021
• SOME APPLICATIONS OF SECTIONAL CURVATURE IN DIFFERENTIAL GEOMETRYAbdel Radi Abdel Rahman Abdel Gadir Abdel Rahman, Adam Haroun Ishag Gary, Anoud Hassan Elzain Ageeb — 2023
• The Analysis of Effects of Curvature Attribute on Interference in Freeform Surface Blade NC MachiningMing Hai Wang, Xiaopeng Li, Yue Sun — 2011
• THE INTERACTION POTENTIAL BETWEEN MICRO/NANO CURVED SURFACE BODY WITH NEGATIVE GAUSS CURVATURE AND AN OUTSIDE PARTICLEDan Wang, Yajun Yin, Jiye Wu — 2015