Many-body correlations from integral geometry

Abstract

In a recent letter we presented a framework for predicting the concentrations of many-particle local structures inside the bulk liquid as a route to assessing changes in the liquid approaching dynamical arrest. Central to this framework was the morphometric approach, a synthesis of integral geometry and liquid state theory, which has traditionally been derived from fundamental measure theory. We present the morphometric approach in a new context as a generalisation of scaled particle theory, and derive several morphometric theories for hard spheres of fundamental and practical interest. Our central result is a new theory which is particularly suited to the treatment of many-body correlation functions in the hard sphere liquid, which we demonstrate by numerical tests against simulation.

arXiv comment12 pages, 6 figures

References in corpus (20)

• Theory of Structural Glasses and Supercooled Liquids
• Dynamics on the Way to Forming Glass: Bubbles in Space-time
• Rigorous Inequalities between Length and Time Scales in Glassy Systems
• Density functional theory for hard-sphere mixtures: the White-Bear version Mark II
• Morphological Thermodynamics of Fluids: Shape Dependence of Free Energies
• Equilibrium sampling of hard spheres up to the jamming density and beyond
• Robust Morphological Measures for Large-Scale Structure in the Universe
• Geometric interpretation of pre-vitrification in hard sphere liquids
• Hard-Sphere Fluids in Contact with Curved Substrates
• Point-to-set lengths, local structure, and glassiness
• Non-analytic curvature contributions to solvation free energies: influence of drying
• Depletion potentials in highly size-asymmetric binary hard-sphere mixtures: Comparison of accurate simulation results with theory
• Wetting at Curved Substrates: Non-Analytic Behavior of Interfacial Properties
• Interfacial free energy of a hard-sphere fluid in contact with curved hard surfaces
• Class of consistent fundamental-measure free energies for hard-sphere mixtures
• Bending rigidity and higher order curvature terms for the hard-sphere fluid near a curved wall
• The existence of a bending rigidity for a hard sphere liquid near a curved hard wall: Helfrich or Hadwiger?
• Morphometric approach to many-body correlations in hard spheres
• Scaled Particle Theory for Hard Sphere Pairs. I. Mathematical Structure
• Scaled Particle Theory for Hard Sphere Pairs. II. Numerical Analysis