arXiv subjects

H. J. H. Brouwers

Publications and source records attributed to H. J. H. Brouwers.

4 recordsLinked to original sources

arXiv2026

Excluded volume geometry and packing fraction in binary convex hyperparticle mixtures

In this paper the excluded volume of binary similar hyperparticles with small size difference in D-dimensional Euclidean spaces R2, R3, and R4 is studied using two different statistical geometry approaches. These geometric approaches, concerning orientation geometry and integral geometry, yield the excluded volume of particle pairs. The excluded volume of rectangles, based on orientation geometry, in Euclidean space R2 is used to derive an explicit equation for the bidisperse packing fraction, which is compatible with the expression published previously. Next, the excluded volume of pairs of convex particles in D = 2, 3 and 4, resulting from integral geometry, are presented. These excluded volumes are identical with the specific ones for circles and rectangles (D = 2) and (sphero)cylinders (D = 3), derived by orientation geometry. Furthermore, these orientation geometry-based excluded volumes contain geometric measures: particle volume, surface area, mean curvature and the second quermassintegral. They allow for the derivation of closed-form expressions for the random packing fraction of binary convex similar hyperparticles in Euclidean spaces R2 , R3 and R4.

cond-mat.soft↗

arXiv2025

Random packing fraction of binary hyperspheres with small or large size difference: a geometric approach

The random packing fraction of binary particles in D-dimensional Euclidean space R^D is studied using a geometric approach. First, the binary packing fraction of assemblies with small size difference are studied, using the excluded volume model by Onsager for particles in three-dimensional space (D = 3). According to this model the packing increase by bidispersity is proportional to (1 - f)(u^D - 1)^2, with f as monosized packing fraction, u as size ratio and D as space dimension. The model predictions are compared with computational results for disks in two dimensions (D = 2) and hyperspheres in the large-dimension limit (D to infinity), yielding good agreement. Subsequently, the packing of hyperspheres with large size difference is modeled, employing the classic theory of Furnas. This theory, developed for three dimensions, starts from an infinite size ratio of larger and smaller particles (u to infinity). Here, the pertaining equations are applied to hyperspheres, and successfully compared with computational results for hyperspheres in the large-dimension limit. Furthermore, an asymptotic approximation of the binary packing fraction for large size ratio is derived, which shows that the first order variation of the Furnas packing fraction (u^-1 = 0) is proportional to (2 - f)u^-1. Finally, a scaled D-dimensional binary packing graph is presented, governing a simplified phase diagram that borders the binary random packing fraction of amorphous assemblies. To summarize, basic space-filling and geometric (athermal) theories on simple hard spheres appear to be a valuable tool for the study of hyperspheres packing and amorphization.

cond-mat.soft↗

arXiv2024

Random packing fraction of binary similar particles: Onsager's excluded volume model revisited

In this paper, the binary random packing fraction of similar particles with size ratios ranging from unity to well over 2 is studied. The classic excluded volume model for spherocylinders and cylinders proposed by Onsager [1] is revisited to derive an asymptotically correct expression for these binary packings. the packing fraction increase by binary polydispersity equals 2f(1 - f)X1(1 - X1)(u - 1)^2 + O((u - 1)^3), where f is the monosized packing fraction, X1 is the number fraction of a component, and u is the size ratio of the two particles. This equation is in excellent agreement with the semi-empirical expression provided by Mangelsdorf and Washington [2] for random close packing (RCP) of spheres. Combining both approaches, a generic explicit equation for the bidisperse packing fraction is proposed. This expression is extensively compared with computer simulations of the random close packing of binary spherocylinder packings, spheres included, and random loose sphere packings (1 < u < 2 and beyond). The derived generic closed-form equation appears to be in excellent agreement with the collection of computer-generated packing data using four different computer algorithms and RCP and random loose packing (RLP) compaction states. Furthermore, the present analysis yields a monodisperse packing fraction map of a wide collection of particle shapes at different compaction states. The explicit boundaries of this map appear to be in good agreement with a broad collection of random close and random loose packing data. Appendix A presents an overview of published monodisperse packing fractions of (sphero)cylinders for aspect ratios from zero to infinity, and at RLP and RCP packing configurations, and they are related to Onsager's theory. Appendix B presents a derivation the binary packing fraction of disks in a plane (R^2) and hyperspheres in R^D (D > 3) with small size difference.

cond-mat.other↗

arXiv2023

A geometric probabilistic approach to random packing of hard disks in a plane

In this paper the random packing fraction of hard disks in a plane is analyzed, following a geometric probabilistic approach. First, the random close packing (RCP) of equally sized disks is modelled. Subsequently, following the same methodology, a simple, statistical geometric model is proposed for the random loose packing (RLP) of monodisperse disks. This very basic derivation of RLP leads to a packing value (~ 0.66) that is in very good agreement with values that have been obtained previously for 2D disk packings. The present geometrical model also enables closed-form expression for the contact (coordination) number as function of the packing density at different states of compaction. These predictions are thoroughly compared with empirical and simulation results, among others the Rényi parking model, yielding good agreement.

cond-mat.soft↗