Distance of closest approach of two arbitrary hard ellipsoids

Zheng, Xiaoyu; Iglesias, Wilder; Palffy‐Muhoray, Peter

doi:10.1103/physreve.79.057702

Cited by 35 publications

(44 citation statements)

References 7 publications

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“…Apparently, the slope of the line corresponding to the nearest distance from the origin to the new ellipse must occur between k 1 and k 2 . According to the golden section search [42], two golden section points p 1 , and p 2 are in the interval [k 2 , k 1 ], and they satisfy…”

Section: Description Of the Overlapping Detection Algorithm Of Elliptmentioning

confidence: 99%

An overlapping detection algorithm for random sequential packing of elliptical particles

Chen

2011

Physica A: Statistical Mechanics and its Applications

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a b s t r a c tRandom sequential packing of particles is a subject of intense research in many branches of physics and engineering. The preponderance of preview work has focused on spherical particles and little is known about non-overlapping elliptical particles. In the present work, a new numerical algorithm is developed to detect overlapping of ellipses by a series of sequential coordinate transformations and a novel golden section search algorithm. The accuracy and efficiency of the numerical algorithm are tested and compared with algorithms developed in previous literature. Its stability is verified by visualizations of random sequential packing of monodispersed and polydispersed ellipses with different boundary conditions. Then, the algorithm is applied to investigate the influence of the shape of ellipses on the random packing fraction, as well as to study the influence of the shape and size of ellipses on the wall effect in the particle packing structure, and some numerical results are demonstrated. Finally, the reliability of the numerical algorithm extended to the three-dimensional space is also evaluated by checking overlapping of ellipsoidal particles.

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Section: Description Of the Overlapping Detection Algorithm Of Elliptmentioning

confidence: 99%

An overlapping detection algorithm for random sequential packing of elliptical particles

Chen

2011

Physica A: Statistical Mechanics and its Applications

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“…The evaluation for non-spherical particles is quite challenging. There is no closed analytical formula to determine whether two arbitrarily oriented ellipsoids overlap (Zheng, Iglesias & Palffy-Muhoray 2009). Hence, for the determination of the dynamic kernel (2.3), which amounts to counting collisions per time interval, we have to use an iterative approach for the collision detection.…”

Section: Collision Detectionmentioning

confidence: 99%

Collision rates of small ellipsoids settling in turbulence

2014

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We propose that the collision rates of non-spherical particles settling in a turbulent environment are significantly higher than those of spherical particles of the same mass and volume. The theoretical argument is based on the dependence of the particle drag force on the particle orientation, thus varying gravitational settling velocities, which can remain different until contact due to the particle inertia. Therefore, non-spherical particles can collide with large relative velocities. Direct numerical simulations (DNS) of streamwise decaying isotropic turbulence seeded with small, heavy, rotationally symmetric ellipsoids of five different aspect ratios are performed to confirm these arguments. The motion of 21 million ellipsoids is tracked by a Lagrangian particle solver assuming creeping flow conditions and neglecting the influence of the particles on the flow. We find that ellipsoids collide considerably more often than spherical particles of the same volume and mass due to a drastically increased mean relative velocity at contact.

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“…(10) in p 1 . The contact distance is in general a highly complicated function, which already in the case of ellipsoids can not be expressed in closed form [39]. Solving Eq.…”

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Shape Universality Classes in the Random Sequential Adsorption of Nonspherical Particles

Baule

2017

Phys. Rev. Lett.

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Random sequential adsorption (RSA) of particles of a particular shape is used in a large variety of contexts to model particle aggregation and jamming. A key feature of these models is the observed algebraic time dependence of the asymptotic jamming coverage ∼ t −ν as t → ∞. However, the exact value of the exponent ν is not known apart from the simplest case of the RSA of monodisperse spheres adsorbed on a line (Renyi's seminal 'car parking problem'), where ν = 1 can be derived analytically. Empirical simulation studies have conjectured on a case-by-case basis that for general non-spherical particles ν = 1/(d +d), where d denotes the dimension of the domain andd the number of orientational degrees of freedom of a particle. Here, we solve this long standing problem analytically for the d = 1 case -the 'Paris car parking problem'. We prove that the scaling exponent depends on particle shape, contrary to the original conjecture, and, remarkably, falls into two universality classes: (i) ν = 1/(1 +d/2) for shapes with a smooth contact distance, e.g., ellipsoids; (ii) ν = 1/(1 +d) for shapes with a singular contact distance, e.g., spherocylinders and polyhedra. The exact solution explains in particular why many empirically observed scalings fall in between these two limits.The question of how particle shape affects the dynamical and structural properties of particle aggregates is one of the outstanding problems in statistical mechanics with profound technological implications [1][2][3]. Jammed systems are particularly challenging, since they are dominated by the geometry of the particles and are not described by conventional equilibrium statistical mechanics [4]. Exploring the effect of shape variation thus relies on extensive computer simulations [5][6][7][8] or mean-field theories whose solutions require similar computational efforts [9,10]. From a theoretical perspective it is striking that so far there has been hardly any insight from exactly solvable analytical models, even though these are most suitable to identify and classify shapes in the infinite shape space.In this letter, we consider the probably simplest nontrivial packing model that takes into account excluded volume effects due to shape anisotropies: random sequential adsorption (RSA). Since Renyi's seminal work on the 'car parking problem' (the RSA of monodisperse spheres on a line) [11,12], RSA models have been widely used to model particle aggregation and jamming in physical, chemical and biological systems [13][14][15]. Their great appeal is the paradigmatic nature of the adsorption mechanism: the particles' positions and orientations are selected with uniform probability and then placed sequentially into the domain if there is no overlap with any previously placed particles. Particles are not able to move or reorient once being placed.Two key features of RSA models are: (i) the existence of a finite jamming density φ in the infinite time limit φ(∞) = lim t→∞ φ(t) and (ii) the algebraic time dependence of the approach to jamming, which has been conj...

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Distance of closest approach of two arbitrary hard ellipsoids

Cited by 35 publications

References 7 publications

An overlapping detection algorithm for random sequential packing of elliptical particles

An overlapping detection algorithm for random sequential packing of elliptical particles

Collision rates of small ellipsoids settling in turbulence

Shape Universality Classes in the Random Sequential Adsorption of Nonspherical Particles

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