Shape Universality Classes in the Random Sequential Adsorption of Nonspherical Particles

Shape Universality Classes in the Random Sequential Adsorption of Nonspherical Particles 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 nonspherical particles, ν=1/(d+d˜), where d denotes the dimension of the domain, and d˜ 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, in particular, that the scaling exponent depends on the 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, and (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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review Letters American Physical Society (APS)

Shape Universality Classes in the Random Sequential Adsorption of Nonspherical Particles

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Shape Universality Classes in the Random Sequential Adsorption of Nonspherical Particles

Abstract

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 nonspherical particles, ν=1/(d+d˜), where d denotes the dimension of the domain, and d˜ 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, in particular, that the scaling exponent depends on the 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, and (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.
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Publisher
The American Physical Society
Copyright
Copyright © © 2017 American Physical Society
ISSN
0031-9007
eISSN
1079-7114
D.O.I.
10.1103/PhysRevLett.119.028003
Publisher site
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Abstract

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 nonspherical particles, ν=1/(d+d˜), where d denotes the dimension of the domain, and d˜ 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, in particular, that the scaling exponent depends on the 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, and (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.

Journal

Physical Review LettersAmerican Physical Society (APS)

Published: Jul 14, 2017

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