Speaker
Dr
Adrian Baule
(School of Mathematical Sciences Queen Mary, University of London)
Description
Random sequential adsorption (RSA) of particles is used in a large variety of contexts to model particle aggregation and jamming. In RSA, a particle's position is selected with uniform probability over the domain and it is then placed sequentially if there is no overlap with any previously placed particles. Particles are not able to move or reorient once being placed. A key feature of these models is the observed algebraic time dependence of the asymptotic jamming coverage. However, the exact value of the scaling exponent is not known apart from the simplest case of the RSA of monodisperse spheres adsorbed on a line (Renyi's seminal `car parking problem' [1]).
In this talk, I show that exact results on the scaling exponent can be derived for three variants of RSA processes on the line: (i) particles interacting by a finite-range potential; (ii) polydisperse hard spheres; (iii) non-spherical hard particles. These results resolve in particular a long-standing conjecture that the exponent depends solely on the degrees of freedom of a particle [2]. Instead, it is shown that the exponent depends sensitively on both particle shape and the size distribution underlying the polydispersity. Remarkably, for non-spherical particles, the exponent falls into at least two universality classes depending on whether the contact distance has singular features (e.g., for spherocylinder and polyhedra) or not (smooth convex shapes like ellipsoids) [3].
For problems (i,ii) the exact time dependent solution for the interval distribution of the RSA can be found, which reveals that a unique potential/size distribution exists that leads to a maximally dense coverage of the line, which is approached infinitesimally slowly in time [4].
[1] A. Rényi, Publ. Math. Res. Inst. Hung. Acad. Sci. 3, 109 (1958).
[2] P. Viot and G. Tarjus, Europhys. Lett. 13, 295 (1990). J. W. Evans, Rev. Mod. Phys. 65, 1281 (1993). G. Tarjus and J. Talbot, J. Phys. A 24, L913 (1991).
[3] A. Baule, Physical Review Letters 119, 028003 (2017)
[4] A. Baule, submitted (2018)
Primary author
Dr
Adrian Baule
(School of Mathematical Sciences Queen Mary, University of London)
