Random sequential covering

Abstract

In random sequential covering, identical objects are deposited randomly, irreversibly, and sequentially; only attempts increasing the coverage are accepted. A finite system eventually gets congested, and we study the statistics of congested configurations. For the covering of an interval by dimers, we determine the average number of deposited dimers, compute all higher cumulants, and establish the probabilities of reaching minimally and maximally congested configurations. We also investigate random covering by segments with ℓ sites and sticks. Covering an infinite substrate continues indefinitely, and we analyze the dynamics of random sequential covering of Z and R d .

Dynamic space packing

“…These Fano factors differ by 2 • (−1) n from the Fano factors in the problem of random sequential covering of the one-dimensional lattice by dimers [84]. In the covering problem, the system falls into a jammed state while the DSP process continues forever.…”

“…Moreover, the steady state in the DSP is universal, while jammed states in the covering problem depend on the initial condition. (Jammed states formed in an initially empty system were studied in [84].) Still, the relation between the Fano factors hints at a connection between the statistics of the occupancy in the jammed state in the dimer covering problem and steady states in the DSP.…”

“…The probability of no desorption, p 0 = 1 − p 1 − p 2 − p 3 − p 4 , is fixed by normalization. The time-dependent solution for the desorption probabilities is thus given by ( 96) with ρ determined by (79), H by (82), D by (84), C(∴) by (88), and C ⋄ by (91):…”

Випадкова Послідовна Адсорбція Дископрямокутників, Покритих Відштовхуючими Оболонками

“…The model of random sequential adsorption (RSA) is widely used to study the structure of adsorption layers on the surface [1,2]. In this model, every subsequent attempt to adsorb a new particle is accompanied by a check for the absence of its intersection with previously deposited ones.…”

Impact of ageing on structure of random sequential adsorption packings of discorectangles

“…These findings stimulated a great interest to the fundamental investigations of deposition of such particles on the two-dimensional (2D) solid substrates, their packing properties, and equilibrium phase behavior of such systems. In many works the deposition kinetics and different packing problems have been analyzed using the model of random sequential adsorption (RSA) [3][4][5]. The RSA model assumes random and sequential adsorption of particles on a substrate without overlapping with previously deposited species.…”