Optimal random deposition of interacting particles
arXiv:1903.02101 · doi:10.1103/PhysRevLett.122.130602
Abstract
Irreversible random sequential deposition of interacting particles is widely used to model aggregation phenomena in physical, chemical, and biophysical systems. We show that in one dimension the exact time dependent solution of such processes can be found for arbitrary interaction potentials with finite range. The exact solution allows to rigorously prove characteristic features of the deposition kinetics, which have previously only been accessible by simulations. We show in particular that a unique interaction potential exists that leads to a maximally dense line coverage for a given interaction range. Remarkably, this distribution is singular and can only be expressed as a mathematical limit. The relevance of these results for models of nucleosome packing on DNA is discussed. The results highlight how the generation of an optimally dense packing requires a highly coordinated packing dynamics, which can be effectively tuned by the interaction potential even in the presence of intrinsic randomness.
arXiv commentPhys. Rev. Lett. (in print)
References in corpus (7)
- Kinetic constraints, hierarchical relaxation and onset of glassiness in strongly interacting and dissipative Rydberg gases
- Random Sequential Adsorption: From Continuum to Lattice and Pre-Patterned Substrates
- Fractal formation and ordering in random sequential adsorption
- Shape universality classes in the random sequential addition of non-spherical particles
- Edwards-like statistical mechanical description of the parking lot model for vibrated granular materials
- Fractal dimension and degree of order in sequential deposition of mixture
- Self-similar non-equilibrium dynamics of a many-body system with power-law interactions