Dynamics of Self-Assembling Systems: Analogy with Chemical Kinetics

Abstract

In this article, we propose a new analyzing method for self-assembling systems. Its initial purpose was to predict the yield—the final amount of desired product—of our original self-assembling mechanical model. Moreover, the method clarifies the dynamical evolution of the system. In this method, the quantity of each intermediate product is adopted as state variables, and the dynamics that dominates the state variables is derived. The behavior of the system is reduced to a set of difference equations with a small degree of freedom. The concept is the same as in chemical kinetics or in population dynamics. However, it was never applied to self-assembling systems. The mathematical model is highly abstracted so that it is applicable to other self-assembling systems with only small modifications.

Beyond molecules: Self-assembly of mesoscopic and macroscopic components

“…Macroscopic self-assembly, however, typically involves much smaller numbers of components than does molecular self-assembly, and the degree of perfection required to generate a particular material also may be lower than that required of a molecular crystal. The compromise between numbers of particles, rates of equilibration, and number of defects in all forms of self-assembly, from molecular to macroscopic, remains to be established (45,46).…”

Basic Problems in Self-Assembling Robots and a Case Study of Segregation on Tribolon Platform

“…The problem of producing a desired configuration in large quantities (while avoiding incomplete assemblies) by homogeneous system is known as the parallel yield problem and has been studied in the context of biological and non-biological selfassembling systems [18] 5 . Here, we term the problem that specifically occurs when components assemble in a right manner, however do not complete the targeted final structure, for combinatorial reasons ( Figure 5; we assume the circular sector components connect side-by-side).…”

The statistical dynamics of programmed self-assembly

“…The present paper owes much to the work of Hosokawa, Shimoyama and Miura who described a self-assembling system using chemical kinetics [7]. Their system consisted of passive triangular parts in a vertical shaker.…”