In the way of computational study one reveals the opportunity for employing changes in ambient conditions to regulate outcome of evolution of an ensemble composed of systems of nanowires that are assembling quasi two-dimensional functional networks over prepatterned surfaces. The component systems are of the same type but different in details, evolve simultaneously and independently, under influence of stochastic factors, within equivalent finite spatial domains and in the same ambient conditions. One assumes that evolutions within all the component systems of the ensemble result in the corresponding ensemble of various patterns of expanding spatial regions specified with the same feature and these regions affect simultaneously and independently certain receiver system. Moreover, differences between contributions, which distinct component systems have to the effect of their influence on the receiver system, are attributed only to differences between spatial arrangements of the regions specified within these component systems. Accordingly, one assumes that this ensemble of patterns corresponds to the outcome that is recognized by certain receiver system as a collective effect (CE) represented by a pattern of distinguished regions within a spatial domain being equivalent to a component system domain. The situation assumed here can be considered as relevant to regulating the low cost process of self-assembling of functional systems such as sensors, extraordinary shells and covers (then, they would be the receiver systems).
It is shown that a prerequisite for employing changes in ambient conditions to regulate the CE is presence of finite-size effects (F-SE), i.e. specific features of the CE accomplishment which result from the fact that elements constituting the component systems of the evolving ensemble system are one dimensional, finite-size elements able to change their positions in finite discrete space while transmitting certain signals between their ends. The signal is considered as finite portion of information transmitted discretely between an element ends. Accordingly, each such element is represented by the pair of its ends only, one end that only sends a signal and the other receiving it. Hopping of the pair to a separate position close by requires obeying certain stochastic condition. The expansion in the ensemble systems is modeled as a random expansion process (REP) simulated as Markov process of covering sites of the finite regular hexagonal array. Whole the pattern within each component system is being accomplished at each step of the evolution and can be composed only of sites being destinations for the receiving ends of the pairs that have experienced hopping at this step. In all the M systems, area covered expands to certain stable limits from the same initial structure with one determined gradient of a forcing factor, P and with the same efficiency, 0 < A < 1 of projecting the hexagonal order of the finite array onto the simulation results. Accomplishing of the CE in course of the REP is represented by the sequence of patterns, MMS(T) being mean expected forms of the M patterns characterizing all the evolution realizations at the respective stages T. We show how changes in the sequence MMS(T) can be regulated by varying the parameters, M, P, A of the model ambient conditions.
Aknowledgment: Parallel computations have been performed by using computer Cray-T3E with computational grant at The Interdisciplinary Centre for Mathematical and Computational Modelling at The Warsaw University, support from NATO Collaborative Linkage Grant PST.CLG.976545 and Polish-British Research Partnership Programme WAR/341/202 are acknowledged.