By S.V. Adamenko, F. Selleri, A. van der Merwe
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Additional info for Controlled Nucleosynthesis: Breakthroughs in Experiment and Theory (Fundamental Theories of Physics)
12) where |pT max | is the maximum absolute value of the momentum for the proper (uncoordinated) thermal motion of any element of the ensemble in the same phase space over the whole period of transition from the initial state (before the common dominating disturbance appeared) into the steady ﬁnal state. A fundamental distinctive feature of the proposed new approach toward the synthesis is the search for and the selection of such a mechanism of initiating the self-sustaining and self-consistent process using the criterion of optimality of the process of transition of the dynamic system (ensemble of interacting particles) from the initial state/conﬁguration into a new state/conﬁguration being “energy-eﬃcient” not only at the ﬁnal point, but also integrally over the whole duration of the transient process.
It was proposed to use the so-called binary synthesis method (see Refs. 13–15). 2) where K0 is the unknown optimal control k × n matrix. 3) the achievement, in the course of the transition of the system into the undisturbed state, xk ≡ 0, of the minimum of the a posteriori quality functional ∞ I= xTk Qxk + UT0k B T BU0k = k=0 ∞ xTk Q + K0T B T BK0 xk → min . 5) i with the positively deﬁned matrix of quadric quantics of the so-called optimal goal function that reﬂects the optimization goals which are known 22 S.
In the general case, we are talking about a new approach towards the synthesis of multiparticle multilinked stable systems or structures of any physical nature. The distinctive feature of this new approach is the thesis that, in the Nature, the synthesis of a system or the self-organization of its structure is always a self-consistent collective response of elements in the source ensemble to the common dominating force which disturbs their state of rest or a nonaccelerated motion in the system’s eigenfunction space.