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The first and the most dramatic example of the macroscopic explosive power of the Multi-agent auto-catalytic systems the nuclear ('Atomic') bomb. The simple microscopic interaction underlying it is that the U235 nucleus, when hit by a neutron splits in a few energetic fragments including neutrons:

n + U ---> n + n + etc. (autocatalysis equation 1)

On the basis of (autocatalysis equation 1) even without knowing what is a neutron or a U235 nucleus, it is clear that a macroscopic 'reaction chain' may develop: if there are other U235 nuclei in the neighborhood, the neutrons resulting from the first (autocatalysis equation 1) may hit some of them and produce similar new reactions. Those reactions will produce more neutrons that will hit more U235 that will produce more neutrons...

http://tqd.advanced.org/3471/nuclear_weapons_fission_diag.html

Figure 1: At the left of the diagram, a neutron hits a U-235 nucleus causing it to fission (this is symbolized by the green arrow) which results in 2 nuclear fragments, energy and 3 neutrons. In the middle section of the diagram, two of the resulting neutrons hit each a new U-235 nucleus (one depicted in the upper part of the diagram and one at the lower part of the diagram). In the right section of the diagram, each of the newly hit U-235 nuclei fission (green arrows) each into 2 nuclear fragments, energy and 3 new neutrons.

The result will be a chain (or rather "branching tree") of reactions in which the neutrons resulting from one generation of fission events induce a new generation of fission events by hitting new U235 nuclei (Figure 1).

This "chain reaction" will go on until eventually, the entire available U235 population (of typically some 10**23 nuclei) is exhausted and their corresponding energy is emitted: the atomic explosion.

http://www.ccnr.org/fission_ana.html

http://www.chem.uidaho.edu/~honors/fission.html

The crucial feature in the equation above, which we call "auto-catalysis", is that by inputting one neutron n in the reaction one obtains two (or more) neutrons (n+n).

The theoretical possibility of iterating it and have an exponentially increasing macroscopic number of reactions was explained in a letter from Einstein to President Roosevelt. In turn this lead to the initiation of the Manhattan project and the eventual construction of the A-bomb.

It is not by chance that the basic Multi-Agent method (the Monte Carlo simulation algorithm used until this very day in physics applications) was invented by people [Metropolis, Metropolis, Teller, Teller and Ulam] involved in the Manhattan project (and the subsequent thermo-nuclear reactions projects): the Multi-Agent method is the best fit method to compute realistically the macroscopic effects originating in microscopic interactions!

The crucial fact is that one can understand the chain reaction while knowing virtually nothing of nuclear physics. After the Multi-Agent method reduces the systems to their relevant elements one is left with abstract systems which admit an universal formalism [Mack] and method of treatment [S95].

Beyond its utility in each field Multi-Agents Modeling constitutes a major unifying factor for the various human fields of activity and a strong communication tool across the disciplinary borders. Any researcher involved in complexity has had the personal experience in which people from various disciplines with virtually no common background were able to carry lively and productive dialogues based on the Multi-Agent formulations of the systems under discussion.

This can be done with no compromise on the specificity of each system: the particular circumstances of each system are readily included in the Multi-Agent formulation of the system. This is very different from usual analytical models whose applicability is very sensitive to the smallest changes in the circumstances (even within the same scientific subject).

Next: The Logistic Bomb: Malthus-Verhulst-Lotka-Volterra-Montroll-May-Eigen-Schuster systems
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