Problem: We do not fully understand the behavior of the flow of capital in the globalized world.
Solution: We have established a mathematical model do describe this phenomenon. The problem is solved numerically but we are searching for an analytical solution.
TREATMENT OF THE FLOW OF CAPITAL IN A GLOBALIZED WORLD"
Recently, we have studied the neutronic physics problem of a so called Fast Soliton Reactor in which a neutron flux penetrates into an extended zone of fertile material. Thereby, new critical zones are created successively and a neutron flux soliton wave phenomenon, very similar to a water wave on shallow water , will evolve. This theory will appear under the title, "On the Burn-up Theory of Soliton Reactors" in the January issue of the International Journal of Hydrogen Energy, on the occasion of the 90th birthday of Edward Teller.
We have further found that this kind of non-linear theory may be useful to describe the capital flow in a globalized world. Here, one notes the fact that free capital is being invested at those places in the world where the return on investment is highest. One important condition for this is that the labor cost in those economically active places are sufficiently low. However, after some time, when labor costs increased ( due to increased salaries and other additional social costs) the profit reduces and the capital "hops" to the next cheaper production site.
We believe that we can describe this globalization effect by the above mentioned mathematical treatment because there is an astonishing analogy between the neutron flux in the reactor and the capital in the globalized world.
The analogy to our actual globalization problem lies in the fact that "fertile material" can be identified with a poor or a low cost workmanship, whereas "fissile material" can be identified with the converted part of it reaching thereby a higher educational and wealth level. The role of neutrons are identical with the role of capital in this picture and the self limiting effect of the whole process; i.e., that the neutrons "move forward" when a certain burn-up is reached, is exactly identical with the fact that the capital moves also if a certain "burn-up of the poverty" is reached. A wave phenomenon is the logic consequence of this behavior because the mobility or "fluidity" of the capital is very much larger than that of labor.
From a global ethical point of view one has to admit that principally such a process is morally acceptable , because the driving mechanism works in such a way that it pumps capital always to the poorest parts of the world thereby staying a certain time and creating a certain amount of economical growth and therefore wealth in its "wake".
However, at the end of the analysis we had to solve the following autonomous non-linear differential equation of second order for y(x):
y" + y' = A*sin(by)
where A and b are constants . [The sum of the first and second derivatives of the function is proportional to the sine of the function itself.]
We have solved this equation numerically , yielding a shock -like function , but we challenge all mathematically interested people in the world to find an analytical solution to this interesting problem. The above equation is in principal a sine-Gordon equation type, but with an additional friction term.
Professor Walter Seifritz is a retired Professor for Reactor Technology (Technical University of Hannover, Germany). and has presently a cooperation with the Federal University of Rio Grande do Sul , Brazil, in the field of Fluidized Bed Nuclear Reactors and also Globalization.