But existing methods of forecasting hardly take into account one of objects of industry and factors infrastructure the most important for functioning is social. Not because this factor is not important, its importance is not called in question in socially-technical systems. There is not any mathematical apparatus for its accounting. Before statistical prognosis techniques of USSR Academy of Sciences existed, but they took into account only one component of human factor is demography that is presence of human resources. But it is only one component of such important factor, as social. And experience of the last years shows, what exactly influence of social factors can kill the most promising undertakings.

It is necessary to note that the apparatus of the account of social interaction exists; there are even a few different approaches to its description on the basis of the theory of the ethos’s interaction. For description of the models of interaction the systems of differential equations realizing mathematical apparatus of dynamics of average (the equations of Lanchester) are applied [5,6,7,8]. The systems of the equations on the basis of dynamics of average show enough adequately the tendencies of interaction and dissemination of ethnical areas at studying of historical retrospective show.

But, as statistical analysis shows, adequacy of the systems of the equations of such type at simulation of modern ethnical process is low. Interaction of ethoses in modern conditions no longer is process with constant parameters: temporary gallops are present in it. Continuity of flow interaction, which is adopted in the equations of dynamics of average, leads to large errors in the forecasts. On this basis, it is impossible to use them for receipt of reliable evaluations. What is the reason of these errors?

With states occurrence, establishing of international law, besides natural areas and levels of passionarity one more factor affecting dissemination of an ethnos, factor of state borders emerged. Presence of the boundaries plays constraining role, similar to the role of physics-geographical landscape parameters, but with determined features [9,10].

For creation of the model accounting influence of state boundary, it is offered to enter concepts “difference of social potentials” and the vector of tension of socially-ethnical area describing this phenomenon [11,12].

Size and the direction of this vector, will designate as “U”, depends on many factors. In overall view as can be specified in matrix form or to be described by the family of functions characterizing various parameters of quality of the live and interethnic complementarity (living standard, safety, the level of related and ethnical communications, the level of activity of the population of given district and so forth). The magnitude of vector “U” between two points (by the regions) describes the value of tension of socially-ethnical area.

Many objective reasons do not allow calculating the precise magnitude of the vector “U”.  But its size and direction can be evaluated on indirect to factors.  One of these indicators is the intensity of a cross-border or an internal flow of migrants. We will designate its “I”. Size “I” in direct ratio depends on distinction of the potentials “U”. The rating “I” describes by statistics and it can be studied.

As a practice shows there is one more indicator which determines the resistance to migration flows. We will designate its “R”. The indicator “R” defines artificial and natural reasons complicating alignment of the potentials “U”. The reasons are defined, both by physics-geographical and political factors, including influence of boundaries. Boundaries up to determined moment can constrain dissemination of ethos’s, or to change the directions of migration flows. Exactly it induces step-type behavior of process of interaction marked in statistics. Statistics does not define size “R”, as opposed to migration ratings. But to define this size easier, than to calculate the vector “U”. For it is enough to enter the mechanism of transformation of aggregated quality indicators which stand in the way of or contribute migration to quantitative evaluations.

The analysis of ratings ”U”, “I” and “R” allows drawing the conclusion that  formulated model of the account of boundaries in the interethnic interaction can be shown as mathematical apparatus, which is similar to that which is used in physics and is described by Ohm’s law (Fig.1):

As the practice of application of the model shows for analysis of various situations generated the model which not only proves versatility of physical laws, it can have a diverse practical application: from the forecast of influence of social factors to functioning of separate objects to forecasting of stability of whole state formations [13,14,15,16].

The offered dependence does not replace model based on apparatus of dynamics of average [17,18,19]:

where dB/dt - rate of change;
              S_B - the value streams “flowing” and “flowing” of energy, depending on its sign.

They take into account ethnic’s interaction inside state formations still enough adequately. The offered equations only complement the systems of the equations for account exactly for the account of influence of boundary limitations [20,21,22].