Probability Density, Diagrammatic Technique, and Epsilon Expansion in the Theory of Wave Turbulence

We apply the methods of Field Theory to study the turbulent regimes of statistical systems. First we show how one can find their probability densities. For the case of the theory of wave turbulence with four-wave interaction we calculate them explicitly and study their properties. Using those densities we show how one can in principle calculate any correlation function in this theory by means of direct perturbative expansion in powers of the interaction. Then we give the general form of the corrections to the kinetic equation and develop an appropriate diagrammatic technique. This technique, while resembling that of $\varphi^4$ theory, has many new distinctive features. The role of the $\epsilon=d-4$ parameter is played here by the parameter $\kappa=\beta + d - \alpha - \gamma$ where $\beta$ is the dimension of the interaction, $d$ is the space dimension, $\alpha$ is the dimension of the energy spectrum and $\gamma$ is the ``classical'' wave density dimension. If $\kappa > 0$ then the Kolmogorov index is exact, and if $\kappa < 0$ then we expect it to be modified by the interaction. For $\kappa$ a small negative number, $\alpha<1$ and a special form of the interaction we compute this modification explicitly with the additional assumption of the irrelevance of the IR divergencies which still needs to be verified.Comment: 26 pages, PUPT-146

Orthodiagonal anti-involutive Kokotsakis polyhedra

We study the properties of Kokotsakis polyhedra of orthodiagonal anti-involutive type. Stachel conjectured that a certain resultant connected to a polynomial system describing flexion of a Kokotsakis polyhedron must be reducible. Izmestiev \cite{izmestiev2016classification} showed that a polyhedron of the orthodiagonal anti-involutive type is the only possible candidate to disprove Stachel's conjecture. We show that the corresponding resultant is reducible, thereby confirming the conjecture. We do it in two ways: by factorization of the corresponding resultant and providing a simple geometric proof. We describe the space of parameters for which such a polyhedron exists and show that this space is non-empty. We show that a Kokotsakis polyhedron of orthodiagonal anti-involutive type is flexible and give explicit parameterizations in elementary functions and in elliptic functions of its flexion

Compatibility of The Dimensions of Polymer Molecular Aggregates to The Pore Throat of a Reservoir

The compatibility of the dimensions of the polymer molecular aggregates and the pore throat of the reservoir were studied. The W section of Tuha oilfield was the study area and polymers produced by Daqing Refining and Chemical Company were used. The permeability limit of the polymer molecules with different molecular masses and concentrations, matching relationship between the dimension of polymer molecular aggregates and pore throat were obtained by experiments. The results of the research are important for the development and implementation of a polymer flooding technical scheme in the middle and late stages of the operation of the Tuha oilfield

Integrate, Adapt, Collaborate: Comecon Architecture in Socialist Mongolia

This paper conceptualizes the uneven dynamics of architectural mobilities between member states of the Council for Mutual Economic Assistance (Comecon) and socialist Mongolia, a member of the Comecon since 1962. These long, intense, multilateral, and coordinated exchanges decisively contributed to the development of the "material-technical base" for construction in Cold War Mongolia, including planning institutions as well as construction and construction-materials industries. Based on archival research and interviews in Mongolia, Russia, Germany, and Poland, we introduce the concept of "concern" and argue that the priorities, motivations, and aspirations of the professionals involved were informed by three concerns. They included, first, the concern for integrating Mongolian design and construction industries into a comprehensive network of organizations in charge of the urbanization processes; second, the concern for adapting foreign resources to the conditions on the ground; and, third, the concern for an increasing collaboration between Mongolian, Soviet, and Eastern European actors. We study how these actors followed, exploited, and sometimes challenged the political economy of the Comecon, and how they negotiated it with feedback from specific investments. We argue that the concept of the three concerns is useful for studying architectural mobilities in global socialism and across competing 20th-century developmental regimes

Place of manufacture diversification in cyclical development of the enterprise

The relevance of the researched problem is caused by the fact that diversification is one of the best options for reforming enterprises. The aim of the research: to consider changes in production of outputs in development cycles of the enterprise. This will help to reveal the nature of manufacture diversification. The leading method to the research of this problem is the system approach, which allows to elicit factors promoting formation of business mechanism of manufacture diversification under the conditions of volatile economic environment. The results of the research are: it is offered to enhance the existing classification of enterprises by nomenclative and technological characteristic, taking into account the specific nature of processing capacity. The materials of the research can be useful for control bodies of enterprises when taking constructive steps in the sphere of manufacture diversification and strategy development. © 2016 Erofeev and Smolin