Phenomenological model of creep under variable loads

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 4, pp. 123–127, July–August, 1993.     

Enumeration of Full Graphs: Onset of the Asymptotic Region

A full graph on n vertices, as defined by Fulkerson, is a representation of the intersection and containment relations among a system of n sets. It has an undirected edge between vertices representing intersecting sets and a directed edge from a to b if the corresponding set A contains B;. Kleitman, Lasaga, and Cowen gave a unified argument to show that asymptotically, almost all full graphs can be obtained by taking an arbitrary undirected graph on the n vertices, distinguishing a clique in this graph, which need not be maximal, and then adding directed edges going out from each vertex in the clique to all vertices to which there is not already an existing undirected edge. Call graphs of this type members of the dominant class. This article obtains the first upper and lower bounds on how large n has to be, so that the asymptotic behavior is indeed observed. It is shown that when n > 170, the dominant class predominates, while when n < 17, the full graphs in the dominant class compose less than half of the total number of realizable full graphs on n vertices.     

Poisson-Lie T-duality and complex geometry in N = 2 superconformal WZNW models

Poisson-Lie T-duality in N = 2 superconformal WZNW models on the real Lie groups is considered. It is shown that Poisson-Lie T-duality is governed by the complexifications of the corresponding real groups endowed with Semenov-Tian-Shansky symplectic forms, i.e. Heisenberg doubles. Complex Heisenberg doubles are used to define on the group manifolds of the N = 2 superconformal WZNW models the natural actions of the isotropic complex subgroups forming the doubles. It is proved that with respect to these actions N = 2 superconformal WZNW models admit Poisson-Lie symmetries. The Poisson-Lie T-duality transformation maps each model onto itself but acts non-trivially on the space of classical solutions.     

Problem of the Sand Production in a Producing Well

The problem of sand production (dilatant-plastic reservoir fragmentation) in the process of pumping-out fluid through an uncased borehole is considered. Taking the dilatant change in reservoir porosity into account makes it possible to find a relation between the fluid and solid mass flow rates. There is no steady-state solution if the elasto-plastic boundary does not coincide with the supply contour. In this case a self-similar problem of well start-up with a constant production rate is considered.     

Research in the field of functionally substituted azines. Syntheses of imidazolidinyl-sym-triazines

New approaches have been developed for the application of cyanamino-sym-triazines in the synthesis of imidazolidinyl-sym-triazines.     

Chaotic synchronization as an information process

The chaotic synchronization phenomenon is studied from the information point of view. Synchronization of a chaos receiver by a chaos source is considered as copy recovery of the chaotic signal transmitted by the source. The main idea of this paper is to show that the necessary condition of chaotic synchronization is not the level of physical action of one system on another but the transmission of a certain volume of information on the chaotic process and, therefore, the capacity of the “communication channel” between the source and the receiver. This work was presented at the Summer Workshop “Dynamic Days” (Nizhny Novgorod, June 30–July 2, 1998). Institute of Radioengineering and Electronics of the Russian Academy of Sciences, Moscow, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 12, pp. 1497–1509, December, 1998.     

Recurrent solar wind streams

A new approach to investigating the statistical relationship between certain solar features and recurrent wind streams is presented. This approach is based, on a comparative analysis of the distributions of lifetimes of a set of solar features, recurrent geomagnetic disturbances, and geomagnetic “calms.” Correlation coefficients of 0.81, 0.85, 0.79, and 0.77 are found for the distributions of several solar features—filaments, large-scale magnetic fields, coronal features, and coronal holes, respectively—and recurrent geomagnetic disturbances. A correlation factor of 0.97 between the distributions of geomagnetic “calms” and active regions is found. The combined evidence indicates that no specific type of solar feature is responsible for the recurrent stream activity. Rather, the configuration of the large-scale magnetic field of the Sun appears to control the permanently existing corpuscular activity. Since prominences trace polarity division lines of the large-scale magnetic field structure of the Sun, they have been checked as a possible general predictor of recurrent corpuscular activity; their parameters could present the most reliable indices that relate closely with trends in geomagnetic disturbances. A comparative analysis of cyclic variations of sunspot numbers, the total number of prominences, the relative number of low-height (<-20″) prominences, and recurrent geomagnetic storms is made for solar cycle N16. The relative number of low-height prominences is found to correlate broadly (0.83) with recurrent wind streams. P. K. Shternberg State Astronomical Institute, Moscow, Russia; National Solar Observatory, Sacramento Peak, U.S. Published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 2, pp. 145–151, February, 1998.