Dorodnitsyn Computing Centre

The prerequisites for the emergence of the theory of hierarchical games are described. The models are described and linked to a set of articles that give an idea of the key problems and the fundamental results obtained. Attention is paid to practical applications. The basic concepts and provisions are illustrated by solutions in the case of linear problems. In conclusion, the need for further research in the field of computational methods is noted.

Исследуются свойства антикоммутатора Паули-Йордана-Дирака квантовой теории поля свободных электронов Дирака в дискретном представлении в пространственно трехмерном случае. Устанавливаются условия сходимости ряда Паули-Йордана-Дирака. Библиография: 23 названия.

The instability of an incompressible boundary layer on a compliant plate with respect to inviscid perturbations in the limit of high Reynolds numbers is analyzed using triple-deck theory. It is shown that unstable inviscid perturbations can exist only if the inertia and/or damping of the plate are taken into account. A twofold role of damping is revealed: it suppresses instability under certain conditions, while leading to its generation under other conditions.

The influence of nonlinearity on the displacement of a singular point in a system of two connected Duffing oscillators when coupling coefficients and insertion losses change. It is shown that the displacement of the singular point when the nonlinearity coefficient changes is accompanied by a decrease in the amplitude of the excited oscillations and a shift in the resonant frequency. The threshold values of the nonlinearity, coupling, and insertion loss coefficients at which a singular point occurs are numerically found. It is shown that an increase in the nonlinearity coefficient leads to a decrease in the threshold value of the insertion losses required for the formation of a singular point.

Based on experimental data, one can note the abnormally large contribution of alanine to the stabilization of the alpha helix and other protein conformations. Independent (including experimental) data indicate a particularly large contribution of alanine to the stabilization of the alpha helix. At the same time, positive contributions were revealed, both to the entropy and to the enthalpy of the system. The high contribution of alanine to the enthalpy of alpha helix formation contradicts the generally accepted view that entropy should decrease during the formation of regular structures in proteins. Alanine stabilizes two types of secondary structure out of three, the alpha helix and the left helix of the “polyproline II” type; alanine also stabilizes the beta structure in fibrillar proteins. The stabilizing effect of alanine on the structure of the alpha helix extends to both natively unfolded proteins and alpha helix–substrate conjugates. In short, it would not be an exaggeration to say that the problem of the formation of the secondary structure of protein is reduced to the problem of alanine. The revealed contradictions are paradoxical and their interpretation (first of all, the substantiation of the contribution of alanine to the enthalpy of melting in terms of fundamental physics) is currently absent. However, the data and comments presented in this paper inspire hope for progress in resolving thes contradictions.

A model of a financial pyramid is proposed in which each participant makes a decision about entering and exiting the pyramid based on the maximin principle using his (or her) ideas about the characteristics of other participants. If the pyramid organizers are able to carry out the whole process quickly enough (so that the payoffs to agents who participated in the pyramid and left it in time do not matter too much), then exactly those agents who overestimated the share of losers in the total mass of agents will lose.

A model of a financial pyramid is proposed in which each participant makes a decision about entering and exiting the pyramid based on the maximin principle using his (or her) ideas about the characteristics of other participants. If the pyramid organizers are able to carry out the whole process quickly enough (so that the payoffs to agents who participated in the pyramid and left it in time do not matter too much), then exactly those agents who overestimated the share of losers in the total mass of agents will lose.

Introduction. Recent studies into the properties of spintronic oscillators have led to broadening their scope of practical application as devices for generating and processing signals. The practical implementation of spintronic oscillators is, however, significantly limited by their low power capacity, thus requiring synchronization between devices.Aim. Determination of conditions for the implementation of the synchronous regime of two antiferromagnetic spintronic oscillators coupled by a common current.Materials and methods. To simplify the numerical simulation of a system of coupled resistively antiferromagnetic oscillators, the method of multiple-time-scale analysis was used. This allowed a system of Kuramoto equations to be considered instead of the original system. To determine the locking band of the Kuramoto model, the homoclinic trajectory approximation method was applied.Results. A system of Kuramoto equation for the phases of partial oscillators under the influence of the inertial term and phase shift was obtained. Expressions describing the locking and synchronization band as functions of the system parameters (bias currents and sizes) were derived. The numerically simulated Kuramoto model was used to determine the bands of the synchronous and asynchronous regimes.Conclusion. The results of numerical simulations of the system of Kuramoto equations and the Adler equation for two coupled spintronic oscillators agree well with the theoretically calculated values of locking and synchronization ranges. The scheme for reducing the model of antiferromagnetic oscillators to a Kuramoto model can be further extended to the case of a larger number of coupled oscillators, which will simplify computational experiments and significantly reduce the time required for numerical simulations.

A subsonic rarefied gas flow past a rectangular cylinder of infinite span is studied by applying a numerical method based on the solution of the S-model kinetic equation. The effect exerted on the resulting flow field by the Reynolds number Re∞ ranging from 10 to 200 is analyzed. At Re∞ = 200 the effect of the cylinder geometry on the flow field is investigated by varying the aspect ratio AR of the cylinder from 1 to 8. The results are presented in terms of the drag, lift, and pressure coefficients and the Strouhal number. The flow patterns downstream of the cylinder exhibit a recirculation region whose size and shape depend on both Re∞ and AR. In the case of steady flow, it is found that the flow-characterizing coefficients depend strongly on the Reynolds number. In the case of unsteady flow, this dependence becomes weaker. As AR increases, the recirculation region downstream of the cylinder is reduced, which leads to a decrease in the drag coefficient. Additionally, the reliability of the approach applied to a class of similar problems is estimated by comparing the present results with data available in the literature.

An approach to recognizing the types of seismic event sources is proposed, based on the combination of several heterogeneous parameters of event records and information about the territory where the seismic event occurred. The following recording parameters are used: the ratio of the amplitudes of body waves, the ratio of parts of the spectra at high and low frequencies, the magnitude, and the spectral constancy parameter. Territorial information includes data on the presence of waterbodies, glaciers, mines, and simplified information on natural seismic activity. Their joint use is done with a special type of Bayesian belief network. The decisions made by the network are probabilistic in nature; the probability is understood in the Bayesian sense, i.e., as the degree of confidence in the truth of the judgment, which consists in attributing an event to one of the types (mine explosion, other explosion on land, underwater explosion, earthquake, icequake). The approach is implemented as a software system, which is included in the program for the interactive analysis of seismic event records LOS.