Discrete Nonholonomic LL Systems on Lie Groups

This paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two classical nonholonomic systems, the Suslov top and the Chaplygin sleigh. The preservation of the reduced energy by the discrete flow is observed and the discrete momentum conservation is discussed.Comment: 32 pages, 13 figure

The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation

We consider the motion of a planar rigid body in a potential flow with circulation and subject to a certain nonholonomic constraint. This model is related to the design of underwater vehicles. The equations of motion admit a reduction to a 2-dimensional nonlinear system, which is integrated explicitly. We show that the reduced system comprises both asymptotic and periodic dynamics separated by a critical value of the energy, and give a complete classification of types of the motion. Then we describe the whole variety of the trajectories of the body on the plane.Comment: 25 pages, 7 figures. This article uses some introductory material from arXiv:1109.321

Влияние ДНК-тропных антиканцерогенных соединений на механизмы регуляции экспрессии генов

The presented review is devoted to the analysis of molecular mechanisms of action for different natural DNA-tropic compounds with established tumor preventive activity. Here we present their cancer preventive effects observed in vivo, mechanisms of DNA binding, influence on epigenetic regulation and “housekeeping” protein function. Additionally, the influence of these compounds on DNA helix parameters is discussed that should impact on epigenetic regulation of gene expression and formation of topologically associated domains.Обзор посвящен анализу молекулярных механизмов действия ряда природных ДНК-тропных соединений с установленной антиканцерогенной активностью. Приведены данные исследований антиканцерогенного действия этих соединений в экспериментах in vivo, рассмотрены механизмы их связывания с ДНК, влияния на метилирование ДНК и модификацию гистонов, способность к ингибированию функций ферментов «домашнего хозяйства». Кроме того, проанализированы возможные эффекты этих соединений на характеристики дуплекса ДНК, что должно иметь значение для эпигенетической регуляции экспрессии генов и формирования топологически ассоциированных доменов

Collisionless kinetic theory of rolling molecules

We derive a collisionless kinetic theory for an ensemble of molecules undergoing nonholonomic rolling dynamics. We demonstrate that the existence of nonholonomic constraints leads to problems in generalizing the standard methods of statistical physics. In particular, we show that even though the energy of the system is conserved, and the system is closed in the thermodynamic sense, some fundamental features of statistical physics such as invariant measure do not hold for such nonholonomic systems. Nevertheless, we are able to construct a consistent kinetic theory using Hamilton's variational principle in Lagrangian variables, by regarding the kinetic solution as being concentrated on the constraint distribution. A cold fluid closure for the kinetic system is also presented, along with a particular class of exact solutions of the kinetic equations.Comment: Revised version; 31 pages, 1 figur

Influence of DNA-binding compounds with cancer preventive activity on the mechanisms of gene expression regulation

The presented review is devoted to the analysis of molecular mechanisms of action for different natural DNA-tropic compounds with established tumor preventive activity. Here we present their cancer preventive effects observed in vivo, mechanisms of DNA binding, influence on epigenetic regulation and “housekeeping” protein function. Additionally, the influence of these compounds on DNA helix parameters is discussed that should impact on epigenetic regulation of gene expression and formation of topologically associated domains