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

Poisson structures for reduced non-holonomic systems

Borisov, Mamaev and Kilin have recently found certain Poisson structures with respect to which the reduced and rescaled systems of certain non-holonomic problems, involving rolling bodies without slipping, become Hamiltonian, the Hamiltonian function being the reduced energy. We study further the algebraic origin of these Poisson structures, showing that they are of rank two and therefore the mentioned rescaling is not necessary. We show that they are determined, up to a non-vanishing factor function, by the existence of a system of first-order differential equations providing two integrals of motion. We generalize the form of that Poisson structures and extend their domain of definition. We apply the theory to the rolling disk, the Routh's sphere, the ball rolling on a surface of revolution, and its special case of a ball rolling inside a cylinder.Comment: 22 page

Nanoscale phase separation in La0.7Ca0.3MnO3La_{0.7}Ca_{0.3}MnO_3 films: evidence for the texture driven optical anisotropy

The IR optical absorption (0.1-1.5 eV) in the $La_{0.7}Ca_{0.3}MnO_3$ films on LAO substrate exhibits the drastic temperature evolution of the spectral weight evidencing the insulator to metal transition. Single crystal films were found to reveal strong linear dichroism with anomalous spectral oscillations and fairly weak temperature dependence. Starting from the concept of phase separation, we develop the effective medium model to account for these effects. The optical anisotropy of the films is attributed to the texturization of the ellipsoidal inclusions of the quasimetal phase caused by a mismatch of the film and substrate and the twin texture of the latter.Comment: 6 pages, 5 Encapsulated PostScript figures, uses RevTeX

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

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

О подходе к созданию цифровой модели рельефа дна Арктического бассейна

In the report an approach to developing technology to create digital elevation models of the seabed using heterogeneous data is considered. The technology was tested on material hydrographic work carried out by domestic and foreign researchers in the Central Arctic Ocean with drifting ice, surface ships and submarines. The necessity of systematic analysis of different quality bathymetric information varying by level of reliability when creating common databases and digital models is justified.Описывается подход к разработке технологии создания цифровых моделей рельефа морского дна с использованием данных разнородных съемок. Технология апробирована на материалах гидрографических работ, выполненных отечественными и зарубежными исследователями в центральной части Северного Ледовитого океана с дрейфующего льда, с надводных и подводных носителей. Обоснована необходимость систематического анализа качества неравноточной батиметрической информации, полученной при маршрутных и площадных съемках и различающейся по уровню достоверности, при создании единых баз данных и цифровых моделей