Том 62, № 7 (2017)

The main stages of the formation of a droplet cloud during the disintegration of water masses (with an initial volume of 0.05–1 L) during their free fall from a great height (up to 15 m) have been determined. High-speed (up to 6 × 10⁵ frames per second) video cameras were used to perform 3D video recording of the transformation and destruction of water mass with the formation of a droplet cloud. It is found that the transverse sizes of the newly formed droplet cloud rapidly increase when the mass passes the first few (up to 10) meters from the onset of falling. It is shown that the maximum cross-sectional areas of the water mass change only slightly with an increase in the discharge height at heights above 10 m. A model of limited growth of the transverse sizes of droplet cloud is developed for the first time based on the results of large-scale experiments.

In this work, we consider mixed problems of elasticity theory, in particular, contact problems for cases that are nontraditional. They include mixed problems with discontinuous boundary conditions in which the singularities in the behavior of contact stresses are not studied or the energy of the singularities is unbounded. An example of such mixed problems is contact problems for two rigid stamps approaching each other by rectilinear boundaries up to contact but not merging into one stamp. It has been shown that such problems, which appear in seismology, failure theory, and civil engineering, have singular components with unbounded energy and can be solved by topological methods with pointwise convergence, in particular, by the block element method. Numerical methods that are based on using the energy integral are not applicable to such problems in view of its divergence.

New high-frequency asymptotics of the dispersion relation have been obtained when analyzing the stability of a transonic boundary layer with self-induced pressure. It is shown that the dependence of the perturbation frequency on the wave number (except for the range of small wave numbers), which was previously considered unambiguous, is an exceptional case.

A solution to the problem of a flexible thread rotating around a horizontal axis is presented. Dependences calculated in elementary functions with graphic applications are obtained for determining the parameters of the rotating thread, such as the thread-shape outline, the largest deviation from the axis, the values of curvature angles, and the thread tension, among others.

The coagulation and sedimentation of aerosol droplets are studied experimentally under nonlinear oscillations in closed and open tubes in the mode of transition to shock waves near the first eigenfrequency. In this case, more efficient coagulation and sedimentation than in the shock-free wave mode of oscillations is observed at almost identical amplitude of the piston displacement.

An analytical expansion of the osculating orbital elements for all major planets of the Solar system into compact analytical series is presented. The method of spectral analysis of the numerical planetary ephemerides DE431 over the entire time interval of 30 000 years covered by them has been used. The derived series surpass considerably all of the known analogs in their compactness and accuracy of representing the planetary ephemerides over long time intervals.