Nonlinear dynamics of magnetohydrodynamic flows of heavy fluid over an arbitrary surface in shallow water approximation

The magnetohydrodynamic equations system for heavy fluid over an arbitrary surface in shallow water approximation is studied in the present paper. It is shown that simple wave solutions exist only for underlying surfaces that are slopes of constant inclination. All self-similar discontinuous and continuous solutions are found. The exact explicit solutions of initial discontinuity decay problem over a flat plane and a slope are found. It is shown that the initial discontinuity decay solution is represented by one of five possible wave configurations. For each configuration the necessary and sufficient conditions for its realization are found. The change of dependent and independent variables transforming the initial equations over a slope to those over a flat plane is found.Comment: 43 pages, submitted to Theoretical and Computational Fluid Dynamic

Determination of the strength properties of wood in the inspection of buildings and structures: methods, problems and solutions

The paper considers the ways and methods of determining the strength of wood according to the current norms and rules. The required number of wood samples are tested and compared with the strength characteristics in SP 64.13330.2020 “Wood structures”. It is concluded that it is impossible to use the obtained results for calculations of building structures, due to the lack of coefficients in the norms, taking into account the vices of wood and the scale factor. The existing methods of nondestructive control of wood were analyzed. The tests were carried out and the dependences between the speed of sound along and across the fibers and the strength of the samples were plotted. The conclusions about the possibility of using the ultrasonic method to determine the strength of wood in the examination of buildings are made