The flow of a viscous liquid film over a solid surface deviating slightly from the horizon is considered. Linear and nonlinear waves excited by hydrodynamic instability are investigated. A new system of differential equations for the average thickness, local fluid flow rate, and friction on a solid surface is derived. The stability of a uniform flow with respect to small periodic wave disturbances in the longitudinal coordinate is investigated. It is shown that there is a finite instability interval in the long-wave range and an unlimited instability interval in the wave number in the short-wave range. It is established that with a spectral representation of solutions by a finite number of terms of the Fourier series, the existence of a regular nonlinear wave regime is possible over a large time interval. The regular solution agrees with experimental observations on the boundaries of linear instability and on the parameters of the nonlinear wave regime.
The article presents a calculation for the stability of the straight-line equilibrium shape of a section of a pipeline with elastic support under the action of a moving load. It studies the influence of the stiffness of the pipeline’s fastening on the position of the stability boundary in the plane of two parameters: the relative mass of the flowing liquid and the speed of the liquid flow through the pipeline. The solution of the perturbed motion equation is represented as a series based on the natural oscillations of an elastic rod. The stability regions’ boundaries are constructed by directly calculating characteristic roots and analyzing their trajectories using the Routh–Hurwitz criterion.
The article is devoted to the development of navigation algorithms for ground wheeled vehicles—particularly, agricultural machinery—using measurements from a strapdown inertial navigation system and wheel odometry data. The derivation is based on notations of the mechanics of aided inertial navigation systems.
The asymptotics of computational costs for simulations of gas flow with shock waves using adaptively refined dynamic meshes of the quadtree class is estimated. The Euler equations in Cartesian coordinates are numerically solved using the finite-volume CWENO method with a compact stencil. A simple criterion for splitting and recombination of computational cells is proposed based on an estimate of the local density gradient. A comparison is made with simulations with the finite-difference WENO method of the same order of approximation on a uniform grid. It is shown that the time and memory costs when refining locally-adapted grids increase significantly slower than for uniform grids.
The algorithms and software are elaborated for processing and analysis of digital images of cylindrical metal or polymer samples deformed during tensile, compressive, or impact Taylor’s tests. The goal is to extract a wide range of quantitative characteristics of a sample shape from its single picture and to determine dimensions and mean strains in order to study material properties and to use the data to calibrate and verify material models.
