Moscow University Mechanics Bulletin最新文献

We consider a system of many point particles with arbitrary quadratic interaction and a harmonic force acting on a single fixed particle. Necessary and sufficient conditions for resonance and uniform boundedness of trajectories are obtained; and for the case of resonance the late time asymptotics for energy maximum of the system is obtained as well.

The paper presents the results of simulation with the simplified modified Hodgkin–Huxley model of an afferent primary neuron in the presence of stochastic noise. The transition from the attraction domain of a point attractor like a stable focus to the attraction domain of a periodic attractor and the inverse transition to the attraction domain of the point attractor are considered. Some examples, in which such transitions may be repeatedly alternated, have been obtained as a mathematical interpretation of the principal neurophysiological ‘‘all-or-none’’ law.

The author’s method of thermodynamic analysis is used to single out two equations of state for the laminar combustion process: the classical Hugoniot adiabat, which determines the pressure, and the equation of state, which determines the entropy. This allows constructing a new mathematical model of the laminar process of vibrational combustion of a two-component mixture by closing the classical models of continuum mechanics. The model is phenomenological, which requires its verification. For numerical verification, the well-known experimental fact is chosen, the appearance of high-frequency acoustic vibrations described by B.V. Raushenbakh. The conditions for the origin of high-frequency oscillations are obtained in terms of the standard chemical potential. They can substantially disturb the combustion process and may cause a catastrophic break-up of the furnace of the engine structure. A numerical experiment established critical values of the standard chemical potential when high-frequency vibrations lead to destruction.

The possibilities of various representations of high-rank tensors in three-dimensional space using lower-rank tensors, in particular, the representations of second-rank tensors by vector fields, is discussed. The purpose of these representations is a convenient geometric interpretation of certain mechanical properties of objects described by high-rank tensors. An invariant correspondence between symmetric second-rank tensors in three-dimensional space and pairs of vectors from the same space is proposed. On the basis of this correspondence, a geometric interpretation of the action of an isotropic symmetric tensor function of a tensor argument is given.

Wiener filter and neural network filter are considered in relation to the problem of measuring the road profile. Road profile is identified using the inertial data from a smartphone rigidly fixed inside a moving car. The effectiveness of the approaches is compared by experimentally driving a car through a series of speed bumps.

A plane problem of the formation of a crater as a result of the explosion of a line charge on the surface of the ground is investigated within the solid–liquid formulation. The explosion crater is supposed to be a polygonal line with two angular points. The exact solution to the problem is constructed. A parametric analysis is performed. The calculated profiles of the explosion crater are presented for some governing parameters of the problem. Restrictions on the governing parameters are given, and limiting cases are considered.

A classification option is proposed for the manifestations of Ratcheting—one-sided accumulation of deformation in a material during its cyclic loading—depending on the degree of complexity of the entire deformation process. The absence of experimentally important experiments with extremely small cycle amplitudes is noted and some programs of such experiments are formulated. The names of the two types of ratcheting are offered.

A method for well placement optimization to maximize oil production during a given time interval is proposed. The method is based on an empirical approach related to the enumeration of possible well positions, rather than calculating the gradient of the objective function. This provides, on the one hand, effective paralleling of the well placement optimization algorithm and, consequently, acceleration of the method, and, on the other hand, the global extremum of the objective function. The application of the method to well placement using a digital 3D model of an oil field is considered.

The mutual influence of round and elliptical cracks in three-dimensional space is investigated. The stress intensity factors for various problems are calculated. The dependence of the stress intensity factors on the ratio of the semiaxes of the ellipse is investigated. The computational error does not exceed 1(%).

It is shown on the example of elastic (SH) wave diffraction by an obstacle like a half-plane that barriers can be used to attenuate vibrations and waves in elastic media. It is found that not only a solid barrier, but also a cut or a natural fracture in soil can protect foundations and buildings against shear bulk waves.