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Quaternion signals specifying a group point object located in a three-dimensional space are considered. A similarity measure of these signals is introduced in the form of their scalar product. A quaternion matched filter is synthesized. Using the minimum distance criterion, the problem of recognizing completely known signals, signals with an unknown initial quaternion and unknown rotation angle is solved.

Exact formulas for the characteristics of detecting an inhomogeneous image with unknown area are derived by the maximum likelihood method.

The paper presents solutions to problems of nonstationary filtration to an imperfect well with an arbitrary angle of inclination from the vertical, allowing for the interpretation of data based on pressure transient test and production forecasting. Solutions are obtained for various conditions on the top and bottom of the reservoir, while two algorithms are implemented to describe the bottom-hole pressure: a multi-segment and a single-segment algorithm with the determination of an equal pressure point. A computational experiment shows that the calculation results obtained using single- and multi-segment algorithms are in good agreement.

Results of studying an oblique impact of heavy solid spheres 6 mm in diameter onto an undisturbed surface of water by the method of high-speed visualization are reported. The dynamics of interaction of the body with the liquid in the cases of sphere ricochet and immersion is compared. It is found that air bubbles are intensely captured in the wake behind the body in situations with body immersion owing to a collision of the edges of the “crown” generated at the cavity boundaries and to formation of a jet penetrating through the cavity bottom and entraining air bubbles. The effects of the sphere material density and of the impact velocity and angle on the scenario of sphere-liquid interaction are studied. Comparisons with previous experiments show that a decrease in the sphere size leads to reduction of the critical angle, while the opposite effect (increase in the critical angle) is observed if the impact velocity is increased. Such effects cannot be explained by theoretical approaches developed earlier for impacts of large spheres because these approaches ignore the dynamics of the liquid jet generated ahead of the body and the changes in the flow pattern as a whole.

The influence of various individual and phantom boundary conditions on the results pre-operative numerical simulations of hemodynamics of a fusiform aneurysm of cerebral vessels is numerically simulated. It is found that allowance for individual mechanical properties of the aneurysm tissue affects the results of predicting the aneurysm status, but does not affect predicting the rupture zone, which can be detected by using the CFD approach under the assumption of rigid walls with phantom boundary conditions and with the condition of the maximum shear stresses on the wall as a criterion of rupture zone determination.

Results of a methodical study aimed at modeling a spatially inhomogeneous transition line are reported. The results are obtained by an in-house software module for the CFD package and an in-house program for predicting the laminar-turbulent transition based on the  e<i>^N</i>-method. Numerical simulations are performed for a hybrid laminar-turbulent transition, where the regular and bypass transition scenarios take place in different regions of the flow in the boundary layer on a swept wing.

A method is developed for determining residual stresses in a thin metal plate via shot peening of its surface. The reference configuration of the plate is assumed to be flat with a layer of hardened material of known thickness with a uniform longitudinal initial stress; its value is determined by solving the inverse problem of establishing the equilibrium state of a bent plate. The problem of bending a plate with initial stresses is solved numerically by the finite element method using the model of an isotropic hypoelastic material. As a result of solving the problem, a residual stress field is determined, allowing one to estimate the degree of danger of positive principal stresses that can lead to destruction of the plate material.

One of the most important factors determining dental implants' longevity and effectiveness is the connection between the abutment and the implant. This investigation focuses on studying how bone shielding is affected by the interface between dental implants and abutments. In a computer-aided design (CAD) environment, three dental implant connectors and carbon-reinforced PEEK are modeled. A comparison is made between the modern dental implant locking mechanism and the more traditional internal hexagonal and conical abutment interfaces to evaluate the former's effectiveness. ANN is employed in the process of developing the precise modulus of the dental implant material for the human jaw. Studying the von Mises stress and deformation of dental interface materials makes it possible to discover a unique locking system that exhibits the highest von Mises stress and deformation, virtually on par with the bone. However, the carbon-reinforced PEEK composite material demonstrates high bone shielding.

A method for selecting an appropriate ice model and its parameters using numerical simulation is developed. The process of low-velocity impact of a spherical indenter with an ice plate is studied, and numerical calculation data are compared with experimental data. This paper describes well-known rheological models of elastoplasticity with the von Mises and von Mises-Schleicher yield criteria, as well as an elasticity model with a constant-size elastoplastic inclusion. A system of isotropic linear elasticity equations, solved by the grid-characteristic method, is used as the determining system of equations. The effect of the model parameters on the calculated instantaneous velocities and coordinates of the ball is investigated. Criteria for selecting the model characteristics are formulated, and approximations of dependences of these criteria on various parameters are constructed.

A single integral form of the postulates of continuum mechanics in the form of laws of change (conservation) of certain quantities is represented as a table of postulates. It is assumed that in a continuous medium, both purely mechanical and various non-mechanical interactions occur, which are described by scalar, vector, and second-rank tensor energetically conjugate pairs of quantities, one of which characterizes a process and the other defines the response of the environment to this process. The first three rows of the table of postulates are used to construct the fourth and fifth rows corresponding to the laws of change in internal energy and the quantity that, in the case of the thermodynamic pair “temperature-entropy” coincides with entropy. It is shown that the assignment of sources, flows through the boundary, and productions in the fourth and fifth rows of the table of postulates actually makes these rows definitions. The principles used in nonisothermal mechanics to construct constitutive relations linking dependent and independent state variables for each type of interaction are generalized.