SIMULATION OF REFLECTION OF A PLANE ELECTROMAGNETIC WAVE IN A MULTILAYER MEDIUM: OIL-SATURATED FORMATION ENCLOSING A HYDRAULIC FRACTURE

Propagation of a plane electromagnetic wave of the microwave range is simulated to calculate the coefficient of its reflection from a homogeneous layer. A particular case of a multilayer geomediumis considered: an oil-saturated formation enclosing a hydraulic fracture. When justifying the choice of the frequency range, the value of fracture surface irregularity was taken into account. The dependence of the reflection coefficient on frequency for an electrically less dense non-absorbing layer inside a denser non-absorbing substance (a void layer inside a rock) has been calculated.

Non-destructive testing of multilayer medium by the method of velocity of elastic waves hodograph

The method of velocity of elastic waves hodograph, aimed at non-destructive testing of structurally heterogeneous composite materials and products based on them, as well as multilayer products and constructions, is considered. The theoretical basis for determining the propagation velocity of elastic waves in a multilayer medium by the hodograph method is given. Based on the studies, recommendations are given for determining the propagation velocity of elastic waves in each individual layer of a multilayer medium, which allows non-destructive testing of the physicomechanical characteristics of each layer of a multilayer medium. It is shown that in addition to simple multiple reflections in a homogeneous medium, in a multilayer medium with parallel interfaces consisting of two or more layers, complex types of multiple reflected waves and mixed waves (reflected-refracted and refracted-reflected) can arise. The main task of applying the low-frequency ultrasonic method is to determine the acoustic parameters of the propagation of elastic waves (velocities, amplitudes, spectra). The main methods for determining the elastic wave velocities are considered, based on the hodograph equation of the indicated reflected waves in a multilayer medium.

Correctness conditions for boundary value problems

The article deals with the issues of mathematical modeling of technological systems that contain physical fields’ sources. It is believed that in the case of a simple spatial form of the object under study, the boundary value problems will be correct. The interest lies in mathematical models for nonlinear, multilayer objects under the influence of load sources, for which, using the traditional theory of existence and unity, it is impossible to guarantee the correctness of boundary value problems. The author considers boundary value problems for systems of differential and pseudo differential equations in a multilayer medium which describe the state of the studied systems under the action of discrete load sources. The correctness of such problems is proven using the theory of distributions over the space of generalized functions. The object of research is boundary value problems for systems of differential and pseudo differential equations in a multilayer medium. The aim of the research is to build correct boundary value problems, which underlie the calculated mathematical models of the process of action of physical fields on multilayer objects. The necessary and sufficient conditions for the correctness of the parabolic boundary value problem in the space of generalized functions are obtained in the article. It is shown that its solution is infinitely differentiated by a spatial variable. The results of the research can be used to obtain the conditions for the correctness of the boundary value problem for differential equations with variable coefficients. Note that, in some cases, the correctness of the calculated mathematical models determines the correctness of applied optimization mathematical models. The application of the author's research is possible when proving the correctness of boundary value problems for a number of technological processes. The universality of the research allows to widely usage of the results obtained in this work to improve the quality of technological processes.

Management of Electric Field under the Sag of High Voltage Overhead Transmission Lines

There have been many methods used to determine the electric field strength under the 150 KV overhead transmission lines (OHTL). Since it is simple and can be used for a homogeneous and multilayer medium, the method chosen for modeling the electric field under the OHTL is the complex image method (CIM). The results obtained show that the electric field strength obtained by the CIM is in agreement with that obtained by Complex Determine Method (CDM). Furthermore, the results obtained from the CIM model fit well with the field data. The OHTL height that must be raised so that the electric field strength under the OHTL will meet the WHO quality standards is 3 m at location A and 2 m at location B. These results show that modelling the electric field under the OHTL using CIM is exellent.