математичне моделювання

Simulation model of the mechanical component of the fully differential capacitive MEMS accelerometer has been developed using MATLAB/Simulink environment. The model allows to simulate movement of the proof mass, capacitance changes of the sense capacitors of the sensitive element, sensitivity of the sensor depending on the applied force of acceleration, and to perform the transient analysis of the integrated device at the system level of computeraided design.

Mathematical modeling of effective elastic and acoustic properties of granite reservoir rocks that has different pore space structure was done. The acoustic properties of granite porous-cracks reservoir were determined. The algorithm and software for solving the problem of joint inversion of seismic and gravimetric data based on Born’s approximation for the space-time Green's function with meansquare background velocity for the horizontally-layered medium has been developed and tested (on an example of the Prykerch shelf model).

The dependence of rheological properties fanerozoj rocks from one-directional tectonic forces and comprehensive pressure are investigated using the experimental data. The stress and strain fields are obtained based on the solution of two-dimensional problems of thermo-elasto-plasticity. These fields prove the dependence of comprehensive pressure and plasticity of the rocks from the levels of one-directional tectonic forces.

Questions of the mathematics modeling of local and global processes of Geodynamics are examined. The model of the process must take into account all its sources at the same time. This demand can be ensured by simultaneously calculating variations from all results of observations of geodynamic features. This task is solved by the determination and use of properties of covariance functions for fields of observation results.

In the article the results of studies of stress-strained state of the crust in Chatkal`s mountain zone of west Tan-Shan are shown. In the first approximation the main and paleo-stresses for separate area of the region`s are estimated. For analysis of the stresses the methods of mathematical modeling and tectonophysical methods of stresses fields reconstructions and method of recovering of stresses by earthquakes mechanisms are used.

Purpose. The aim is to conduct mathematical modeling of disturbances and seismic wave field propagation in horizontally layered isotropic elastic half-space; summarizing the results obtained in the case of absorbing media; numerical implementation of the method of calculation of seismic waves in horizontally layered medium with absorption, perturbed point source in a simple force that depends on time; build sustainable programs and algorithms for numerical calculations for synthetic seismograms; and conducting numerical experiments for verification of results.

The research findings in the sphere of mathematical modeling of modern broadband wireless access have been revealed in the article. Detailed description of algorithm program realized in multi- antenna channel has been provided. The distinctive feature of this algorithm is taking into account the digital signal processing correlation properties of multi-antenna channel.

Regression analysis of the population dynamics of hunting mammals based on Khmilnytskyi forestry was made. Correlation analysis of the observations results between the populations of spotted deer and wisent, spotted deer and wild boar, lepus and fox was made. Modelling of the population dynamics of hunting mammals was done using Mathcad based on the system of recurrent logistics equations and the adequacy of the model by the Pearson's criteria was proved.

The mathematical models for spatial analysis of GHG emission processes from pulp, paper, food products and beverages have been developed. Using geoinformation technology the estimates of GHG emissions in Poland at the level of production plants, as well as at the level of elementary areas 2 km  2 km in size have been obtained.

Mathematical models for the spatial analysis of the processes of greenhouse gases emission from the mining and transformation of coal in Poland were elaborated. The digital maps of mines’s and coking’s places were created. GIS technology, which makes it possible to form a geo-distributed database was improved and the necessary calculations were done.  The obtained assessment of greenhouse gas emissions was represented by the digital thematic map.