Ural State Mining University, Yekaterinburg, Russia:

V. B. Surnev, Head of Department, Doctor of Physical and Mathematical Sciences, igg.mt@m.ursmu.ru
N. G. Valiev, Head of Department, Doctor of Engineering Sciences
V. B. Pyatkova, Senior Lecturer

The article describes mathematical modeling of linear parametric systems with concentrated and distributed parameters. The mathematical apparatus of modeling of parametric systems with concentrated parameters using an evolutionary integral equation, announced earlier, is extended to a general case of a system of an arbitrary physical nature. The proposed apparatus can be used for the mathematical modeling of time evolution of a linear parametric system with concentrated parameters, and within the method of automated selection when solving an inverse dynamic problem of the linear parametric system synthesis. In analogy to the mathematical model of a system with concentrated parameters, the model system of equations is written in the theory of wave field scattering by an object with constituent parameters dependent on an exogenous governing variable, i.e. the system of equations modeling the response of a linear physical system with distributed parameters under external effect to another external effect. A significant difference from the existing studies in this respect is the use of the wave field equations with the partial derivatives of the first order instead of the second-order equations. The list of applied geological and mining problems solvable using the proposed methods is given. The scope of the discussion embraces temperature instability of an inductive measuring transducer; seismic and electromagnetic profiling in re-prospecting and monitoring in metallic and nonmetallic mineral mining; mathematical modeling of high-viscosity oil recovery monitoring; monitoring of mineral salt production by vacuum evaporation; monitoring of in-situ uranium leaching.

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