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Utilization of hydraulic-fracturing technology is dramatically increasing in exploitation of natural gas extraction. However the prediction of the configuration of propagated hydraulic fracture is extremely challenging. This paper presents a numerical method of obtaining the configuration of the propagated hydraulic fracture into discrete natural fracture network system. The method is developed on the basis of weighted fracture which is derived in combination of Dijkstra's algorithm energy theory and vector method. Numerical results along with experimental data demonstrated that proposed method is capable of predicting the propagated hydraulic fracture configuration reasonably with high computation efficiency. Sensitivity analysis reveals a number of interesting observation results: the shortest path weight value decreases with increasing of fracture density and length, and increases with increasing of the angle between fractures to the maximum principal stress direction. Our method is helpful for evaluating the complexity of the discrete fracture network, to obtain the extension direction of the fracture. [ABSTRACT FROM AUTHOR]

Numerical simulation of shielding effectiveness (SE) of a perforated shielding enclosure is carried out, using the finite element method (FEM). Possibilities of model definitions and differences between 2D and 3D models are discussed. An important part of any simulation is verification of the model results-here the simulation result are verified in terms of convergence of the model in dependence on the degrees of freedom (DOF) and by measurements. The experimental method is based on measurement of electric field inside the enclosure using an electric field probe with small dimensions is described in the paper. Solution of an illustrative example of SE by FEM is shown and simulation results are verified by experiments. [ABSTRACT FROM AUTHOR]

A single-species population model exhibiting a symmetric slow variation for the carrying capacity and intrinsic growth rate is evaluated explicitly. However, it is unrealistic to eliminate the possibility of a clear separation in the evolution of the biotic environmental elements; thus, this paper considers the situation where these elements have a hierarchical variation on the time scales. Accordingly, two particular situations are recognized, which are the carrying capacity varies faster than the growth rate and vice versa. Applying the multi-time scaling technique in such a system provides a small parameter, which leads us to construct analytical approximate expressions for the population behavior, using the perturbation approach. Such approximations display very good agreement with the numerical simulations. [ABSTRACT FROM AUTHOR]