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Parametric illustration of shapes, mechanical elements modeling with 3D visualization innovations utilizing item orientated programming, the well-known golden ratio software on vertical and horizontal displacement investigations of the floor floor, spatial modeling and simulating of dynamic non-stop fluid move approach, simulation version for waste-water remedy, an interplay of tilt and illumination stipulations at flight simulation and mistakes in taxiing functionality, plant structure optimum plot plan, atmospheric modeling for climate prediction, a stochastic seek process that explores the options for hill mountain climbing approach, mobile automata simulations, thyristor switching features simulation.

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It’s interesting to find that the golden ratio appears in the point sink induced maximum ground surface horizontal displacement and corresponding settlement of a poroelastic half space. 3. 1 Basic Equations Figure 3 presents a point sink buried in a saturated porous elastic aquifer at a depth h . The aquifer is considered as a homogeneous isotropic porous medium with a vertical axis of symmetry. , the flow field is independent from the displacement field. Considering a point sink of constant strength Q located at point 0, h , the basic governing equations of the elastic saturated aquifer for linear axially symmetric deformation can be expressed in terms of displacements ui and excess pore water pressure p in the cylindrical coordinates r , , z as follows (Lu & Lin, 2006, 2008): G u p G 2r 0, r 1 2 r r G p G 2u z 0, 1 2 z z k p Q 2 p n r z h u t 0 , w t 2 r G 2ur (8a) (8b) (8c) where 2 2 r 2 1 r r 2 z 2 is the Laplacian operator.

For example, for 3D simplex pqrs in fig. 3b, there is an empty circumsphere passing through three points p, q,r and s. The center of this sphere is a vertex of the Voronoi tessellation between these points, because this vertex is equidistant from each of these sites and there is no other closer point. This property offers a more adequate discretization among all arbitrary triangular tessellation of the space. In addition, it is frequently used to choose the best place to insert new points within the poor quality elements in refinement methods (please see Shewchuk, 1997).

Point Sink Fundamental Solutions for Subsidence Prediction, Journal of Engineering Mechanics, Vol. 116, No. 5, pp. 11761182. Livio, M. (2002). The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number, Broadway Books, New York. Lu, J. -C. -T. (2006). The Transient Ground Surface Displacements Due to a Point Sink/Heat Source in an Elastic Half-space, Geotechnical Special Publication No. 148, ASCE, pp. 210-218. Lu, J. -C. -T. (2008). Modelling of Consolidation Settlement Subjected to a Point Sink in an Isotropic Porous Elastic Half Space, Proceedings of the 17th IASTED International Conference on Applied Simulation and Modelling, Corfu, Greece, pp.