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Minimization of potential energy with Tikhonov regularization is adopted to solve the singular system of equilibrium equations resulting from the filtered designs.
The first part presented the analytical development of the equations needed to analyze the performance of an active control system based on three performance criteria: the minimization of pressure at a selected set of points within the waveguide, the minimization of potential energy in a selected volume of the waveguide, and the minimization of power in the downstream region of the waveguide.
Microseismic monitoring cannot only delineate and map vertical and horizontal fracture growth patterns, but also provide a dimensional image of the stimulated volume and its propagation, which enables optimization of wellbore and well stage spacing, well production and reservoir development plan, and also minimization of potential environmental impacts.
In this setting we necessarily place much emphasis on specificity, including robust extraction methodologies and minimization of potential for contamination.
CCL studies are also important in terms of the prevention or minimization of potential late effects of therapy.
Prospects ranged from questioning the doctor's authority and competence, to minimization of potential negative side effects, to finding another doctor who was willing to prescribe it" [ 6].
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Although the point set generated through the minimization of electrostatic potential is the gold standard, minimizing the electrostatic potential of one thousand points (or charges) or more remains a formidable task.
The method is based on the minimization of the potential energy of the whole mechanism.
The second method adopts a suitable variational (weak) formulation, based on the minimization of the potential energy.
In this paper, we develop a hierarchical and heterogeneous particle swarm optimizer (HHPSO) to deal with the problem in the minimization of the potential energy.
This shape function is used to obtain a transcendental stiffness matrix for the strip through the minimization of the potential energy technique.
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