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By using the optimal control framework new classes of curves and surfaces can be defined.
Flow/damage surfaces can be defined in terms of stress, inelastic strain rate, and internal variables using a thermodynamics framework.
These blending surfaces can be defined by specifying contact curves on the given primary surfaces and then creating a blend surface that is smoothly joined to the given surfaces.
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end{aligned} (13)Now, sliding surface can be defined in linear mode for the achievement of stability in the states of the subsystem (4): begin{aligned} S=left[ {{begin{array}{l} {s_5 } {s_6 } end{array} }} right] =c_1 e_1 +c_2 e_2 +c_3 e_3 +e_4.
For these, the previously obtained outer surface can be defined as a conformation of this elastic membrane of high potential energy, which is then progressively released to a position of lesser potential energy without penetration of any delimiting structure, for example, bony surfaces or underlying muscles.
b) Again while the pH of the solution remains moderately in a neutral range (pH 7.0), phycoremediation of As III) or As V) on the neutral microalgal biomass surface can be defined by a ligand or ion exchange reaction mechanism, which is characterized as follows (Mandal et al. 2011; Giri et al. 2013): MOH + AsO3 3− → M+…AsO3 3− + OH− (ligand or ion exchange) (6.147).
Definition: The dip of the plane, represented by the inclination of the plane from the earth surface, can be defined more precisely as the linear representing the steepest possible angle between the plane (A B C) and the ground-plane (spanned by the x - and z -axes) (Fig. 4 D).
The ratio of the final structure surface to the original surface area can be defined as the area enhancement ratio (AER), which is defined as AER = Atot/Acell, where Atot is the total surface of the unitary cell after etching and Acell is the area of the unitary cell before etching.
Therefore, the surface energy can be defined as the excess energy at the surface of a material compared to the bulk.
Furthermore, a saturation surface tension can be defined, which is independent on the types of plasma used and of all plasma parameters, whereas the time constant depends strongly on the type of plasma.
In this paper, we present the method in detail, and demonstrate several new extensions of the method to different physical phenomena, including curvature flow with surface energy densities defined on a per-phase basis, as well as multiphase fluid flow in which density, viscosity and surface tension can be defined on a per-phase basis.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com