Local gradient operator

Here, I is the dyadic idemfactor and m = n — n moreover, V = d/dr is the local gradient operator defined only within a unit cell (r e t0). The material functions P, J, and n are the respective dyadic, triadic, and vector fields... 

The attack at a pressure of 240 bar is very severe at temperatures between 300 and 390 °C where the local gradient is steep. In the steady state section at 400 °C, the bite is comparatively moderate. Further corrosion tests indicate that at higher pressures the bite speeds up and that a higher steady state operating temperature has a minor influence on the corrosion rate. 

This program combines a GA and a local gradient minimization with CHARMM as the scoring function for flexible docking of protein complexes. The populations ate modified by standard mutation and crossover operators. 

Here, D is the diffusion coefficient of the solute molecule and V denotes the two-dimensional gradient operator. The quantity n appearing in the boundary condition here refers to the unit vector pointing outward normal to the channel surface (see Fig. 1). It is important to note that Eq. 5 assumes that the analyte molecules move with the local fluid velocity u and diffuse uniformly throughout the channel. The description presented here, therefore, is only valid for... 

Electrodynamics is a typical domain in which space plays an important role. An example of a curve-localized variable is the electric field (It is true that intensity or strengh is sometimes used, but since it is misleading with the electric current or a force, I prefer nothing to use). E resulting from spatial variation of a potential V, which is given by application of the contra-gradient operator ... 

In contradistinction with the previous discussion about reducing scalar state variables, the relationship with the next localized variable cannot be obtained by a differential vector operator, but by an ordinary derivation, becanse here the two variables U/ and U/ are both scalars. Notwithstanding, this is possible between the two last levels by a gradient operator ... 

Well-controlled crystallisation is the best approach for the preparation of material that is uniform in shape, size, structure and purity. However, the local gradient of supersaturation could be a limiting factor in respect to the uniformity of the product quality, as nucleation and crystal growth depend on the degree of supersaturation. If the combination of laminar flux and low shear stress is expected to produce crystals with good structural lattices (Drioli et al, 2006), it is important to note that the choice of the operating conditions can influence the nucleation rate, as described by the following equation ... 

The simplest practicable approach considers the membrane as a continuous, nonporous phase in which water of hydration is dissolved.In such a scenario, which is based on concentrated solution theory, the sole thermodynamic variable for specifying the local state of the membrane is the water activity the relevant mechanism of water back-transport is diffusion in an activity gradient. However, pure diffusion models provide an incomplete description of the membrane response to changing external operation conditions, as explained in Section 6.6.2. They cannot predict the net water flux across a saturated membrane that results from applying a difference in total gas pressures between cathodic and anodic gas compartments. 

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