Continuity requirement

Now, continuity requires that the wronskian/i/j —fifi is preserved, from which it may be verified that... 

In Equation (4.12) the discretization of velocity and pressure is based on different shape functions (i.e. NjJ = l,n and Mil= l,m where, in general, mweight function used in the continuity equation is selected as -Mi to retain the symmetry of the discretized equations. After application of Green s theorem to the second-order velocity derivatives (to reduce inter-element continuity requirement) and the pressure terms (to maintain the consistency of the formulation) and algebraic manipulations the working equations of the U-V-P scheme are obtained as... 

After application of Green s theorem to the second-order velocity derivatives (to reduce inter-element continuity requirement) and algebraic manipulations the working equations of the continuous penalty scheme are obtained as... 

The concentration gradient normal to the outside of the catalyst particle. The rate is expressed on catalyst-filled reactor volume, with e void fraction for this smaller volume the rate must be higher to keep Vrr=Vcr< . This is calculated from the continuity requirement that was mentioned above ... 

For these gradients, continuity requires that everything that reacted inside, had to diffiise through the outside layer of the catalyst. 

The complete set of curves in Fig. 19 show that the adsorption performance of the activated carbon canister is a continuous requirement, and not an occasional need... 

Training Training programs can only be developed after training requirements are established. In reality, training will be a continuous requirement, but this represents a point at which some significant new requirements have been put in place. 

It is becoming increasingly clear that the preponderant amt of modern ordnance requiring the initiation of HE charges utilize electric initiation. However, there still remains a continued requirement for the use of percussion initiation. The use and description of sensitive artillery primers, eg, M29A1, etc, to accomplish this has previously been discussed... 

Fig. 7a-c Phase continuity requirements, a Electron-donating orbitals (denoted by D-D) are out of phase, b Accepting orbitals (denoted by A—A) are in phase, c Donating and accepting orbitals (D-A) are in phase... 

Singlet o-type diradical. Figure 8 shows the phase relationship between the electron donating and accepting orbitals in a o-type diradical (Scheme 4b). It can be seen that the cyclic -p-0j -02 -q-02-0j- orbital interaction satisfies the continuity requirements in the singlet state (Fig. 8) the neighboring orbitals in p(D)-Oj (A)-02 (A)-q(A)-02(D) are all in phase while those in the sequence p(D)-Oj(D)-02(p) are all out of phase. The phase is continuous for the cyclic interaction. 

In the singlet state of Jt-type 1,3-diradical (e.g., TM, 2), there may also exist the through-space interaction between radical centers, i.e., p...q interaction (Fig. 9), in addition to the previously addressed cyclic -p-o -q-o- orbital interactions (Fig. 6). The through-space interaction is indispensable for the bond formation between the radical centers. The corresponding delocalization of the a-spin electron is shown in Fig. 9a. Clearly, the involvement of the through-space p... q interaction gives rise to two cyclic orbital interactions, -p-o -q- and -p-o-q-. From Fig. 9, one can find that the cyclic -p-o -q- orbital interaction can satisfy the phase continuity requirements for the a-spin electron the electron-donating radical orbital, p (D) can... 

Although there are many biocide alternatives available on the market, for example enzyme technology or bio-dispersants, there appears to be a continued requirement for the use of biocides in order to reduce the levels of microbiological contamination entering the paper making process. The increased awareness of environmental and safety aspects will continue to play an important role on the selection of biocides for paper making processes. The use of legislation to select biocides must be done in parallel with each plants internal risk assessment. No one biocide active will meet all the criteria set out by different European countries and hence the use of these actives must be carefully assessed on a plant by plant basis. 

If due to buoyancy the fuel gases attain a velocity vb in the flame zone after leaving the port exit, continuity requires that the effective radial diffusion distance be some value rb. Obviously, continuity requires that p be the same for both cases, so that... 

The fiber continuity requirement for the taper follows from the assumption that all fibers are infinitely long and their number is constant. A mass balance gives the fiber-volume-fraction dependency along the x-axis as... 

The matrix continuity requirement is obtained from consideration of the matrix flux at two control surfaces in the taper—one at an arbitrary coordinate x and one at x = L (see Fig. 11.6). At x the matrix flux is unknown, and at the end of the taper the matrix travels with the same velocity as the fibers due to the plug-flow assumption. Neglecting the difference between the flow component in the x-direction and the component along the fibers, the matrix flux through the respective control surfaces is obtained as... 

Thus continuity requires that there is no axial variation in the axial velocities. The axial momentum equation, Eq. 3.79, also reduces to a very simple form ... 

The design of commercial equipment for carrying out these unit operations continuously requires numerous experimental data. 

If one now chooses x, = S and recalls that the xi (k < n) are fieely adjustable, the Second Law would be violated if S were also adjustable at will (by means of non-static adiabatic transitions). Taking continuity requirements into account, it follows that S can either never decrease or never increase. The single example of the sudden expansion of a real gas shows that it can never decrease. One has the Principle of Increase of Entropy The entropy of an adiabatically isolated system can never decrease. 

An accurate description of the SCL current requires two-dimensional analysis. Current continuity requires that the SCL current equals the current in the shortened saturated transistor, i.e. the saturation current of Eq. (3) multiplied with the factor L/(L — AL). Solving the equations for AL, the drain current reads ... 

It is further assumed that the transverse velocity fluctuations arise from the longitudinal velocity fluctuations in order to satisfy continuity requirements, i.e. ... 

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