Parallel paths

Finally, in yet another variant, the sample liquid stream and the gas flow are brought together at a shaped nozzle into which the liquid flows (parallel-path nebulizer). Again, the intersection of liquid film and gas flow leads to the formation of an aerosol. Obstruction of the sample flow by formation of deposits is not a problem, and the devices are easily constructed from plastics, making them robust and cheap. 

Distributors in industrial units typically have large numbers of injection points of quite diverse design characteristics, some of which are depicted in Eigure 16 for fluidized-bed appHcations. Flow variations through these parallel paths can lead to poor flow distributions within a reactor, thus reducing product yields and selectivity. In some circumstances, undesirable side products can foul portions of the distributor and further upset flow patterns. Where this is important, or where the possibiHties and consequences are insufficiently understood and independent means caimot be employed to assure adequate distribution, the pilot plant must be sized to accommodate such a distributor. Spacing should be comparable to those distributors that are anticipated to be... 

FIG, 12-18 Parallel-path cooling-tower arrangement for plume abatement. (Marley Co.)... 

This can be limited by using a non-linear resistance called Metrosil across the relay, as shown in Figure 15.27. If voltage reaches a dangerous level, this resistance will provide a low-resistance parallel path to the current and limit the voltage across the relay to about I kV. The current / through the non-linear resistance is given by... 

Amster and Hooper, 1986). Other formulations exist for eomponents in parallel with equal reliability values, as shown in equation 4.69, and for eombinations of series, parallel and redundant eomponents in a system (Smith, 1997). The eomplexity of the equations to find the system reliability further inereases with redundaney of eomponents in the system and the number of parallel paths (Burns, 1994) ... 

Axial flow, in which the liquid enters the impeller and discharges along a parallel path to the axis, is shown in Figure 9. The radial and longitudinal components are primarily responsible for the derived mixing action. The tangential component is important when the shaft has a vertical orientation and is positioned near the center of the tank. 

If the order of a reaction with respect to one or more species increases as the concentration of those species increases, it is an indication that the reaction may be proceeding by two or more parallel paths. 

Another type of air washer is the capillary air washer see Fig. 9.16. It consists of many thousands of small glass or plastic filaments (cells) providing a large, wetted surface area. These are placed to allow a parallel path of air through them. The surface of each of these strands is covered with the water that is discharged from sprays. 

Identifying specific quantified building ventilation rates can be difficult due to the number of non-linear parallel paths that may have to be simultaneously considered. 

An additional limit to the size of a passive array relates to the current which flows in an OLED when it is under reverse bias [189]. When a given pixel is turned on in the array, there are many possible parallel paths for the current, each involving two diodes in reverse bias and one forward. Hence, as the number of rows and columns increases, there is a higher level of background emission from non-selected pixels that limits the contrast ratio of the array. As a result, the contrast degrades as N increases. 

Potential for very high cell and battery reliability (small electrolyte shapes have fewer defects small cells offer maintenance-free batteries by providing a multiplicity of parallel paths) ... 

The light produced by a laser has a much more narrow wavelength than the light of an LED or other light sources (Fig. 15.3). In addition, laser light is coherent, i.e., the photons travel in parallel paths from the source. Lasers made of thin-films are similar to bulk lasers (He-Ne, ruby) except that they are more compact and efficient. Due to the short lifetime of the photons, high-frequency modulations are possible. 

Combination of these two models for a combined series- and parallel-path system gives... 

Account for interactions within systems (multiple parallel paths, feedback)... 

The thermal decomposition of peroxydisulphate proceeds by two parallel paths, viz. 

Electrochemical steps are often denoted by the letter E (or e), and chemical steps by the letter C (or c). Thus, the first pathway in the example above can be said to follow an EE scheme, and the second an EC scheme. Except for Section 13.7, the reactions considered below will occur by only a single pathway (in both the forward and reverse directions), and there will be no parallel path. 

Aside from CO, other intermediate species have been detected. The formation of formic acid was detected by DBMS [Jusys and Behm, 2001 Wang and Baltmschat, 2007], whereas formaldehyde was found by fluorescence and DBMS [Korzeniewski and Childers, 1998 Jusys and Behm, 2001 Wang and Baltmschat, 2007]. The presence of formic acid clearly indicates that the mechanism should always have a parallel path, although its contribution to the total CO2 could be minor. In fact, only... 

Ensemble or Third-Body Ejfects. These effects concern the selective blockage of a particular adsorption site by adatom deposition. This can be advantageous when the reaction mechanism contains parallel paths that can be affected differently by blocking particular sites. In some cases, the undesired reaction needs more than one free adjacent site (ensemble), and can be inhibited by blocking particular sites without decreasing the reactivity of the surface for the catalyzed reaction. 

In general the rate equation for a heterogeneous reaction accounts for more than one process. The present consideration is directed to the general problem of combining the rates for processes of different kinds. Let r1( r2,..., rn be the rates of changes for the individual processes that are to be accounted for by an overall rate. If the changes occur by parallel paths, then the overall rate will be greater than the rate for any individual path. In fact, if the different parallel paths are independent of each other, the overall rate will be simply the sum of all the individual rates, or... 

As explained above, the QM/MM-FE method requires the calculation of the MEP. The MEP for a potential energy surface is the steepest descent path that connects a first order saddle point (transition state) with two minima (reactant and product). Several methods have been recently adapted by our lab to calculate MEPs in enzymes. These methods include coordinate driving (CD) [13,19], nudged elastic band (NEB) [20-25], a second order parallel path optimizer method [25, 26], a procedure that combines these last two methods in order to improve computational efficiency [27],... 

The organization of the paper is as follows. In the Methods Section we present a brief review of the procedures employed to determine the MEP, namely QM/MM geometry optimizations and the CD method (Section 3.2.1). NEB and the second order parallel path optimizer methods are reviewed in Section 3.2.2. In Section 3.2.3 we present a modified NEB method which allows the addition of extra images to a converged path. Finally we describe the FEP method developed in our lab in Section 3.2.4. In the Computational Details Section we present a description of the procedures employed for the determination of all four paths. Subsequently, we analyze the results obtained from all four paths and conclude with closing remarks. 

The procedure and methods for the MEP determination by the NEB and parallel path optimizer methods have been explained in detail elsewhere [25, 27], Briefly, these methods are types of chain of states methods [20, 21, 25, 26, 30, 31]. In these methods the path is represented by a discrete number of images which are optimized to the MEP simultaneously. This parallel optimization is possible since any point on the MEP is a minimum in all directions except for the reaction coordinate, and thus the energy gradient for any point is parallel to the local tangent of the reaction path. 

Once the path has been optimized with NEB, it is used as the initial guess for the parallel path optimizer method. In this second step the path is again iteratively optimized with the parallel path optimizer method for the core set, followed by the optimization of the environment set. In this part of the calculation no restraints are imposed on the environment set during the optimization. The iterations are continued until all the convergence criteria are met and the final optimized MEP is obtained. 

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