Close-coupling

Alexander M H and Manolopoulos D E 1987 A stable linear reference potential algorithm for solution of the quantum close-coupled equations in molecular scattering theory J. Chem. Phys. 86 2044-50... 

Solution of this set for F R) represents tire adiabatic close-coupling method. The adiabatic states are nomrally detennined (via standard computational teclmiques of quanUim chemistry) relative to a set of axes (X, Y, Z ) with the Z- axis directed along the nuclear separation R. On transfomring to this set which rotates during the collision, then /(r, / ), for the diatomic A-B case, satisfies... 

B2.2.9.1 CLOSE-COUPLING EQUATIONS FOR ELECTRON-ATOM (ION) COLLISIONS... 

A partial wave decomposition provides the frill close-coupling quantal method for treating A-B collisions, electron-atom, electron-ion or atom-molecule collisions. The method [15] is siumnarized here for the inelastic processes... 

Numerical solution of this set of close-coupled equations is feasible only for a limited number of close target states. For each N, several sets of independent solutions F.. of the resulting close-coupled equations are detennined subject to F.. = 0 at r = 0 and to the reactance A-matrix asymptotic boundary conditions,... 

When the initial and final internal states of the system are not well-separated in energy from other states then the closed-coupling calculation converges very slowly. An effective strategy is to add a series of correlation temis involving powers of the distance r. between internal particles of projectile and target to the tmncated close-coupling expansion which already includes the important states. 

The close-coupling equations are also applicable to electron-molecule collision but severe computational difficulties arise due to the large number of rotational and vibrational channels that must be retained in the expansion for the system wavefiinction. In the fixed nuclei approximation, the Bom-Oppenlieimer separation of electronic and nuclear motion pennits electronic motion and scattering amplitudes f, (R) to be detemiined at fixed intemuclear separations R. Then in the adiabatic nuclear approximation the scattering amplitude for ... 

Alternatively, one can use close-coupling methods. These methods are easiest to understand for single arrangement problems (i.e. when both the AB + C and AC + B product arrangements are very high in energy so that only the A + BC reactant arrangement can be accessed). Then one writes... 

The close-coupling approach works readily and simply if the reaction is purely melastic . The method can also be made to work very simply for a single product arrangement (as in collinear reactions), by using a twisted coordinate system, most conveniently reaction path coordinates [37, 38 and 39] as shown in figure B3.4.3. 

Mowrey R C and Kouri D J 1987 Application of the close coupling wave packet method to long lived resonance states in molecule-surface scattering J. Chem. Phys. 86 6140... 

Enough space must be available to properly service the flow meter and to install any straight lengths of upstream and downstream pipe recommended by the manufacturer for use with the meter. Close-coupled fittings such as elbows or reducers tend to distort the velocity profile and can cause errors in a manner similar to those introduced by laminar flow. The amount of straight pipe required depends on the flow meter type. For the typical case of an orifice plate, piping requirements are normally Hsted in terms of the P or orifice/pipe bore ratio as shown in Table 1 (1) (see Piping systems). 

The proper installation of both orifice plates and Venturi-type flow tubes requires a length of straight pipe upstream and downstream of the sensor, ie, a meter mn. The pressure taps and connections for the differential pressure transmitter should be located so as to prevent the accumulation of vapor when measuring a Hquid and the accumulation of Hquid when measuring a vapor. For example, for a Hquid flow measurement in a horizontal pipe, the taps are located in the horizontal plane so that the differential pressure transmitter is either close-coupled or connected through downward sloping connections to allow any trapped vapor to escape. For a vapor measurement in a horizontal pipe, the taps should be located on the top of the pipe and have upward sloping connections to allow trapped Hquid to drain. 

Close-Coupled Pumps (Fig. 10-38) Pumps equipped with a built-in electric motor or sometimes steam-turbine-driven (i.e., with pump impeller and driver on the same shaft) are known as close-coupled pumps. Such units are extremely compact and are suitable for a variety of services for which standard iron and bronze materials are satisfactory. They are available in capacities up to about 450 mVh (2000 gal/min) for heads up to about 73 m (240 ft). Two-stage units in the smaller sizes are available for heads to around 150 m (500 ft). 

Ball mills or tube mills can be operated in closed circuit with external air classifiers with or without air sweeping being employed. If air sweeping is employed, a cyclone separator may Be placed between mill and classifier. (The principles of size reduction combined with size classification are discussea under Characteristics of Size Classifiers. ) Likewise other types of grinding mill can be operated in closed circmt with external size classifiers (Fig. 20-12), as will be described at appropriate places on succeeding pages. However, many types of grinders are air-swept and are so closely coupled with their classifiers mat the latter are termed internal classifiers. 

Surface combustion devices are designed for fully premixing the gaseous fuel and air and burning it on a porous radiant surface. The close coupling of the combustion process with the burner surface results in low flame temperatures and, consequently, low NO formation. Surface materials can include ceramic fibers, reticulated ceramics, and metal alloy mats. This approach allows the burner shape to be customized to match the heat transfer profile with the application. 

The power turbine is free (i.e., the power turbine is not physically coupled to the gas generator but is closely coupled to the gas generator by a transition duct that transports the gas From the gas generator to the power turbine). The power turbine is an industrial-type turbine in design characterized by heavy wall casings, hydrodynamic (tilting... 

Install flame arresters on atmospheric vents to prevent fire on the outside of the tank from propagating back into the vapor space inside the tank. Provide fire resistant insulation for critical vessels, piping, outlet valves on tanks, valve actuators, instruments lines, and key electrical facilities. Provide remote controlled, automatic, and fire-actuated valves to stop loss of tank contents during an emergency provide fire protection to these valves. Valves should be close-coupled to the tank, and must be resistant to corrosion or other deleterious effects of spilled fluids. Vessels should be provided with overpressure relief protection. 

In this group, the impeller or impellers are mounted on the extreme end of the shaft in a cantilevered condition hanging from the support bearings. This group of pumps is also subdivided into a class known as motor-pumps or close-coupled pumps where the impeller is directly mounted onto the motor shaft and supported by the motor s bearings. 

Use a close coupled ell for drawoff from gravity separators to eliminate backup of hydraulic head. 

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