Expansion cycles, periodic

Reciprocating expanders, in normal operation, should not accept liquid in any form during the expansion cycle. However, the reciprocating device can tolerate some liquid for short periods of time provided that none of the constituents freeze out in the expander cylinder and cause serious mechanical problems. If selected design conditions indicate possibilities of entering the liquid and especially the triple point range on expansion during normal operation, then inlet pressure and temper-... 

In a second technique, a freshly swept surface of a dilute surfactant solution is subjected to periodic compression-expansion cycles. With the... 

Vacuum pump capacity is conventionally based on the total cycle and expressed as mVh-m" (cfi7i/ft ) of filter area measured at pump inlet conditions. Thus, the gas volumes per unit area passing during each dry period in the cycle are totaled and divided by the cycle time to arrive at the design air rate. Since air rate measurements in the test program are based on pressure drop across the cake and filter medium only, allowance must be made For additional expansion due to pressure drop within the filter and auxiliary piping system in arriving at vacuum pump inlet conditions. 

Some manufacturers of this type of boiler claim that water treatment of any kind is not necessary and that no chemicals are required, especially with smaller units below, say, 240 kWh (800 lb/hr). Instead they rely on the on-off expansion-contraction cycles within the vessel to drop scale from the heating elements, or on a daily manual flush of the boiler vessel together with frequent replacement of elements and periodic acid cleaning. (Some improved design models thankfully have an automatic flush system that is actuated upon boiler shutdown.)... 

The amphiphilic material to be studied is dissolved at a known concentration in a volatile solvent which is not miscible with water and a known quantity is spread at the water surface using a micropipette. In order to study the physical properties of the film thus formed, one needs to be able to confine the film to a definite area and to be able to vary this area at will. It might appear that it would be equally possible to maintain a constant area and vary the amount of material which is spread. For the majority of materials this latter procedure is not satisfactory as equilibrium is not arrived at in a reasonable period of time and this method would not allow one to take the material through successive cycles of compression and expansion. We thus turn to a discussion of the various ways in which a film can be confined and its area varied in a systematic manner. Leaving aside methods which are really only of historical interest, for which reference should be made to the book by... 

The second test, developed by the Society of the Plastics Industry, involved preparing an amount of bacon that covered at least 50% of the dinner plate surface area [2], The plate with the bacon layer was heated in a microwave oven set at full power until the temperature at the center of the plate area reached 121°C ( 5°C). The time period required to reach this temperature within the bacon fat was 5 min on the microwave unit used for this test Immediately after the cooking cycle, the plate was cleaned on the lower rack of an automatic dishwasher. The dishwasher cycle was set at normal and included a heated dry cycle. The water temperature reached 66°C ( 5°C). Once the cycle was complete, the plate was inspected for surface blemishes such as cracks or blisters. This test is considered the most severe of the three due to the extreme localized heat generated, which causes the difference between the thermal coefficient of expansion for the two materials to shear the interface resulting in delamination. 

The active phase of the Deacon catalyst is usually assumed to be a complex melt of copper or chromium and alkaline metal chlorides under reaction conditions, which is distributed within the pore network of an inert carrier [42]. Such supported liquid-phase catalysts (SLPC) are eminently suitable for adsorbing large amounts of the reacting components as sorption takes place in a bulk phase and is not restricted to only a limited number of suitable surface sites. The periodic expansion and contraction of the melt as a result of (de) sorption imposes considerable strains on the carrier structure hence, special mechanically robust support materials are needed to withstand such strains and prevent the catalyst crumbling away and disintegrating after a few cycles. In addition, even when it is immobilized on the carrier, the melt is extremely aggressive and resistant materials must be used for reactor construction. 

The word cyclic requires that the system be restored periodically to its original state. In the case of a gas in a piston-and-cylinder assembly the expansion and compression back to the original state constitute a complete cycle. If the process... 

For classically chaotic quantum systems the forward application of the trace formula is difiicult because of the following reasons, (i) In a chaotic system the number of periodic orbits proliferates exponentially (ii) the orbits have to be computed numerically and (iii) there are convergence problems with (4.1.72) that have to be circumvented with appropriate resummation prescriptions such as, e.g., cycle expansions (Cvitanovic and Eckhardt (1989), Artuso et al. (1990a,b)). Nevertheless, sometimes valuable information on the structure of atomic states can be obtained by retaining only the shortest orbits in the expansion (4.1.72). This was... 

The most recent advance in the theory of the helium atom was the discovery of its classically chaotic nature. In connection with modern semiclassical techniques, such as Gutzwiller s periodic orbit theory and cycle expansion techniques, it was possible to obtain substantial new insight into the structure of doubly excited states of two-electron atoms and ions. This new direction in the application of chaos in atomic physics was initiated by Ezra et al. (1991), Kim and Ezra (1991), Richter (1991), and Bliimel and Reinhardt (1992). The discussion of the manifestations of chaos in the helium atom is the focus of this chapter. 

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