Ghosts

I he calculation of the energy of the individual species A is performed in the presence ol ghost orbitals of B that is, without the nuclei or electrons of B. A similar calculation is... 

The excess chemiccil potential is thus determined from the average of exp[—lT (r )/fe In ensembles other than the canonical ensemble the expressions for the excess chem potential are slightly different. The ghost particle does not remain in the system and the system is unaffected by the procedure. To achieve statistically significant results m Widom insertion moves may be required. However, practical difficulties are encounte when applying the Widom insertion method to dense fluids and/or to systems contain molecules, because the proportion of insertions that give rise to low values of y f, dramatically. This is because it is difficult to find a hole of the appropriate size and sha... 

The concept of ghost-atoms only applies to Single Point calculations in the current version of HyperChem. 

Figure 5.17 Rotational Raman spectrum of N2 (the lines marked with a cross are grating ghosts and not part of the spectrum)...

Figure 6,4 Small pits on a 316 stainless steel plate. A light pita, marking ghost images of deposit mounds.

In addition to primary features from copper in Eig. 2.7 are small photoelectron peaks at 955 and 1204 eV kinetic energies, arising from the oxygen and carbon Is levels, respectively, because of the presence of some contamination on the surface. Secondary features are X-ray satellite and ghost lines, surface and bulk plasmon energy loss features, shake-up lines, multiplet splitting, shake-off lines, and asymmetries because of asymmetric core levels [2.6]. 

There are variations of this method. For example may it be argued that the full set of ghost orbitals should not be used, since some of the functions in the complex are used for describing the electrons of the other component, and only the virtual orbitals are available for artificial stabilization. However, it appears that the method of full counterpoise corection (using all basis functions as ghost orbitals) gives the best results. Note that A cp is an approximate correction, it gives an estimate of the BSSE effect, but it does not provide either an upper or lower limit. 

Gespenstf n. specter, ghost, phantom. Gesperr(e), n. locking device, catch, ratchet, gespieen, p.p. (of speien) spat vomited. Gespinst, n. spun yarn spun goods thread (textile) fabric web cocoon, -faser, /. textile fiber, -pflanze,/. textile plant fiber plant. 

Ghosts are caused when two or more frequency components couple, or merge, to form another discrete frequency component in the vibration signature. This generally occurs with multiple-speed machines or a group of single-speed machines. 

Note that the presence of modulation, or ghost peaks, is not an absolute indication of a problem within the machine-train. Couple effects may simply increase the amplitude of the fundamental mnning speed and do little damage to the machine-train. However, this increased amplitude will amplify any defects within the machine-train. 

Sum This type of modulation, which is described in the example above, generates a series of frequencies that include the fundamental shaft speeds, both input and output, and fundamental gear-mesh profile. The only difference between the real frequencies and the ghost is their location on the frequency scale. Instead of being at the actual shaft-speed frequency, the ghost appears at frequencies equal to the sum of the input and output shaft speeds. Figure 44.40 illustrates this for a speed-increaser gearbox. 

Beware that this type of coupling often may go undetected in a normal vibration analysis. Since the ghost frequencies are relatively high compared to the expected real frequencies, they are often outside the monitored frequency range used for data acquisition and analysis. 

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