Extended phase shift

The use of optical Hthography for submicrometer resolutions has been extended by developments such as phase-shift Hthography (35). A... 

A much simpler and more flexible approach, however, extends the scheme of pulsed magnetic field gradients discussed above to include more complex time dependences. To see how this can be done, we write down the general dependence of the phase shift accumulated at time t subject to a space-dependent Larmor frequency ... 

Here t is the resulting shear stress, 6 is the phase shift often represented as tan(d), and (O is the frequency. The term 6 is often referred to as the loss angle. The in-phase elastic portion of the stress is To(cosd)sin(wt), and the out-of-phase viscous portion of the stress is To(sind)cos(complex modulus and viscosity, which can be used to extend the range of the data using the cone and plate rheometer [6] ... 

Because the initial emphasis of this study was on extending ACC to liquid-fueled combustors, a simple closed-loop controller, which had been well tested in the previous studies involving gaseous fuel, was utilized. Such a controller, however, may not be effective in a combustor where the oscillation frequencies drift significantly with the control. The main problem was the frequency-dependent phase shift associated with the frequency filter. For such a case, it would be more useful to employ an adaptive controller that can rapidly modify the phase setting depending on the shift in the dominant oscillation frequencies. 

At small concentrations of Pd there will be a conduction-band resonance at each transitional-metal atom, and the resistance depends on the phase shifts. For Ag-Pd the resonance only just extends over the Fermi energy, giving very small residual resistance and specific-heat enhancement for Cu-Ni they are much larger. 

The density of states so defined can be shown to be connected to the time delay that an electron experiences when scattering off the parent ion. The connection between time delay and energy derivative of the phase shift in the single channel case was first discussed by Eisenbud and Wigner [71,72], and later generalized and extended, with the concept of "dwell time," to the multichannel case by Smith [73]. Smith introduced a time-delay matrix Q, defined as... 

There is no need for a phase shift parameter if the deviation from orthogonality is modeled by a ligand-ligand repulsive term (see below). A similar approach is the use of a multiple harmonic functiont52] and this has the advantage that it can easily be extended to other geometries such as trigonal bipyramids. 

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