Equal-time structure factor

In equation (4.51) of Chapter 4, the equal time structure factor, C (x), was defined. For light scattered from fluctuations in the dielectric properties of a material, it was shown that the light intensity was proportional to this quantity. In the problem of total intensity light scattering discussed in that chapter, the measurement is integrated over time and time-dependent fluctuations are not directly observed. When time-dependent fluctuations are... 

Finally, a quench into the one-phase region of the microemulsion has been investigated. An analysis based on a Ginzburg-Landau model for a single, conserved order parameter predicts [160] that the equal-time structure factor, Eq. (65), approaches its equilibrium form S(k) algebraically for long times t. 

The equal-time structure factor S(k, t) at the time t after the quench is... 

Toik) = 5c-k(0)5ck 0))-j- = Sc-kSck)To simply the equal-time structure factor in thermal equilibrium at temperature Tq before the quench. Note that A k) is positive for 0 < < k, with... 

The simplest case of comb polymer is the H-shaped structure in which two side arms of equal length are grafted onto each end of a linear cross-bar [6]. In this case the backbones may reptate, but the reptation time is proportional to the square of Mj, rather than the cube, because the drag is dominated by the dumb-bell-like frictional branch points at the chain ends [45,46]. In this case the dependence on is not a signature of Rouse motion - the relaxation spectrum itself exhibits a characteristic reptation form. The dynamic structure factor would also point to entangled rather than free motion. 

Because the diffraction experiment involves the average of a very large number of unit cells (of the order of 10 in a crystal used for X-ray diffraction analysis), minor static displacements of atoms closely simulate the effects of vibrations on the scattering power of the average atom. In addition, if an atom moves from one disordered position to another, it will be frozen in time during the X-ray diffraction experiment. This means that atomic motion and spatial disorder are difficult to separate from each other by simple experimental measurements of intensity falloff as a function of sm6/X. For this reason, atomic displacement parameter is considered a more suitable term than the terms that have been used historically, such as temperature factor, thermal parameter, or vibration parameter for each of the correction factors included in the structure factor equation. A displacement parameter may be isotropic (with equal displacements in all directions) or anisotropic (with different values in different directions in the crystal). 

Physical observables that can be measured in both the path-integral representation and the SSE representation include, next to the energy and the specific heat, any expectation value or correlation function that is diagonal in the basis set i). This includes the uniform or staggered magnetization in the z direction, the equal time correlation functions and structure factor of the... 

Product yield is very often a factor that limits the development of a natural product as a lead compound. Traditionally, both chemical synthesis and classical strain improvement technologies have been applied to overcome this limitation. As natural products are often molecules of high structural and stereochemical complexity, their total synthesis is usually difficult, and yields are low. Classical strain improvement represents an equally time-consuming and rather undirected process, during which numerous rounds of mutagenesis and subsequent screening are applied to obtain strains with improved production titers. 

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