Correlation diagrammatical representations

As mentioned in Section 3.1, the incoherent dynamic structure is easily calculated by inserting the expression for the mean square displacements [Eqs. (42), (43)] into Eq. (4b). On the other hand, for reptational motion, calculation of the pair-correlation function is rather difficult. We must bear in mind the problem on the basis of Fig. 19, presenting a diagrammatic representation of the reptation process during various characteristic time intervals. 

Andersen, H. C. Diagrammatic Formulation of the Kinetic Theory of Fluctuations in Equilibrium Classical Fluids. III. Cluster Analysis of the Renormalized Interactions and a Second Diagrammatic Representation of the Correlation Functions. J. Phys. Chem. B 2003, 107, 10234-10242. 

Figure 3. A diagrammatic representation of the cumulant decomposition ([IV, A2]p 2)) for the three-particle operator drawn in Fig. 2. Four kinds of one- and two-particle operators are obtained. The double line is the contraction for the particle-rank reduction (closure), where the correlation is averaged with the effective field (i.e., density matrices).

Figure 9.7. Diagrammatic representation of the fibrinogen molecule and its conversion to the soft clot of fibrin. Reproduced (in modified form) by permission from Textbook of Biochemistry with Clinical Correlations (3rd Ed.) Devlin (1992). This material is used by permission of John Wiley Sons, Inc.

The organization of this chapter is as follows. In Sect. 5.1 we present the basic formalism and work out the Feynman rules for the grand canonical ensemble. Diagrammatic representations valid in the thermodynamic limit are derived for both thermodjmamic quantities and correlation functions. The proof of the Linked Cluster Theorem is given in Appendix A 5.1. Section 5.2... 

We finally need the diagrammatic representation of the correlation functions. As shown in Appendix A 52, as a simple consequence of the general Linked Cluster Theorem all correlation functions or cnmulants defined here... 

Figure 4 Diagrammatic representation of the relaxation and correlation energy corrections needed in deriving accurate IE from Koopmans estimates...

For the purposes of the forthcoming discussion of correlation contributions through, it is profitable to introduce the diagrammatical representation. Let us start with the second and third order contribu-... 

In spite of its value, this method will not be used much in what follows. We shall prefer more expressive diagrammatic representations. In particular, we shall encounter again the correlation < (r) in Chapter 13, when dealing... 

Fig. 7,3. Diagrammatic representation the collision process contributing to the repeated ring operator Each vertex represents an elastic collision between A and S the propagation between these correlating collisions is given by sequences of uncorrelated collisions of A with S and S with S.

Figure 5.15 Diagrammatic representation of HNCA FT 3D NMR correlation experiment involving multiple 90° and 180° pulses with signal observation and acquisition in time domain prior to fourier series transformation of time domain signal information SFiD(ti, t2, ts) into frequency domain (spectral intensity) information, Jnmr (fi, F2, fa).

Figure 5.16 Diagrammatic representation of presentation of data from FT 3D NMR correlation experiments. In this representation, frequency domain (spectral) information, Jnmr (fi, p2, F ) is plotted as a stack or cube of 2D NMR Jnmr(F i, fa) contour plots, each plot resolved at a different value of fa- Frequency resolution is done to aid resolution of individual resonance signals in order to achieve unique and unambiguous assignment of resonance signals to resonating nuclei.

In Eq. (85), B,j(r) is the sum of the so-called bridge graphs. The diagrammatic representations and the interrelations of the correlation functions can be found in textbooks on liquid-state chemical physics. 

DIAGRAMMATIC REPRESENTATION OF THE PERTURBATION EXPANSION OF THE CORRELATION ENERGY... 

Fig. 12.4. Diagrammatic representation of the third-order contribution of the correlation energy (cf. Problem 12.2.)...

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