Diagram technique

At the end of Section 8.16 we mentioned that the Fock representation avoids the use of multiple integrations of coordinate space when dealing with the many-body problem. We can see here, however, that the new method runs into complications of its own To handle the immense bookkeeping problems involved in the multiple -integrals and the ordered products of creation and annihilation operators, special diagram techniques have been developed. These are discussed in Chapter 11, Quantum Electrodynamics. The reader who wishes to study further the many applications of these techniques to problems of quantum statistics will find an ample list of references in a review article by D. ter Haar, Reports on Progress in Physics, 24,1961, Inst, of Phys. and Phys. Soc. (London). 

To make this point clear, one has to look at the involved effects using diagram techniques. Self-energy effects, that is the deformation of the electron cloud around a single electron which then reacts back on this electron, can be divided into two... 

Bruggemann, R., J. Schwaiger, and R.D. Negele. 1995. Applying Hasse diagram technique for the evaluation of toxicological fish tests. Chemosphere 30 1767-1780. 

Indeed, we have discussed the matrix elements involved in these formulas (see Eqs. (36), (52), and (56)) as well as the physical meaning of the Fourier coefficients pk p] t). However, the mathematical expressions are often rather involved and it is convenient, especially in specific applications, to introduce a diagram technique in order to represent the various terms of these general formulas.28 We first notice that in Eqs. (41) and (42), the momenta p,- essentially appear as parameters indeed, according to Eq. (52) only the wave-vectors are explicitly modified by the interactions. This is the reason why we shall only represent these wave numbers graphically it should, however, be kept in mind that the momenta are effectively affected by the interactions through the differential operators d/dp ... 

We shall not dwell upon this diagram technique any further and we refer the interested reader to the references above quoted. Applications will be found in the following sections. 

We first select the class of terms which behave like Eq. (159). For this purpose, it is very convenient to use the diagram technique of Section II. 

In order to classify these terms we could use the diagram technique introduced by Fujita.22 However, since we are interested in the case of a high field H0 and since in that case there are no intermediate states conserving energy, we may simply take the square of the S matrix and obtain for the transition probabilities the expression... 

Acronym for Critical Path Method. A network diagramming technique that places emphasis on time, cost, and the completion of events. 

MSN.25.1. Prigogine and R. Balescu, Irreversible processes in gases, I The diagram technique, Physica 25, 281-301 (1959). 

Impedance diagram technique. The polarization cell consisted in a transparent plastic tube that was adhered to the paint surface by means of a silicone sealer. The tube contained distilled water and a 25 cm platinized titanium sheet, which was used as auxiliary electrode. Measurements were made with... 

The flow diagram technique can also be used to illustrate clearly the rather limited effects on autocatalytic systems which arise from the reversibility of chemical reactions. For this we replace step (6.8) by its reversible counterpart... 

The flow diagram technique works very well for this adiabatic case. This is because, as noted above, the reaction curve R does not vary with the residence time, whereas the gradient of the flow line L does. The condition for an ignition or an extinction point is that R and L should become tangential, as shown in Fig. 7.3. We should simultaneously satisfy... 

Graph theory provided various fields of physical chemistry and chemical physics with a technique that has been extensively used in theoretical physics (the well-known Feynman diagram technique). It also appeared to be extremely effective in both chemical kinetics and chemical polymer physics. The major advantage of this technique is the extremely simple derivation of equations and the possibility of their direct physical interpretation. 

G. E. Stedman, Diagram Techniques in Group Theory, Cambridge University Press, Cambridge, 1990. 

For multicomponent systems, the expression for y here employed may be shown equivalent to that involved in the cluster diagram technique (6), which is currently being employed in a variety of problems. The present derivation shows that the starting expressions satisfy the thermodynamic consistency relation embodied by the adsorption isotherm. It is, however, important to observe that any direct application of these alternative rigorous approaches, which is of necessity of an approximate nature, leads to some violation of the complete internal equilibrium conditions. Similarly, calculations of surface tension which employ the adsorption equation as a starting point invariably violate mechanical equilibrium in some order of approximation. 

Predictions can be made about the suitability of different system trajectories on the basis of orbital symmetry conservation rules (207). The most suitable trajectory is an approximation to the reaction path of the reaction under study. The rules can also yield information about the possible structure of the activated complex. The correlation diagram technique has been improved in a series of books by Epiotis et al. (214-216). The method is based on self-consistent field-configuration interaction or valence bond (SCF-CI or VB) (including ionic structures) wave functions. Applications on reactions in the ground states as well as in the excited electronic states are impressive however, the price to be paid for the predictions seems to be rather high. 

Use a Cause Effect Diagram (Technique 53) to document all the important causal relationships in the system. Then prioritize these relationships using a Cause Effect Matrix (Technique 54). These then become the initial focus of an attempt to trim the system using a trimming worksheet. 

Use a Cause Effect Diagram (Technique 53) to determine the root cause for each potential error. This is a critical step in mistake proofing that is often missed because too many people confuse errors with defects. For example, motion sensor failure is a defect motion sensor zone set incorrectly is an error. You can only truly solve a problem at the error level, so make sure you understand the difference. 

Scenario In the DVD-by-mail example from the Cause Effect Diagram (Technique 53), we looked for the root causes (inputs) contributing to customer dissatisfaction. We can also use a Cause Effect Matrix to discover... 

You can gather this information from your Process Map or Value Stream Map (Technique 46), or even a Cause Effect Diagram (Technique 53). 

The spider diagram technique (p. 326) is a speedy way of doing this. If you have time to read several sources, consider their content in relation to the essay title. Can you spot different approaches to the same subject Which do you prefer as a means of treating the topic in relation to your title Which examples are most relevant to your case, and why ... 

Keldysh, L.V. (1965) Diagram Technique for Nonequilihrium Processes. Sov. Phys. Jetp-USSR 20, 1018-1026. 

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