Reciprocal relations analysis

Fourier transform, molecular systems, component amplitude analysis cyclic wave functions, 224-228 reciprocal relations, 216-217 Four-state system loop construction ... 

Cauchy-integral method, 219-220 cyclic wave functions, 224-228 modulus and phase, 214-215 modulus-phase relations, 217-218 near-adiabatic limit, 220-224 reciprocal relations, 215-217, 232-233 wave packets, 228-232 electron nuclear dynamics (END), 337-351 final-state analysis, 342-349 intramolecular electron transfer,... 

Restriction equations, molecular systems, component amplitude analysis, reciprocal relations, 215-217 Robb, Bemardi, and Olivucci (RBO) method, conical intersection location, 489—490 Rotational couplings ... 

Far from thermodynamic equiHbrium we find nonfinear interdependence of thermodynamic fluxes and forces. In this case, the Onsager reciprocal relations are generally not satisfied, and the formafism developed in Chapter 2 is not fuUy applicable for analysis of the state of open systems. Analysis of systems that are far from thermodynamic equilibrium is the subject of nonlinear nonequilibrium thermodynamics. 

Two important conclusions foUow from the analysis of the Horiuti Boreskov Onsager reciprocity relations (4.97) for the rates in different channels of catalytic transformations ... 

Electrophoresis and sedimentation potential also offer a test of predictions of thermodynamics of irreversible processes, provided these are supplemented by classical analysis of the data. Few measurements of sedimentation potential have been reported [1] and the theories due to Kruyt [2], Debye and Huckel [3] and Henry [4] are not in complete agreement. The thermodynamics of irreversible processes [5] may be helpful since the theory does not depend on any model. In the present chapter it is intended (i) to test linear phenomenological relations, (ii) to test the Onsager s reciprocal relation and (iii) to examine the validity of conflicting theories of electrophoresis. 

Compliance, elastic n. Symbol S. An elastic constant, which is the ratio of a strain or strain component to a stress or stress component. For a perfectly elastic material it is the reciprocal of the elastic modulus. For a viscoelastic material the modulus and compliance are not reciprocally related due to their different time dependencies. Sepe MP (1998) Dynamic mechanical analysis. Plastics Design Library, Norwich, New York. 

The validity of the reciprocal relations was shown by Yablonsky et al. (201 lb) using the technique of Temporal Analysis of Products (TAP) developed by Cleaves in 1988 (Cleaves et al., 1988 see Chapter 5). The reactor used was a so-called thin-zone TAP reactor (TZTR), in... 

Moyne C, Murad MA (2006) A two-scale model for coupled electro-chemo-mechanical phenomena and Onsager s reciprocity relations in expansive clays I homogenization analysis. Transp Porous Media 62 333-380... 

The observation of images of composites may lead to qualitative conclusions only, but it does mean that the existence of certain objects and their reciprocal relations may be confirmed. The quantitative data and their analysis is necessary for rational design of composite materials and for effective determination of the relation between the materials structures and properties. Computer image analysis has been developed over the last 20 years to enable quantitative analysis on the basis of images of any kind. Using a basically similar approach to an image as in manual or semi-automatic methods, the fully automatic approach offers much greater possibilities of quantitative determination of various parameters that characterize the structures of the materials. 

Assume that the entropy production function two times continuously differentiable function with respect to fluxes. Then from the previous first equations and the Young-theorem of the analysis we get the generalized reciprocal relations... 

It is important to understand how the over-pressure can develop (source) and what might be the eventual results. The mere sohdng of a formula to obtain an orifice area is secondary to an analysis and understanding of the pressure system. Excess pressure can develop from explosion, chemical reaction, reciprocating pumps or compressors, external fire around equipment, and an endless list of related and unrelated situations. In addition to the... 

EveretP discusses pulsation associated with reciprocating compression and presents several points of analysis and diagrams primarily related to the pipe vibration. 

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