Reciprocity principle

When comparing (5.106) with (5.105), it becomes evident that these expressions coincide to make the interchange xo . This fact demonstrates the so-called reciprocity principle In any linear system, some effect does not vary if the source (at position x = xo) and the observation point (x = ) will be interchanged. The linearity of our system is represented by the linearity of the Fokker-Planck equation (5.72). 

Incorrect conclusion 1 above is sometimes said to derive from the reciprocity principle, which states that light waves in any optical system all could be reversed in direction without altering any paths or intensities and remain consistent with physical reality (because Maxwell s equations are invariant under time reversal). Applying this principle here, one notes that an evanescent wave set up by a supercritical ray undergoing total internal reflection can excite a dipole with a power that decays exponentially with z. Then (by the reciprocity principle) an excited dipole should lead to a supercritical emitted beam intensity that also decays exponentially with z. Although this prediction would be true if the fluorophore were a fixed-amplitude dipole in both cases, it cannot be modeled as such in the latter case. 

In the bare glass case, note that the decay is not exponential, as otherwise would be expected if the reciprocity principle had been misapplied here. Nevertheless, by viewing only supercritical angles, one can selectively observe only those fluorophores within several hundred nanometers of the surface, even if the excitation (rather than the emission) is not surface-selective at all. 

FIG. 7. The importance of the tip state is highlighted by applying the reciprocity principle to imaging a free electron metal surface with a d/ tip. (From Ref. 39.)... 

THL.3. 1. Prigogine, Remarque sur le principe de reciprocite d Onsager et le couplage des reactions chimiques (Remarks on Onsager s reciprocity principle and the coupling of chemical reactions). Bull. Cl. Set Acad. Roy. Belg. 32, 30-35 (1946). 

The effect of p,- or dangling bonds on STM resolution can be understood in the light of the reciprocity principle (Chen, 1988), which is the fundamental microscopic symmetry between the tip and the sample By... 

Fig. 1.30. Origin of atomic resolution on metal surfaces. According to the reciprocity principle, the image taken with a d,- tip state (which exists on a W tip) on a free-electron-metal surface is equivalent to an image taken with a point tip on a fictitious sample surface with a d state on each top-layer atom, which obviously has a strong corrugation. (Reproduced from Chen, 1990, with permission.)...

As we have discussed in Chapter 2, a direct consequence of the Bardeen tunneling theory (or the extension of it) is the reciprocity principle If the electronic state of the tip and the sample state under observation are interchanged, the image should be the same. An alternative wording of the same... 

Naturally, we observed the reciprocity principle. By interchanging the tip state and the sample state, the conductance distribution, and consequently, the apparent radius of the image, are unchanged. 

See Lead zirconate titanate ceramics Quality number 219 Quantum transmission 59 Reciprocal space 123, 353 Reciprocity principle 88 Reconstruction 14, 327 Au(lll) 327 DAS model 16 Si(lll)-2X1 14 Recursion relations 352 Repulsive atomic force 185, 192 Resonance frequency 234, 241 piezoelectric scanners 234 vibration isolation system 241 Resonance interactions 171, 177 and tunneling 177 Resonance theory of the chemical bond 172... 

In order to generally categorize the reaction schemes mentioned previously and the following ones in the course of indirect enantioseparation techniques, it has to be emphasized again, that the reciprocity principle should always be applicable. This means that if a chiral acid as the CDA can be used successfully to resolve the enantiomers of a chiral amine, then this optically pure amine as the CDA will equally well separate the enantiomers of the acid by the indirect method. The OPA reaction (see Figure 4) is therefore equally well suited for analyzing the optical purity of thiols, amines or amino acids. 

Saunders, D. and Kirby, J. (1996) light-induced damage investigating the reciprocity principle. Preprints of the 11th Triennial Meeting of the International Committee for Conservation ICOM-CC, Edinburgh, Vol. 1, pp. 87-90. 

We can give a simple, but important physical interpretation of the expressions for sensitivities, (9.55), based on the reciprocity principle. Note that, according to definition (see Chapter 8), the Green s tensors (r r") and Gh (r r"), are the electric and magnetic fields at the receiver point, r, due to a unit electric dipole source at the point r" of the conductivity perturbation. Let us introduce a Cartesian system of coordinates x,y,z, and rewrite these tensors in matrix form ... 

We can reduce significantly the number of the required iterations using the reciprocity principle (Madden, 1972 Rodi, 1976 Madden and Mackie, 1989 McGillivray and Oldenburg, 1990 de Lugao and Wannamaker, 1996 and de Lugao et ah, 1997) for Frechet derivative calculations. Due to reciprocity, the field is equal to the... 

The reciprocity principle plays an important role in the theory of wavefield propagation and in the inversion of wavefield data. It is based on an application of the integral formula (14.17) to two Green s functions, G (r" r ti ) and G " (r lriw), satisfying the... 

To date, BWFs have been developed for a variety of aquatic organisms ranging from marine phytoplankton [89-91], to marine copepods and fish [92,93], freshwater copepods [94], and freshwater cladocerans [95]. The application of BWFs is dependent upon the reciprocity principle, which states that the effect of a given dose is independent of the rate at which the dose is administered [89,96]. In essence, the reciprocity principle is not valid if a high dose rate administered over a short period of time gives a different response than a low dose rate of the same total dose administered over a longer time period. 

According to Onsager s reciprocity principle, for the steady-state condition of very small volume elements and close to equilibrium, we can write for the inverse-indexed phenomenological coefficients... 

The directional/hemispherical reflectance is the fraction of flux incident within a small solid angle about the direction 6 that is reflected into the hemisphere above the surface and will be denoted by the symbol p. By the Helmholtz reciprocity principle (9,10), a measurement in the InfO geometry will yield the same reflectance value. In practice, actual measurement geometries only approximate the ideal geometry due to the presence of ports and other factors. The directional/hemispherical reflectance is composed of a diffuse and a specular or regular component. 

A mathematical model for the scattering indicatrix that meets the normalizing condition over final velocities and satisfies reciprocality principle has been proposed by Cercignani (Cercignani 1975). It contains accommodation coefficients of taingen-tial momentum (ar) aird normal energy (a ) and has the form... 

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