Resonant transmission

Even for the resonant transmission through the Sinai billiard, computations show that many eigenfunctions contribute to the scattering wave function as shown in fig. 1. An assumption of a complex RGF for the scattering function (9) means that the joint probability density has the form... 

Figure 1. The coefficients cn in the expansion (8) for the resonant transmission through the Sinai billiard with numerical sizes 500 x 500, R = 50 with energy e = 10.425. 

Fig. 8.9 (a) Round trip amplitude attenuation factor and (b) OFF resonance transmission of the singly coupled microring as a function of W and R0. Reprinted from Ref. 45 with permission. 2008 Institute of Electrical and Electronics Engineers... 

An MNF/microcylinder sensor exploits WGMs resonances in a cylinder (optical fiber), which are excited by an MNF. The arrangement of an MNF and a cylinder is shown in Fig. 13.li. As opposed to the WGM in a microsphere and microdisk considered in Sect. 13.3.1, the beam launched from the MNF into the cylinder spreads along the cylinder surface and eventually vanishes, even if there is no loss. The theory of resonant transmission of the MNF/microcylinder sensor was developed in Ref. 18. The resonant transmission power of this device can be modeled by a self-interference of a Gaussian beam that made n turns along the cylinder circumference ... 

Fig. 1.1 Dielectric dispersion spectra for a polar solvent with a single Debye relaxation process in the micro-wave region and two resonant transmissions in the IR and UV ranges [5 b].

Fig. 6. Transmission coefficient T(E,Vb) versus electron energy E. The electrode separation is 11.7 A, Vg = 0. The three curves correspond to three different bias voltages V. In each curve, a transmission peak dominates. This peak results from resonance transmission through LUMO-derived molecular levels (RMLs) which are depicted as symbols over the peaks of T(E, Vb). The circles, triangles, and squares correspond to Vb = 0 V, Vb = 0.2 V, and Vb = 0.4 V, respectively. The inset shows the calculated I-V curve from which the metallic behavior of the junction is evident.

As an example, some details of transport features of Au-Cgo-Au molecular tunnel junctions were discussed. The physical mechanism of resonance transmission through the molecule was responsible for most of the transport properties. The resonance is mediated by the LUMO-derived states, and charge transfer plays a very important role. The I-V curves show metallic... 

Assuming that resonance, steric and inductive effects are additive, an inductive polar substituent constant (qj) may be defined by employing standard reactions reasonably assumed to possess no resonance transmission or steric effect. 

Table 1 Attenuation factors, f for Hammett p values transmitted through various groups. All groups except the methylene and ethylene also involve some form of resonance transmission.

Strong contribution Scheme 4 Resonance transmission of charge withdrawal in phenolate ions... 

A small amount of resonance transmission is suffered by meta substituents and is due to the ii-inductive effect where electrostatic charge at a conjugated atom adjacent to the substituent polarises the corresponding 7c-electron system. For our purposes this contribution is taken to be negligible... 

Poor Hammett a correlations are often obtained for reactions in which a positively charged centre is formed that can resonate with an electron donating substituent, because of the additional resonance transmission for these substituents This phenomenon is illustrated by the solvolysis of substituted 2-phenyl-2-chloropropane (Figure 5). Scheme 6 shows how a transition structure may obtain extra stabilisation by resonance interaction between carbenium ion and 4-methoxy and 4-dimethylamino groups. In these cases there is no effect on the energy of the reactant molecules. 

Maximum resonance interaction is likely to occur in the transition structure for the solvolysis reaction of Scheme 6 when the transition structure fully resembles a carbenium ion. In reactions where the transition structure does not completely resemble the reference state the substituent will not exert its full potential in resonance transmission with the reaction centre. The r parameter of Yukawa and Tsuno (Equation 12) provides a measure of the extent of the resonance interaction for a reaction centre which builds up positive charge. 

The Dewar-Grisdale Equation An approach to field and resonance transmission of the polar effect essentially the same as that of Taft s group was suggested by Dewar and Grisdale. The localised and delocalised polar effects are represented by F and M which are taken to be additive in any given a value. The value a,y is related to the sum of... 

Plot the pX of substituted anilines (given in Table 4) against the corresponding Hammett a and a" values. Explain your results in terms of a separation of inductive and resonance transmission of the polar effect. 

The Ojy, values for the substituents are in the series CH3- < CH3O- < H- < Cl- CH3CO- CH3OCO- < NC- < O2N-. Note that these are inductive effects and do not include resonance interactions. A slightly different order would be obtained if Op were used, owing to the possible incursion of resonance transmission effects. 

Provided there is no resonance transmission in the effect of substituents on the dissociation of acetic acids (as would be expected) then the linear equation indicates that the transmission of the effect of the meta substituent does not involve resonance either. The correlation shows that provides a useful secondary definition of Oi. This relationship is a Class II free energy correlation between the dissociation of substituted acetic acids and weZa-substituted benzoic acids. 

The fit (Figures 11 and 12) indicates that there is substantial resonance transmission to the leaving oxygen in the transition structure by substituents in the para position which can withdraw electrons by resonance interaction. This is consistent with a concerted displacement mechanism at the silicon atom. 

Fig. 1.6 Schematic representation of parameters used in calculating resonant transmission for source and absorber of finite thickness.

Figure 1. Transmission spectra of several 8-Iayer QW multilayer structures. One period is depicted. It can be seen that in each plot there are 8 (more or less pronounced) resonance transmission peaks.

R 324 O. N. Antzutkin, Amyloidosis of Alzheimer s Ap Peptides Solid-State Nuclear Magnetic Resonance, Electron Paramagnetic Resonance, Transmission Electron Microscopy, Scanning Transmission Electron Microscopy and Atomic Force Microscopy Studies , Magn. Reson. Chem., 2004, 42,231... 

Fig. 10. A plot of the ratio AJA vs. na PJA for various AjF, Here A is the measured area of the resonance transmission dip in ev (see text of article), A is the Doppler width of the level, F is the level width, n is the sample thickness in atoms/cm, and Cq is the peak total cross section in cm /atom. This extremely useful figure was prepared by the BNL...

Example 1.7 With a resonator transmission T2 = 0.02 (a figure that can be readily realized in practice) the enhancement factor becomes = 50, as long as saturation effects can be neglected and provided the absorption is sufficiently small that it does not noticeably change the laser intensity. 

Band splitting and low S H2O freqnency component attributed to Fami resonance transmission of KBr pellets NaAl(S04)2 12H20(y) ... 

A medium with saturable absorption can also be used for the nonlinear medium. In this case, the resonance condition is always met as far as the wavelength is concerned, but the feedback from the second mirror, which is required for resonant transmission, is not obtained until sufficient light is present inside the cavity to bleach the nonlinear medium. Devices of this type can show differential gain and optical bistability but not optical limiting. 

Chichester, D.L. and Sterbentz, J.W. (2011). A second look at neutron resonance transmission analysis as a spent fuel NDA. Idaho Falls, ID Idaho National Laboratory, INMM 2011 INL/CON-11-20783. 

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