Resonant domain

At the opposite limit yn < ye, sparsely distributed resonant domains scatter the light in all directions of space and the specular reflection becomes negligible. (In the case where y, > ynr, the condition of weak specular reflection becomes r0 < An.) This behavior of the resonant reflection optical response should be observable for real systems as a function of the temperature, ynr(T) being70,127 a rapidly growing function of T see Fig. 4.4. 

Figure 2 The scattering resonance domain of the NEXAFS data. The following experimental spectra are shown as-deposited (20 K), irradiated at 20 K (20 + hv), then warmed at 50 K. The dotted and dashed experimental curves correspond to a subtraction of the experimental data (A dotted line A dashed line) (see text). The calculations of the resonances H2O...HO2, A and A are achieved using different clusters which are drawn below the graph (see text).

The analytic part is the following. In the domain Q of the actions we isolate a non-resonance domain V, characterized by a resonance module M, a real constant a and an integer N, where the following inequality holds true ... 

The conclusion is illustrated in Figure 4 until the orbit remains in the non-resonance domain V it lies in a small neighborhood of the plane of fast drift nx(po)- However, this is not enough to assure the long-time preservation of the actions, because the analytic theory does not assure that the orbit will be confined for a long time in V. The question is what happens if the orbit leaves the non-resonance domain ... 

Figure 4 The local dynamics in a non-resonance domain. The orbit lies in a neighborhood of the plane of fast drift.

According to the definitions given in Poschel (Poschel 1993), the resonant domain associated to a lattice A is a neighborhood of the resonance defined in the following way first we require that the action is suitably close to the resonance through the inequality ... 

C. The truncated normal form approximation. Consider a resonant motion with initial condition in the resonant domain of a lattice A and replace the true solution with... 

In the resonant domain the sensitivity, fi equency and bandwidth depend on the load. With an increasing load resistance the resonant frequency moves from the series resonance to the parallel resonance. The bandwidth or damping of the resonator runs through a maximum if the impedance of load and sensor capacitance exhibit approximately the same values. With additional inductive adjustment a continuous tuning of the resonant behaviour is possible. 

The more conventional, energy domain fonnula for resonance Raman scattering is the expression by Kramers-Heisenberg-Dirac (KHD). The differential cross section for Raman scattering into a solid angle dD can be written in the fomi... 

Equation (A 1.6.94) is called the KHD expression for the polarizability, a. Inspection of the denominators indicates that the first temi is the resonant temi and the second temi is tire non-resonant temi. Note the product of Franck-Condon factors in the numerator one corresponding to the amplitude for excitation and the other to the amplitude for emission. The KHD fonnula is sometimes called the siim-over-states fonnula, since fonnally it requires a sum over all intennediate states j, each intennediate state participating according to how far it is from resonance and the size of the matrix elements that coimect it to the states i. and The KHD fonnula is fiilly equivalent to the time domain fonnula, equation (Al.6.92). and can be derived from the latter in a straightforward way. However, the time domain fonnula can be much more convenient, particularly as one detunes from resonance, since one can exploit the fact that the effective dynamic becomes shorter and shorter as the detuning is increased. 

Remade F and Levine R D 1993 Time domain information from resonant Raman excitation profiles a direct inversion by maximum entropy J. Chem. Phys. 99 4908-25... 

Johnson A E and Myers ABA 1996 A comparison of time- and frequency-domain resonance Raman spectroscopy in triiodide J. Cham. Phys. 104 2497-507... 

Other types of mass spectrometer may use point, array, or both types of collector. The time-of-flight (TOF) instrument uses a special multichannel plate collector an ion trap can record ion arrivals either sequentially in time or all at once a Fourier-transform ion cyclotron resonance (FTICR) instrument can record ion arrivals in either time or frequency domains which are interconvertible (by the Fourier-transform technique). 

Confirmation analysis In most cases, the occurrence of dynamic resonance can be quickly confirmed. When monitoring phase and amplitude, resonance is indicated by a 180° phase shift as the rotor passes through the resonant zone. Figure 44.44 illustrates a dynamic resonance at 500 rpm, which shows a dramatic amplitude increase in the frequency-domain display. This is confirmed by the 180° phase shift in the time-domain plot. Note that the peak at 1200 rpm is not resonance. The absence of a phase shift, coupled with the apparent modulations in the FFT, discount the possibility that this peak is resonance-related. 

More recently, the method of scanning near-field optical microscopy (SNOM) has been applied to LB films of phospholipids and has revealed submicron-domain structures [55-59]. The method involves scanning a fiber-optic tip over a surface in much the same way an AFM tip is scanned over a surface. In principle, other optical experiments could be combined with the SNOM, snch as resonance energy transfer, time-resolved flnorescence, and surface plasmon resonance. It is likely that spectroscopic investigation of snbmicron domains in LB films nsing these principles will be pnrsned extensively. 

The requirement I > 2 can be understood from the symmetry considerations. The case of no restoring force, 1=1, corresponds to a domain translation. Within our picture, this mode corresponds to the tunneling transition itself. The translation of the defects center of mass violates momentum conservation and thus must be accompanied by absorbing a phonon. Such resonant processes couple linearly to the lattice strain and contribute the most to the phonon absorption at the low temperatures, dominated by one-phonon processes. On the other hand, I = 0 corresponds to a uniform dilation of the shell. This mode is formally related to the domain growth at T>Tg and is described by the theory in Xia and Wolynes [ 1 ]. It is thus possible, in principle, to interpret our formalism as a multipole expansion of the interaction of the domain with the rest of the sample. Harmonics with I > 2 correspond to pure shape modulations of the membrane. 

Figure 14. Tunneling to the alternative state at energy can be accompanied by a distortion of the domain boundary and thus populating the ripplon states. All transitions exemplified by solid lines involve tunneling between the intrinsic states and are coupled linearly to the lattice distortion and contribute the strongest to the phonon scattering. The vertical transitions, denoted by the dashed lines, are coupled to the higher order strain (see Appendix A) and contribute only to Rayleigh-type scattering, which is much lower in strength than that due to the resonant transitions.

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