Weak modulation

Extended energy-loss fine structures (EXELES) are analogous to the EXAES effect observed in X-ray absorption [2.224, 2.225]. These weak modulations (cf Eig. 2.39a), still observable ca. 100 eV away from the edge onset, occur because the excited elec-... 

Since the surface atoms are likely to be relatively strong backscatterers the extended fine structure will be dominated by the scattering from the substrate. This relatively weak modulation at higher energy is referred to as the surface EXAFS, or SEXAFS. An analysis of the SEXAFS can give further structural information, most valuably, on the adsorption site (for further details, see Ref. [2]). 

Figure 3 shows the transmittance function for molecular chains with various lengths using the same parameters as in Fig. 2. The functions are shifted for better visibility. For n — 2, it is a Lorentzian as suggested by the exact result (equation (40)). With growing chain length, the transmittance function shows weak modulations within the band, and drops sharply outside of the band. We also show the exact result obtained in the limit of infinite chain length (equation (41)).

A possibility to achieve negative (positive) A5 by its minimization (maximization) even for weak modulation (i.e., for small E) is to adapt the temperature of the bath such that for an undriven system Hamiltonian Hq, no change is observed, A5 = 0, which is a necessary condition for a system-bath equilibrium. This would require nonunitary system modulation, for example, the effect of repeated measurements [92-94],... 

As it follows from the method of derivation of expressions (59) and (60), they are valid, strictly speaking, only if 1. This condition is satisfied not only in the trivial case of 1 (that is, for weakly modulated illumination intensity), but also for 2 1 if d is sufficiently small, i.e., in a rather important case of high spatial frequencies d1. From the physical point of view, this is related to the fact that for high d 1 values the spreading of nonequilibrium holes is so large that their spatial modulation becomes quite weak. 

For either of these techniques, the period of the modulation should be of the order of the lifetime. If the period chosen is too small, the fluorescent emissions are weakly modulated. On the other hand, if they are too long, the phase shift may become too small to measure with accuracy.. ... 

Xr is the readout wavelength and s the sample thickness. Q < 1 indicates thin, Q > 1 thick grating conditions,which are prevalent in the present case with Q 5. An extensive treatment of the diffraction theory of phase gratings has been given by Kogelnik [48]. All experiments discussed here have been conducted within the weak modulation depth limit, where the heterodyne or electric field diffraction efficiency Chet(t) is simply proportional to the refractive index modulation depth ... 

Adey, W. R. Bawin, S. M. Lin-Liu, S. Increased calcium efflux from cerebral tissue exposed to weak modulated microwave fields. Physiological Society, London, July 1980. Proceedings, 23P. 

Although originally mainly the more pronounced near-edge features were observed and compared or interpreted (usually empirically), it is evident from a recent review (18) that today considerably greater emphasis is given to the study of the extended fine structure. This stands in relation to the improved experimental methods for detection of weak modulations and to the currently more advanced theoretical description of the EXAFS part of the spectrum. Complete understanding of the Kossel structure at the threshold part of an element s inner-shell spectrum, which contains among others valence orbital, ionization, and chemical shift information, is relatively slow due to the... 

Figure 20 shows how flow changes the signal when a thin slice of excited spins is moving through the detecting coil. The frequency of the weak modulation is determined by the product of the first moment of Siq) and the flow velocity. 

A Bose or Fermi gas weakly modulated by the lattice potential yields... 

Fig. 2. (A) Fluorescence yield (in arbitrary units) for isolated, dark-adapted chloroplasts as a function of time in the absence (a) and presence (b) of DCMU. (B) Light-induced fluorescence-yield change in lyophilized chloroplasts (control), in hexane-methanol extracted chloroplasts, and in extracted chloroplasts reconstituted with PQ-9. Small upward arrows indicate weak, modulated green monitoring light turned on larger arrows for intense actinic light on (upward arrow) and off (downward arrow). (A) adapted from Zankel and Kok (1972) Estimation of pool size and kinetic constants. In A San Pietro (ed) Methods in Enzymology 24 222 (B) from Liu, Hoff, Gu, Li and Zhou (1991) The relationship between the structure of plastoquinone derivatives and their biological activity in photosystem II of spinach. Photosynthesis Res 30 100.

The short-time spike in the decay, which can be attributed to the dephasing of many quantum beat terms (all with + 1 phases), represents the irreversible flow of vibrational energy out of the zero-order state prepared by the laser. The long-time component, although weakly modulated, represents an equilibration in the distribution of vibrational energy subsequent to the initial energy flow process. 

In case 5, since v R T we can approximate the exact results by considering small v limit in Eqs. (A.47) and (A.48) for Q, and Eq. (A.3) for the line shape. By taking this limit, we find that the line shape is well described by a single Lorentzian given by Eq. (4.65), and Q by Eq. (4.67). Note that for all weak modulation cases, cases 2, 4, and 5, both the slow and fast modulation approximate results are valid (see Table IV.2). Also, a simple relation between and Q holds in the limit, v 0,... 

Figure 4.15. Phase diagram of q versus R/T. Symbols are the results of exact calculations based on Eqs. (A.47) and (A.48) as v/F is varied from the lower left to the upper right cases 0.01 (downward triangle), 0.1 (upward triangle), 1 (diamond), 10 (square), and 100 (circle). The dashed curves are calculations based on appropriate approximate expressions of Q for each case, Eqs. (4.80) (weak modulation), (4.64), (strong, slow modulation), and (4.77) (strong, fast modulation).

Table IV.2 summarizes various expressions for the line shape and Q found in the limiting cases of the two-state jump model investigated in this work. For simplicity, we have set fj = 1. We see that although the fluctuation model itself is a simple one, rich behaviors are found. We believe that these behaviors are generic (although we do not have a mathematical proof). In the weak modulation cases, both and Q can be described by a single expression, irrespective of the fluctuation rate R. However, in the strong modulation cases, and Q change their qualitative features as R changes.

Envelope-free intact thylakoid vesicles were isolated from spinach. Membrane-free PSII -particles were prepared from spinach as in [3]-Fluorescence of a weak modulated measuring beam (< 1 pE m s" ) was measured with a PAM fluorimeter. Redox-potentials were measured in an 02 free chamber with a Pt-calomel-electrode (Ingold). 

The ratio of variable (Fv) to maximal (Fm) fluorescence, Fv/Fm, was measured using a modulated fluorimeter (6). Leaves were dark adapted for 10 to 15 minutes prior to measuring minimal fluorescence (Fo) using a weak modulated yellow light (1 pmol.m". s" ). Fm was determined by exposing the leaf to white actinic light with a PPFD of 1600 pmol.m" .s". ... 

FO was induced by a very weak modulated light Ll. Fv was induced by a second light L2, non-modulated and of an intensity of 450 pmol/s/m2. qQ can be used as an indicator of the rate of reduced QA. 

The correspondent X-ray picture consists of a set of narrow discrete equidistant spots dX q = mqo along the direction of periodicity. The angular spectrum of the structure factor is shown schematically in Fig. 5.17b. The amplitudes of harmonics depend mostly on the shape of the density curve and determine a number and the height of the 8-type maxima. The peak amplitudes are weakly modulated by the molecular form factor (MFF) and additionally by thermal fluctuations through the factor of Debye-Waller (DWF) for the one-dimensional case 7 oc exp(—q /3) [1]. Here < > is the mean square amplitude of the ther-... 

The EMT expressions given above are independent of A/Ao and are called the zero-order effective indices. They provide accurate results for weakly modulated gratings (As = limit A/Xq 1. The applica-... 

---