The case of large

Now let us consider the wavevector broadening of the upper polariton states for large q. At large wavevectors the upper polariton dispersion curve tends to that of the cavity photon, and 5q 7o(A2e63/2/cj2h c3) C q. Thus, independently of the value of the Rabi splitting, for large q the upper cavity polariton branch contains the coherent states only. 

From this macroscopic consideration it is seen that the states for which the wavevector is not a good quantum number do not form in a certain vicinity of q = 0 for both branches, and for q q lx for the lower branch. In other words, the states with the well-defined wavevector exist in the intermediate region of the wavevectors only q n q qitlx for the lower branch, and q q Pn for the upper branch. However, in contrast to the case of vanishing q, one can say that for q A 1 the coherent polaritonic states do not form at all. The excited states from this part of the spectrum are not resonant with the cavity photon, and as a result no hybridization happens. Instead, these excited states are similar to the localized excited states in a non-cavity material, i.e. they are to be treated just as incoherent excited states. 

The spectrum of the excitations is shown in Fig. 10.5 for 2 A = 80 meV. The dashed lines show the uncoupled molecular excitons and photons, and the solid lines show the coherent part of the spectrum with well-defined wavevector. The crosses show the end-points of the spectrum of excitations for which q is a good quantum number. The spectrum of incoherent (weakly coupled to light) states is shown by a broadened line centered at the energy Eq. It follows from the expression for the dielectric tensor that this spectrum is the same as the spectrum of out-of-cavity organics. The spectrum of absorption as well as the dielectric tensor depend on temperature. This means that in the calculation of the temperature dependence of the polariton spectrum we have to use the temperature dependence of the resonance frequency Eo as well as the temperature dependence of 7 determining the width of the absorption maximum. However, the spectrum of emission of local states which pump polariton states can be different from the spectrum of absorption. The Stokes shift in many cases 

The dispersion curves of the coherent polaritonic states (solid lines) and of uncoupled cavity photons and the molecular excitation (dashed lines). The crosses show the end-points of the part of the spectrum with well-defined wavevector. On the right, the broadened line of the molecular resonance is shown. The inset shows the excitonic weights (10.26) for upper ( cix ) 2) and lower ( cix ) 2) polaritonic branches. Reprinted with permission from Agranovich et al. (15). Copyright 2003, American Physical Society. 

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If agitation and heating are not practical as in the cases of large volumes, it is better to withdraw samples from various levels in order to get an average sample. 

Therefore an expression which is equivalent to Eq. (1.21) for the case of large... 

Supports. The spaciag of supports is governed by the hot allowable stress of the piping materials stabiUty, ia the case of large-diameter thin-wall pipe deflection to avoid sagging or pocketing and the natural frequency of the unsupported length to avoid susceptibiUty to undesirable vibration. 

Description A tray or compartment diyer is an enclosed, insulated housing in which solids are placed upon tiers of trays in the case of particulate solids or stacked in piles or upon shelves in the case of large objects. Heat transfer may be direct from gas to sohds by circulation of large volumes of hot gas or indirect by use of heated shelves, radiator coils, or refractoiy walls inside the housing. In indirec t-heat units, excepting vacuum-shelf equipment, circulation of a small quantity of gas is usually necessary to sweep moisture vapor from the compartment and prevent gas saturation and condensation. Compartment units are employed for the heating and diying of lumber, ceramics, sheet materi s (supported on poles), painted and metal objects, and all forms of particulate solids. 

It is recommended that further evaluation be carried out by direct measurement according to the data in Section 3.7.1 because of possible errors caused by foreign sources in the case of large readings. 

Since in oilfields or reservoirs borehole casings are frequently sited close to one another, they can be affected by the voltage cone of the anode bed and the cathodic voltage cone of other casings. Thus, in the case of large oilfields and reservoirs, it is appropriate to protect all wells cathodically. 

Our conclusions about the case of large /tls have a rather speculative character, and pursue merely an illustrative goal, since (2.41) and (2.42) are obtained in the weak-coupling limit. 

The cross-linking reaction is carried out after the resin has been applied to the glass fibre. In practice the curing is carried out either at elevated temperatures of about 100°C where press mouldings are being produced, or at room temperature in the case of large hand lay-up structures. 

These simple models are based on the assumption of constant drift velocity i.e., particles are assumed to achieve their final charge instantaneously. This is a reasonable assumption in the case of large particles, the charging of which is governed by field-driven ion motion. The characteristic distance, x% corresponding to the time constant in Eq. (13,53) is given by... 

It is additionally recommended in the British Gas publication Guidance Notes on the Installation of Gas Pipework, Boosters and Compressors in Customers Premises (lM/16) that for buildings containing plant over 2 MW total heat input and being supplied with gas at pressures above 1 bar, a remotely operable valve shall be fitted in the gas supply to the building. In the case of large boiler houses, provision for remote operation of the valves shall be provided both inside and outside the building. 

Several methods for the evaluation of the MDF have been put forward, notably that processed by Tchebycheff, which gives a high degree of accuracy in the case of large cooling ranges. In the form in which it is most commonly used, it reads ... 

Perhaps the most complete description was given by Cox [74], who derived an expression for the dynamic contact angle which is also valid in the case of large angles. The Cox prediction was tested experimentally and a good agreement between theory and experiment was found. 

This is our final equation. A simplified form is found if the matrices W defined in eqn 28 are neglected (so that X and the matrices S are ignored). This is possible, for example, in the case of large energy differences between MO s whose occupations are different. Then... 

Oil spill-treating agents may be applied from boats, hydrofoils, aircraft, or helicopters in the case of large-scale pollution. For minor incidents such as car accidents, the application is done by hand. 

Small to medium size water-to-water heat pumps are considered in this system. Since the primary pumps are common to all the heat pumps, this system may not be ideal for projects where large size multiple heat pumps are used. It is better if dedicated primary pumps are used in the case of large multiple heat pumps. This is discussed in Section 6.4.1. 

Our discussion of complex formation in electron-ion recombination, field effects, and three-body recombination has perhaps posed more questions than it has answered. In the case of H3 recombination, the experimental observations suggest but do not prove that complex formation is an important mechanism. Three-body recombination involving complex formation is not likely to have much effect on the total recombination coefficients of diatomic ions, but it may alter the yield of minor product channels. Complex formation may be most prevalent in the case of large polyatomic ions, but there is a serious lack of experimental data and theoretical calculations that can be adduced for or against complex formation. 

To derive the transmittance noise for the case of large scintillation noise, we begin at a somewhat earlier point than we did for the low-noise case, with equation 41-14 [2] ... 

Controlled potential methods have been successfully applied to ion-selective electrodes. The term voltammetric ion-selective electrode (VISE) was suggested by Cammann [60], Senda and coworkers called electrodes placed under constant potential conditions amperometric ion-selective electrodes (AISE) [61, 62], Similarly to controlled current methods potentiostatic techniques help to overcome two major drawbacks of classic potentiometry. First, ISEs have a logarithmic response function, which makes them less sensitive to the small change in activity of the detected analyte. Second, an increased charge of the detected ions leads to the reduction of the response slope and, therefore, to the loss of sensitivity, especially in the case of large polyionic molecules. Due to the underlying response mechanism voltammetric ISEs yield a linear response function that is not as sensitive to the charge of the ion. 

Here F is the Faraday constant C = concentration of dissolved O2, in air-saturated water C = 2.7 x 10-7 mol cm 3 (C will be appreciably less in relatively concentrated heated solutions) the diffusion coefficient D = 2 x 10-5 cm2/s t is the time (s) r is the radius (cm). Figure 16 shows various plots of zm(02) vs. log t for various values of the microdisk electrode radius r. For large values of r, the transport of O2 to the surface follows a linear type of profile for finite times in the absence of stirring. In the case of small values of r, however, steady-state type diffusion conditions apply at shorter times due to the nonplanar nature of the diffusion process involved. Thus, the partial current density for O2 reduction in electroless deposition will tend to be more governed by kinetic factors at small features, while it will tend to be determined by the diffusion layer thickness in the case of large features. 

The last term Tt is the rest of the development, involving all the orthogonal operators, with the exclusion of M. Caspers assumes that the contribution of the terms which are not principal diagonal may be neglected in the case of large fields. He then finds that for large H and t, Q fulfils the integral equation... 

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