Coefficient transmission

The transmission coefficient Cl (Qj,t), considering transient (broadband) sources, is time-dependent and therefore accounts for the possible pulse deformation in the refraction process. It also takes account of the quantity actually computed in the solid (displacement, velocity potential,...) and the possible mode-conversion into shear waves and is given by... 

The use of air-bome ultrasound for the excitation and reception of surface or bulk waves introduces a number of problems. The acoustic impedance mismatch which exists at the transducer/air and the air/sample interfaces is the dominant factor to be overcome in this system. Typical values for these three media are about 35 MRayls for a piezo-ceramic (PZT) element and 45 MRayls for steel, compared with just 0.0004 MRayls for air. The transmission coefficient T for energy from a medium 1 into a medium 2 is given by... 

Figure A3.6.11. Viscosity dependence of transmission coefficient of the rate of cyclohexane chair-boat inversion in liquid solution (data from [100]).

Voth G A 1990 Analytic expression for the transmission coefficient in quantum mechanical transition state theory Chem. Phys. Lett. 170 289... 

There is still some debate regarding the form of a dynamical equation for the time evolution of the density distribution in the 9 / 1 regime. Fortunately, to evaluate the rate constant in the transition state theory approximation, we need only know the form of the equilibrium distribution. It is only when we wish to obtain a more accurate estimate of the rate constant, including an estimate of the transmission coefficient, that we need to define the system s dynamics. 

The symmetric transmission coefficients are defined = LijMi. The general solutions are of the form... 

Now we can compute the transmission coefficient [17,24]. It will be the difference between the positive and negative contributions, or... 

The transition described by (2.62) is classical and it is characterized by an activation energy equal to the potential at the crossing point. The prefactor is the attempt frequency co/27c times the Landau-Zener transmission coefficient B for nonadiabatic transition [Landau and Lifshitz 1981]... 

This discussion of geometric effects ignored the attenuation of radiation by material through which the radiation must travel to reach the receptor. The number of particles, dN, penetrating material, equals the number of particles incident N times a small penetration distance, dx, divided by the mean free path length of the type of particle in the type of material (equation 8.3-8). Integrating gives the transmission coefficient for the radiation (equation 8.3-9). 

For gas-phase reactions, Eq. (5-40) offers a route to the calculation of rate constants from nonkinetic data (such as spectroscopic measurements). There is evidence, from such calculations, that in some reactions not every transition state species proceeds on to product some fraction of transition state molecules may return to the initial state. In such a case the calculated rate will be greater than the observed rate, and it is customaiy to insert a correction factor k, called the transmission coefficient, in the expression. We will not make use of the transmission coefficient. 

Many computational studies in heterocyclic chemistry deal with proton transfer reactions between different tautomeric structures. Activation energies of these reactions obtained from quantum chemical calculations need further corrections, since tunneling effects may lower the effective barriers considerably. These effects can either be estimated by simple models or computed more precisely via the determination of the transmission coefficients within the framework of variational transition state calculations [92CPC235, 93JA2408]. 

Decide the heat transmission coefficient (U values) for the outside walls and glass, roof and bottom floor, and the inside walls, ceilings, or of heated spaces adjacent to non-heated spaces. 

Measure up the area of each type of surface and compute the loss through each surface by multiplying the transmission coefficient by the measured area by the difference between the inside and the outside temperatures. 

If insulation panels are not of uniform construction (as in the case of a wall containing a window) the average sound-insulation value must be derived for use in calculations. The total transmission coefficient for the composite panel will equal the sum of the individual coefficient times their respective areas divided by the total area. Thus ... 

Some gas phase data suggest that a certain fraction of the transition states for some reactions are reflected back to products. One can multiply the right side of Eq. (7-55) by k, the transmission coefficient, to account for this, in which case k < 1. We shall ignore this factor k, taking it as unity. Indeed, we shall ignore a large body of experimental research on gas phase reactions and the theoretical calculations on them. 

Cope, W.F. Ptvc. Inst. Mech. Engrs. 45 (1941) 99. The friction and heat transmission coefficients of rough pipes. 

Phenomenological evidence for the participation of ionic precursors in radiolytic product formation and the applicability of mass spectral information on fragmentation patterns and ion-molecule reactions to radiolysis conditions are reviewed. Specific application of the methods in the ethylene system indicates the formation of the primary ions, C2H4+, C2i/3+, and C2H2+, with yields of ca. 1.5, 1.0, and 0.8 ions/100 e.v., respectively. The primary ions form intermediate collision complexes with ethylene. Intermediates [C4iZ8 + ] and [CJH7 + ] are stable (<dissociation rate constants <107 sec.-1) and form C6 intermediates which dissociate rate constants <109 sec. l). The transmission coefficient for the third-order ion-molecule reactions appears to be less than 0.02, and such inefficient steps are held responsible for the absence of ionic polymerization. 

A low ion pair yield of products resulting from hydride transfer reactions is also noted when the additive molecules are unsaturated. Table I indicates, however, that hydride transfer reactions between alkyl ions and olefins do occur to some extent. The reduced yield can be accounted for by the occurrence of two additional reactions between alkyl ions and unsaturated hydrocarbon molecules—namely, proton transfer and condensation reactions, both of which will be discussed later. The total reaction rate of an ion with an olefin is much higher than reaction with a saturated molecule of comparable size. For example, the propyl ion reacts with cyclopentene and cyclohexene at rates which are, respectively, 3.05 and 3.07 times greater than the rate of hydride transfer with cyclobutane. This observation can probably be accounted for by a higher collision cross-section and /or a transmission coefficient for reaction which is close to unity. 

In the case where they represent quantum vibrational modes, this leads to the appearance of a small tunnel factor in the transmission coefficient k. ... 

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