Phenomenological cross-section

Values are computed from phenomenological cross-sections using Equation 5. 

There is a little information available from repeller studies. In their paper on methanol, Thynne et al. (40) present, without analysis, data on the variation of the phenomenological cross-sections of Reactions J and K with the ion-exit energy obtained from conventional low pressure measurements. These data can be used to examine the dependence of k(Ee) upon Ee via the relation ... 

A phenomenological description of the differential cross-section for emission of photoelectrons into solid angle O in the lab frame can be written, assuming random molecular orientation and an axis of cylindrical symmetry defined by the photon polarization, as... 

Since we don t usually know enough about pore structure and other matters to assess the relative importance of these modes, we fall back on the phenomenological description of the rate of diffusion in terms of Fick s (first) law. According to this, for steady-state diffusion in one dimension (coordinate x) of species A, the molar flux, NA, in, say, mol m-2 (cross-sectional area of diffusion medium) s-1, through a particle is... 

While the ability to treat capture cross sections theoretically is very primitive and the experimental data on capture cross sections are very limited this phenomenological parameter seems to be an appropriate meeting place for experiment and theory. More work in both of these areas is needed to characterize and understand the important role of surface states in electron transfer at semiconductor-electrolyte interfaces. 

Various computer codes exist which are used to simulate nuclear weapons effects on various targets. Variations of codes on radiation transport, shielding and cross sections also can be considered. A directory of currently used codes was compiled by Martin, Reitz and Root (Ref 23), which for the most part is a rather complete tabulation of computer programs applied to the numerical simulation of nuclear weapon expls phenomenology and effects... 

The microscopic theory derived in the previous section describes the evolution of the molecular system under the influence of the electric field of the light beam. In this section, following Loudon (1983 ch.l), we use (2.22) to deduce an expression for the phenomenological absorption cross section cr(u>) defined in (2.1). See Loudon for a more detailed discussion. 

A theoretical determination of the rate constant for a chemical reaction requires a calculation of the reaction cross-section based on the dynamics of the collision process between the reactant molecules. We shall develop a general relation, based on classical dynamics, between reaction probabilities that can be extracted from the dynamics of the collision process and the phenomenological reaction cross-section introduced in Chapter 2. That is, we give a recipe for how to calculate the reaction cross-section in accord with the general definition in Eq. (2.7). 

Here x is a phenomenological parameter measuring the chirality and / is a size scale factor. Since here the Reynolds number is small ( 10 s), the Stokes equation can be used to get r = DS2. where D is the hydrodynamic drag coefficient and 2 is the rotational speed. The drag coefficient for a cylindrical object rotating about its axis with cross-sectional radius r and length L is D = 4ztT)r2L, where tj is the viscosity of the medium [19]. Therefore, D /3 and the rotational speed 2 of the rotor will scale as... 

Dipole scattering does not require an atomistic theory. A phenomenological theory suffices, which includes a response function dependent on dielectric constants. The cross-section for dipole scattering based on these assumptions is given in Eqs, 3.7 and 3.9 of Ibach and Mills./61/ These formulae include plane-wave reflection coefficients from the surface, which are solutions of the standard LEED problem. Since dipole scattering involves essentially only forward scattering, it is not necessary in practice to adopt the spherical-wave picture of our step 2 (cf. section 3.4.3), the plane-wave approach is adequate in this situation. 

The matter discussed in sec. 2.3 concerned the phenomenology of adsorption from solution. To make further progress, model assumptions have to be made to arrive at isotherm equations for the individual components. These assumptions are similar to those for gas adsorption secs. 1.4-1.7) and Include issues such as is the adsorption mono- or multlmolecular. localized or mobile is the surface homogeneous or heterogeneous, porous or non-porous is the adsorbate ideal or non-ideal and is the molecular cross-section constant over the entire composition range In addition to all of this the solution can be ideal or nonideal, the molecules may be monomers or oligomers and their interactions simple (as in liquid krypton) or strongly associative (as in water). 

In Eq. (3), is the relevant molecular transition frequency, y is a dam >ing rate, is a polarizability, and (/) is the z-component of the total electric field in the vicinity of the molecule. If (t) were simply of the form i)Cos(fijr), then Eq. (3) is the well-known phenomenological Lorentzian oscillator model of absorption which leads to an approximate Lorentzian form for the absorption cross section [1]. Similar remarks hold for the SP dipole, fi/f), if E t) = ocos(mr), where E t) is the z-component of the total electric field near the SP dipole. The parameters 04,74 and a, in this case are chosen such that the resulting Lorentzian cross section proximates the known exact sur ce plasmon absorption cross section or its appropriate form in the quasistatic (a A=2 tic/cs) limit. Note that I am using a simplified notation compared to the various notations of Refs. [13-15]. (Relative to Ref. [13], for example, my definitions of surface plasmon dipole... 

This chapter demonstrates the important role chemical dynamics play in the phenomenology of meteors and the associated ionospheric consequences. Although considerable work has been done to derive the important parameters of the relevant molecular and atomic collisions under extreme conditions, there are still many poorly known cross sections that are required to properly model the macroscopic observables based on microscopic processes. The current state of knowledge is best for low energy metal ion collisions, where the extensive work of the Armentrout group at the University of Utah (see Sec. 3.3.2) has made the most valuable and extensive contribution. A missing component are cross sections for Me+ -t- O3 reactions which could be an efficient source of metal oxide ions that dissociatively... 

Figure 3.12 shows how the r(aj)-isotherm is affected when the number of the hydrocarbon chains in the surfactant molecule is doubled. A monolayer of cationic-anionic surfactant pairs, behaves phenomenologically as if it consisted of double chain molecules in the condensed phase the molecular eirea more or less doubles as compared to single chains. For the distearoyl phosphatidyl choline the more bulky phosphate head group further increases the cross-sectional area per molecule. This is consistent with some tilt in the orientation of the molecules with respect to the normal of the interface (cf. sec. 3.3b, ad (iv)). 

Boltzmann constant. The effective path length of the collision cell is X, while T and p are the temperature and the pressure of the reactant gas, respectively. Pressure dependent cross section data were plotted and then extrapolated to zero pressure using the method of Armentrout and coworkers [44]. The reaction rate coefficients, which are dependent on the lifetime of the ion molecule complex, were calculated and converted to an expression for the phenomenological rate coefficient [44] by (14.2). 

The theoretical approaches range from the simplest phenomenological models to complex quantum calculations. They can be split into two main strategies. The first one consists in keeping the classical Mie expression for the absorption cross section... 

That is, the heat flux is constant at any cross section of the plate. However, for the size of a heat transfer device, say for a heater providing this flux through the walls of a room to be heated, we need the specific value of this constant. Thermodynamics is silent to this need, The attempt to find an answer for this need is the origin of (conduction) heat transfer. Since the statement of our example specifies the temperatures of two surfaces, we need a relation between heat flow and temperature, Q = f(T), which is phenomenologically provided by heat transfer. Observations show that any relation of this nature is dependent on the medium it applies to and, consequently, is a particular law. The remainder of this section is devoted to particular laws of heat transfer. We begin with the particular law associated with our illustrative example. 

Whilst the term macroscopic cross-section is used for the phenomenological cross-section defined here, it should be noted that it is also used to mean the quantity a[M] which is the effective cross-section of all the target particles in 1 cm and has dimension of cm". ... 

As is evident from the above definition, the phenomenological cross-section Q is an energy-average of the microscopic cross-section o E) over the energy range between 0 and Ef, and accordingly is a function of Ef, viz. 

---