Classical model/physics

Most of the four above-mentioned properties for Raman spectra can be explained by using a simple classical model. When the crystal is subjected to the oscillating electric field = fioc " of the incident electromagnetic radiation, it becomes polarized. In the linear approximation, the induced electric polarization in any specific direction is given by Pj = XjkEk, where Xjk is the susceptibility tensor. As for other physical properties of the crystal, the susceptibility becomes altered because the atoms in the solid are vibrating periodically around equilibrium positions. Thus, for a particular... 

Equations 7.57 and 7.58 that are developed above use the as the velocity component as shown for screw rotation physics. As previously discussed, the classic drag flow model [8] assumed that the equivalent flow rate will be obtained if the barrel is rotated in the direction opposite to that of the screw as long as the linear velocity of the unwound barrel Is numerically equal to the linear velocity of the screw core. For this classic barrel rotation model, is used as the velocity component instead of V(,z-Since is less than the drag flow rate would be reduced. It Is Interesting to note here that the classical model using reduced the drag flow rate such that It provided a better estimate of the actual rotational flow rate, but for the wrong reason. 

It is instructive to analyze the hydrophobic bond by a simple classical model of surface tension. The model is correct in principle but not in detail. It does, however, illustrate the basic physical principles and is useful in comparing hydrophobic binding in model systems using the transfer of solutes from water to hydrocarbons with proteins and model experiments. The transfer of a hydrocarbon solute from water to a hydrocarbon solvent consists of the following notional steps (Figure 11.4) (1) removal of the hydrocarbon to vacuum (2) creation of a cavity in the hydrocarbon solvent and (3) transfer of the solute to the... 

The classic models for physical adsorption are those of Langmuir and of Bru-nauer, Emmett and Teller. Langmuir proposed a model of gas adsorption involving monomolecular adsorption and constant AHads, independent of the extent of surface coverage ... 

So long as, however, the driving-field intensity is far above the threshold, the S -matrix amplitude (4.1) and its classical limit (4.27) yield practically identical results. This shows that, in this regime, NSDI is (apart from its initiation via tunneling) an essentially classical phenomenon. This provides a physical justification for extending the classical model to more complex scenarios, such as, for instance, more than two electrons (Sect. 4.8). 

Finally, in some of the most widely used classical models - the free-volume models of Fujita, Vrentas and Duda and their alternatives (171-175) - more than a dozen structural and physical parameters are needed to calculate the free-volume in the penetrant polymer system and subsequently the D. This might prove to be a relatively simple task for simple gases and some organic vapors, but not for the non-volatile organic substances (rest-monomers, additives, stabilizers, fillers, plasticizers) which are typical for polymers used in the packaging sector. As suggested indirectly in (17) sometimes in the future it will maybe possible to calculate all the free-volume parameters of a classical model by using MD computer simulations of the penetrant polymer system. 

Kappeler F., Beer H., and Wisshak K. (1989) s-Process nucleosynthesis-nuclear physics and the classical model. Rev. Prog. Phys. 52, 945-1013. 

As seen in the previous chapter, all the approaches used to solve the dynamie optimization problem integrate, at some point, the dynamical system of the ehemieal proeess. In order to obtain more effieiently the values of the optimum profile of the control variable, a suitable model of the system should be developed. That means that the complexity of the model should be limited, but, in the same time, the model should represent the plant behaviour with good accuracy. The best way to obtain such a model is by using the model reduction techniques. However, the use of a classical model reduction approach is not always able to lead to a solution [6]. And very often, the physical structure of the problem is destroyed. Thus, the procedure has to be performed taking into account the process knowledge (units, components, species etc.). 

Using the methods of classical statistical physics one may more or less rigorously solve problems where the system on a microscopic level is either in a state of complete chaos (perfect gas) or total order (solid perfectly crystalline bodies). In contrast, disordered media and processes in which there is neither crystalline order nor complete chaos on the microscopic level have not yet had an adequate description. This problem is connected with the condition that the macroscopic variables must considerably exceed the correlation scales of microscopic variables, a condition which is not met by disordered media. Consequently in order to describe such systems, fractal models and phased averaging on different scale levels (meso-levels) should be effective. 

Kabbeler, F., Beer, H. WlSSHAK, K. 1989 s-process nucleosynthesis - nuclear physics and the classical model. Kept. Prog. Physics 52, 945. 

Arguments for recent developments of the spherical harmonics approach for the analysis of the macroscopic strain and stress by diffraction were presented in Section 12.2.3. Resuming, the classical models describing the intergranular strains and stresses are too rough and in many cases cannot explain the strongly nonlinear dependence of the diffraction peak shift on sin even if the texture is accounted for. A possible solution to this problem is to renounce to any physical model to describe the crystallite interactions and to find the strain/ stress orientation distribution functions SODF by inverting the measured strain pole distributions ( h(y)). The SODF fully describe the strain and stress state of the sample. 

Once the continuum hypothesis has been adopted, the usual macroscopic laws of classical continuum physics are invoked to provide a mathematical description of fluid motion and/or heat transfer in nonisothermal systems - namely, conservation of mass, conservation of linear and angular momentum (the basic principles of Newtonian mechanics), and conservation of energy (the first law of thermodynamics). Although the second law of thermodynamics does not contribute directly to the derivation of the governing equations, we shall see that it does provide constraints on the allowable forms for the so-called constitutive models that relate the velocity gradients in the fluid to the short-range forces that act across surfaces within the fluid. 

The numerical calculations are based on a classical model for the ion-molecule collision. The potential energy, of course, includes both ion-dipole and ion-polarizability terms. It is necessary to use definite values of all physical constants in order to make a calculation. In all studies values of the... 

Enhancement of Capacitance. The agreement between (modified) Verwey-Niessen models and experiment is less satisfactory for lower-polarity organic media (e.g., DCE, as opposed to NB) and for lower electrolyte concentrations [13]. What is the physical origin of the higher experimental capacitances seen for these conditions As noted by Schmickler and co-workers [59], this enhancement of capacitance at the ITIES relative to the classical model stands in contrast to the response of electrode-electrolyte interface, where the capacitance is often found to be lower than the Gouy-Chapman function. 

In the classical model of physical vapour deposition, the atoms or molecules leave the vapourizing molten or solid surface with directions defined by the cosine law. They travel to the substrate without any interactions in the residual atmosphere and they impinge on the substrate, meeting only substrate atoms or atoms of their own kind. In reality, however, some events can occur to an atom between evaporation source and substrate. 

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