The physical phenomenon

The rotational speed may range between some metres per second to more than 100 m s The tornado also moves horizontally and its translational speed is usually rather low (up to a few tens of metres per second), which generally allows people who see it arriving to run away in time. 

The tornado is part of the same family of tropical hurricanes, but its size is much smaller. The dimension of the vortex is of 10-100 m, while the central vortex of a hurricane may be 100-1000 times higher. 

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Focusing Laser Light. One of the most important properties of laser radiation is the abiHty to coUect all of the radiation using a simple lens and to focus it to a spot. It is not possible to focus the laser beam down to a mathematical point there is always a minimum spot size, set by the physical phenomenon of diffraction. A convenient equation is... 

Scaling by use of dimensionless numbers only is limited in two-phase flow to simple and isolated problems, where the physical phenomenon is a unique function of a few parameters. If there is a reaction between two or more physical occurrences, dimensionless scaling numbers can mainly serve for selecting the hydrodynamic and thermodynamic conditions of the modelling tests. In... 

The theory behind every measurement method can be generalised by Eq (1) [1]. Some quantity (or quantities, measurands) is measured, which has a specific relationship to the sought quantity. The measurand can be regarded to be a stochastic variable associated with an uncertainty, which implies that the sought quantity is also a random variable. The mathematical relationship depends on the physical model, that is, the model of the physical phenomenon of interest, for example temperature, pressure, and volume flow. The physical model always includes limitations, which implies that the measurement method has restrictions that is, it will only function in a certain measuring range and according to the assumption of the model. 

The physical phenomenon of current generation in simple D/A systems can be thought of in terms of the six chemical steps depicted in Fig. 4. (1) The absorption of a photon leads to a localized exciton with energy oo on either the donor or... 

For a solid surface with two-dimensional periodicity, such as a defect-free crystalline surface, all the measurable quantities have the same two-dimensional periodicity, for example, the surface charge distribution, the force between a crystalline surface and an inert-gas atom (Steele, 1974 Goodman and Wachman, 1976 Sakai, Cardino, and Hamann, 1986), tunneling current distribution, and STM topographic images (Chen, 1991). These quantities can be expanded into two-dimensional Fourier series. Usually, only the few lowest Fourier components are enough for describing the physical phenomenon, which requires a set of Fourier coefficients. If the surface exhibits an additional symmetry, then the number of independent Fourier coefficients can be further reduced. 

The idea of the effective mass of an electron is known not to be strict in particular, the definition of the effective mass depends, generally speaking, on the physical phenomenon under consideration. For instance, when one analyses electron motion in a periodic crystal, the effective mass is usually determined as [13]... 

Measurements of the physical phenomenon present in the world we live in often demonstrate far more complexity and variety than our preconceived models allow. When we first develop a new measurement technique, its use may open a new window on the world. During the first few years of measurements in a new field, discoveries often come rapidly with exciting expansion of our understanding. After a few years, however, the discoveries slow down, and when a field has been open for a century, new information and measurement capability come only at the expense of major effort. 

The solvent polarization can be formally decomposed into different contributions each related to the various degrees of freedom of the solvent molecules. In common practice such contributions are grouped into two terms only [41,52] one term accounts for all the motions which are slower than those involved in the physical phenomenon under examination (the slow polarization), the other includes the faster contributions (the fast polarization). The next assumption usually exploited is that only the slow motions are instantaneously equilibrated to the momentary molecule charge distribution whereas the fast cannot readjust, giving rise to a nonequilibrium solvent-solute system. 

Inspection of Tables I and II shows that corresponding values of SD differ by almost a factor of 3. This difference is caused by the physical phenomenon of "backmixing." Hot products mix with cold reactants in the second case, and because of the strong non-linearity the average rate is enhanced. 

Retarders are usually devices which rotate the polarization plane of radiation or convert linearly polarized radiation into a elliptically or circularly polarized one. Their basic physical function consists in decomposing the electric vector of the linearly polarized radiation into two mutually orthogonally polarized components between which a phase difference retardation) is created. Depending on the physical phenomenon that causes the retardation effect practical retarders based on birefringence and total internal reflection are known and used. 

A model is a representation or a description of the physical phenomenon to be modelled. The physical model (empirical by laboratory experiments) or conceptual model (assembly of theoretical mathematical equations) can be used to describe the physical phenomenon. Here the word model refers to a mathematical model. A (mathematical) model as a representation or as a description of a phenomenon (in the physical space) is a systematic collection of empirical and theoretical equations. In a model (at least in a good model) both approaches explain and predict the phenomenon. The phenomena can be predicted either mechanistically (theoretically) or statistically (empirically). 

Once this relationship is formulated, all we need to know is the general nature of the physical phenomenon and variables. Specific values for variables (size of components, fluid proprieties, etc.) are not needed to perform the dimensional analysis. This relationship could be applied to any system, if it is governed by the same variables and laws. If Eq. (6.204) describes the behaviour of a laboratory device, a similar relationship can be written for evolution of the phenomenon in the prototype ... 

EXAFS theory was developed in the early 1970s by Sayers et al., providing XAS experimentalists a model in which data could be fit to. In their pioneering work it was observed that the physical phenomenon that gives rise to EXAFS oscillations has two major components, i.e., that of amplitnde and phase as described by the following equations amplitude ... 

As the case previously explained was comparable with fusion and solidification, and the velocity then discussed with the rate of solidification, so here the phenomena may be brought into delation with the physical phenomenon of evaporation, which, in analogy with the change of moving force just referred to, goes more slowly up to the occurrence of equilibrium, here reached when the vapour pressure has risen to a maximum. 

In most experimental devices, the main problem is to eliminate the different sources of error. For pressure drop measurements, the pressure sensors must not be intrusive and interfere with the physical phenomenon. In most pubhshed works, the pressure sensors are added to the circuit and the fitting itself can create a singular pressure loss. Two experiments are presented. The first one has a rectangular channel whose hydraulic diameter varies from 100 pm to 1 mm with pressure sensors on either side of the test channel and includes entrance effects. The second one whose hydrauhc diameter is 7.1 pm has the pressure taps far from the inlet and outlet to eliminate entrance and exit effects. 

A broad range of physical and chemical processes occur as a result of an encounter between pairs of particles. Depending on the physical phenomenon being investigated, the particles may range in size from the atomic scale to colloidal, while the bath density may range from that of a low-pressure gas to a dense liquid. The primary aim of this chapter is to show that a simple model for encounter dynamics can be derived from the Fokker-Planck equation (FPE), which applies, within limits, over the entire range of particle size and bath density. 

Sonochemistry is the research area in which molecules undergo chemical reaction due to the application of powerful ultrasound radiation (20 KHz-10 MHz) [4]. The physical phenomenon responsible for the sonochemical process is acoustic cavitation. Let us first address the question of how 20 kHz radiation can rupture chemical bonds (the question is also related to 1 MHz radiation), and try to explain the role of a few parameters in determining the yield of a sonochemical reaction, and then describe the unique products obtained when ultrasound radiation is used in materials science. 

In order to appreciate the different methods of data analysis, it is helpful to have a clear idea of the mathematics of the physical phenomenon of fluorescence [9]. On a Jablonski diagram is shown in Figure 1, Sg represents the energy level... 

The formulation above is known in mathematics as a Dirac delta function. The delta function is everywhere zero except when some condition is satisfied (here, a - (k — k) being integral), and then it suddenly attains its maximum possible value. This is equivalent to the physical phenomenon we know of in diffraction analysis and crystallography as the constructive interference of waves. As we will see in the next chapter, Bragg s law is simply one expression of this function. 

Even meteorologists used another terms, a very rough or random surface at the early history of their recent theories, [522], The terms penetrable obstruction or a grid [554] are evidently incorrect for such extensive and lengthy structures. The term the porous medium also used by some researchers resembles some features of the object under investigation but has already been employed in filtration theory and thus is associated with theoretical approaches of the latter theory. The term a layer with distributed force suggested by Hunt et al. [50, 319] clearly expresses the mathematical idea used but does not reflect the physical phenomenon under focus. 

All the effects reflect the physical phenomenon of acoustic or ultrasonic cavitation. With this, to initiate the cavitation one must apply a certain threshold sound pressure designated as a cavitation threshold and determine the cavitation strength of a liquid. 

The physical phenomenon utilized for the first time by Field [31a] and Munson [31b] is as old as the universe itself. In the MS source, a gas plasma is produced at a pressure of O.I-l Torr (in electron impact, this pressure is of the order of 10 -10" Torr). If the reagent gas is methane, CH5, CjH, etc., are produced after reaction. These ions have been detected in the gas plasmas surrounding Jupiter and Saturn [32] and those which compose certain stars. 

The theory of molecular diffusion has been derived from the theory of Brownian motion, which is the physical phenomenon that small particles immersed in a fluid move randomly. Let us briefly touch on Brownian motion. The theory of Brownian motion was established by Einstein in... 

In the hypersurface portions where polarization effects may be considered inessential to the understanding of the physical phenomenon under investigation, the model may be limited to electrostatic interactions. This further reduction is less well justified than the preceding ones, although in some cases (see, e.g. Section IX) a mutual cancellation of other effects enhances the reliability of the electrostatic approximation. 

As is well known, the selection rules allow RSL by polaritons only in crystals without a center of inversion. This is precisely the kind of crystal in which Fermi resonance with polaritons (to be discussed below) was found to be the physical phenomenon in which the special features of the biphonon spectrum were most evident. 

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