Real physical phenomena

Existing correlations of phase equilibrium data contain many regressed parameters, they are often semi-empirical, and they may be successful in fitting the data in parts of the phase diagram -even with high accuracy. As far as prediction is concerned, models developed for that purpose attempt to justify theoretically a link between the model parameters and real physical phenomena. However, the distinction between these two methods is often lost, since theoretically based models are forced to fit the data better by the introduction of additional adjustable parameters. 

Other tests have been used in the past, particularly for aviation gasoline, where it was more important to discriminate accurately between fuels with ON > 100. These had the advantage of being more related to real physical phenomena. For example, the performance number [11] was based on a single standard fuel, iso-octane, and the relative indicated mean effective power (imep) (defined in terms of the cylinder pressure [3]), and so is directly related to combustion. The performance number was 100 times the ratio of the knock limited imeps of the fuel and iso-octane. Much of the API 45 project on octane number of mixtures of pure hydrocarbons (see Section 7.2.5) was reported in terms of performance number. This project of the American Petroleum Institute ran from 1938 to 1957, and has provided an invaluable source of basic data. The articles by Lovell [10] and Scott [12] review and interpret these data. Whilst this criterion and these values of CCRs [10,13] are no longer in widespread use for automotive fuels, the data available in the older literature could still be useful in testing chemical models. Because the octane number scale is based on two reference fuels, modelling the octane number of any hydro-... 

Large tension in water and aqueous solutions at typical sizes of the system 3-300 micrometers is real physical phenomena but not artifact. 

However, charges, dipoles, etc. do not correspond to real physical phenomena when assigned to atomic centers. Similarly, point-charge representations of lone pairs do not represent real physically observable quantities. With this understood, one can appreciate that atomic charges and so on can be looked upon not as physical quantities, but rather as adjustable parameters. These parameters can be fit to best reproduce certain desired quantities, either experimental or theoretical [14,19-21]. Of most relevance are those which are geared toward the electrostatic interactions of the molecule in question. 

Simulation of a mixing process by using a computer provides a better alternative. Monte Carlo simulation techniques are often utilized. Monte Carlo techniques are numerical methods that involve sampling from statistical distributions, either theoretical or empirical, to approximate the real physical phenomena without reference to the actual physical systems. For the general discussion of Monte Carlo methods, readers are referred to Hammersley and Handscomb [19] and Tocher [20]. 

Statistical fractals are generated by disordered (random) processes. An element of disorder is typical of most real physical phenomena and objects. The fact that disorder, i.e., the absence of any spatial correlation, is a sufficient condition for the formation of fractals was first noted by Mandelbrot [1]. A typical example of this type of fractal is the random-walk path. However, real physical systems are often inadequately described by purely statistical models. Among other reasons, this is due to the effect of excluded volume. The essence of this effect lies in the geometric restriction that forbids two different elements of a system to occupy the same volume in space. This restriction is to be taken into account in the corresponding modelling [10, 11]. The best-known examples of this type of models are self-avoiding random walk, lattice animals and statistical percolation. 

Such concepts as configuration interaction, resonance, hybridization, and exchange are not real physical phenomena, but only artifacts of the approximations used in the calculations. Likewise, the concept of orbitals is but an approximation, and, strictly speaking, orbitals do not exist. 

Good models for bubble swarm dynamics, coalescence and breakup rates, interfacial area transport, and bubble size distributions must be based on real physical phenomena. Bubbly flow instability, for example, has typically been treated as a... 

Essentially only the total 9 has a meaning, because this describes the stationary state. The splitting 9 = 91 9n is artificial and this forms only a means of finding an approximate solution of the wave equation, thus a necessary consequence of our mathematical incapacity. Resonance is therefore also not a real physical phenomenon but a human mnemonic. It is the same as when we say of a cnild, just like his mother and later just like his father . We do not really mean that the person of the child alternates, resonates , between that of mother and father or that these latter are present as parts but only that to a first approximation we try to describe his personality as a sum of two other entities. An analysis of an entity such as a human being into intelligence, character etc, can be very useful for an opinion but is not based on the presence of distinct parts which are themselves the subject of investigation. 

Resonance, strictly speaking, is not a real physical phenomenon but only an interpretation, as a consequence of the way in which the wave function of the stationary state, for example of the benzene molecule, can be constructed approximately by linear combination of other wave functions. This construction is possible in a way which fits in well with the interpretation of these systems based on the theory of chemical structure. 

Figures 3a and 3b show the calculated flow fields for the 260 mm immersion case. The predominant flow direction in the slag was upwards from the interface to the top and back down in a loop. This flow was driven by both natural convection and the buoyancy generated by the carbon monoxide gas produced by the electrode-slag reactions. Hence, it was strongest around the electrodes, oftheordra-of 0.1 m/s, and decreased to die ordra-ofO.OI m/s away from the electrodes. In addition to the principal recirculatory flow loop around the electrodes, a second weaker recirculatory loop formed below the electrodes due to the temperature difference between the electrode and the interface. By contrast, the bullion was relatively quiescent, except for a weak flow loop near the side wall, apparently in a counterintuitive direction (Figure 3b). More work is required to establish whether this loop is a real physical phenomenon or an artefact of the mesh geometry.

When a problem is reformulated to improve its conditioning, it is important that the new formulation replicates the real physical phenomenon and not a similar one. 

The "electron-spin hypothesis was formulated in 1925 by George Uhlenbeck and Samuel Goudsmit to account for the splitting of spectral lines in a magnetic field. The spinning of the electron is not known to be a real physical phenomenon. 

In addition, an intense peak at the proton Larmor frequency was observed, and in some spectra this peak appeared to be split. Due to the use of the maximum entropy method (MEM, as opposed to the far more common Fourier transformation) for spectral processing, they could not determine whether the splitting was due to a real physical phenomenon or simply an artifact of the MEM method, precluding further analysis. The appearance of this matrix peak did, however, indicate the presence of waterborne protons weakly coupled to the paramagnetic vanadyl nucleus. 

Fig. 30, while level-off phenomenon can be observed from the simulation result given in Fig. 33 for the rough surface in mixed lubrication. It is unclear at the present whether the downward turn shown in Fig. 30 is a manifest of real physical process, or a false phenomenon due to numerical inaccuracy. 

Experimentally undefined parameters, which have a real physical meaning that is, they reflect an actual physical phenomenon but cannot be determined from the experimental data (even a thought experiment to measure them cannot be conceived) or by a thermodynamic calculation. In isolated cases such parameters can be calculated on the basis of nonthermodynamic models. The equations used for calculations generally contain sums, differences, or other combinations of such parameters that are measurable. The Galvani potential at the interface between two dissimilar conducting phases is an example. 

About 50 years ago, physicists were amazed to discover that the universe, which had previously been regarded as completely symmetrical, had a certain preference for left-handedness. It had been considered impossible that basic natural laws would distinguish between left and right. This assumption formed the basis for the physical law of the conservation of parity according to this, the sum of the parities before and after each physical process must be equal. In other words the mirror image of each physical phenomenon is also a real phenomenon (Ball, 1994). 

As a final note, it should be emphasized that like the phenomenon of resonance, hybridization is not a real physical process (atoms don t hybridize any more than molecules resonate). It is a man-made process for describing an already existing situation, the molecular bond, when the simple model using single AOs fails to work. 

Photoemission — Photoemission is the effect first discovered by H. R. Hertz (1857-1894) in Karlsruhe and W. Hallwachs (1859-1922) in Dresden in 1887, which is now known to be the emission of electrons from solids under illumination by electromagnetic radiation. The significance of the phenomenon historically is that it gave the first clear indication that the photons postulated by -> Planck to explain the energy distribution of light emitted from a black body had a real physical existence. -> Einstein was able to show that the energy of electrons emitted by the solid should obey the law = hi/-o,... 

To reveal the essence of the notion of the structure of real (physical) space, from Vernadsky s viewpoint, is not so easy. He used different terms in works which were written at different times to characterise this phenomenon a property of space, a geometrical structure of space, and a structure of space, and, ultimately, a state of space. He did not give, as a rule, clear definitions of the differences between these terms. Therefore, I shall use the terminology preferred in the latest works of Vernadsky. This will help to some extent to achieve terminological consistency. 

A few comments on idealization are in order here. We obtain physical laws by abstracting reality. Often, only the concept of simplification of the real world by abstraction allows a mathematical description of a physical phenomenon. On the other hand, problems and inconsistencies arise by the simplification procedure. Here we present some examples ... 

It is often better to avoid any manipulation of the system if the aim is to reduce its dimensions. In fact, it is advisable to leave the nonlinear system in its original form since it is derived from the modeling of a physical phenomenon. In doing so, there is greater certainty that the numerical system is well conditioned because it describes a real problem. 

This is a real pity, because many interesting and fnndamental properties of the physical phenomenon are missed. In the following sections, the demonstration will allow one to define a crucial concept, the wave function, by going through the definition of the imaginary nnm-ber and of the exponential fnnction. All are fnndamental tools that are not just mathanatical beings but important concepts helping to understand physics as much as possible. 

The zero flow pressure, a well known phenomenon in the coronary bed, is commonly known in other vascular beds as the critical closing pressure . Many theories attempt to explain the reason for the existance of the critical closing pressure (Hoffman, 1978 Archie, 1978 Bellamy, 1978). Is this a real physical closure of the micro vessel lumen, or is it a function of the yield stress of the blood attributed to its cassonian rheological properties The zero flow pressure, Pjf, is in fact a combination of the critical closing pressure, the compressive effects and the autoregulating effects. 

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