Physical phenomena

The principle physical phenomenon of applying the eddy current method for evaluating the amount of residual austenite in the structure of quenched steel is magnetic induction, involving the influence of the changeable magnetic field on the studied area, found under the probe. 

Let us consider one more physical phenomenon, which can influence upon PT sensitivity and efficiency. There is a process of liquid s penetration inside a capillary, physical nature of that is not obvious up to present time. Let us consider one-side-closed conical capillary immersed in a liquid. If a liquid wets capillary wall, it flows towards cannel s top due to capillary pressure pc. This process is very fast and capillary imbibition stage is going on until the liquid fills the channel up to the depth l , which corresponds the equality pcm = (Pc + Pa), where pa - atmospheric pressure and pcm - the pressure of compressed air blocked in the channel. 

When considering mathematical models of plates and shells, the authors clearly perceived the necessity for a reasonable compromise so that, on the one hand, the used models should describe the principle of a physical phenomenon and, on the other, they should be quite simple in order that the mathematical tool could be usefully employed. 

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... 

An appropriate set of iadependent reference dimensions may be chosen so that the dimensions of each of the variables iavolved ia a physical phenomenon can be expressed ia terms of these reference dimensions. In order to utilize the algebraic approach to dimensional analysis, it is convenient to display the dimensions of the variables by a matrix. The matrix is referred to as the dimensional matrix of the variables and is denoted by the symbol D. Each column of D represents a variable under consideration, and each tow of D represents a reference dimension. The /th tow andyth column element of D denotes the exponent of the reference dimension corresponding to the /th tow of D ia the dimensional formula of the variable corresponding to theyth column. As an iEustration, consider Newton s law of motion, which relates force E, mass Af, and acceleration by (eq. 2) ... 

As indicated earlier, the vaUdity of the method of dimensional analysis is based on the premise that any equation that correcdy describes a physical phenomenon must be dimensionally homogeneous. An equation is said to be dimensionally homogeneous if each term has the same exponents of dimensions. Such an equation is of course independent of the systems of units employed provided the units are compatible with the dimensional system of the equation. It is convenient to represent the exponents of dimensions of a variable by a column vector called dimensional vector represented by the column corresponding to the variable in the dimensional matrix. In equation 3, the dimensional vector of force F is [1,1, —2] where the prime denotes the matrix transpose. 

Suppose that there are variables Q2,. .., that are involved in a physical phenomenon whose dimensional vectors are D, D2,. .., D, respectively. This phenomenon can generally be expressed by (eq. 4) ... 

Theorem 1. The number of products in a complete set of B-numbers associated with a physical phenomenon is equal to n — r, where n is the number of variables that are involved in the phenomenon and ris the rank of the associated dimensional matrix. 

Theorem 4. The set of B-numbers associated with a physical phenomenon is invariant with respect to the choice of the reference dimensions provided that the reference dimensions are considered independent, and that the number of these reference dimensions is not altered. 

The implication of this theorem is important in that in computing a complete set of dimensionless products or B-numbers associated with a physical phenomenon, it does not matter which set of dimensions are chosen as the reference dimensions as long as they are independent and their number is not altered. 

In applying dimensional analysis, it is first necessary to be able to identify the variables that govern a particular physical phenomenon. The naming of the governing variables requites some prior knowledge of a particular branch of physics involved. This may include analytical studies, experimental observations, or both. Whatever the source, there must be some prior knowledge upon which a selection can be made. 

Let Dhe the dimensional matrix of order mhy n associated with a set of variables of a physical phenomenon, where m is the number of chosen reference dimensions and n the number of variables of the set. Without loss of generaUty, it may be assumed that n > m. Consider the augmented matrix (eq. 21) ... 

Mass Transport. Probably the most iavestigated physical phenomenon ia an electrode process is mass transfer ia the form of a limiting current. A limiting current density is that which is controlled by reactant supply to the electrode surface and not the appHed electrode potential (42). For a simple analysis usiag the limiting current characteristics of various correlations for flow conditions ia a parallel plate cell, see Reference 43. 

Laser sampling is more a physical phenomenon than a chemical one. The energy of the laser is used to nonselectively ablate the sample. This insures homogeneous sampling of a physically defined area regardless of the nature of the components Solubilities are not a factor. This technique shows much promise for ceramics, glasses, and geologic samples. 

Theoretical representation of the behaviour of a hydrocyclone requires adequate analysis of three distinct physical phenomenon taking place in these devices, viz. the understanding of fluid flow, its interactions with the dispersed solid phase and the quantification of shear induced attrition of crystals. Simplified analytical solutions to conservation of mass and momentum equations derived from the Navier-Stokes equation can be used to quantify fluid flow in the hydrocyclone. For dilute slurries, once bulk flow has been quantified in terms of spatial components of velocity, crystal motion can then be traced by balancing forces on the crystals themselves to map out their trajectories. The trajectories for different sizes can then be used to develop a separation efficiency curve, which quantifies performance of the vessel (Bloor and Ingham, 1987). In principle, population balances can be included for crystal attrition in the above description for developing a thorough mathematical model. 

An important recent trend is the tendency for the two processes, CVD andPVD, to merge. For instance, CVD now makes extensive use of plasma (a physical phenomenon) and reactive PVD (evaporation or sputtering) occurs in a chemical environment. Much ofthenew equipment reflects this process integration in the concept of cluster tools which may incorporate CVD, etching, sputtering, and ion implantation in one piece of equipment. 

Diffusion is a physical phenomenon, which occurs when the atoms of a solid move into another solid above a certain temperature. Diffusion is particularly pronounced with silicon into aluminum, as mentioned in Sec. 2.2 above. It occurs during subsequent processing steps when the temperature exceeds 400°C. 

An important recent trend is the tendency for the two processes, CVD and PVD, to merge. CVD for instance, now makes extensive use of plasma (a physical phenomenon) and conversely. 

Porphyrin is a multi-detectable molecule, that is, a number of its properties are detectable by many physical methods. Not only the most popular nuclear magnetic resonance and light absorption and emission spectroscopic methods, but also the electron spin resonance method for paramagnetic metallopor-phyrins and Mossbauer spectroscopy for iron and tin porphyrins are frequently used to estimate the electronic structure of porphyrins. By using these multi-detectable properties of the porphyrins of CPOs, a novel physical phenomenon is expected to be found. In particular, the topology of the cyclic shape is an ideal one-dimensional state of the materials used in quantum physics [ 16]. The concept of aromaticity found in fuUerenes, spherical aromaticity, will be revised using TT-conjugated CPOs [17]. 

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. 

Several models are just different ways of representing the same physical phenomenon. For example, the lattiee-gas model, eapillary waves, and the density functional calculations presented above basically have the same view of the interface. However,... 

The term inversion is used here to refer to a feasible physical phenomenon, whioh in this case is similar to an umbrella that turns inside-out in the wind. The word has already been used twice in different senses (i) the inversion of coordinates, e.g. the passage from a right-handed system to a left-handed one and (ii) a traditional symmetry operation applied to a molecule with a center of invmioa. Accordingly, this term must be used with care ... 

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... 

Hybridization is not a physical phenomenon. It is a mathematical operation that is used to construct localized orbitals to describe the bonding in a molecule. 

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). 

It can also happen, and is perhaps more common, in the case of diffuse reflectance. In that measurement technique, absent a rigorous theory to describe this physical phenomenon, the concept of a variable pathlength is used as a first approximation to the nature of the change in the measurements. 

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