Hypothetical particle

The Maxwell-Boltzmann velocity distribution function resembles the Gaussian distribution function because molecular and atomic velocities are randomly distributed about their mean. For a hypothetical particle constrained to move on the A -axis, or for the A -component of velocities of a real collection of particles moving freely in 3-space, the peak in the velocity distribution is at the mean, Vj. = 0. This leads to an apparent contradiction. As we know from the kinetic theor y of gases, at T > 0 all molecules are in motion. How can all particles be moving when the most probable velocity is = 0 ... 

Fig. 8-12 Hypothetical particle arrangement in a sediment and a clay aggregate. (Adapted from Casa-grande, 1940.)...

Figure5.9. Hypothetical particle of cubic MgO, exhibiting three crystallographic surfaces. The (100) and (110) surfaces are nonpolar, implying that Mg and O ions are present in equal numbers, but the polar (111) surface can be terminated either by Mg cations or O anions. In practice, MgO crystals predominantly show (100) terminated surfaces. 

Equation (6.11) is the Schrodinger equation for the translational motion of a free particle of mass M, while equation (6.12) is the Schrodinger equation for a hypothetical particle of mass fi. moving in a potential field F(r). Since the energy Er of the translational motion is a positive constant (Er > 0), the solutions of equation (6.11) are not relevant to the structure of the two-particle system and we do not consider this equation any further. 

The kinetic energy of the hypothetical particle of perpendicular to the z axis can be expressed by... 

The result of a binary collision is specified in classical mechanics by the angle of deflection, x It is defined in Fig. 10, where the trajectory of the hypothetical particle of mass fi is illustrated. It can be seen that when r is minimal, that is at the distance of closest approach, the angle is related to the angle of deflection by... 

This has also commonly been termed direct interception and in conventional analysis would constitute a physical boundary condition imposed upon the particle path induced by action of other forces. By itself it reflects deposition that might result with a hypothetical particle having finite size but no mass or elasticity. 

Consequently, we are forced to admit that compact massive objects are not the main component of the dark halo of our Galaxy, or any of its kind. This in turn implies that the Sun and stars are lost amongst a halo of darkness, in the middle of a haze of neutralinos, hypothetical particles predicted by so-called supersymmetric particle theories. 

Pauli called his hypothetical particle the neutron. Naturally it bore no relationship to the neutron of which Rutherford spoke, which Chadwick was soon to discover. But the confusion that might have resulted was avoided when Enrico Fermi suggested adding the Italian diminutive suffix -ino to the name. Pauli s particle was thus christened the neutrino ( little neutral one ). 

The eightfold-way theory had its first success when Gell-Mann used it to predict the existence of an as-yet-undiscovered particle, just as Mendeleev had predicted the existence of undiscovered evidence. Gell-Mann called the hypothetical particle the omega-minus (it had a negative charge). In 1964 experimentalists found the particle and confirmed that it had exactly the mass Gell-Mann said it would have. 

Research on liquid-phase oxidation processes has opened up a tremendous area for research on free radical mechanisms. Such research will be concerned, not with hypothetical particles like those studied a few years ago, but with thoroughly material active centers, amenable to investigation by experimental techniques currently in use. Problems of foremost importance are involved in correlating data on unit processes... 

The chemists of the nineteenth century once thought that all material substances were comprised of only 36 elements,3 Over the years, these expanded to over 100 elements. Fifty years ago, it was proclaimed that the elements were made of electrons, protons, and neutrons. Then, commencing in the 1940s, many other particles were found, as described here. Then for a while it seemed that elementary matter could be reduced to three particles—the quarks. But quarks have multiplied in number, with a sixth quark now seriously proposed. Will there be too many quarks Perhaps hypothetical particles will be proposed from which the quarks are comprised. Possibly the ultimate answer will lie with the mathematical groups that order the particles rather than in truly elementary objects. ... 

The surface mean diameter ds is the diameter of a hypothetical particle having the same averaged surface area as that of the given sample ds is given by... 

Consider a system of a mixture of a minor component of uniform size in a major component, which can be solid or liquid. In either case, we shall measure the amount of major component in a withdrawn sample as the number of hypothetical particles, each having the same volume as a minor-component particle. If the volume fraction of minor component is p and we withdraw samples containing n particles, the fraction of samples containing k minor particles is given by... 

The three active neutrinos are our only known particle candidates for non-baryonic dark matter. Since they fail to be cold dark matter, we are lead to consider hypothetical particles. 

Current cosmological data imply the existence of non-baryonic dark matter. We have discussed some of the most popular candidates and shown that none of the candidates known to exist, i.e. the active neutrinos, can be non-baryonic cold dark matter. Hence to explain the nature of cold dark matter we need to invoke hypothetical particles that have not been detected yet. Some of these hypothetical particles have been suggested for reasons different than the dark matter problem (such as sterile neutrinos, neutralinos, and axions), some others have been proposed mainly as a solution to the cold dark matter problem (e.g., self-interacting dark matter, WIMPZILLAs, etc.). Although most studies focus on the first category of candidates, especially neutralinos and axions, we should keep an open mind. 

The diameter ds of a hypothetical particle having an average surface-area is given by Eq (3-10). The total surface is measured by 2nd2 where, as before, n is the number of particles having a diameter d. Since 2n is the total number of particles, then... 

Determination of Surface-Shape Factor—The shape-factor is one which, when multiplied by the square of the diameter of a hypothetical particle having an average surface, gives the true surface. The shape-factor is given by Eq (3-41)... 

The theoretical analysis of atmospheric aerosols just described focuses on a population of typical yet hypothetical particles that have the average chemical characteristics of the ambient mix. Yet, the nature of actual, individual particles remains largely a mystery due to the difficulties in collecting and probing single submicron particles. 

Figure 3. Depth profiling of a hypothetical particle by the techniques of Table 5.

Figure 5. A hypothetical particle size distribution curve of low temperature ash and product coal.

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