Rotation in spherical mode

Should a fermion represent some special distortion, or knot, in the aether, spherical rotation allows it to move freely through the space-time continuum without getting entangled with its environment, which consists of the same stuff as the fermion. While rotating in spherical mode adhesion to the environment is rythmically stretched and relaxed as the fermion moves through space. This half-frequency disturbance of the wave-field, that supports the fermion in space, constitutes the effect observed as spin. 

To understand the appearance of spin it is necessary to consider a fermion as some inhomogeneity in the space-time continuum, or aether. In order to move through space the fermion must rotate in spherical mode, causing a measurable disturbance in its immediate vicinity, observable as an angular momentum of h/2, called spin. The inertial resistance experienced by a moving fermion relates to the angular velocity of the spherical rotation and is measurable as the mass of the fermion. 

An elegant description of rotation in spherical mode is provided in terms of a special unitary matrix of order 2, known as SU(2) in Lie-group space (T2.8.2). The matrices that form a basis for the algebra of SU(2) are those already introduced to represent quaternions. The important result is that the group space SU(2) is compact compared to a noncompact group R that characterizes cylindrical rotation about an axis of infinite extent. If an object... 

Like its energy, the angular momentum of the valence electron also becomes spherically averaged. It rotates in spherical mode and its total angular momentum appears as quantum torque. Like a spinning electron this orbital quantum torque sets up a half frequency wave field that resonates non-locally with the environment. The most general solution to the wave equation of a spherically confined particle therefore is the Fourier transform of the spherical Bessel function... 

It is important to note that the property of spin is only defined in quanternion notation, which specifies a conserved quantity J. It may be viewed as a fourdimensional symmetry operator, approximated by a three-dimensional angular-momentum operator L and a one-dimensional spin, on separation of space and time variables. The approximation J = L - - S implies that neither L nor S is a three-dimensional vector, both of them implying rotation in spherical mode [3]. The one-dimensional projections, and S, in an applied magnetic field or in a molecular environment are vector quantities. 

These relations are together generally referred to as single correlation time theory and used to correlate the relaxation phenomena for monomeric substances in solution to their molecular motion. Nevertheless, in the case of macromolecules, the C-H vectors in the molecular structure are not thought to undergo such isotropic spherical diffusional rotation. In fact, the relaxation phenomena of macromolecules seldom follow these relations and particular modes of motion must be assumed for the internuclear vectors considering the detailed molecular structure. 

As with spherical particles the Peclet number is of great importance in describing the transitions in rheological behaviour. In order for the applied flow field to overcome the diffusive motion and shear thinning to be observed a Peclet number exceeding unity is required. However, we can define both rotational and translational Peclet numbers, depending upon which of the diffusive modes we consider most important to the flow we initiate. The most rapid diffusion is the rotational component and it is this that must be overcome in order to initiate flow. We can define this in terms of a diffusive timescale relative to the applied shear rate. The characteristic Maxwell time for rotary diffusion is... 

The most convincing physical model [63] explains electron spin in terms of spherical rotation, another way of rotating a solid object, different from the well-known mode of rotation about an axis. It starts as a slight wobble, which, by continuous exaggeration of the motion, develops into a double... 

When R2 is spherical with Cx symmetry, the preferred mode of energy minimization will be bond bending as in the hindered rotation of biphenyls. 

Figure 6.4. The powder diffraction pattern collected from a sample of LaNi4 35800.15 using Cu Ka radiation on a Rigaku TTRAX rotating anode diffractometer. The divergence slit was 0.75° and the receiving slit was 0.03°. The experiment was carried out in a continuous scanning mode with a rate 0.5 deg/min and with a sampling step 0.02°. The powder used in this experiment was prepared by gas atomization from the melt and therefore, particles were nearly spherical (see inset in Figure 3.32).

There are few methods suitable for on-line chemical analysis of aerosol particles. Raman spectroscopy offers the possibility of identifying the chemical species in aerosol particles because the spectrum is specific to the molecular. structure of the material, especially to the vibrational and rotational modes of the molecules. Raman spectra have been obtained for individual micron-sized particles placed on surfaces, levitated optically or by an eiectrodynamic balance, or by monodisperse aerosols suspended in a flowing gas. A few measurements have also been made for chemically mixed and poly disperse aerosols. The Raman spectrum of a spherical particle differs from that of the bulk material because of morphology-dependent resonances that re.su It when the Raman scattered photons undergo Mie scattering in the particle. Methods have been developed for calculating the modified spectra (McNulty el al., 1980). 

When the pseudo-spherical ammonium ion is mostly replaced by a truly spherical ion the complex sequence of phase changes found in the pure ammonium halides is suppressed. The mixed potassium ammonium halide salts retain their NaCl cubic structure down to the lowest temperatures. The alkali metal ions support the structure leaving the ammonium ions as free to rotate at 1 K as at 300K [13]. The INS spectrum of this system is quite different from the pure salt and there are no sharp features in any region of the spectrum. We shall analyse the impact that this freedom has on the internal modes about 1400 cm. ... 

K by the forcible pressure swing adsorption method (ca. 13 MPa). The adsorbed methane molecules are located in the pocket-like narrow corners of the necks of the ID channel [20]. Because the thermal motion of the pseudo-spherical methane molecules seems to be effectively suppressed in its translation mode but rotation is allowed, the forcible adsorption of methane gas produces an inclusion plastic crystal [20], which can be regarded as a mesophase between the fluid and solid state of the phase of a guest incorporated in a crystal host the guest molecules are randomly oriented, but their alignment follows the crystal periodicity. 

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