Mechanical moment

This simplified treatment does not account for the fine-structure of the hydrogen spectrum. It has been shown by Dirac (22) that the assumption that the system conform to the principles of the quantum mechanics and of the theory of relativity leads to results which are to a first approximation equivalent to attributing to each electron a spin that is, a mechanical moment and a magnetic moment, and to assuming that the spin vector can take either one of two possible orientations in space. The existence of this spin of the electron had been previously deduced by Uhlenbeck and Goudsmit (23) from the empirical study of line spectra. This result is of particular importance for the problems of chemistry. 

BACK-GOUDSMIT EFFECT. An effect closely related to the Zeeman effect. It occurs in the spectrum of elements having a nuclear magnetic and mechanical moment. See also Hyperfine Structure and Paschen-Back Effect. 

The emulsion of a fatliquor should not be too stable. The leathermaker wants to control its depth of penetration into the leather by the tendency of the surfactant to adsorb to the protein of the hide. This adsorption depletes the micelles of surfactant, causing the emulsion to break before it permeates the interior of the hide, releasing the oil somewhat superficially. The untreated interior thereby retains its stiffness, but with only a small mechanical moment. The product is then firm but resilient (not like cardboard). The released oil, with the surfactant tightly bound to the fibers, also resists being washed out of the leather by water. Suede leather, on the other hand, requires full penetration of the fatliquor and, therefore, an emulsifier that does not bind tightly to the protein. 

After Sommorfeld, j is called the inner quantum number it represents the total mechanical moment of the atom. It too must of course be quantised. Since s — there are only the two possibilities,... 

We shall now show that the electron s own magnetic moment, which is bound up with its mechanical moment, supplies the explanation of the anomalous Zeeman effect, i.e. the observed phenomenon that in a (weak) magnetic field a spectral line is split up into a considerable number of lines (fig. 2, Plate VII) while, according to classical theory, and also according to wave mechanics when spin is not taken into account, we can only have the normal Zeeman effect, i.e. the splitting up of every spectral line into a Lorentz triplet. 

We may briefly recall the explanation of the normal Zeeman effect. The revolution of the electron produces a mechanical moment j>i of the orbital motion, and this is quantised by known rules ... 

The factor 2 here arises from the anomaly in the relation between magnetic and mechanical moment in the spin, as compared with the similar relation in the orbit—an anomaly mentioned on p. 142, and explained by Thomas as a consequence of the theory of relativity. In this equation s is the operator of the total spin moment, and cS s cos(,9, H) is its component in the direction of the field. 

Closely connected with the mechanical moment of nuclei is their magnetic moment. We have already ( 7, p. 166) made some remarks about the determination of this quantity, particularly for the proton. We may add here that it is also possible to evaluate magnetic nuclear moments by the theoretical calculation of the dimensions of the fine structure, and comparison with the measurements. 

Clearly, CTI leads to a periodic backbone contraction/expansion of the polypeptide chain involved, as could be inferred from the isomer-specific distances of the Ca atoms directly attached to the isomerizing peptide bond. For prolyl bonds in native proteins this distance is about 0.8 A shorter in the cis isomer when compared to the respective trans isomer [12]. This atomic translation produces a mechanical moment that was hypothesized to be involved in the functional cycle of motor proteins [13]. 

In the theory of elastic plates and shells it is sometimes natural to introduce explicitly not only the external forces g(r) acting on the surface, but also external shearing forces Q and mechanical moments M applied to the edges. The equilibrium conditions are then (see Ref. 86, Section 23)... 

In the first place, it appears from delicate measurements on the mechanical moment acquired by a body when it is magnetized that the spin moments rather than the orbital moments of electrons are those chiefly responsible for ferromagnetism. This finding points to some hypothesis about the mode of coupling of electron spins. The ordinary magnetic interaction of the spin moments is much too small to account for the powerful mutual effect. 

Integration in Eqn (10.2) is performed over V area occupied by the current sources. As (r, (p, z) one can mark cylindrical coordinates of a free point in space, and as (p,6,Q—cylindrical coordinates of a point that belongs to V area. The magnetic induction vector is determined from the equality B = rotA.. Magnetic carriers (separate nanoparticles or their aggregates) can be considered as magnetic dipoles. In general, the dipole is influenced by the force F and mechanical moment M which are defined by the known formulas ... 

Due to the mechanical moment, free dipoles orient along the field, and then M = 0. Dipoles turn quite quickly, we can assume that they are always focused along the field. The force of magnetic interaction depends not only on change of magnetic field, but also variations of magnetic moment of the carrier. If these values are constant in space then F = 0. Hence, to obtain the required values of the forces, the magnetic field should vary in space. 

The electric current in the electromagnetic coil is chosen such that the resulting mechanical moment (M ) of the magnetic forces keeps the beam exactly horizontal. Then the balance of moments is... 

Here Ms and are the mechanical moments of the gravity forces of the beam, wire, and basket of the balance on its sorbent sample site (s) and ballast or tare site (k) respectively. Likewise Bs and Bk indicate the moments of the buoyancy forces of beam, wire, and basket on the sorbent site (s) and ballast or tare site (k) respectively. Tbe other quantities and parameters in Eq. (3.1)... 

Here the symbol M indicates any of the electromagnetically measured mechanical moments occurring on the r. h. s. ofeq. (3.10), the uncertainties of which having been assumed to be equal for all four types of... 

An angular momentum vector L, associated with a magnetic moment will precess in a magnetic field, as illustrated in Fig.2.3. Frequently we encounter this phenomenon in the description of atomic and molecular processes. To demonstrate the phenomenon, imagine magnetic poles q in analogy with the electrical case, for which we have the same mathematical description. For the mechanical moment M we then have... 

Radiation pattern Source mechanism Moment tensor. Source inversion... 

Fault-plane solutions Focal mechanisms Moment-tensor solutions... 

C. Lacabanne I don t know. What I can say is that the relative magnitude of the Tg and Tji is strongly affected by the kind of measurement. It s quite amazing that in some materials we can relate the relative magnitude of the Tg and Tji. It is the same, say, by DMA and TSC in the case of poly(cyclohexyl methacrylate). Generally speaking, the relative magnitude of both transitions is a characteristic of the type of laboratory data taken, either dipole or mechanical moments of the chains. That s all I can say for now. 

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