Transition pole

Connection formula pertaining to a first-order transition pole at the origin... 

Now we assume that in a certain region of the complex 2-plane around a first-order transition pole at the origin, i.e., a first-order pole of Q2(z) at the origin, we have... 

Quadmpoles or hexapoles are used as transmission guides for both slow and fast ions. In both cases, the objective is to ensure that as many ions as possible are guided from the entrance of the device to its exit. The ions are usually in transit in a straight line between an ion source and a mass analyzer. Any ions within the transmission guides that are deflected from the desired trajectory are pushed or pulled back on course by the action of the inhomogeneous RF fields applied to the poles of the guides. 

The poles con espond to excitation energies, and the residues (numerator at the poles) to transition moments between the reference and excited states. In the limit where cj —> 0 (i.e. where the perturbation is time independent), the propagator is identical to the second-order perturbation formula for a constant electric field (eq. (10.57)), i.e. the ((r r))Q propagator determines the static polarizability. 

Naqvi [134] has proposed an alternative model to the Frye and Horst mechanism for the degradation and stabilization of PVC. At room temperature, PVC is well below its glass transition temperature (about 81°C). The low thermal stability of the polymer may be due to the presence of undesirable concentrations of like-poles in the more or less frozen matrix with strong dipoles. Such concentrations, randomly distributed in the polymer matrix, may be considered to constitute weak or high energy spots in the polymer, the possible sites of initiation of thermal dehydrochlorination. 

On heating PVC, as the glass transition temperature is approached, the tensions within the concentrations of like-poles may be released by atoms being pushed apart to an extent that some break from the polymer backbone, resulting in the initiation of dehydrochlorination of the polymer. Unstabilized PVC is known to start degrading at approximately its glass transition temperature [135]. 

Since the excited levels are determined by searching the poles of the polarization propagator, the poles corresponding to very small dipole transition strengths are difficult to identify. This is particularly the case for the highest energy poles and, consequently, it is not possible to determine by such procedure the top of the conduction band. 

In anisotropic crystals, the amplitudes of the atomic vibrations are essentially a function of the vibrational direction. As has been shown theoretically by Karyagin [72] and proved experimentally by Goldanskii et al. [48], this is accompanied by an anisotropic Lamb-Mossbauer factor/which in turn causes an asymmetry in quadra-pole split Mossbauer spectra, for example, in the case of 4 = 3/2, f = 1/2 nuclear transitions in polycrystalline absorbers. A detailed description of this phenomenon, called the Goldanskii-Karyagin effect, is given in [73]. The Lamb-Mossbauer factor is given by... 

Loss of sister chromatid cohesion would therefore be sufficient for the sudden movement of chromatids to opposite poles at the metaphase to anaphase transition. According to this hypothesis, a specific apparatus binds chromatids together during replication, holds them in an orientation that facilitates the attachment of sister kinetochores to spindles extending to opposite poles, and resists the splitting force that results from this bipolar attachment to the spindle. Destruction of this specialized cohesive structure triggers movement of chromatids to opposite poles at the onset of anaphase. 

The pall of fog that has shrouded the sister separation process for over a century is starting to lift and this long mysterious process has started to reveal its secrets. There is now convincing evidence that the sudden movement of chromosomes to the poles at the onset of anaphase is triggered by cleavage of specific sister chromatid cohesion proteins. Future research must address the structural basis of cohesion and how it is established only at replication forks. It must also address the generality of mechanisms that dismantle cohesion at the metaphase to anaphase transition and how mistakes in this process contribute to human disease. 

The transition from laminar to turbulent flow on a rotating sphere occurs approximately at Re = 1.5 4.0 x 104. Experimental work by Kohama and Kobayashi [39] revealed that at a suitable rotational speed, the laminar, transitional, and turbulent flow conditions can simultaneously exist on the spherical surface. The regime near the pole of rotation is laminar whereas that near the equator is turbulent. Between the laminar and turbulent flow regimes is a transition regime, where spiral vortices stationary relative to the surface have been observed. The direction of these spiral vortices is about 4 14° from the negative direction of the azimuthal angle,. The phenomenon is similar to the flow transition on a rotating disk [19]. 

Because T -> V energy transfer does not lead to complex formation and complexes are only formed by unoriented collisions, the Cl" + CH3C1 -4 Cl"—CH3C1 association rate constant calculated from the trajectories is less than that given by an ion-molecule capture model. This is shown in Table 8, where the trajectory association rate constant is compared with the predictions of various capture models.9 The microcanonical variational transition state theory (pCVTST) rate constants calculated for PES1, with the transitional modes treated as harmonic oscillators (ho) are nearly the same as the statistical adiabatic channel model (SACM),13 pCVTST,40 and trajectory capture14 rate constants based on the ion-di-pole/ion-induced dipole potential,... 

Fig. 46 Schematic diagram of elemental process during transition from Hex cylinder to bcc sphere (i) undulation of interface (a, b), (ii) break-up of cylinders into ellipsoids (b, c), (iii) relaxation of domains from ellipsoids into spheres (c, d), and (iv) relaxation in junction distribution to attain uniform distribution (d, e). Pole where concentration of junction points is low may work as memory of grain conservation upon reverse transition from bcc sphere to Hex cylinder. Small arrows in part (b) indicate diffusion of chemical junctions along interface in process (ii). From [136], Copyright 2000 American Chemical Society...

The electrodeposited precursor films, annealed in air at 870 °C in the presence of a TBSBCCO pellet, produce a biaxial textured Tl-1223 phase, as confirmed by an XRD pole-figure measurement. The omega and phi scans indicate full-width at half-maximum (FWHM) values of only 0.92° and 0.6°, respectively, which indicates a very high-quality film. The superconductive transition temperature of the Tl-1223 film, determined resistively, was about 110 K. Figure 7.11... 

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