Thresholds, behavioral

Figure 10-15. Output vs. input energy characteristic of our laser device. The horizontal dashed curve indicates the zero line. A clear laser threshold behavior at an excitation pulse energy ol 1.5 nJ is observed. Below the lasing threshold only isotropic phololuminesccncc is entitled. Above threshold the device emits low divergence single mode laser emission perpendicular to the surface, as schematically shown in the inset. The laser light is polarized parallel to the grating lines.

Catalyst Decay. Asymmetric hydrogenation of the SM using the Et-DuPhos-Rh catalyst exhibits a catalyst threshold behavior. When the initial charge of the catalyst is below this threshold value, the reaction is not completed. This indicates that the catalyst may become deactivated. 

The small cluster threshold behavior, suggested by the kinetics scheme presented earlier, is apparent in this data set. Assuming (1) the RRK form for k n, (2) the addition reactions are not activated, and (3) the number of participating modes are independent of the element type, the M-CO bond strengths can be grouped by energy. For... 

The rate of dye decomposition should be negligible at exposure energies up to several thousand times the energy absorbed during the read process and increase rapidly thereafter. Dye compositions which exhibit this type of threshold behavior must have relatively high photochemical and thermal stability and decompose by a free radical process above the melting point of the substrate.199... 

We have already mentioned the threshold behavior of photodetachment. Morrison (1957) postulated the rule that at or near threshold, the cross section for a process should vary as cr°c( - ) , where is the energy transferred, 0 is the minimum energy required for the process, and n equals the number of outgoing electrons minus 1. Thus, as shown schematically in Figure 4.4, the threshold cross section should vary linearly with energy for... 

FIGURE 4.4 Schematic of threshold behavior of ionization processes. Under ideal conditions, one expects a step function for photoionization, a linear variation with energy under electron impact, and a parabolic dependence for double ionization by electron impact. 

The different threshold behaviors for heads and tails orientations shown in Figures 7 and 8 indicate that, at very low energies, reaction is restricted to only one end of the molecule. We directly observe that there is no reaction for attack in the unfavored orientation. The different thresholds for attack at different ends of these molecules requires the final state of the system, at the respective thresholds, to be somehow different for attack at the opposite ends of the molecule. For CFjBr, we believe that different products may be formed, depending on the end attacked, but the same species in different internal states could also be a possibility. In these experiments there are two likely low-energy reaction channels. 

Matkovic, V., and Heaney, R. P. (1992). Calcium balance during human growth Evidence for threshold behavior. Am. J. Clin. Nutr. 55, 992-996. 

Based on the preceding results, we can say that linearly polarized light from the band-gap absorption region can induce either transitory changes or crystallization transformation in amorphous Sbj Sei alloys. These two phenomena critically depend on exposure, show threshold behavior, and seem to arise from apparently different mechanisms defect states or some kind of structural units given preferential orientation under the action of linearly polarized light. 

Since photodecomposition appears to occur randomly throughout the UP crystals, the influence of cooperative intermolecular effects at conversions as low as 0.06% indicates that reactivity in single crystals can be controlled by defects far beyond the first coordination sphere of the reaction center, and that caution must be used when interpreting product ratios, even after low levels of decomposition. The threshold behavior for such influence also warms against extrapolation of product ratios at finite decomposition levels to those expected after infinitesimal amounts of conversion. 

Figure 10.10 Near threshold behavior of neutron and charged-particle-induced reactions. [From Ehmann and Vance (1991).]...

Threshold Behavior of the Formation of a Quasi-Bound State 225... 

The asymptotic overcritical dipole potential also affects the threshold behavior of the phase shift [60, 72, 83, 84]. Thus, the eigenphase sum includes a term S ip(E) that diverges logarithmically toward the threshold E for these sublevels, S ip(E) satisfying a formula... 

THRESHOLD BEHAVIOR OF THE FORMATION OF A QUASI-BOUND STATE... 

J. Ludlow, G.F. Gribakin, Effect of a finite-energy spread of the positron beam on the threshold behavior of the positron annihilation cross section, Phys. Rev. A 66 (2002) 064704. 

TCDD, both biochemical and biological, do or do not demonstrate threshold behavior. 

The sub-threshold behavior for gate voltages slightly positive to Vr, is described using the expression ... 

Figure 4.2. Variation of the radiative width y, or coherent emission rate, of a 2D disordered exciton as a function of the disorder strength A. For A > g,r, the emission becomes incoherent. For all distributions, including the gaussian distribution, there is threshold behavior with a sudden takeoff of the coherent emission.

K. Shima, T. Nakagawa, K. Umetani, T. Mikumo, Threshold behavior of Cu-, Ge-, Ag-K-, and Au-L3-shell ionization cross sections by electron impact, Phys. Rev. A 24 (1981) 72. 

It must be underlined that the central manifold theorem, extending the linear center manifold into the nonlinear regime, is way less powerful than its stable/ unstable counterpart. There is no limit t —> oo and even no unicity of nonlinear center manifolds. Consequently, it is not well known how this whole beautiful stmcture bifurcates and disappears as E > E. There has been virtually no study of the bifurcation stmcture (see, however, Ref. 55), and the transition from threshold behavior to far-above-threshold behavior is an open question, as far as I am aware. 

Kawakubo et al. studied the behavior of a self-exdted oscillator under the influence of an extomal noise. Th found that the self-osdUations are suppressed by the external noise with a threshold behavior reminiscent of the phase transitions of a ferroelectric sample. 

The threshold behavior seen in Fig. 8 suggests that CO does not react readily with the nearly defect-free stoichiometric surface, but that some O ions must be removed, forming 0-vacancy point defects, before a significant reaction can... 

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