Localized behavior

From our transport measurements, we can conclude that at low temperatures, the conductivity of the bundle of buckytubes shows two-dimensional weak localization behavior and the MR is negative above 60 K the MR is positive and increases approximately... 

Solutions to models with different length scales may contain regions such as shocks, steep fronts and other near discontinuities. Adaptive meshing strategies, in which a spatial mesh network is adjusted dynamically so as to capture the local behavior accurately, will be described. The algorithm will be tested on an example of filtration combustion. 

The solution to these models will have regions of strongly localized behavior such as shocks, steep fronts and other near discontinuities. 

Gas holdup and liquid circulation velocity are the most important parameters to determinate the conversion and selectivity of airlift reactors. Most of the reported works are focused on the global hydrodynamic behavior, while studies on the measurements of local parameters are much more limited [20]. In recent years, studies on the hydrodynamic behavior in ALRs have focused on local behaviors [20-23], such as the gas holdup, bubble size and bubble rise velocity. These studies give us a much better understanding on ALRs. 

Most XYZ molecules, especially those with mx very different from mz (for example, HCN) have local behavior. The situation is very different in XY2 molecules, for which the two bonds are identical. Thus, one must have... 

If Xy = 0 the vibrations have local behavior. As the XyS increase, one goes more and more into normal vibrations. 

Langley, W. M. (1988). Spiny mouse s (Acomys cahirinus) use of its distance senses in prey localization. Behavioral Processes 16,67-73. 

Imperfect though they are, the impact of these functionals on later, more refined developments cannot be overstated. To this end, some general observations can be made. Eq. (53) certainly lacks flexibility, since once 9(72) is chosen, G[g] will have a fixed value for all systems. Eq. (54) is better due to the global dependence of G(N, Z) on specific system parameters. Eq. (55) is the best among these three, since it accoimts for the local behavior of the OF-KEDF. 

While all the previous methods use two points, the correction (2.10) is based exclusively on the local behavior of the function as shown on Fig. 2.4. 

Because the flow of electric current always involves the transport of matter in solution and chemical transformations at the solution-electrode interface, local behavior can only be approached. It can be approximated, however, by a reference electrode whose potential is controlled by a well-defined electron-transfer process in which the essential solid phases are present in an adequate amount and the solution constituents are present at sufficiently high concentrations. The electron transfer is a dynamic process, occurring even when no net current flows and the larger the anodic and cathodic components of this exchange current, the more nearly reversible and nonpolarizable the reference electrode will be. A large exchange current increases the slope of the current-potential curve so that the potential of the electrode is more nearly independent of the current. The current-potential curves (polarization curves) are frequently used to characterize the reversibility of reference electrodes. 

Alternatively, such prepared excited states may prove useful photochemically under particular circumstances. This is especially true for local-mode-type molecules [461, 462], that is, molecules for which vibrational eigenstates resemble localized excitation in individual bonds. As an example, in the case of HOD, the large frequency difference between the OH and OD oscillators is such that intramolecular vibrational relaxation does not destroy the localized excitation. (Similar effects arise if one excites a resonance state that displays local behavior see, for example, Ref. [463] for an ABA-type molecule.) As shown theoretically [464, 465], and confirmed experimentally [53-60], preparation of the OH stretch followed by an excitation laser leading to dissociation gives a marked enhancement of the H atom photodissociation in many molecules. 

The positive-definiteness of H is a useful concept in analysis of general functions. Smooth functions can be approximated by quadratic models within a sufficiently small neighborhood of a given point. The local behavior of f can then be analyzed in terms of the properties of H. 

A dependence close to a linear law is observed down to 100 K. At low temperature, both the thermal expansion and the pressure coefficient are small. Therefore, the constant-volume temperature dependence of the resistivity does not deviate from the quadratic law observed under constant pressure. At this stage it is interesting to stress that the theory of the resistivity in a half-filled band conductor [63], including the strength of the coulombic repulsions as derived from NMR data (Section III.B), should lead to a more localized behavior than that observed experimentally in Fig. 14. 

It is easily understood that local heat transfer coefficient is closely related to the local behaviors of gas and particles. When the heat transfer surface is suspended in the column for heat transfer coefficient measurements, a certain connecting stick is usually used. The use of the connecting stick will disturb the flow pattern of the particles around the probes, so that local heat transfer coefficients measured for probes pointing upward is expected to be different from those obtained for downward probes. 

The local behavior of the rest point set on the boundary is summarized in Table 4.1, where 0 < A < A2 < 1 is assumed. The more interesting case is that of an interior rest point. Let <. = (xf, X2c, pi) denote the coordinates of a possible interior rest point. First of all, it must be the case that... 

The first study of this type in the Moerner lab explored the histidine kinase PleC, which localizes at one of the poles of the cell during the cell cycle. PleC fusions to EYFP were easily observed at the single-molecule level in C. crescentus cells, mostly diffusing via attachment to the inner membrane [114]. Because no directed transport or motional asymmetry was observed, the authors were able to conclude that a diffusion-to-capture model could explain the observed localization behavior. 

The normalized variable (NV) approach of Leonard [109, 107] uses the locally normalized variable ip to predict the local behavior of the converted variable ip ... 

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