Local calculations

SOURCE LOCALIZATION CALCULATE THE X COORDINATE OF THE SOURCES THAT HAVE OVERCOME SCREENING... 

Electrophilic substitution reactions of unsubstituted quinoxaline or phenazine are unusual however, in view of the increased resonance possibilities in the transition states leading to the products one would predict that electrophilic substitution should be more facile than with pyrazine itself (c/. the relationship between pyridine and quinoline). In the case of quinoxaline, electron localization calculations (57JCS2521) indicate the highest electron density at positions 5 and 8 and substitution would be expected to occur at these positions. Nitration is only effected under forcing conditions, e.g. with concentrated nitric acid and oleum at 90 °C for 24 hours a 1.5% yield of 5-nitroquinoxaline (19) is obtained. The major product is 5,6-dinitroquinoxaline (20), formed in 24% yield. 

The shared memory OpenMP library is used for parallelization within each node. The evaluation of the action of potential energy, rotational kinetic energy, and T2 kinetic energy are local to each node. These local calculations are performed with the help of a task farm. Each thread dynamically obtains a triple (/2, il, ir) of radial indices and performs evaluation of first the kinetic energy and then the potential energy contribution to hps local( , i2, il, ir) for all rotational indices. 

The nonlocal results for C(F) are consistent with local calculations. Introducing softening of the, s-modes at short k only changes the undulative contribution to Cby 10-15%. 

Typically, the insertion induces sharp variation of the membrane profile at the distances 0.5-1.0nm from the membrane-peptide interface [79-82]. The steepness of this perturbation indicates that the short-A, behavior of membrane moduli must be important in the estimates of the elastic energy. In addition, a peptide inserted in a membrane almost certainly perturbs the membrane s elastic moduli in the immediate vicinity of the inclusion. Both these effects, membrane nonlocality and nonuniform modification of elastic properties by insertions, might play an important role in resolving the contradiction between the local calculations [80] and the experimental data for the mean lifetime of a gramicidin channel [81,109,110]. ... 

From these time-scales, it may be assumed in most circumstances that the free electrons have a Maxwellian distribution and that the dominant populations of impurities in the plasma are those of the ground and metastable states of the various ions. The dominant populations evolve on time-scales of the order of plasma diffusion time-scales and so should be modeled dynamically, that is in the particle number continuity equations, along with the momentum and energy equations of plasma transport theory. The excited populations of impurities on the other hand may be assumed relaxed with respect to the instantaneous dominant populations, that is they are in a quasi-equilibrium. The quasi-equilibrium is determined by local conditions of electron temperature and electron density. So, the atomic modeling may be partially de-coupled from the impurity transport problem into local calculations which provide quasi-equilibrium excited ion populations and effective emission coefficients (PEC coefficients) and then effective source coefficients (GCR coefficients) for dominant populations which must be entered into the transport equations. The solution of the transport equations establishes the spatial and temporal behaviour of the dominant populations which may then be re-associated with the local emissivity calculations, for matching to and analysis of observations. 

The reactivity of the hetero ring, with electron deficient 2(3)-positions, has been compared to glyoxal diimine." Quinoxalines are deactivated towards electrophilic substitutions, however, substitution is most likely to occur at the equivalent positions 5 and 8, where electron-localization calculations show the highest electron density to be. Electron-donor substituents in the benzenoid ring facilitate electrophilic substitution and, when activating substituents are present in the hetero ring, the site of reaction depends on the reaction conditions. In deprotonated alkyl-substituted quinoxalines an increased number of resonance possibilities exists and mildly basic conditions arc usually required for condensation reactions. 

These local calculations predict the formation of planar, hyperbolic, parabolic (cylindrical) and elliptic (globular) interfaces as the volume fraction of the iMger block increases from 50%. The compositional range of existence of the various interfacial geometries depends to a limited extent on the effective surface tension acting at the interface. 

Thermal equilibrium between solid and gas locally. Calculations including energy transferred between char and gas by radiation and convection support this statement. The equations are illustrated in the section Temperature differences between the gas and solid phases ... 

This equation serves as the foundation of all that we will have to say about hardening. We begin by noting that the numerator is a reflection of the interaction between a single obstacle and a single dislocation. As a result, it is something that we can expect to understand on the basis of local calculations that concern themselves only with the properties of a single such interaction. By way of contrast, the denominator reflects the statistical properties related to the distribution of obstacles. As we will see below, there are a number of different ways of... 

The MRI-based viscosity measurement relies on local calculations of the velocity gradient based on using MRI velocity profiles to provide a wide range of shear viscosity-shear rate data. Two observations are used to characterize fully developed and steady laminar flow in a MRI-based viscometer the velocity profile and the pressure drop per unit tube length measurements. Viscosity measurements were acquired on strawberry milk samples using H P LG tubing for the sample channel. 

The block-localized calculations are conceptually similar to NBO analysis (see Section 1.4.2) in that they compare a calculation in which the orbitals are strictly localized with the unrestricted calculation to estimate the effect of delocalization. Y. Mo and S. D. Peyerimhoff, J. Chem. Phys., 109, 1687 (1998). T. Kundu, L. Goodman, and J. Leszczynksi, J. Chem. Phys., 103, 1523 (1995). 

Calculation of a perturbed distribution function can be approached in various ways (1) direct solution of the Boltzmann equation for the distribution function in the perturbed system, (2) distribution-difference methods, (3) local calculations, and (4) normal-mode expansion methods. 

If the perturbation in the neutron flux is restricted to the small region P, it is neither necessary nor economical to solve the perturbed flux equation of the flux-difference equations over the entire volume (P -t- U) of the reactor. In the following we outline the approaches used for applying these equations for local calculations, and describe some applications for these calculations. 

Similar procedures can also be applied for local calculations in inhomogeneous systems. Such local calculations are useful (77, 19, 28) for deep-... 

Equation (33), or the first component (n = 0) of Eq. (35), can also be solved for the perturbed region P. For these local calculations, the equations to be solved become inhomogeneous equations for a subcritical system bounded by region P. The accuracy of this approach has recently been investigated by Lineberry (29) and by Akl and Laponche (30). They showed that the results of these local distribution-difference calculations are not very sensitive to the location of the boundary of the buffer zone B, as long as the latter is thicker than about three mean-free-paths. 

The Wheland calculations did not include effects of ground state resonance, which certainly would be important in comparisons of reactivities between different C HsX derivatives. Some rather crude but illustrative localization calculations are available where ground state resonance has been taken into account. 

One might well wonder why the localization method is not used exclusively in calculations of substitution on aromatic systems. The principal reason is laziness. Calculation of E. for a 16-atom system, such as pyrene, is considerably simplified by the I v symmetry operations to the solution of two five- and two three-row determinants. The corresponding localization calculation for attack on pyrene at the 1 position requires solution of a 15—row determinant. However, a calculation of this sort is child s play for a modern high-speed digital computer. 

Locally calculated Reynolds numbers determine the magnitude of a viscosity-increase ratio used in the solution of Reynolds equation, and in calculating power and temperature rise. An exponential curve-fit to the results of C61 is used of the form Hj/. i=aRe° where a and b depend upon the use as follows ... 

To compensate, Nordholm et al. [7] introduced a non-local calculation based upon the van der Waal model. Percus [3] provided a general framework for the NLDFT that follows these lines ... 

---