Nearby

Within the same geographicai region, the crude specific gravity varies from one reservoir to another, in Saudi Arabia, for example, the crude from the Ghawar field has an average standard specific gravity on the order of 0.850 (34° API) while the specific gravity of the crude from the nearby Safaniyah field is 0.893 (27° API). 

Special configurations to reduce probe wobble and sensitivity to geometry changes and to allow inspection nearby both sides of a support plate in one pass... 

Therefore, we may say that head wave is the excited shear wave when longitudinal wave is spreading along boundaries. This is the head wave which we often call. In Fig.3 the wavefront of head wave is indicated by AB. The biggest circular arc AC in Fig.3 is the wavefront of longitudinal wave. The small arrow beside the circular line indicates the direction of displacement after the wavefront arrives and the written character 8 nearby indicates its... 

Because of the charged nature of many Langmuir films, fairly marked effects of changing the pH of the substrate phase are often observed. An obvious case is that of the fatty-acid monolayers these will be ionized on alkaline substrates, and as a result of the repulsion between the charged polar groups, the film reverts to a gaseous or liquid expanded state at a much lower temperature than does the acid form [121]. Also, the surface potential drops since, as illustrated in Fig. XV-13, the presence of nearby counterions introduces a dipole opposite in orientation to that previously present. A similar situation is found with long-chain amines on acid substrates [122]. 

What is the interaction between the iron and the nearby histidines ... 

The shielding at a given nucleus arises from the virtually instantaneous response of the nearby electrons to the magnetic field. It therefore fluctuates rapidly as the molecule rotates, vibrates and interacts with solvent molecules. The changes of shift widi rotation can be large, particularly when double bonds are present. For... 

A second type of relaxation mechanism, the spin-spm relaxation, will cause a decay of the phase coherence of the spin motion introduced by the coherent excitation of tire spins by the MW radiation. The mechanism involves slight perturbations of the Lannor frequency by stochastically fluctuating magnetic dipoles, for example those arising from nearby magnetic nuclei. Due to the randomization of spin directions and the concomitant loss of phase coherence, the spin system approaches a state of maximum entropy. The spin-spin relaxation disturbing the phase coherence is characterized by T. ... 

The interaction of the electron spin s magnetic dipole moment with the magnetic dipole moments of nearby nuclear spins provides another contribution to the state energies and the number of energy levels, between which transitions may occur. This gives rise to the hyperfme structure in the EPR spectrum. The so-called hyperfme interaction (HFI) is described by the Hamiltonian... 

If one has available the. values for the system from a calculation perfonued at a nearby geometry, one can use these C. values. 

The expense is justified, however, when tackling polymer chains, where reconstruction of an entire chain is expressed as a succession of atomic moves of this kind [121]. The first atom is placed at random the second selected nearby (one bond length away), the third placed near the second, and so on. Each placement of an atom is given a greater chance of success by selecting from multiple locations, as just described. Biasing factors are calculated for the whole multi-atom move, forward and reverse, and used as before in the Metropolis prescription. For fiirther details see [122, 123. 124. 125]. A nice example of this teclmique is the study [126. 127] of the distribution of linear and branched chain alkanes in zeolites. 

Even expression ( B3.4.31), altiiough numerically preferable, is not the end of the story as it does not fiilly account for the fact diat nearby classical trajectories (those with similar initial conditions) should be averaged over. One simple methodology for that averaging has been tln-ough the division of phase space into parts, each of which is covered by a set of Gaussians [159, 160]. This is done by recasting the initial wavefunction as... 

Symplectic integration methods replace the t-flow (pt,H by the symplectic transformation which retains Hamiltonian features of They poses a backward error interpretation property which means that the computed solutions are solving exactly or, at worst, approximately a nearby Hamiltonian problem which means that the points computed by means of symplectic integration, lay either exactly or at worst, approximately on the true trajectories [5]. 

Recent mathematical work suggests that—especially for nonlinear phenomena—certain geometric properties can be as important as accuracy and (linear) stability. It has long been known that the flows of Hamiltonian systems posess invariants and symmetries which describe the behavior of groups of nearby trajectories. Consider, for example, a two-dimensional Hamiltonian system such as the planar pendulum H = — cos(g)) or the... 

Note the curious return property exhibited by the energy in the symplectic method this is a manifestation of the nearby Hamiltonian mentioned in the introduction (see [7, 18, 28]). 

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