Intuitions

Only the simulations in which the transducer is coupling either to the V-butt weld or to the surrounding steel can be analyzed in a simple and intuitive way, which means that the different pulses in the A-scan signals can be related uniquely to the reflection or diffraction of the wavefront at the weld, the backwall, and/or the notch. 

This is a third set of equations that essentially allows us to locate a virtual source for every two adjacent measurements. Intuitively this can be simply described as finding the point of intersection of two radii of lengths and Therefore the simplifying assumptions... 

The adhesion between two solid particles has been treated. In addition to van der Waals forces, there can be an important electrostatic contribution due to charging of the particles on separation [76]. The adhesion of hematite particles to stainless steel in aqueous media increased with increasing ionic strength, contrary to intuition for like-charged surfaces, but explainable in terms of electrical double-layer theory [77,78]. Hematite particles appear to form physical bonds with glass surfaces and chemical bonds when adhering to gelatin [79]. 

The preceding derivation, being based on a definite mechanical picture, is easy to follow intuitively kinetic derivations of an equilibrium relationship suffer from a common disadvantage, namely, that they usually assume more than is necessary. It is quite possible to obtain the Langmuir equation (as well as other adsorption isotherm equations) from examination of the statistical thermodynamics of the two states involved. 

Another connnon approximation is to construct a specific fonn for the many-body waveftmction. If one can obtain an accurate estimate for the wavefiinction, then, via the variational principle, a more accurate estimate for the energy will emerge. The most difficult part of this exercise is to use physical intuition to define a trial wavefiinction. 

A more intuitive, and more general, approach to the study of two-level systems is provided by the Feynman-Vemon-Flellwarth geometrical picture. To understand this approach we need to first introduce the density matrix. 

The reason for this enliancement is intuitively obvious once the two reactants have met, they temporarily are trapped in a connnon solvent shell and fomi a short-lived so-called encounter complex. During the lifetime of the encounter complex they can undergo multiple collisions, which give them a much bigger chance to react before they separate again, than in the gas phase. So this effect is due to the microscopic solvent structure in the vicinity of the reactant pair. Its description in the framework of equilibrium statistical mechanics requires the specification of an appropriate interaction potential. 

An eiegant theoreticai treatise of poiymer physics which conveys an intuitive understanding of the behaviour of macromoiecuies. Charrier J-M 1990 Polymeric Materials and Processing Plastics, Elastomers and Composites (Munich Hanser)... 

The simplest way to add a non-adiabatic correction to the classical BO dynamics method outlined above in Section n.B is to use what is known as surface hopping. First introduced on an intuitive basis by Bjerre and Nikitin [200] and Tully and Preston [201], a number of variations have been developed [202-205], and are reviewed in [28,206]. Reference [204] also includes technical details of practical algorithms. These methods all use standard classical trajectories that use the hopping procedure to sample the different states, and so add non-adiabatic effects. A different scheme was introduced by Miller and George [207] which, although based on the same ideas, uses complex coordinates and momenta. 

The main application of the loop method is to analyze complex systems, that can support several low-lying conical intersections. The idea is to provide a simple systematic, not intuition dependent, method for finding the accessible conical intersections. 

According to Eq. (A.4), if < 0, the ground state will be the in-phase combination, and the out-of-phase one, an excited state. On the other hand, if > 0, the ground state will be the out-of-phase combination, while the in-phase one is an excited state. This conclusion is far reaching, since it means that the electronic wave function of the ground state is nonsymmetric in this case, in contrast with common chemical intuition. We show that when an even number of electron pairs is exchanged, this is indeed the case, so that the transition state is the out-of-phase combination. 

The first technique is very intuitive. Out of the few proteins that could be crystallized in a number of different conformations, adenylate kinase is probably the best-studied example. By combining nine observed crystal structures and interpolating between them, a movie was constructed that visualized a hypothetical path of its hinge-bending transition (jVonrhein et al. 1995]). 

SLN is easy to learn and its use is intuitive. The language uses only six basic components to specify chemical structures. Four of them are hsted in Table 2-3 and can be compared directly with the SMILES notation of Section 2,3.3. 

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