Idea behind

Scaiming probe microscopies have become the most conspicuous surface analysis tecimiques since their invention in the mid-1980s and the awarding of the 1986 Nobel Prize in Physics [71, 72]- The basic idea behind these tecimiques is to move an extremely fine tip close to a surface and to monitor a signal as a fiinction of the tip s position above the surface. The tip is moved with the use of piezoelectric materials, which can control the position of a tip to a sub-Angstrom accuracy, while a signal is measured that is indicative of the surface topography. These tecimiques are described in detail in section BI.20. 

Modem photochemistry (IR, UV or VIS) is induced by coherent or incoherent radiative excitation processes [4, 5, 6 and 7]. The first step within a photochemical process is of course a preparation step within our conceptual framework, in which time-dependent states are generated that possibly show IVR. In an ideal scenario, energy from a laser would be deposited in a spatially localized, large amplitude vibrational motion of the reacting molecular system, which would then possibly lead to the cleavage of selected chemical bonds. This is basically the central idea behind the concepts for a mode selective chemistry , introduced in the late 1970s [127], and has continuously received much attention [10, 117. 122. 128. 129. 130. 131. 132. 133. 134... 

On metals in particular, the dependence of the radiation absorption by surface species on the orientation of the electrical vector can be fiilly exploited by using one of the several polarization techniques developed over the past few decades [27, 28, 29 and 30], The idea behind all those approaches is to acquire the p-to-s polarized light intensity ratio during each single IR interferometer scan since the adsorbate only absorbs the p-polarized component, that spectral ratio provides absorbance infonnation for the surface species exclusively. Polarization-modulation mediods provide the added advantage of being able to discriminate between the signals due to adsorbates and those from gas or liquid molecules. Thanks to this, RAIRS data on species chemisorbed on metals have been successfidly acquired in situ under catalytic conditions [31], and even in electrochemical cells [32]. 

The examples of modelling discussed in section C2.5.2 and section C2.5.3 are meant to illustrate tlie ideas behind tlie tlieoretical and computational approaches to protein folding. It should be borne in mind tliat we have discussed only a very limited aspect of tlie rich field of protein folding. The computations described in section C2.5.3 can be carried out easily on a desktop computer. Such an exercise is, perhaps, tlie best of way of appreciating tlie simple approach to get at tlie principles tliat govern tlie folding of proteins. 

Based on the polarization curves of figure C2.8.4 tliere are several possibilities for reducing or suppressing tire corrosion reaction. The main idea behind every case is to shift tire corroding anode potential away from E. This can be done in tire following ways. 

The first requirement is the definition of a low-dimensional space of reaction coordinates that still captures the essential dynamics of the processes we consider. Motions in the perpendicular null space should have irrelevant detail and equilibrate fast, preferably on a time scale that is separated from the time scale of the essential motions. Motions in the two spaces are separated much like is done in the Born-Oppenheimer approximation. The average influence of the fast motions on the essential degrees of freedom must be taken into account this concerns (i) correlations with positions expressed in a potential of mean force, (ii) correlations with velocities expressed in frictional terms, and iit) an uncorrelated remainder that can be modeled by stochastic terms. Of course, this scheme is the general idea behind the well-known Langevin and Brownian dynamics. 

The principal idea behind the CSP approach is to use input from Classical Molecular Dynamics simulations, carried out for the process of interest as a first preliminary step, in order to simplify a quantum mechanical calculation, implemented in a subsequent, second step. This takes advantage of the fact that classical dynamics offers a reasonable description of many properties of molecular systems, in particular of average quantities. More specifically, the method uses classical MD simulations in order to determine effective... 

This algorithm is an improvement over the algorithms described in the previous subsections. The idea behind this algorithm is fairly simple. To ensure load balance, the rows of the force matrix will be allocated in such a way that the load on all processor is equal. 

The idea behind this approach is simple. First, we compose the characteristic vector from all the descriptors we can compute. Then, we define the maximum length of the optimal subset, i.e., the input vector we shall actually use during modeling. As is mentioned in Section 9.7, there is always some threshold beyond which an inaease in the dimensionality of the input vector decreases the predictive power of the model. Note that the correlation coefficient will always be improved with an increase in the input vector dimensionality. 

The selection function is used to choo.se chromosomes which can then mate and thus give their coded information to the next generation. The idea behind the selection mechanism is to obtain more copies of better chromosomes in the next generation. 

The natural process of bringing particles and polyelectrolytes together by Brownian motion, ie, perikinetic flocculation, often is assisted by orthokinetic flocculation which increases particle coUisions through the motion of the fluid and velocity gradients in the flow. This is the idea behind the use of in-line mixers or paddle-type flocculators in front of some separation equipment like gravity clarifiers. The rate of flocculation in clarifiers is also increased by recycling the floes to increase the rate of particle—particle coUisions through the increase in soUds concentration. 

Classification Process simulation refers to the activity in which mathematical models of chemical processes and refineries are modeled with equations, usually on the computer. The usual distinction must be made between steady-state models and transient models, following the ideas presented in the introduction to this sec tion. In a chemical process, of course, the process is nearly always in a transient mode, at some level of precision, but when the time-dependent fluctuations are below some value, a steady-state model can be formulated. This subsection presents briefly the ideas behind steady-state process simulation (also called flowsheeting), which are embodied in commercial codes. The transient simulations are important for designing startup of plants and are especially useful for the operating of chemical plants. 

Nonlinear Programming The most general case for optimization occurs when both the objective function and constraints are nonlinear, a case referred to as nonlinear programming. While the idea behind the search methods used for unconstrained multivariable problems are applicable, the presence of constraints complicates the solution procedure. 

The basic idea behind the Euler method is to set the change in w per increment of time as... 

The idea behind this model is that in regions with high turbulenee levels the eddy lifetime k/ will be short, the mixing fast, and as a result the reaetion rate is not limited by small-seale mixing. On the other hand, in regions with low turbulenee levels, small-seale mixing may be slow, whieh will limit the reaetion rate. 

The idea behind OELs is to identify the highest level of exposure concentration and the corresponding reference time period for which we can be confident that there will be no adverse effects on health. However, the concentrations and lengths of exposure at which the presence of airborne chemical agents could damage health have not been clear for many years, and even today there are many questions to be answered. 

Most integral equations are based on the Ornstein-Zernike (OZ) equation [3-5]. The idea behind the OZ equation is to divide the total correlation function h ri2) iiito a direct correlation function (DCF) c r 12) that describes the fact that molecules 1 and 2 can be directly correlated, and an indirect correlation function 7( 12), that describes the correlation of molecule 1 with the other molecules that are also correlated with molecule 2. At low densities, when only direct correlations are possible, 7(r) = 0. At higher densities, where only triplet correlations are possible, we can write... 

You should remember the basic physical idea behind the HF model each electron experiences an average potential due to the other electrons (and of course the nuclei), so that the HF Hamiltonian operator contains within itself the averaged electron density due to the other electrons. In the LCAO version, we seek to expand the HF orbitals i/ in terms of a set of fixed basis functions X X2 > and write... 

The idea behind energy independence is that if all energy production occurs within a country s borders, then that country s economy will be insulated from any energy supply disruptions. The country would then have less unemployment and less economic decline if and when the world s energy exporters, especially OPEC members, cut their supplies. France, has developed a strong nuclear power industry so that it would not have to import as much oil... 

Two methods are used in practice to obtain enantiomerically pure amino acids. One way is to resolve the racemic mixture into its pure enantiomers (Section 9.8). A more direct approach, however, is to use an enantioselective synthesis to prepare only the desired 5 enantiomer directly. As discussed in the Chapter 19 Focus Oil, the idea behind enantioselective synthesis is to find a chiral reaction catalyst that will temporarily hold a substrate molecule in an unsymmetrical environment. While in that chiral environment, the substrate may be more... 

The whole idea behind PLS is to try to restore, to the extent possible, the optimum congruence between the each spectral factor and its corresponding concentration factor. For the purposes of this concept, optimum congruence is defined as a perfectly linear relationship between the projections, or scores, of the spectral and concentration data onto the spectral and concentration factors as exemplified in Figure 73. Since the spectral noise is independent from the concentration noise, a perfectly linear relationship is no longer possible. So, the best we can do is restore optimum congruence in the least-squares sense. 

Steam-Moderated Process. The basic idea behind this approach is to limit the extent of conversion of the methanation reaction, Reaction 1, by adding steam to the feed gases. This process simultaneously provides for (46) elimination of the CO shift, Reaction 2, to get a 3 1 H2 CO ratio from the make-up gas ratio of about 1.5 1 and avoidance of carbon laydown by operation under conditions in which carbon is not a thermodynamically stable phase (see Chemistry and Thermodynamics section above). 

Proof of Theorem 4-9. The proof of Theorem 4-9 is somewhat lengthy, but the intuitive idea behind it is simple. We will first show that the equivocation per digit between source and output is at least (BT — CT)Tt. This average uncertainty about the input given the output can be broken into two terms first the uncertainty about whether an error was made and second the uncertainty about the source digit when errors are made. These are the terms on the right side of Eq. (4-66). 

The key idea behind STM is that, because electrons have wavelike properties (Section 1.5), they can penetrate into and through regions where classical mechanics would forbid them to be. This penetration is called tunneling. The effect is used in STM (hence the tunneling in the name) by bringing... 

The main idea behind the Ritz method is to take into consideration... 

The co-equivalence property of homogeneous schemes lies in the main idea behind a new approach to the further estimation of the order of accuracy of a scheme on account of (9) or (10) its coefficients a, d, ip should be compared with coefficients d, d, (p of a simple specimen scheme, the accuracy order of which is well-known (see Section 7). 

The main idea behind regularization of dilference schemes is that the schemes of a desired quality should be sought in the class of stable schemes starting from an original scheme and replacing it, by changing the operator R, by another scheme of a desired quality belonging to the class of stable schemes. 

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