Direct evaluation

The technique of mudlogging is covered in this section because it is one of the first direct evaluation methods available during the drilling of an exploration well. As such, the mudlog remains an important and often under-used source of original information. 

Here is a complex time which is given by t = t- hl2kT. Methods for evaluating this equation have included path integrals [45], wavepackets [48, 49] and direct evaluation of the trace in square integrable basis sets [ ]. 

DeRege P J F, Williams S A and Therien M J 1995 Direct evaluation of electronic coupling mediated by hydrogen bonds—implications for biological electron transfer Sc/e/ ce 269 1409-13... 

Fig. 1. CPU times (in hours) for 1 ps MD runs for various proteins using three different methods, direct velocity Verlet with a time-step 0.5 fs, r-RESPA with direct evaluation of electrostatic forces and an overall time-step of 4.0 fs, and r-RESPA/TFMM with an overall time-step 4.0 fs (combination of (2,2,2,2) in force breakup).The energy conservation parameter log AE for the three methods are comparable. The CPU time (hours) is for RISC6000 /MODEL 590 computer.

The direct evaluation of velocities gives a useful handle for controlling the simulation temperature (via velocity scaling). 

NRA as in RBS or ERDA, and possible modification of the target composition as a result of irradiation must be considered. Nuclear reaction cross-sections are also usually not available in analytical form for direct evaluation of measured data. Concentrations are, therefore, often obtained by comparison of the measured data with results from standard samples of known concentration. 

It should be observed that, in the most general case, interpretation of the mechanical responses requires time-resolved wave-profile measurements. As shown in Eqs. (2.2) and (2.3), direct evaluation of the response requires quantitative description of derivatives of kinetic and kinematic variables. 

The shock-compression events are so extreme in intensity and duration, and remote from direct evaluation and from other environments, that experiment plays a crucial role in verifying and grounding the various theoretical descriptions. Indeed, the material models developed and advances in realistic numerical simulation are a direct result of advances in experimental methods. Furthermore, the experimental capabilities available to a particular scientist strongly control the problems pursued and the resulting descriptions of shock-compressed matter. Given the decisive role that experimental methods play, it is essential that careful consideration be given to their characteristics. 

Each time step thus involves a calculation of the effect of the Hamilton operator acting on the wave function. In fully quantum methods the wave function is often represented on a grid of points, these being the equivalent of basis functions for an electronic wave function. The effect of the potential energy operator is easy to evaluate, as it just involves a multiplication of the potential at each point with the value of the wave function. The kinetic energy operator, however, involves the derivative of the wave function, and a direct evaluation would require a very dense set of grid points for an accurate representation. 

Tests carried out for particular purposes may make use of other special means to measure the progress of corrosion. For example, changes in the reflectivity of polished surfaces have been used as a sensitive means of following changes in the very early stages of corrosion in laboratory studies. A similar technique has been applied on a practical scale in connection with the direct evaluation of the relative merits of different alloys as used for mirrors in searchlights exposed to corrosive natural atmospheres. 

Methods are described for determining the extent to which original natural color is preserved in processing and subsequent storage of foods. Color differences may be evaluated indirectly in terms of some physical characteristic of the sample or extracted fraction thereof that is largely responsible for the color characteristics. For evaluation more directly in terms of what the observer actually sees, color differences are measured by reflectance spectrophotometry and photoelectric colorimetry and expressed as differences in psychophysical indexes such as luminous reflectance and chromaticity. The reflectance spectro-photometric method provides time-constant records in research investigation on foods, while photoelectric colorimeters and reflectometers may prove useful in industrial color applications. Psychophysical notation may be converted by standard methods to the colorimetrically more descriptive terms of Munsell hue, value, and chroma. Here color charts are useful for a direct evaluation of results. 

In conclusion it should be added that, during the last few years, even methods for the direct evaluation of the first-order density matrix p(xlt x2) have been developed (McWeeny, 1956). 

Table 4 shows that the results obtained with this procedure for LiBF4 in DME at 25 °C are significantly more precise than those obtained from use of Eq. (16). The. direct evaluation of the data, by Eq. (7) 1100],... 

It is impossible to carry out this program of directly evaluating the energy integral except in the simplest cases but rough energy curves for various electronic structures can often be constructed by semi-empirical methods, and the discussion outlined above carried out with them. Thus information regarding the repulsive forces between ions obtained from the observed properties of ionic crystals can be used for ionic states of mole-... 

Statistical Wavefront Sensing A direct evaluation of Eq. 49 gives... 

It is possible to use full or limited configuration interaction wavefunctions to construct poles and residues of the electron propagator. However, in practical propagator calculations, generation of this intermediate information is avoided in favor of direct evaluation of electron binding energies and DOs. 

The approach to the evaluation of vibrational spectra described above is based on classical simulations for which quantum corrections are possible. The incorporation of quantum effects directly in simulations of large molecular systems is one of the most challenging areas in theoretical chemistry today. The development of quantum simulation methods is particularly important in the area of molecular spectroscopy for which quantum effects can be important and where the goal is to use simulations to help understand the structural and dynamical origins of changes in spectral lineshapes with environmental variables such as the temperature. The direct evaluation of quantum time- correlation functions for anharmonic systems is extremely difficult. Our initial approach to the evaluation of finite temperature anharmonic effects on vibrational lineshapes is derived from the fact that the moments of the vibrational lineshape spectrum can be expressed as functions of expectation values of positional and momentum operators. These expectation values can be evaluated using extremely efficient quantum Monte-Carlo techniques. The main points are summarized below. 

Amides, alkaline hydrolysis, 215 Anharmonic systems, direct evaluation of quantum time-correlation functions, 93 Apollo DSP—160, CHARMM performance, 129/ simulations, solvent effects, 83... 

Knackstedt, MA Zhang, X, Direct Evaluation of Length Scales and Structural Parameters Associated with Flow in Porous Media, Physical Review E 50, 2134, 1994. 

The ZN formulas can also be utihzed to formulate a theory for the direct evaluation of thermal rate constant of electronically nonadiabatic chemical reactions based on the idea of transition state theory [27]. This formulation can be further utilized to formulate a theory of electron transfer and an improvement of the celebrated Marcus formula can be done [28]. 

Instead of using repeated solution of a suitable eigenvalue equation to optimize the orbitals, as in conventional forms of SCF theory, we have found it more convenient to optimize by a gradient method based on direct evaluation of the ener functional (4), ortho normalization being restored after every parameter variation. Although many iterations are required, the energy evaluation is extremely rapid, the process is very stable, and any constraints on the parameters (e.g. due to spatial symmetry or choice of some type of localization) are very easily imposed. It is also a simple matter to optimize with respect to non-linear parameters such as orbital exponents. 

In general, adiabatic calorimeters are more sensitive than TPA techniques. The induction time can be u.sed for direct evaluation of boundaries for safe operation. Obviously, the time of a corrective action must be less than t d. The fully safe operational temperature is that corresponding to tad = 24 h and is denoted as ADT24 (Adiabatic Decomposition Temperature for 24 hours). 

Although the evaluation of partial derivatives is not usually an insurmountable obstacle in networks involving one-phase flow in pipes, several investigators (C3, L2) have explored alternative iterative methods which do not require direct evaluation of partial derivatives. These methods are generally based on linearized approximations using secants rather than tangents. ... 

So far, the existence of a well-defined entanglement length in dense polymer systems has been inferred indirectly from macroscopic experiments like measurements of the plateau modulus. However, its direct microscopic observation remained impossible. The difficulty in directly evaluating the entanglement... 

A. A. Ischenko, J. D. Ewbank, and L. Schafer, Direct Evaluation of Equilibrium Molecular Geometries Using Real-Time Gas Electron Diffraction, J. Phys. Chem., 98 (1994) 4287-4300. 

Model Fit or Direct Evaluation Similar to the ID case we can now fit a model to the projected intensity or to the CLD. What we get in this case is the needle-diameter distribution of the microfibrils. Nevertheless, there are two other possibilities to directly evaluate the data. 

Kofke, D. A., Gibbs-Duhem integration a new method for direct evaluation of phase coexistence by molecular simulation, Mol. Phys. 1993, 78, 1331-1336... 

Fig. 2.6. The thermodynamic cycle for estimating the hydration free energy, zl/Ihydration, of a small solute (the right side of the figure). One route is the direct evaluation of A/lhydrauon along the upper vertical arrow. The solute, originally placed in vacuum (a) is moved to the bulk water (b). Another route consists of annihilating, or creating, the solute both in vacuo and in the aqueous medium and corresponds to the vertical lines in the thermodynamic cycle. As suggested by the cycle, these two routes are formally equivalent, as A/lhydrnt,ion = A A0 — A A1...

Bahar, I., Atilgan, A. R., Erman, B., Direct evaluation of thermal fluctuations in proteins using a single-parameter harmonic potential, Fold. Des. 1997, 2, 173-181... 

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