When using computational chemistry to answer a chemical question, the obvious problem is that the researcher needs to know how to use the software. The difficulty sometimes overlooked is that one must estimate how accurate the answer will be in advance. The sections below provide a checklist to follow. [Pg.135]

The eigenvalue problem defined by equations (12.56) and (12.37) has been studied by Lee and Luss l79j and, more recently, in considerable detail by Villadsen and Michelsen When - I it is easy to show [Pg.173]

In section 11.3 vie showed that the difficult problem of solving the flux relations can be circumvented rather simply when the stoichiometric relations are satisfied by the flux vectors, but the treatment given there was limited to the case of a single Independent chemical reaction, when the stoichiometric relations permit all the flux vectors to be expressed in terms of any one of them. The question then arises whether any comparable simplification is possible v en the reactants participate in more than one independent reaction. [Pg.150]

There was a time when one could use only a few molecular descriptors, which were simple topological indices. The 1990s brought myriads of new descriptors [11]. Now it is difficult even to have an idea of how many molecular desaiptors are at one s disposal. Therefore, the crucial problem is the choice of the optimal subset among those available. [Pg.217]

Case-Based Reasoning. Case-Based Reasoning (CBR) systems base their solutions on previously solved problems (cases) which are stored in a case-base [Watson Marir, 1994]. When a new problem is presented to a CBR system a similar case(s) is/are retrieved from the case-base. Depending on the differences between the retrieved and the presented problem the retrieved solution may have to be more or less adapted to obtain a solution to the new problem. The solved problem may be retained in the case base if deemed useful. [Pg.99]

How many iterations does it take to achieve self-consistency for the helium problem treated (partially) in Exercises 8-3 and 8-4 What is the % discrepancy between the calculated value of the first ionization potential and the experimental value of 0.904 hartiees when the solution has been brought to self-consistency [Pg.260]

Moreover, well away from the critical point, the range of correlations is much smaller, and when this range is of the order of the range of the intenuolecular forces, analytic treatments should be appropriate, and the exponents should be classical . The need to reconcile the nonanalytic region with tlie classical region has led to attempts to solve the crossover problem, to be discussed in section A2.5.7.2. [Pg.648]

This paper presents solutions of two different NDT problems which could not be solved using standard ultrasonic systems and methods. The first problem eoncems the eraek detection in the root of turbine blades in a specified critical zone. The second problem concerns an ultrasonie thiekness measurement for a case when the sound velocity varies along the object surface, thus not allowing to take a predetermined eonstant velocity into account. [Pg.764]

A large percentage of eddy-current inspections are conducted in the field, away from the home base and often in remote or inaccessible locations. Using local telephone lines or mobile phone lines would allow the inspector to beam his data back to the office. In this way highly qualified personnel can be consulted when problems or difficult to interpret results occur. Inspectors no longer need to feel isolated on site. [Pg.1020]

Another option is a q,p) = p and b q,p) = VU q). This guarantees that we are discretizing a pure index-2 DAE for which A is well-defined. But for this choice we observed severe difficulties with Newton s method, where a step-size smaller even than what is required by explicit methods is needed to obtain convergence. In fact, it can be shown that when the linear harmonic oscillator is cast into such a projected DAE, the linearized problem can easily become unstable for k > . Another way is to check the conditions of the Newton-Kantorovich Theorem, which guarantees convergence of the Newton method. These conditions are also found to be satisfied only for a very small step size k, if is small. [Pg.285]

© 2019 chempedia.info