Brute-force

In the last two sections, we have applied increasingly tricky devices to solve what amounts to systems of equations, in order to make their solution efficient. Even the two-species uncoupled case involved the generation of the u and v vectors and the solution of small (2 x 2) systems to obtain the boundary values. In the case of coupled systems, the problems mount and matrix-vector equations had to be used. 

A simple example would be the single-species case and Cottrell. Then, the system (6.2) would be augmented by adding, at the top, the Cottrell condition Cq = 0 and the matrix equation is 

The totally irreversible case is again obtained by setting Ki, to zero in the above equations. 

This leaves the controlled current case. As noted above (Sect. 6.3), it is the current, not the gradient, that is controlled, so the equation is 

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Loesch H J and Remscheid A 1990 Brute force in molecular reaction dynamics a novel technique for measuring steric effects J. Chem. Phys. 93 4779-90... 

Molecular dynamics consists of the brute-force solution of Newton s equations of motion. It is necessary to encode in the program the potential energy and force law of interaction between molecules the equations of motion are solved numerically, by finite difference techniques. The system evolution corresponds closely to what happens in real life and allows us to calculate dynamical properties, as well as thennodynamic and structural fiinctions. For a range of molecular models, packaged routines are available, either connnercially or tlirough the academic conmuinity. 

To obtain an effective algorithm for substructure searching the factorial degree of the brute force algorithm has to be drastically deaeased. In the next sections we discuss several approaches where combination leads to a much more effective and apphcable approach for substructure searching. In the process of searching the isomorphism between Gq and a substructure of Gx, the partial mappings Gq —> Gj can be used as well. In these cases, not all atoms from Gq are mapped and, for those which are not, the array value Mj is set to 0. 

It can be said that these three main strategies have been applied equally and very often in combination. Basically, the first approach implies the use of a faster computer or a parallel architecture. To some extent it sounds like a brute force approach but the exponential increase of the computer power observed since 1970 has made the hardware solution one of the most popular approaches. The Chemical Abstracts Service (CAS) [10] was among first to use the hardware solution by distributing the CAS database onto several machines. 

If it is known that a drug must bind to a particular spot on a particular protein or nucleotide, then a drug can be tailor-made to bind at that site. This is often modeled computationally using any of several different techniques. Traditionally, the primary way of determining what compounds would be tested computationally was provided by the researcher s understanding of molecular interactions. A second method is the brute force testing of large numbers of compounds from a database of available structures. 

Now, contrary to popular opinions, this method need not be conducted in a sealed pipe bomb. Secondary amination by substitution is as much a reaction of opportunity as it is of brute force and heat. In fact, heating can tend to cause the reformation of safrole and isosafrole. So the simplest way to do this would be to use 500mL of ammonium hydroxide or alcoholic ammonia or, for those wishing to make MDMA or meth, 40% aqueous methylamine or alcoholic methylamine (to tell you the truth, methylamine is preferable in this method because it is more reactive that ammonia so yield will increase). This 500mL is placed in a flask and into it is poured a solution of 35g bromosafrole (30g phenylisopropyl-bromide) mixed with 50mL methanol. The flask is stoppered and stirred at room temperature for anywhere from 3 to 7 days. The chemist could also reflux the same mixture for 6-12 hours or she could throw the whole mix into a sealed pipe bomb (see How to Make section) and cook it for 5 hours in a 120-130°C oil bath. 

Solvent cleaning is a much more delicate technique than the brute force of abrasion. In reality, there will almost always be some abrasive action involved. The idea is to dissolve the deposit in a solvent. The solution must... 

The method of optimization is a brute-force search technique. All the possible laminates that can be obtained by changing the individual laminae orientations by 5° increments are candidates for the optimization process. We consider RC7 because this program is widely used and because it is representative of the brute-force search technique. The basic question is because we must carry a certain load, what laminate do we need We have no idea how many layers are required, much less their orientation, but we must start someplace. 

This brute-force search strategy is followed as more layers are added because we do not know how many layers we need for the prescribed load. If the load is very high, perhaps we will need 19 layers, and we will work our way up to that laminate by adding one layer at a time and finding the best laminate of that number of laminae. 

Reducing infiltration. Traditional brute force approaches to weather stripping were redesigned to reduce infiltration with less material that contacted a larger surface area. New materials such as thermoplastic elastomers offered additional potential to control for infiltration. But perhaps the most important way to control infiltration is proper installation. 

This is a quadratic equation as usual, we look for ways to avoid solving it by brute force. Note that because BaS04 is very insoluble, a reasonable approximation would seem to be... 

Start with 1 mol of and let it age for 10 billion years or so. Refer to Table 2.1. What is the maximum number of atoms of " Po that will ever exist Warning This problem is monstrously difficult to solve by brute force methods. A long but straightforward analytical solution is possible. See also Section 2.5.3 for a shortcut method. 

Solution The most straightforward way to optimize a function is by a brute force search. Results from such a search are shown in Table 6.2. 

Search for the overall optimum within the available parameter space Factorial, simplex, regression, and brute-force techniques. The classical, the brute-force, and the factorial methods are applicable to the optimization of the experiment. The simplex and various regression methods can be used to optimize both the experiment and fit models to data. 

What strategy should one follow In the classical experiment, one factor is varied at a time, usually over several levels, and a functional relationship between experimental response and factor level is established. The data analysis is carried out after the experiment(s). If several factors are at work, this approach is successful only if they are more or less independent, that is, do not strongly interact. The number of experiments can be sharply increased as in the brute-force approach, but this might be prohibitively expensive if a single production-scale experiment costs five- or six-digit dollar sums. Figure 3.4 explains the problem for the two-factor case. 

Figure 3.4. Optimization approaches. The classical approach fixes all factors except one, which is systematically varied (rows of points in left panel) the real optimum (x) might never be found this way. The brute-force approach would prescribe experiments at all grid points (dotted lines), and then further ones on a finer grid centered on 80/1 2, for example.

The brute force method depends on a systematic variation of all involved coefficients over a reasonable parameter space. The combination yielding the lowest goodness-of-fit measure is picked as the center for a further round with a finer raster of coefficient variation. This sequence of events is repeated until further refinement will only infinitesimally improve the goodness-of-fit measure. This approach can be very time-consuming and produce reams of paper, but if carefully implemented, the global minimum will not be missed, cf. Figures 3.4 and 4.4. 

The algebraic/iterative and the brute force methods are numerical respectively computational techniques that operate on the chosen mathematical model. Raw residuals r are weighted to reflect the relative reliabilities of the measurements. 

By brute-force iteration, the highest Y within the cube spanned in 3-space is located with a resolution of a few percent of the parameter ranges. The cube s center is accordingly moved, and the model is reevaluated in this fashion a track of steadily higher T-values in the immediate... 

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