Vectorization software

A major disadvantage is the time required for the computation. The entire algorithm (generation of 3-D structure, conformation analyses, property calculation, property mapping on surface or field and autocorrelation transformation) needs between 100 and 100000 s for one molecule. With today s computer technology, using multi-processor compute servers and highly vectorized software, it is possible to calculate up to several thousand three-dimensional autocorrelation descriptors vtithin a day (Table 7). 

Figure Bl.21.1. Atomic hard-ball models of low-Miller-index bulk-temiinated surfaces of simple metals with face-centred close-packed (fee), hexagonal close-packed (licp) and body-centred cubic (bcc) lattices (a) fee (lll)-(l X 1) (b)fcc(lO -(l X l) (c)fcc(110)-(l X 1) (d)hcp(0001)-(l x 1) (e) hcp(l0-10)-(l X 1), usually written as hcp(l010)-(l x 1) (f) bcc(l 10)-(1 x ]) (g) bcc(100)-(l x 1) and (li) bcc(l 11)-(1 x 1). The atomic spheres are drawn with radii that are smaller than touching-sphere radii, in order to give better depth views. The arrows are unit cell vectors. These figures were produced by the software program BALSAC [35]-...

Band structure calculations have been done for very complicated systems however, most of software is not yet automated enough or sufficiently fast that anyone performs band structures casually. Setting up the input for a band structure calculation can be more complex than for most molecular programs. The molecular geometry is usually input in fractional coordinates. The unit cell lattice vectors and crystallographic angles must also be provided. It may be nee-... 

Some more recent software uses the tensor LEED approximation of Rous and Pen-dry which can save a substantial amount of computer time [2.268-2.270]. In tensor LEED the amplitudes (0) of all escaping electron waves (spots) are first calculated conventionally as described above for a certain reference geometry. Then the derivatives of these amplitudes 5Ag/5ri with respect to small displacements of each atom i in this reference geometry are calculated. These derivatives are the constituents of the "tensor". The wave amplitude for a modified model geometry where atom i is displaced by the vector Aq is then approximately given by ... 

Mathematical models require computation to secure concrete predictions. Successes in relatively simple cases spurs interest in more complex situations. Somewhat specialized computer hardware and software have emerged in response to these demands. Examples are the high-end processors with vector architecture, such as the Cray series, the CDC Cyber 205, and the recently announced IBM 3090 with vector attachment. When a computation can effectively utilize vector architecture, such machines will out-perform even the most powerful conventional scalar machine by a substantial margin. Such performance has given rise to the term supercomputer. ... 

Consider Equations (6-10) that represent the CVD reactor problem. This is a boundary value problem in which the dependent variables are velocities (u,V,W), temperature T, and mass fractions Y. The mathematical software is a stand-alone boundary value solver whose first application was to compute the structure of premixed flames.Subsequently, we have applied it to the simulation of well stirred reactors,and now chemical vapor deposition reactors. The user interface to the mathematical software requires that, given an estimate of the dependent variable vector, the user can return the residuals of the governing equations. That is, for arbitrary values of velocity, temperature, and mass fraction, by how much do the left hand sides of Equations (6-10) differ from zero ... 

The task of the problem-independent chemistry software is to make evaluating the terms in Equations (6-10) as straightforward as possible. In this case subroutine calls to the Chemkin software are made to return values of p, Cp, and the and hk vectors. Also, subroutine calls are made to a Transport package to return the ordinary multicomponent diffusion matrices Dkj, the mixture viscosities p, the thermal conductivities A, and the thermal diffusion coefficients D. Once this is done, finite difference representations of the equations are evaluated, and the residuals returned to the boundary value solver. 

Velocity maps of simple or complex liquids, emulsions, suspensions and other mixtures in various geometries provide valuable information about macroscopic and molecular properties of materials in motion. Two- and three-dimensional spin echo velocity imaging methods are used, where one or two dimensions contain spatial information and the remaining dimension or the image intensity contains the information of the displacement of the spins during an observation time. This information is used to calculate the velocity vectors and the dispersion at each position in the spatially resolved dimensions with the help of post-processing software. The range of observable velocities depends mainly on the time the spins... 

Fig. 2.1.12 Vector diagram of the velocity distribution of flowing water driven by a paddle with holes. The diagram was calculated by the AM IRA software (http //ami ra.zib.de).

Other pattern recognition strategies have been used for bacterial identification and data interpretation from mass spectra. Bright et al. have recently developed a software product called MUSE, capable of rapidly speciating bacteria based on matrix-assisted laser desorption ionization time-of-flight mass spectra.13 MUSE constructs a spectral database of representative microbial samples by using single point vectors to consolidate spectra of similar (not identical) microbial strains. Sample unknowns are then compared to this database and MUSE determines the best matches for identification purposes. In a... 

The seven ways (r, through r7) for calculating correlation as the square root of the ratio of the explained variation over the total variation between X (concentration of analyte data) and Y (measured data) are described using many notational forms. For example, many software packages provide built-in functions capable of calculating the coefficient of correlation directly from a pair of X and Y vectors as given by rx (Equation 59-7). 

Unfortunately, the lab used in the creation of the circuits in this book closely resembles the lab of other engineering companies around the world. We use 5% tolerance resistors and 10% tolerance capacitors that are either soldered to a vector board or plugged into a solderless breadboard. This introduces various parasitics and inaccuracies in the results. In order to be more precise in showing the accuracy of SPICE simulation software, we frequently run the simulations with the stated values of the resistors or capacitors used in our lab breadboards. The measured values for each resistor and capacitor used in our breadboard configuration which may be different, are shown in Fig. 3.3. 

The new scores vector, Ui ew ( white column in Figure 4.6) will be a better estimation than our preliminary estimation ( black column in Figure 4.6). Next, this newly calculated u vector is used as the input to start again the process above. After several iterations (the procedure is very fast), all vectors will converge to a stable solution (convergence is usually set by the software according to a rounding error) and we can finish the calculation of the first factor. 

Following the very brief introduction to the method of lines and differential-algebraic equations, we return to solving the boundary-layer problem for nonreacting flow in a channel (Section 7.4). From the DAE-form discretization illustrated in Fig. 7.4, there are several important things to note. The residual vector F is structured as a two-dimensional matrix (e.g., Fuj represents the residual of the momentum equation at mesh point j). This organizational structure helps with the eventual software implementation. In the Fuj residual note that there are two timelike derivatives, u and p (the prime indicates the timelike z derivative). As anticipated from the earlier discussion, all the boundary conditions are handled as constraints and one is implicit. That is, the Fpj residual does not involve p itself. 

---