Timing for computers

For n-alkane melts on the 2nnd lattice, the time for computation of a single MC step scales approximately as N11, where N denotes the number of beads. This exponent was evaluated for simulations with 1500, 2844, and 3950 beads. The exponent for N seems to decrease slightly as N increases it may be closer to 1 for larger systems. 

FIG. 21-47 Illustration of the influence of the measurement s accuracy on the variance as a function of the mixing time [following K. Sommer, How to Compare the Mixing Properties of Solids Mixers (in German), Frep. Technol. no. 5, 266-269 (1982)]. A set of samples have been taken at different mixing times for computing the sample variance. Special attention has to be paid whether the experimental sample variance monitors the errors of the analysis procedure (x) or detects really the mixing process C). Confidence intervals for the final status o are shown as hatched sections. 

Distillation column models are well known to be nonlinear. This implies that a +10% step perturbation in the feed composition could display different dynamics and nonsymmetrical responses to a -10% step perturbation. Six different input sequences were studied and in each case, the computational time for computing the process transient was recorded, for both the open- and closed-loop configurations. 

The overall computation time for computing the forces with the Ewald method is approximately given by [46]... 

Table 6.6 Comparison of the normalized CPU-time for computations with and without exploiting the special structure of the characteristic lines...

The partitioning just described avoids the inversion of matrices since,is a 1 x 1 matrix. The time for computing each is greatly reduced by the fact... 

From a reading of this chapter, which methods do you find are best suited, in terms of accuracy and economy of time, for computation of the following properties of CPs bandgaps band structures band structure evolutions rotational barriers UV-Vis-NIR absorption spectra far-IR absorption and Reflectance spectra Pauli susceptibility optical transition probabilities (intensities). 

The effect of water on polypeptide conformations has been presented by Krimm and Venkatachalam (1971) for poly-L-proline. Their approach has limitations. The main limitation is that it requires excessive time for computation because of the large number of degrees of freedom, and it does not account for the interactions of all groups with water, but rather it considers only interactions due to water molecules in the vicinity of the carbonyl group. 

The computer subroutines for calculation of vapor-phase and liquid-phase fugacity (activity) coefficients, reference fugac-ities, and molar enthalpies, as well as vapor-liquid and liquid-liquid equilibrium ratios, are described and listed in this Appendix. These are source routines written in American National Standard FORTRAN (FORTRAN IV), ANSI X3.9-1978, and, as such, should be compatible with most computer systems with FORTRAN IV compilers. Approximate storage requirements and CDC 6400 execution times for these subroutines are given in Appendix J. 

Also included in this table are some average execution times for the thermodynamic subroutines measured for the CDC 6400 of the Computer Center, University of California, Berkeley. 

Execution times for the higher level subroutines FLASH and ELIPS will be highly dependent on the problems involved. The times required per iteration can be estimated from times for lower level subroutines and the descriptions given for FLASH and ELIPS. Computation times for two specific cases calculated with FLASH and one case claculated with ELIPS are included in Table J-1 to show approximate magnitudes required. 

The results obtained with the two methods confirm the measured data with a good precision, with less computational time for the specialised code than the general code. This validation on three representative test bloeks can lead to many applications of modelling of the thin-skin regime. 

The first of them to determine the LMA quantitatively and the second - the LF qualitatively Of course, limit of sensitivity of the LF channel depends on the rope type and on its state very close because the LF are detected by signal pulses exceeding over a noise level. The level is less for new ropes (especially for the locked coil ropes) than for multi-strand ropes used (especially for the ropes corroded). Even if a skilled and experienced operator interprets a record, this cannot exclude possible errors completely because of the evaluation subjectivity. Moreover it takes a lot of time for the interpretation. Some of flaw detector producers understand the problem and are intended to develop new instruments using data processing by a computer [6]. 

Before the data can be visualised, ie displayed in a two or three-dimensional representation, the ultrasonic responses from the interior of the test-piece must be reconstructed from the raw ultrasonic data. The reconstruction process projects ultrasonic indications into 3D space. As well as reconstructing the entire ultrasonic data set within an acquisition file, it is possible to define an arbitrary sub-volume of the test object over which reconstruction will take place. The image resolution may also be defined by the user. Clearly, larger volumes or greater resolution will increase the computation time for both the reconstruction and visualisation processes. 

Fig. 3. Average computation time for one step using EGO.VIII on a DEC-Alpha 3300L workstation (175 MHz) for simulation systems of varying size. The insets show some of the protein-water systems used for the benchmark simulations.

Nevertheless, the technique suffers from a severe time scale problem -the trajectories are computed for (at most) a few nanoseconds. This is far too short compared to times required for many processes in biophysics. For example, the ii to T conformational transition in hemoglobin lasts tens of microseconds [1], and the typical time for ion migration through the gramicidin channel is hundreds of nanoseconds. This limits (of course) our ability to make a meaningful comparison to experiments, using MD. 

Table 1. CPU Time for 1000 MD steps of 50 H2O molecules in a box with L = 15 Ausing the LFV and the SISM for equal time step of 1 fs computed on an HP 735 workstation...

The primary reason for interest in extended Huckel today is because the method is general enough to use for all the elements in the periodic table. This is not an extremely accurate or sophisticated method however, it is still used for inorganic modeling due to the scarcity of full periodic table methods with reasonable CPU time requirements. Another current use is for computing band structures, which are extremely computation-intensive calculations. Because of this, extended Huckel is often the method of choice for band structure calculations. It is also a very convenient way to view orbital symmetry. It is known to be fairly poor at predicting molecular geometries. 

Ah initio trajectory calculations have now been performed. However, these calculations require such an enormous amount of computer time that they have only been done on the simplest systems. At the present time, these calculations are too expensive to be used for computing rate constants, which require many trajectories to be computed. Semiempirical methods have been designed specifically for dynamics calculations, which have given insight into vibrational motion, but they have not been the methods of choice for computing rate constants since they are generally inferior to analytic potential energy surfaces fitted from ah initio results. 

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