SHAKE procedure

The most commonly used method for applying constraints, particularly in molecula dynamics, is the SHAKE procedure of Ryckaert, Ciccotti and Berendsen [Ryckaert et a 1977]. In constraint dynamics the equations of motion are solved while simultaneous satisfying the imposed constraints. Constrained systems have been much studied in classics mechanics we shall illustrate the general principles using a simple system comprising a bo sliding down a frictionless slope in two dimensions (Figure 7.8). The box is constrained t remain on the slope and so the box s x and y coordinates must always satisfy the equatio of the slope (which we shall write as y = + c). If the slope were not present then the bo... 

In other cases, modifications were conducted to modify the standard manual shaking procedure. Hoffman et al. [225] modified the method substituting manual shaking by a special stirring vessel. 

Fig. 3. Surface inactivation rate of prostatic acid phosphatase by shaking and protection by added surface-active agent. Shaking mixtures (20 ml) contained purified enzyme (056 /ug of protein/ml) in 0.05 M acetate buffer at pH 5.5. The solutions were shaken in 50 ml volumetric flasks using a mechanical shaker (Burrell, model CC). Temperatures were maintained by immersion of the flasks in an appropriately set water bath. After specified intervals of shaking, duplicate 0.1 ml ahquots were removed into tubes containing Triton X-100. All tubes were assayed simultaneously, following the shaking procedure, with 0.05 M phenyl phosphate as substrate. Curve 1 Enzyme + Triton X-100 at 0°C and 29°C. Curve 2 Enzyme alone at 0°C. Curve 3 Enzyme alone at 29°C. From Tsuboi and Hudson (88).

However, there are potential objections to the use of a one atmosphere foaming experiment. These must be considered to determine the relevance of these experiments to surfactant performance in a formation. Bikerman has stated that in one atmosphere experiments the height and volume of the foam obtained depend on the details of the shaking procedure...and thus cannot be used to characterize the foaminess of a liquid in a (reasonably) absolute manner...the foam heights reproduced are specific for the test procedure selected and have no general validity. (10)... 

MD simulations can also be used for the pmf calculations with umbrella sampling or the perturbation method. An effective procedure for implementing isothermal-isobaric conditions is to couple the system to a constant temperature and pressure bath. A leap-frog algorithm is then preferred for integrating Newton s equations. " In addition, the SHAKE procedure can be applied to constrain intramolecular degrees of freedom, This is often done to eliminate bond vibrations which permits use of a larger time step, about 1-2 fs. 

Examples of the shaking procedure can be found in several ISO standards for the determination of organic micro-pollutants in soil, such as PAH, OCB and PCB, mineral oil and herbicides. 

The matrix method solution of Eq. [56] consists of finding the total displacement, Eq. [54], of a particle, needed to satisfy simultaneously all the constraints in which the particle is involved. In contrast, the SHAKE procedure consists of finding incrementally the displacement a particle needs to satisfy successively all those constraints. From Eq. [54], the displacement needed to satisfy separately a constraint a, is... 

Either matrix inversion or SHAKE can be used to solve the set of / linear equations Eq. [130] for the t. As discussed before, solution for the 7 and (t)] by matrix techniques becomes computationally expensive for systems with large numbers of coupled constraints, so the following presentation is confined to the solution by the SHAKE procedure. Andersen discusses why the velocity Verlet algorithm cannot be incorporated into the method of undetermined parameters in as straightforward a manner as can the basic Verlet algorithm. 

Agitation is the easiest way of producing foam, but the results are very dependent on the details of the shaking procedure. Foam height, or for more viscous fluids specific gravity changes, are usually measured. 

Methods and algorithms for molecular dynamics simulations of molecular fluids are described. Those techniques are emphasized that in the experience of the authors are reliable and easy to implement. This implies the use of cartesian coordinates throughout, the use of the SHAKE procedure to satisfy constraints and the incorporation of an adjustable coupling to an external bath with constant temperature and pressure. 

Eor a same teether sample and using the same shaking procedure two laboratories measured a release rate differing by a factor of 200 (Table 6.35). The reason for this huge discrepancy is not clear. Actions are being undertaken in the framework of EC Measurement and Testing to increase the reliability of the migration data. 

Precision data have not been established for all types of samples on which this test method is used. Limited cooperative tests were conducted in 1961, principally to establish equality with the previously used shaking procedure. Preci-... 

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