PHASE algorithm

In general, any sequence which introduces a delay between the pulse(s) and the beginning of data collection will produce this type of phase error. Inevitably, there is always a short delay between the end of the pulse and the beginning of acquisition, but if the delay is only a few microseconds then the frequency-dependent phase error is less than 360° and is easily removed. However, in the spectrum above, the delay is 14 ms so that frequency differences of several kHz will introduce phase errors of thousands of degrees these are virtually impossible to remove with currently available phasing algorithms. 

The above-mentioned advances in dataset collection and phasing algorithms enable several high throughput applications of X-ray crystallography (a) target,... 

A two phase algorithm is used here. On the first phase, the balancing problem as assignment operations to different SMMs is solved and after that the necessary number of every kind of SMMs to provide feasible flow of materials is determined so the capacity of each section of the technological chain would be almost the same. The procedure is based on an assembly line balancing algorithm for single-model and mixed-model cases [4]. 

The demodulation algorithm is very simple the DSP multiplies the received signal by each carrier, and then filters the result using a FIR filter. This kind of digital filter is phase linear, (constant group delay important for the EC combinations). Other filters may be programmed, other demodulation algorithms may be used. 

The results of both experiments showed that the analysis in the frequency domain provides new technological possibilities of testing characteristics of austenitic steels. Using known phase-frequency characteristics of structural noises it is possible to construct algorithms for separation of useful signal from the defect, even through amplitude values of noise and signal are close in value. 

The velocity Verlet algorithm may be derived by considering a standard approximate decomposition of the Liouville operator which preserves reversibility and is symplectic (which implies that volume in phase space is conserved). This approach [47] has had several beneficial consequences. 

Leontidis E, Forrest B M, Widmann A FI and Suter U W 1995 Monte Carlo algorithms for the atomistio simulation of oondensed polymer phases J. Chem. Soc. Farad. Trans. 91 2355- 68... 

Cao, J., Voth, G.A. The formulation of quantum statistical mechanics based on the Feynman path centroid density. I. Equilibrium properties. J. Chem. Phys. 100 (1994) 5093-5105 II Dynamical properties. J. Chem. Phys. 100 (1994) 5106-5117 III. Phase space formalism and nalysis of centroid molecular dynamics. J. Chem. Phys. 101 (1994) 6157-6167 IV. Algorithms for centroid molecular dynamics. J. Chem. Phys. 101 (1994) 6168-6183 V. Quantum instantaneous normal mode theory of liquids. J. Chem. Phys. 101 (1994) 6184 6192. 

The force decomposition algorithm maps all possible interactions to processors and does not require inter-processor communication during the force calculation phase of MD simulation. However, to obtain the net force on each particle for the update phase would need global communication. In this section, we will present parallel algorithms based on force decomposition. 

A molecular dynamics simulation samples the phase space of a molecule (defined by the position of the atoms and their velocities) by integrating Newton s equations of motion. Because MD accounts for thermal motion, the molecules simulated may possess enough thermal energy to overcome potential barriers, which makes the technique suitable in principle for conformational analysis of especially large molecules. In the case of small molecules, other techniques such as systematic, random. Genetic Algorithm-based, or Monte Carlo searches may be better suited for effectively sampling conformational space. 

The main difference between the force-bias and the smart Monte Carlo methods is that the latter does not impose any limit on the displacement that m atom may undergo. The displacement in the force-bias method is limited to a cube of the appropriate size centred on the atom. However, in practice the two methods are very similar and there is often little to choose between them. In suitable cases they can be much more efficient at covering phase space and are better able to avoid bottlenecks in phase space than the conventional Metropolis Monte Carlo algorithm. The methods significantly enhance the acceptance rate of trial moves, thereby enabling Icirger moves to be made as well as simultaneous moves of more than one particle. However, the need to calculate the forces makes the methods much more elaborate, and comparable in complexity to molecular dynamics. 

---