Period, dynamics averaging

Averages or plotted values at regular time intervals. You specify an Average/Graph period in the Molecular Dynamics Averages dialog box. 

The distribution function P(A) may describe not only the dynamic displacements of the atom due to thermal vibrations, but also static displacements. In this latter case a disordered atom can occupy different sites at random which are themselves periodic. The average structure is then a spatial average taken over a large number of unit cells. For this reason T(S) is called the displacement factor thus avoiding the use of the more traditional term of temperature factor. 

Snapshots at regular time intervals that store atomic coordi-riaies and velocities. You can play back these snapshots to inspect the simulated structures or to average values. Yon specify a Snapshot period in the Molecular Dynamics Snapshots dialog box. 

HyperChem run s the molecular dynain ics trajectory, averaging and analyzing a trajectory and creating the Cartesian coordinates and velocities, fhe period for reporting these coordinates and velocities is th e data collection period. At-2. It is a m iiltiplc of the basic time step. At = ii At], and is also referred to as a data step. The value 1I2 is set in the Molecular Dynamics options dialog box. 

HyperChem includes a number of time periods associated with a trajectory. These include the basic time step in the integration of Newton s equations plus various multiples of this associated with collecting data, the forming of statistical averages, etc. The fundamental time period is Atj s At, the integration time step stt in the Molecular Dynamics dialog box. 

Fig. 1 Water flow dynamics in the Llobregat River (NE Spain) close to its mouth, (a) Monthly average flow rates between 1968 and 2008. (b) Daily average flow rates in 2007-2008 during a remarkably dry period (data Catalan Water Agency data base)...

The dynamics for each solute concentration study were run 10 times and averaged for each 10 iteration periods. Water molecules from the upper and lower compartments, within the membrane, are designated Wi and W2, respectively. It can be seen from these results that the presence of solutes in the lower compartment, W2, retards the flow of water into the membrane, relative to the flow from the upper compartment, Wi. In addition, this retardation of flow increases as the concentration of solute in W2 increases. We anticipate that these results are comparable to the situation at the earliest manifestation of the osmotic effect [5]. 

Monomer concentrations Ma a=, ...,m) in a reaction system have no time to alter during the period of formation of every macromolecule so that the propagation of any copolymer chain occurs under fixed external conditions. This permits one to calculate the statistical characteristics of the products of copolymerization under specified values Ma and then to average all these instantaneous characteristics with allowance for the drift of monomer concentrations during the synthesis. Such a two-stage procedure of calculation, where first statistical problems are solved before dealing with dynamic ones, is exclusively predetermined by the very specificity of free-radical copolymerization and does not depend on the kinetic model chosen. The latter gives the explicit dependencies of the instantaneous statistical characteristics on monomers concentrations and the rate constants of the elementary reactions. 

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