Virtual time

Bhawe (14) has simulated the periodic operation of a photo-chemically induced free-radical polymerization which has both monomer and solvent transfer steps and a recombination termination reaction. An increase of 50% in the value of Dp was observed over and above the expected value of 2.0. An interesting feature of this work is that when very short period oscillations were employed, virtually time-invariant products were predicted. 

The notation of eqns. (195b) and (195c) is such that cR and cB stand for the small-amplitude parts of the concentrations of R and B, while eg is the d.c. part of the R concentration. It is assumed that eg is virtually time-independent on the a.c. time scale. 

The manufacturers use this procedure to extrapolate their cmves below 0.01 sec and C is therefore a theoretical time. Virtual time is related to the prospective current by definition and so the manufacturer will quote the maximum prospective current that can be used in conjunction with his curves. At this point the engineer is encouraged to consult the manufacturers for advice on the selection of fuses for current-limiting duty. 

The above discussion on current limiting and virtual time have been included for completeness so that the reader is made aware of their significance. 

LCPT [46, 47, 51, 52, 56] first developed by a Japanese astrophysicist, Hori [51, 52], is superior to all the most traditional methods, in that no cumbersome functions of mixed variables appear and all the terms in the series are repeating Poisson brackets. The crux is the use of Lie transforms, which is regarded as a virtual time evolution of phase-space variables z( = (p,q)) along the time e driven by a Hamiltonian W that is. 

Figure 2.15 shows pictorially what the Lie transforms and its inversion perform 7i(0) transforms, for example, a point A in the (p,q) coordinate system to a point B in the other (p,q) system, which corresponds to a virtual time evolution of the phase-space variable from time 0 to... 

The proof that the Nose thermostat samples a canonical ensemble of noicrostates, provided that g = Ndf + l (virtual-time sampling) ox g = Ndf (real-time sampling), is as follows [53]. The partition function of the microcanonical ensemble generated for the extended system using virtual-time sampling (i.e., using the natural time evolution of the extended system) reads... 

Equation (96) shows that the virtual-time extended-system ensemble average of any quantity A depending on the real-system coordinates r = f and momenta p =... 

From Eq. (96), the real-system phase-space probability density for the Nosd thermostat (virtual-time sampling) can be written... 

Sampling, real-time 131, 139-141 virtual-time 131, 139, 140 SAW 20 Scaling 116... 

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