Temperature configurational

Butler B D, Ayton C, Jepps C G and Evans D J 1998 Configurational temperature verification of Monte Carlo simulations J. Chem. Phys. fOS 6519-22... 

Once fundamental data have been obtained, the goal is to develop a mathematical model of the process and to utilize it to explore such possibilities as produc t selectivity, start-up and shut-down behavior, vessel configuration, temperature, pressure, and conversion profiles, and so on. 

The intent of this study is to demonstrate the temperature uniformity and stability of the sterilizing medium throughout the sterilizer. Temperature distribution studies should be conducted on both empty and loaded chambers with maximum and minimum load configurations. Temperature uniformity may be influenced by the type, size, design, and installation of the sterilizer. The manufacturer of the vessel, based on the variables mentioned, should determine a satisfactory empty chamber temperature uniformity. 

The reaction proceeded in all cases with excellent stereocontrol to afford exclusively products having the (3R) configuration. Temperature was observed to exert a strong influence on the cis/trans selectivity, allowing the obtention of single trans or cis cycloadducts in most cases, simply by performing the reactions at 80°C or room temperature, respectively. 

Equation (18) requires that the temperature be known as a function of energy. Evans et al. [20] have shown that an intrinsic temperature can be assigned to an arbitrary configuration of a system. This so-called configurational temperature is based entirely on configurational information and is given by... 

In random walk simulations with configurational temperature, the calculations are started with a convergence factor / = exp(O.l). When / > exp(10 ), the density of states calculated from the temperature is used as the initial density of states for the next stage, the convergence factor is reduced by and the temperature accumulators are reset to zero... 

Fig. 2. Systematic errors in configurational temperatures in the first 4 stages of the simulation. With decreasing magnitude of the errors, the corresponding modification factors are In/ = 0.1, 0.01, 0.001, and 0.0001, respectively...

Fig. 3. Statistical errors in heat capacity as a function of CPU time. The squares are the results from the Wang-Landau algorithm the circles are the results from configurational temperature calculations, and the diamonds are the results from multi-microcanonical ensemble simulations [17]...

The effective kinetic energy of the ions is modified by the fictitious electronic mass /i and this leads to uncertainties in the temperature of the system. This could be circumvented by defining the temperature as the configurational temperature [182] but this is too expensive in ab initio calculations and has not been tried so far. At a more empirical level, appropriate corrections to the atomic masses can be applied [183]. By satisfying the first condition given in the previous paragraph we can make the uncertainties for the temperature determination small. 

The theoretical predictions of drop deformation and breakup are limited to infinitely diluted, monodispersed Newtonian systems. However, it is possible to obtain valid relationships between processing parameters and morphology. Thus it was found that in the system PS/HDPE the viscosity ratio, blend composition, screw configuration, temperature, and screw speed significantly influence the blend morphology [Bordereau et al., 1992]. For more detail on the topic see Chapter 9, Compounding Polymer Blends, in this Handbook. 

One salient feature of the results of Fig. 7.7, is that for the BAOAB] scheme there is consistently less than a 1 % error in the computed configurational temperature (for moderate friction) across all step sizes, even the largest stable timesteps tested. The relative errors obtained were so small that no discernable trend (with step size) can be shown (due to the sampling error), whereas the other schemes tested show an error consistent with second-order discretization. 

Noticeably the BAOAB] scheme provides an order of magnitude improvement in the configurational temperature results at all step sizes tested. However, the results for its average kinetic temperature are rather poor, especially compared to its conjugate method OABAO] produced from shuffling the terms around. This emphasizes the potentially misleading assumption of equivalence between the two... 

Fig. 8.9 Log-log plot of the relative error in kinetic temperature left) and configurational temperature (right) against stepsize by using various numerical methods. The system was simulated for 1,000 reduced time units but only a trajectory s tail of time length 800 was used to calculate the static quantity to make sure the system was well equilibrated. The stepsizes tested begtm at h = 0.05 and were increased incrementally by 15 % until all methods either were above 100% relative error or became unstable...

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