Simulation Results Analysis

In the hybrid intelligent algorithm, population size = 100, crossover probability Pc = 0.6, mutation probability = 0.5, number of iterations Gmax = 20,000, rank-based evaluation function a = 0.05 and there are 3000 random simulation. The main frequency of the PC for calculating is 2400 MHz, and all the algorithm program is realized by C++ language. 

The optimal objective value of each stage after 20,000 iterations is shown in Table 4.8. The maximum profit of the entire supply chain is 2155.014000. Tables 4.9, 4.10, 4.11, 4.12, 4.13, 4.14, 4.15, 4.16, 4.17, 4.18, 4.19, 4.20, 4.21, 4.22, 4.23, 4.24 and 4.25 are the optimal strategic decision found among all strategic decision variables after 20,000 iterations (optimal decision value of variable 0-1 is corresponding to the optimal decision value of real number, so it is omitted). 

To further verify the validity of the algorithm and the random expected value model, we simulate different values of parameters of hybrid intelligent algorithm  

In the hybrid intelligent algorithm, set population size N = 130, crossover probability p = 0.4, mutation probability = 0.5, number of iterations 

Manufacturer code Finished goods code Production capability Inventory capability Setup cost Variable production cost Inventory cost Transportation capability 

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One of the flexibilities of eomputer simulation is that it is possible to define the themiodynamie eonditions eorresponding to one of many statistieal ensembles, eaeh of whieh may be most suitable for the purpose of the study. A knowledge of the underlying statistieal meehanies is essential in the design of eorreet simulation methods, and in the analysis of simulation results. Flere we deseribe two of the most eommoir statistieal ensembles, but examples of the use of other ensembles will appear later in the ehapter. 

Visuahzation and analysis of structure and dynamics simulation results. Free of charge for academic use. Available for different platforms. Imports TINKER results and accepts various file formats. hitp //www.csc.ji/gopenmol/... 

In the next section we describe the basic models that have been used in simulations so far and summarize the Monte Carlo and molecular dynamics techniques that are used. Some principal results from the scaling analysis of EP are given in Sec. 3, and in Sec. 4 we focus on simulational results concerning various aspects of static properties the MWD of EP, the conformational properties of the chain molecules, and their behavior in constrained geometries. The fifth section concentrates on the specific properties of relaxation towards equilibrium in GM and LP as well as on the first numerical simulations of transport properties in such systems. The final section then concludes with summary and outlook on open problems. 

In another study Milehev and Landau [27] investigated in detail the transition from a disordered state of a polydisperse polymer melt to an ordered (liquid erystalline) state, whieh oeeurs in systems of GM when the ehains are eonsidered as semiflexible. It turns out that in two dimensions this order-disorder transition is a eontinuous seeond-order transformation whereas in 3d the simulational results show a diseontinuous first-order transformation. Comprehensive finite-size analysis [27] has established... 

An analysis of the hydration structure of water molecules in the major and minor grooves in B-DNA has shown that there is a filament of water molecules connecting both the inter and the intra phosphate groups of the two strands of B-DNA. However, such a connectivity is absent in the case of Z-DNA confirming earlier MC simulation results. The probability density distributions of the counterions around DNA shows deep penetration of the counterions in Z-DNA compared to B-DNA. Further, these distributions suggest very limited mobility for the counterions and show well defined counter-ion pattern as originally suggested in the MC study. 

Such an analysis indicates that the zero-sink assumption must be used with extreme caution if accurate flux calculations are required at the local root level. Potassium, for example, is close to the limiting value of A, for the zero sink assumption to be fulfilled, and simulations with larger roots or larger buffer powers could well lead to inaccurate simulation results. Any zero-sink model involving nitrate should be treated with some suspicion. The zero-sink assumption is also widely used in root architecture models (see later). 

A rather crude, but nevertheless efficient and successful, approach is the bond fluctuation model with potentials constructed from atomistic input (Sect. 5). Despite the lattice structure, it has been demonstrated that a rather reasonable description of many static and dynamic properties of dense polymer melts (polyethylene, polycarbonate) can be obtained. If the effective potentials are known, the implementation of the simulation method is rather straightforward, and also the simulation data analysis presents no particular problems. Indeed, a wealth of results has already been obtained, as briefly reviewed in this section. However, even this conceptually rather simple approach of coarse-graining (which historically was also the first to be tried out among the methods described in this article) suffers from severe bottlenecks - the construction of the effective potential is neither unique nor easy, and still suffers from the important defect that it lacks an intermolecular part, thus allowing only simulations at a given constant density. 

Figure 2 shows that, for all but the shortest chains, the Flory-Vrij analysis predicts a slightly higher melting temperature than the present mean-field model. Both approximations are give values higher than the simulation results, but the overall agreement is reasonable. 

Fig.2 Melting temperatures of polymers (faTm/Ec) with variable chain lengths. The solid line is calculated from Eq. 10, the dashed line is calculated from Flory-Vrij analysis (Eq. 11), and the circles are the simulation results in the optimized approach. In simulations, the occupation density is 0.9375, and the linear size of the cubic box is set to 32 for short chains and 64 for long chains (Hu and Frenkel, unpublished results)...

We first summarize the salient features of the Langevin dynamics simulation results followed by a theoretical analysis. 

Note that with respect to the usual adiabatic analysis we have ad hoc substituted the approximate Kramers time by the exact one, Eq. (6.16), and found a surprisingly good agreement of this approximate expression with the computer simulation results in a rather broad range of parameters.]... 

The experimental and simulation results presented here indicate that the system viscosity has an important effect on the overall rate of the photosensitization of diary liodonium salts by anthracene. These studies reveal that as the viscosity of the solvent is increased from 1 to 1000 cP, the overall rate of the photosensitization reaction decreases by an order of magnitude. This decrease in reaction rate is qualitatively explained using the Smoluchowski-Stokes-Einstein model for the rate constants of the bimolecular, diffusion-controlled elementary reactions in the numerical solution of the kinetic photophysical equations. A more quantitative fit between the experimental data and the simulation results was obtained by scaling the bimolecular rate constants by rj"07 rather than the rf1 as suggested by the Smoluchowski-Stokes-Einstein analysis. These simulation results provide a semi-empirical correlation which may be used to estimate the effective photosensitization rate constant for viscosities ranging from 1 to 1000 cP. 

In Fig. 9, the distribution of reactant C is shown in each environment. As cc is a linear combination of and Y2 (Eq. 78), we can distinguish features of both Fig. 7 and Fig. 8 in the plots in Fig. 9. In particular, because C is injected in the right-hand inlet stream, cC2 and 2 appear to be quite similar. Finally, as shown in Liu and Fox (2006), the CFD predictions for the outlet conversion X are in excellent agreement with the experimental data of Johnson and Prud homme (2003a). For this reactor, the local turbulent Reynolds number ReL is relatively small. The good agreement with experiment is thus only possible if the effects of the Reynolds and Schmidt numbers are accounted for using the correlation for R shown in Fig. 4. Further details on the simulations and analysis of the CFD results can be found in Liu and Fox (2006). 

The simulation control includes the methods of generating price simulation scenarios either manually, equally distributed or using stochastic distribution approaches such as normal distribution. In addition, the number of simulation scenarios e g. 50 is defined. The optimization control covers preprocessing and postprocessing phases steering the optimization model. The optimization model is then iteratively solved for a simulated price scenario and optimization results including feasibility of the model are captured separately after iteration. Simulation results are then available for analysis. 

The evenly distributed price points ensure result analysis maps based on a standard grid. Core analysis of simulation results considers profit and utilization of the value chain as illustrated in fig. 106. 

Dynamic models explicitly categorize the causes for model results instead of simply calculating combinations of statistical distributions. Analysis of simulation results can categorize not only what happened but also why it happened. 

In an extensive study, Okamoto and co-workers [76-86] introduced a biochemical switching device based on a cyclic enzyme system in which two enzymes share two cofactors in a cyclic manner. Cyclic enzyme systems have been used as biochemical amplitiers to improve the sensitivity of enzymatic analysis [87-89], and subsequently, this technique was introduced into biosensors [90-93], In addition, cyclic enzyme systems were also widely employed in enzymic reactors, in cases where cofactor regeneration is required [94-107], Using computer simulations, Okamoto and associates [77,80-83] investigated the characteristics of the cyclic enzyme system as a switching device, and their main model characteristics and simulation results are detailed in Table 1.1, as is a similar cyclic enzyme system introduced by Hjelmfelt et al. [109,116], which can be used as a logic element. 

Experimental and simulation results presented below will demonstrate that barrel rotation, the physics used in most texts and the classical extrusion literature, is not equivalent to screw rotation, the physics involved in actual extruders and used as the basis for modeling and simulation in this book. By changing the physics of the problem the dissipation and thus adiabatic temperature increase can be 50% in error for Newtonian fluids. For example, the temperature increase for screw and barrel rotation experiments for a polypropylene glycol fluid is shown in Fig. 7.30. As shown in this figure, the barrel rotation experiments caused the temperature to increase to a higher level as compared to the screw rotation experiments. The analysis presented here focuses on screw rotation analysis, in contrast to the historical analysis using barrel rotation [15-17]. It was pointed out recently by Campbell et al. [59] that the theory for barrel and screw rotation predicts different adiabatic melt temperature increases. 

These two facts motivated a critical check of the validity of Eq. 4.11 in a wide Q-range [9,105,154,155]. For this purpose the information obtainable from fully atomistic MD simulations was essential. The advantage of MD simulations is that, once they are validated by comparison with results on the real system, magnitudes that cannot be accessed by experiments can be calculated, as for example the time dependence of the non-Gaussian parameter. The first system chosen for this goal was the archetypal polymer PL The analysis of the MD simulations results [105] on the self-motion of the main chain hydrogens was performed in a similar way to that followed with experimental data. This led to a confirmation of Eq. 4.11 beyond the uncertainties for Q<1.3 A (see Fig. 4.15). However, clear deviations from the Q-dependence of the Gaussian behaviour... 

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