Sample Simulation Results

As indicated earlier in the chapter, simulation modeling is used to evaluate temporal aspects of supply chain cmifiguration. Sample simulation results illustrate evalua-timi of the robustness of supply chain configuration in the case of disruptive events (the sample is adopted from the case study of establishing an automotive supply chain in emerging markets (Chandra and Grabis 2002). 

Simulation is used to compare two alternative supply chain configurations differing by the number of suppliers. The first configuration (Dl) uses MSI as a 

---

On the other hand, however, it is not straightforward to calculate the MWDs for intermediate cases using the conventional approach. A notable advantage of using an MC simulation technique is that it can be applied to virtually any type of emulsion polymerization, and can account for the chain-length-dependent bimolecular termination reactions in a straightforward manner [265]. Sample simulation results for instantaneous MWDs were shown [265] that were obtained using parameters for styrene polymerization that were reported by Russell [289]. 

The system of equations (Equations 3.117 and 3.119) is then solved by an ODE solver for a given set of data and initial conditions. For each time step air parameters T and tg are found by solving Equations 3.118 and 3.120. Sample simulation results for this case are plotted in Figure 3.18. Note that at the end of drying, the tanperature in the dryer increases excessively due to constant power being supplied to the internal heater. The model may serve as a tool to control the process, e.g., increase the ventilation rate Wb when drying becomes too slow or reduce the heater power when temperature becomes too high as in this case. 

However, for the conducting Cu sample, simulation results indicate that the temperature is usually lower than that of AI2O3 case, whereas the temperature difference inside the sample at steady state is higher for Cu than for AI2O3. Figure 6.28 shows the radial mechanical displacement distribution at steady state, as the system is applied with a current of 1000 A and a pressure of 140 MPa for the case of alumina and copper sample. The corresponding radial and axial components of the stress distribution field, due to thermal and Poisson-type expansion, are illustrated in Fig. 6.29, for the AI2O3 (a and c) and Cu (b and d) samples [41]. 

The model was further validated simulating the N2O decomposition/reactivity onto core monolith samples simulation results were in fairly good agreement with both the N2O and the NH3 concentration traces. 

In this chapter, fundamentals of particle transport, deposition, and removal were reviewed, and some of their biomedical applications were described. Particular attention was given to recent advances in computational modeling of nano and microparticle transport and deposition in human airways. Transport and deposition processes in lung bifurcations, nose and oral passages, as well as in alveolar cavities were discussed. Rheological properties of blood are also discussed, and sample simulation results are presented. The presented results showed the following ... 

Here, a numerical example is presented which is taken from the test results of Chap. 9. The parameter values are selected according to the sample simulation results/measurements depicted in Fig. 9.21. The identified coupling stiffness, damping coefficient, and all the friction parameters are given, for reference, in Table B.l. The applied axial force and input angular velocity values are also listed in this table. 

With the Monte Carlo method, the sample is taken to be a cubic lattice consisting of 70 x 70 x 70 sites with intersite distance of 0.6 nm. By applying a periodic boundary condition, an effective sample size up to 8000 sites (equivalent to 4.8-p.m long) can be generated in the field direction (37,39). Carrier transport is simulated by a random walk in the test system under the action of a bias field. The simulation results successfully explain many of the experimental findings, notably the field and temperature dependence of hole mobilities (37,39). 

Recently, many experiments have been performed on the structure and dynamics of liquids in porous glasses [175-190]. These studies are difficult to interpret because of the inhomogeneity of the sample. Simulations of water in a cylindrical cavity inside a block of hydrophilic Vycor glass have recently been performed [24,191,192] to facilitate the analysis of experimental results. Water molecules interact with Vycor atoms, using an empirical potential model which consists of (12-6) Lennard-Jones and Coulomb interactions. All atoms in the Vycor block are immobile. For details see Ref. 191. We have simulated samples at room temperature, which are filled with water to between 19 and 96 percent of the maximum possible amount. Because of the hydrophilicity of the glass, water molecules cover the surface already in nearly empty pores no molecules are found in the pore center in this case, although the density distribution is rather wide. When the amount of water increases, the center of the pore fills. Only in the case of 96 percent filling, a continuous aqueous phase without a cavity in the center of the pore is observed. 

A particular problem is the number of events that should be simulated before the results are stabilized about a mean value. This problem is comparable to the question of how many runs are required to simulate a Gaussian distribution within a certain precision. Experience shows that at least 1000 sample arrivals should be simulated to obtain reliable simulation results. The sample load (samples/day) therefore determines the time horizon of the simulation, which for low sample loads may be as long as several years. It means also that in practice many laboratories never reach a stationary state which makes forecasting difficult. However, one may assume that on the average the best long term decision will also be the best in the short run. One should be careful to tune a simulator based on results obtained before equilibrium is reached. 

Each simulation example is identified by a file name and title, and each comprises the qualitative physical description with drawing, the model equation development, the nomenclature, the ISIM program, suggested exercises, sample graphical results and literature references. The diskette in the pocket at the back of the book contains the programs and the ISIM software. 

As discussed in Sect. 6.1, the bias due to finite sampling is usually the dominant error in free energy calculations using FEP or NEW. In extreme cases, the simulation result can be precise (small variance) but inaccurate (large bias) [24, 32], In contrast to precision, assessing the systematic part (accuracy) of finite sampling error in FEP or NEW calculations is less straightforward, since these errors may be due to choices of boundary conditions or potential functions that limit the results systematically. 

Figure 11, Density of states of a water sample, referring to two-, three-, tetra- and penta-coordinated 3D clusters and to the total of the sample, as resulting from MD simulation, T=305 K. Dotted lines indicate vibrational frequencies for a single water molecule in gas phase.

The fundamental perspective of this review is that simulation results are not absolute, but rather are intrinsically accompanied by statistical uncertainty [4-8]. Although this view is not novel, it is at odds with informal statements that a simulation is "converged." Beyond quantification of uncertainty for specific observables, we also advocate quantification of overall sampling quality in terms of the "effective sample size" [8] of an equilibrium ensemble [9,10]. 

Mori et al. s results for three PBLG samples in m-cresol. For every sample, Dr decreases monotonically with increasing c, in a way resembling the simulation results shown in Fig. 16b. These Dr data, as well as the dynamic light scattering data, will be compared with Eqs. (50)- (52) in Sect. 8 together with zero-shear viscosity data. 

It is theoretically predicted that the formation of the breather is accompanied by the collective oscillation of the bond-length, which can be detected in the pump-probe experiment as modulation of the instantaneous vibrational frequencies. The simulation of a frequency distribution of the vibrational frequencies and a spectrogram was made with a modulation period of 44-fs and a modulation duration time of 50-fs. The evidence of the modulation appears in the spectrogram in the shape of satellite-bands S , S and D , D on both sides of the main vibrational modes S and D, respectively with the same separation. These sidebands do not appear in cis-rich samples. These results clearly suggests that the unidentified... 

TB Whitaker, F Giesbrecht, J Wu. Suitability of several statistical models to simulate observed distribution of sample test results in inspections of aflatoxin-contaminated peanut lots. J AOAC Int... 

Simulate the change of the substrate and product concentrations for batch and continuous reactors based on the kinetic parameters obtained. Compare one batch run with the simulated results. For this run, take samples every 5 to 10 minutes for 1 to 2 hours. 

---