Monte Carlo calculations, simulated spectra

To demonstrate the capability of the LXe-CAT as an imaging 7-ray telescope, we have carried out Monte Carlo calculations that simulate the response of the instrument to several source distributions. In particular, we simulate the imaging process for a coded aperture imaging system in response to photon continuum spectra from point sources and to a 7-ray line from localized sources. The background rates expected in a balloon or satellite based observation were calculated. Fig. 5 shows the total background spectrum, together with its individual components, calculated for 3 gem over Palestine, TX. A 5 cm Csl thick shield was assumed for the calculation. 

Figure 9. The measured momentum density of an aluminium film. In the left panel we show the measured momentum density near the Fermi level (error bars), the result of the LMTO calculations (dashed line) and the result of these calculations in combination with Monte Carlo simulations taking into account the effects of multiple scattering (full line). In the central panel we show in a similar way the energy spectrum near zero momentum. In the right panel we again show the energy spectrum, but now the theory is that of an electron gas, taking approximately into account the effects of electron-electron correlation (dashed) and this electron gas theory plus Monte Carlo simulations (solid line).

One way to include these local quantum chemical effects is to perform ab initio calculations on an HOD molecule in a cluster of water molecules, possibly in the field of the point charges of the water molecules surrounding the cluster. In 1991 Hermansson generated such clusters from a Monte Carlo simulation of the liquid, and for each one she determined the relevant Bom Oppenheimer potential and the vibrational frequencies. The transition-dipole-weigh ted histogram of frequencies was in rough agreement with the experimental IR spectrum for H0D/D20 [130],... 

If the spectral lines are broadened but have the same profile, the moments of the spectrum can be expressed in terms of the moments of the non-broadened spectrum and the moments of a separate line. When the moments of the separate line do not exist (for natural line shape), the global characteristics of the spectrum can be found simulating its structure by Monte-Carlo or distribution function methods and then convoluting each calculated line. 

In the Monte Carlo simulation, a few hundreds (100-2000) of scans are calculated, and the Fourier transform of their sum gives the simulated spectrum. The trajectories of spin sets are individual which makes their scans different providing the variety of the samples necessary for the simulation, similar to the case of the single spin interpretation. The calculation of the scans remains independent of each other thus the calculation can be parallelised in the case of coupled spin systems as well.101 The density matrix introduced because of the coupling and the increased amount of calculations on the matrix elements emphasise the use of modern architectures in parallel computation.104... 

In addition to conventional shell fitting, authors have used Monte Carlo simulation. During MC calculation, the Cm atom was positioned at random position in the 10 A diameter sphere formed by three coordinating BTP molecules, and the corresponding theoretical EXAFS spectra were calculated and compared with the experimental spectrum. From the best agreement between the theoretical and experimental EXAFS spectra, the Cm-N distances equal to 2.52 A and 2.57, 2.59 A for nitrogen atoms of pyridine and triazine rings, respectively, were obtained. 

Statistical models for the analysis of NMR data are used in two complementary approaches (Fig. 2) an analytical (model fitting) approach and a synthetic (computer simulation) approach. In the analytical approach, assigned NMR resonance intensities are fit to expected intensities based on statistical models. In the synthetic approach, spectral intensities are first calculated using reaction probabilities predicted by theoretical models these theoretical intensities are matched with those observed in the NMR spectrum. The calculation is based on theoretical probability expressions or Monte Carlo simulation. In an integrated approach, both methods are used for more complex systems. 

A calculation of the aperture flux was performed by Monte-Carlo simulation of a setup equivalent to GRIS (see point 3 of this section) using the y-spectrum given in [1] but divided by 1.28 to account for the different y-flux over Alice Springs [7] ... 

An analytical mockup of the experimental system was made and the GEM c e (Monte Carlo) was used to calculate Ms for a scries of plutonium-polystyrene cubes. Calculations were made using two simulated beams whose spectra arc assumed to bracket the experimental beam spectrum. The peak of the spectra for C and D are at 1.8 and 2.2 MeV, respectively. The code, inserts source neutrons perpendicular to the front face of the cube and tracks a neutron until it is lost by leakage or absorption. All neutron progeny are similarly treated. The results are also shown in Fig. 1. 

Figure 6 On the accuracy of the Point Estimate technique for calculating the spectrum of the unconditional standard deviation of SDOF displacement. Solid line Point Estimate method. Dashed line Monte Carlo simulation (1,000 samples). The dotted line corresponds to the standard deviation without considering uncertainties in the Kanai-Tajimi model and using the mean values of the parameters.

The results are shown in Fig. 6. Notice that with only six calculation of the SDOF system per period, the results are in excellent agreement with the estimation yielded by Monte Carlo simulation obtained as the average of 1,000 calls of Eq. (68) for each period. The figure also displays the spectrum of the standard deviation without considering the uncertainties of the model parameters. The effect of such a consideration can be better appreciated in Fig. 7, which corresponds to the increment of the standard deviation using the uncertain stochastic model with respect to its use with... 

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