Monte Carlo simulations background

Marek, P.-Brozzetti, J.-Gustar, M. 2001. Probabilistic Assessment of Structures using Monte Carlo Simulations, Background, Exercises and Software, ITAM Academy of Sciences of the Czech Republic, GLOS s.r.o., Semily Czech Republic, Prague. 

Marek, R, Brozzetti, J., Gustar, M., Tikalsky, P. 2003. Probabilistic Assessment of Structures Using Monte Carlo Simulation Background, Exercises and Software, (2nd extended edition), ISBN 80-86246-19-1, ITAM CAS, Prague, Czech Republic, pp. 471. 

There are more complicated cases, like measurements with non-zero background, measurement times comparable with the activity lifetimes, variation of counting efficiency in time and so forth. Then the likelihood L(k ) cannot be evaluated analytically, but only using Monte Carlo simulations of a model of the data this will be demonstrated below. It is possible to describe data dependent on more parameters. 

The goal of Monte Carlo simulations is to obtain a histogram of the likelihood of observing 13 and 4 counts (including the background) for different values of r c. Because experimenters were only interested in Bis for r c, the simulation procedure... 

Estimate the (1 — a)-quantile Scrit (i-e. the critical value) of the corresponding background spectrum by Monte Carlo simulations. Depending on the chosen background model and the chosen normalization of the spectral estimator, the critical value in general depends on scale. 

Only the valence Compton profiles are needed for the reconstruction of the momentum density and the occupation number density. So one has to subtract an appropriate core Compton profile. Furthermore the contribution of the multiple scattered photons to the measured spectra has to be taken into account (for example by a Monte Carlo simulation [6]). Additionally one has to take heed of the fact that the efficiency of the spectrometer is energy dependent, so the data must be corrected for energy dependent effects which are the absorption in the sample and in the air along the beam path, the vertical acceptance of the spectrometer and the reflectivity of the analyzing crystal. The relativistic derivation of the relationship between the Compton cross section and the Compton profile leads to a further correction factor [7j. Finally a background subtraction and a normalization of the valence profiles to the number of valence... 

The present study is concerned with an important question which pertains to the Monte Carlo simulation, and which arose during the study of the fate of solitary oil ganglia (5). Simply stated, this question is what, if any, is the effect of the oil ganglion shape on the fate of the ganglion We will attempt to answer this question here. To make the treatment comprehensible and self-contained we will start by reviewing briefly some background material, without proof or unnecessary detail. The interested reader is referred to the original references (see above) for particulars. Then, we proceed to treat the problem at hand. 

Fig. 3. Fractal growth patterns in lipid monolayers, (a) Fluorescence microscopic picture of a dimyristoyl phosphatidylethanolamine monolayer doped with a fluorescent dye impurity. The monolayer has been rapidly compressed through a fluid-solid phase transition. The dark fractal patterns are solid domains being formed in the fluorescing fluid phase. The radius is about 50 /im. [From Ref. 13 by courtesy of Helmuth Mohwald.] (b) Fractal domains of solid as obtained from Monte Carlo simulation of the growth model of the present paper. The dark dots in the white background denote lipid chains in the fluid conformational state.

The theoretical background of the confinement effect in (artificial) tubes was recently examined in detail with the aid of an analytical theory as well as with Monte Carlo simulations [70]. The analytical treatment referred to a polymer chain confined to a harmonic radial tube potential. The computer simulation mimicked the dynamics of a modified Stockmayer chain in a tube with hard pore walls. In both treatments, the characteristic laws of the tube/reptation model were reproduced. Moreover, the crossover from reptation (tube diameter equal to a few Kuhn segment lengths) to Rouse dy-... 

Limits to the mean and standard deviation have been discussed in the previous sections based upon Student s t function and the Chi-squared function. While the theory of confidence intervals for these two quantities is well developed, such is not the case for the general nonlinear fitting of parameters to a data set. This will be discussed in the next chapter on general parameter estimation. For such cases, about the only approach to confidence intervals is through the Monte Carlo simulation of a number of test data sets. This approach is also applicable to limits on the mean and standard deviation and will be discussed here partly as background for the next chapter and as another approach to obtaining confidence intervals on statistical quantities. 

Nonequilibrium molecular dynamics (NEMD) Monte Carlo heat flow simulation, 71-74 theoretical background, 6 Nonequilibrium probability, time-dependent mechanical work, 51-53 Nonequilibrium quantum statistical mechanics, 57-58... 

Figure 2. The distribution of the compactness parameter for Monte Carlo protons and gammas as well as data (which is mostly protons). 8% of the background data pass the compactness cut of 2.5 (shown above), while simulations show that 50% of gamma rays are retained.

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