Measurement Monte Carlo method

Instead of calculations, practical work can be done with scale models (33). In any case, calculations should be checked wherever possible by experimental methods. Using a Monte Carlo method, for example, on a shape that was not measured experimentaUy, the sample size in the computation was aUowed to degrade in such a way that the results of the computation were inaccurate (see Fig. 8) (30,31). Reversing the computation or augmenting the sample size as the calculation proceeds can reveal or eliminate this source of error. 

Figure 1.10. The figure demonstrates what is obtained when the Monte Carlo method (cf. Section 3.5.5) is used to simulate normally distributed values each histogram (cf. Section 1.8.1) summarizes 100 measurements obviously, many do not even come close to what one expects under the label bell curve. ...

Special considerations are required in estimating paraimeters from experimental measurements when the relationship between output responses, input variables and paraimeters is given by a Monte Carlo simulation. These considerations, discussed in our first paper 1), relate to the stochastic nature of the solution and to the fact that the Monte Carlo solution is numerical rather than functional. The motivation for using Monte Carlo methods to model polymer systems stems from the fact that often the solution... 

Napier began by using Monte Carlo methods to establish that an essential precondition for a rigorous analysis of the type proposed was the availability of a sufficiently large sample of redshifts, each with formal accuracy better than 5 km/s anything less would result in even a real signal at 36 km/s being washed out by measurement errors. 

All these contributions add up to a total antihydrogen formation cross section of approximately 2 x 10-15 cm2 in the antiproton energy range 2-10 keV where the charge-exchange production mechanism is likely to be most effective. This value is consistent with results obtained by Ermolaev, Bransden and Mandal (1987), who used the classical trajectory Monte Carlo method, and also with the results of a recent experiment (Merrison et al., 1997) which measured the hydrogen atom formation cross section via reaction (8.22). 

The activation energy for the roll-over reaction was determined from the above mentioned Monte-Carlo based method19 the Monte-Carlo method was used to accurately determine the contribution of the TT-r) intermediate leading to D2-D10 and the amount of this 7t-r intermediate that rolls over, giving D6-D10. The ratio of the two intermediates indicates how much of the 7t-r 2 intermediate rolls over via the di-a-t]1 intermediate. This roll-over is an activated mechanism, and by measuring the amount of roll-over as a function of temperature the activation energy for roll-over can be determined. 

The intensity calculation is based on the knowledge of qKpr), the primary X-ray intensity distribution function as a function of mass depth pz (Fig. 8.9). Some experimental calculations of (iKp ) have been conducted using the tracer method proposed by Castaing. These measurements have only covered a limited number of experimental situations but have enabled adjustment of the parameters used in simulations by the Monte Carlo method or matrix effect correction models using a parameterisation of the function [Pg.164]

Many quality assurance procedures in diagnostic radiology require the use of a phantom to simulate the X-ray attenuation of the patient. The phantom should transmit the same quantity and quality (i.e. spectrum) of radiation as that transmitted by the patient. The knowledge of photon spectra at the position of measurement on the surface, inside and behind standard dosimetric and imaging phantoms is helpful for performing dosimetric or calibration measurements and hence helpful in the course of quality control. The experimental approach is limited however, simulation with Monte Carlo methods has been proved to be a very powerful technique (Petoussi et al., 1992). 

Shyichuk has developed a Monte Carlo method of computer-aided simulation of the MWDs of degraded polymer derived from the MWD of the unexposed polymer and assuming scission and cross-linking are random events. The results of trial scission cross-linking concentrations are compared with measured MWDs for the exposed samples using the sum of the squares of the... 

Husar( 1971) studied the coagulation of ultrahne particles produced by a propane torch aerosol in a 90-m polyethylene bag. The size distribution was measured as a function of time with an electrical mobility analyzer. The results of the experiments are shown in Fig. 7.11 in which the size distribution is plotted as a function of particle diameter and in Fig. 7.12 in which is shown as a function of t) both based on particle radius. Numerical calculations were carried out by a Monte Carlo method, and the results of the calculation are also shown in Fig. 7.12. The agreement between experi ment and the numerical calculations is quite satisfactory. 

In order to test observational errors nsing a fnll sample of unblended spectral lines, the Monte-Carlo method with a generator of normally distributed numbers was used. For N = 2545 measurements of magnetic fields on four yellow supergiants Aqr, a Aqr, e Gem, e Peg), including weak unblended spectral lines, the relation between mean the Monte-Carlo simulated standard error and the mean experimental standard error was estimated as = 1.033<(t>. Further, weak spectral lines for which z ro - rj < 0.2 were eliminated to strengthen the data uniformity. For A= 1844 measurements = 0.968<(t>. The discrepancy is 3.3 % in the first case and 3.2 % in the second case both appear to be very small. 

In 1998. Andrec and Prestegard- measured the coupling constants in antiphase patterns. They introduced a variant using a Metropolis-Hasting Monte Carlo method. Application to the measurement of coupling constants smaller than linewidth is shown to be applicable to simulations and experimental data stemming from INADEQUATE experiments. 

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