Influence Of Statistical Fluctuations Research Articles

LUMINI PACKAGE FOR AB INITIO MODELING OF DOSIMETRIC EXPERIMENTS

The paper presents the capabilities of the new Lumini code for ab initio modeling of dosimeter efficiency parameters. It is based on a scaling method that allows unifying the parameters of the kinetic model of the dosimeter without the numerous approximations used to interpret experimental results of thermal-, phosphorescence, and partial illumination of irradiated semiconductors. For the first time, the Monte Carlo method was used to consider the influence of statistical fluctuations in the energy and kinetic parameters of the model on the dosimetric parameters of typical dosimeters. As a first step, the data of Lumini's interpretation of the experimental TLD spectra of 500K dosimeters irradiated on the M-30 microtron was discussed.

Statistical fluctuation analysis of measurement-device-independent quantum random-number generation

Without any assumption on detectors, measurement-device-independent quantum random-number generators (MDI QRNGs) with high generation rates have attracted lots of attention lately. However, the influence of statistical fluctuations on randomness extraction rate has not been taken into full consideration, which is crucial in the practical applications of MDI QRNGs. We propose a solution for MDI QRNGs, study the influence of statistical fluctuations, and apply an optimizing method to solve the lower bound of randomness extraction rate. Then the rate is simulated under reasonable values of some observed parameters, and it displays that the QRNG generates $6\ifmmode\times\else\texttimes\fi{}{10}^{4}\phantom{\rule{4pt}{0ex}}\text{bit}/\text{s}$, if the transmission loss is 10 dB and the number of pulses sent from the source is $N={10}^{12}$. Compared with the rates of other MDI QRNGs, our simulation outputs are with genuine randomness, since the statistical fluctuations of all parameters are considered.

The long-term stability on basic performances of a diisopropylnaphthalene-based liquid scintillation cocktail

The long-term stability of a cocktail is very important for liquid scintillation counting. The expiry date of a cocktail labeled on the container is usually one to three years later than the manufacture date, which is fairly short for the convenience of purchase, storage and use. Three batches of a diisopropylnaphthalene-based aqueous-miscible cocktail, Ultima Gold AB, with a span of 18 years of storage, have been compared on their basic performances, i.e. background count rate, counting efficiency, quench resistance, and α/β discrimination. We found that the 18-year storage has less impact on the basic performances than batch-to-batch variability in cocktail compositions, which means Ultima Gold AB has very good long-term stability. Therefore, in practice Ultima Gold AB can be used even beyond its expiry date, if it is properly stored for less than 18 years. This result will bring much convenience to plan the purchase, storage and use of the cocktail. In addition, the influence of statistical fluctuations on the quench parameter SQP(E) has been studied.

Bayesian estimation of 2-dimensional complicated distributions

In a previous paper (Zong Z, Lam KY. Estimation of complicated distributions using B-spline functions. Structural Safety 1998;20:323–32), we used a linear combination of B-spline functions to approximate a 1-dimensional or 2-dimensional complicated distribution. The method works well for large samples. In a recent paper (Zong Z, Lam KY. Bayesian estimation of complicated distributions. Structural Safety 2000;22:81–95), the method was extended to small samples for 1-dimensional p.d.f.. In this paper, we will continue to extend the method to small samples for 2-dimensional p.d.f. We still use a linear combination of B-spline functions to approximate a complicated 2-dimensional p.d.f. Strongly influenced by statistical fluctuations, the combination coefficients (unknown parameters) estimated from a small sample are highly irregular. Useful information is, however, still contained in these irregularities, and likelihood function is used to pool the information. We then introduce smoothness restriction, based on which the so-called smooth prior distribution is constructed. By combining the sample information (likelihood function) and the smoothness information (smooth prior distribution) in the Bayes' theorem, the influence of statistical fluctuations is effectively removed, and greatly improved estimation can be obtained by maximizing the posterior probability. Moreover, an entropy analysis is employed to find the most suitable prior distribution in an “objective” way. Numerical experiments have shown that the proposed method is useful to identify an appropriate p.d.f. for a continuous random variable directly from a sample without using any prior knowledge of the distribution form. Especially, the method applies to large or small samples.

Bayesian estimation of complicated distributions

In a previous paper (Zong Z, Lam KY. Estimation of complicated disributions using B-spline functions. Structural safety 1998; 20(4): 323–32), we used a linear combination of B-spline functions to approximate complicated distributions. The method works well for large samples. In this paper, we extend the method to small samples. We still use a linear combination of B-spline functions to approximate a complicated probability density function (p.d.f). Strongly influenced by statistical fluctuations, the combination coefficients (unknown parameters) estimated from a small sample are highly irregular. Useful information is, however, still contained in these irregularities, and likelihood function is used to pool the information. We then introduce smoothness restriction, based on which the so-called smooth prior distribution is constructed. By combining the sample information (likelihood function) and the smoothness information (smooth prior distribution) in the Bayes' theorem, the influence of statistical fluctuations is effectively removed, and greatly improved estimation, which is close to the true distribution, can be obtained by maximizing the posterior probability. Moreover, an entropy analysis is employed to find the most suitable prior distribution in an “objective” way. Numerical experiments have shown that the proposed method is useful to identify an appropriate p.d.f. for a continuous random variable directly from a sample without using any prior knowledge of the distribution form. Especially, the method applies to large or small samples.

The influence of statistical fluctuations on the erraticity behavior of multiparticle system

It is demonstrated that in a low-multiplicity sample, the increase of the fluctuation of event factorial moments with decreasing phase-space scale, called “erraticity”, is dominated by the statistical fluctuations. The erraticity behavior observed in the NA27 experiment can be readily reproduced by purely statistical fluctuations. Applying the erraticity analysis to a high-multiplicity sample is, however, recommended and the method is improved for the very-high-multiplicity case.

Determination of the centroid and sigma values of the central Gaussian part of a spectral line and their use for detection of spectral interference

The centroid x 0 and the sigma values, i.e. (σ g ) left and (σ g ) right, of the central part of an experimental line profile in inductively coupled plasma emission spectrometry, which can be described by a Gaussian function, can be very useful for the detection of spectral interference. The methods of Boekelheide, Zimmermann, Mundschenk, Caruana et al., which can be used for the determination of these Gaussian parameters, are critically evaluated. The influence of statistical fluctuations on the accuracy of these parameters is studied using a Gaussian pseudo-random generator as described by Brent. It is shown that with the polynomials of Taylor and Schutyser, introduced for computer implementation of Boekelheide's method, no perfect linearization of the central part of a spectral line is obtained. It appears that with the expressions, proposed in this paper, more accurate full-width at half-maximum (FWHM) values can be obtained than with those of Taylor and Schutyser and, that they are better resistant to statistical fluctuations. Problems arise when the parameters of overlapping Gaussian distributions are to be determined since with Boekelheide's method the surface under each single Gaussian profile has to be known exactly a priori for the computation of the percentiles. It is found that with this method spectral interference can be detected only if two overlapping Gaussians are not too close (i.e. the difference of the centroids Δ x o≡( x o ) 1–( x o) 2 should exceed ca 0.5 FWHM). Zimmennann's method gives excellent results for the centroids and sigma values of Gaussian profiles and spectral interference can be detected fairly easily in most cases. The method has the additional advantage of performing well for relatively large statistical fluctuations. The method of Caruana et al. yields the same information as Zimmermann's procedure but appears to be more sensitive to statistical fluctuations especially when smaller fitting regions for the least-squares procedure are employed. Compared to Zimmermann's method it is, however, not so easy to detect spectral interference.

Fusion and deep inelastic collisions studied on the Ar + Au system

We investigated the Ar + Au system at two different bombarding energies 201 and 248 MeV. The mass and the energy of the products have been measured at different angles. Mass distributions exhibits two components separated at the low bombarding energy and partly merging into each other at the high bombarding energy. One of them can be attributed to fission following complete fusion, the other one is centered around mass 40 and corresponds to deep inelastic products. These two different mechanisms correspond to different time scales. Angular distributionsd 2 σ/dθdM are peaked a little bit forward the grazing angle for products close to the projectile and, when the mass transfer increases, becomes constant. For deep inelastic collisions the mass transfer occurs in the way predicted using potential energy considerations, but the small FWHM and the slight shift of the position of the maximum of these distributions indicates a short contact time. Due to the increase of the temperature, the FWHM of the mass distribution of deep inelastic products increases with the bombarding energy. The mean total kinetic energy studied as a function of the detection angle shows the influence of statistical fluctuations at backward angles. One also observes for this system that the relaxation time connected with the mass asymmetry degree of freedom is larger than the one associated to the energy damping. Complete fusion cross sections measurements were also done at 183, 189 and 195 MeV which allowed to draw the excitation function for this process. Calculations of the fusion cross section using the concept of critical distance are in agreement with the data.

Influence of statistical fluctuations on the angular distribution of deep inelastic reactions

We apply the Fokker Planck equation in phase space of the collective degrees to compute the angular distribution for deep inelastic reactions. Within this approach, statistical fluctuations and trajectories are treated simultaneously in a consistent way. A comparison with experimental results shows a rather good agreement.

On the influence of statistical fluctuations of concentration on the I s vs. T curve of disordered ferromagnetic alloys

On the influence of statistical fluctuations of concentration on the I s vs. T curve of disordered ferromagnetic alloys