Radiation statistical nature

The measurement accuracy was experimentally determined by positioning the tracer in known locations inside the bed (Moslemian, 1987). The apparent tracer positions were calculated from the linear regression formulation Eq. 9.13, based on the measured detector count rates and the predetermined calibrations. Sufficient data were taken at each location to allow for statistical determination of mean and standard deviations of the tracer position and velocity. In general, the axial errors were often greater than the radial errors because of the longer axial distance of the bed that the detectors had to monitor. For an empty bed, the mean axial error in determining the tracer position was 4.7 mm and the mean radial error was 3.9 mm The corresponding standard deviations were 1.6 mm in the axial direction and 1.2 mm in the radial direction. These deviations were due to the statistical nature of the radiation detection and are the minimum deviations obtainable for the tracer position. The measured mean axial and radial velocities were approximately zero (<1 cm/s) at all locations inside the bed. However, the standard deviations of the velocities were 7.6 cm/s in the... 

Infrared and optical detector technology is a deterministic area of knowledge in which it is possible to analyze the performance of detectors in terms of the properties of the materials employed in the detectors. It is also possible to determine analytically the ultimate limits to the detector performance set by the statistical nature of the radiation to which it responds. There are two such limits. 

Theoretical work has focused on two aspects of the problem perturbation theory and other calculations of the transition probabilities in the material, and the effect on the transition probability of the statistical nature of the radiation field. Makinson and Buckingham [7,29] were the first to predict the second-order effect and calculate its magnitude based on a surface model of photoemission this work was expanded by Smith [7.30], Bowers [7.31], and Adawi [7.32], The analogous volume calculation was performed by Bloch [7.33] and later corrected by Teich and Wolga [7.24, 25],... 

The number of counts registered in a certain channel (energy interval), plotted against channel number, is called a y (or or P) spectrum. The y-radiation of a simple radionuclide having a unique y-energy does not produce a sharp spectral line, but a peak, owing to the statistical nature of the interaction of y-rays with matter. 

It is assumed that within the range of exposure conditions usually encountered in radiation work, the risks of cancer and hereditary damage increase in direct proportion to the radiation dose. It is also assumed that there is no exposure level that is entirely without risk. Thus, for example, the mortality risk factor for all cancers from uniform radiation of the whole body is now estimated to be 1 in 25 per sievert (see below for definition) for a working population, aged 20 to 64 years, averaged over both sexes. In scientific notation, this is given as 4 X 10 per sievert. Effects of radiation, primarily cancer induction, for which there is probably no threshold and the risk is proportional to dose are known as stochastic, meaning of a random or statistical nature. ... 

The inherent noise fluctuations of a radio receiver usually determine the weakest signal strength that can be measured with a radio telescope. The statistical nature of noise radiation is such that statistical fluctuations are proportional to the noise power itself. Furthermore, the average of N independent measurements of the noise power is Va times more accurate than a single measurement. Noting that a single independent measurement can be made in the minimum time interval /dv, we see that the maximum number of independent measurements that can be made in time t vs, tdv. Thus, the sensitivity equation for an ideal receiver is given by... 

The fundamental problem is that statistical methods, only, are inadequate tools in trying to determine whether a small increase in radiation affects cancer rates. Any effect is likely to be lost against the natural variation in the disease. Once more infbrmation becomes available about the mechanism by which radioactivity causes cancerous growth, it may become easier to resolve this issue, but there is little indication when this might happen. 

Pohl, E., F. Steinhausler, W. Hofmann, and J. Pohl-Ruling, Methodology of Measurements and Statistical Evaluation of Radiation Burden to Various Population Groups From All Internal and External Natural Sources, in Proceedings of Biological and Environmental Effects of Low-Level Radiation, International Atomic Energy Agency), Vol.II, pp. 305-315, Vienna, Austria (1976). 

Smirnova and coworkers studied the influence of various types of ionizing radiations on the physiomechanical characteristics of a statistical polymer of butadiene and acrylonitrile137. Although the polymer is a statistical polymer, the nature of its thermo-mechanical curve indicates a block nature of the polymeric basis of the rubber there is a... 

The accumulation of human data on a wider scale, and in quantitative form, has enabled radiation epidemiology to advance from an essentially descriptive stage to an analytic one in which numerical, dose-spedfic, risk estimates have begun to be treated statistically in order to identify determinants of risk. As presently conceived, these determinants include characteristics of the radiation exposure, underlying dose-response relationships, host factors, other environmental factors, differential tissue sensitivity, time after exposure, and natural levels of incidence. 

In Chap. 2 and Chap. 3, Sect. 1.2, the appropriate boundary and initial conditions for reactions between statistically independent pairs of reactants were formulated to model a homogeneous reaction. In these cases, if there is no inter-reactant force, all that is required is one or other reactant to be in vast excess on the other. Since the excited donor or the electron donor has to be produced in situ by photostimulation or high-energy radiation, it is natural to choose [D ] < [A], though there are exceptions. Locating the donor at the origin in a sea of acceptor molecules distributed randomly leads to the initial condition, as before... 

Perrin s argument that the very nature of a unimolecular reaction demands independence of collisions, and therefore dependence on radiation, is adequately met both by the theory of Lindemann and by that of Christiansen and Kramers. Both these theories have the essential element in common that the distribution of energy among the molecules is not appreciably disturbed by the chemical transformation of the activated molecules thus the rate of reaction is proportional simply to the number of activated molecules and therefore to the total number of molecules, sinc in statistical equilibrium the activated molecules are a constant fraction of the whole. Thus the radiation theory is not necessary to explain the existence of reactions which are unimolecular over a wide range of pressures. 

Equation (2.2.24) means homogeneous generation of particles A and B with the rate p (per unit time and volume), whereas (2.2.25) comes from the statistical independence of sources of a different-kind particles. Physical analog of this model is accumulation of the complementary Frenkel radiation defects in solids. Note that depending on the irradiation type and chemical nature of solids (metal or insulator), dissimilar Frenkel defects could be either spatially correlated in the so-called geminate pairs (see Chapter 3) or distributed at random. We will focus our attention on the latter case. 

Having explicit formulas for a number of first moments we can approximately restore the envelope line of the radiation spectrum without its detailed calculations. If lines in the spectrum have one symmetric maximum, then its envelope line is approximated by a normal function whose reconstruction requires only the mean energy and variance of the spectrum. Such an approach is useful for the case of complex spectra consisting of many lines, which, due to low resolutions as well as Doppler and collisional broadening or large natural width, form continuous or quasi-continuous bands. Studies of variation of these statistical characteristics along isoelectronic sequences give a wealth of information on intra-atomic interactions. 

An important limitation that is sometimes encountered is due to the particulate nature of electricity (electrons, ions) and of radiation (photons). The measurement of radiation intensities is in certain cases (e.g., X rays) performed by counting particles or photons one at a time. The number A counted in a time interval of given magnitude is subject to statistical fluctuations a count of A is subject to an estimated standard error given by... 

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