Poisson distribution law

The law which applies in problems of this kind is the Poisson distribution law, developed by the French mathematician Simeon Denis Poisson (1781-1840). According to this law, if the mean value is m counts, the probability of finding a value of x counts is... 

In contrast to most analytical operations, radioactive counting does not, in general, follow the normal distribution law. It follows the Poisson distribution law, an asymmetric distribution function described by... 

It should be noted that the solubilisate will be distributed among the water pools according to the Poisson distribution law [129]. That is, the probability Pk of having/ monomers per water pool such that the average occupancy number is av is given by... 

The initial distribution of the metal salt molecules is guided by the Poisson distribution law (Section 3.7), and also shows the same for the metal atoms. 

In the very initial stage of a phase transition, the appearance of nuclei on the electrode surface can be considered as a flux of random independent events along the time axis [3.1-3.16]. Therefore the probability Pm to form exactly m nuclei within a time interval [0,t] can be expressed by the Poisson distribution law ... 

Poisson distribution, multiparticle collision dynamics, macroscopic laws and transport coefficients, 102-104 Polyatomic molecules, coherence... 

Our first chapter in this set [4] was an overview the next six examined the effects of noise when the noise was due to constant detector noise, and the last one on the list is the first of the chapters dealing with the effects of noise when the noise is due to detectors, such as photomultipliers, that are shot-noise-limited, so that the detector noise is Poisson-distributed and therefore the standard deviation of the noise equals the square root of the signal level. We continue along this line in the same manner we did previously by finding the proper expression to describe the relative error of the absorbance, which by virtue of Beer s law also describes the relative error of the concentration as determined by the spectrometric readings, and from that determine the... 

Debye and Huckel applied the Boltzmann statistical distribution law and the Poisson equation for electrostatics in the model above (1,6, 10). In the calculations using the model above they considered one particular ion (the reference ion, or central ion) with... 

Adsorption. In the simple theory of the space charge inside a semiconductor, it was assumed that all the electrons and holes are free to move up to the surface. Being susceptible to thermal motion, their concentrations from a- = 0 to x — °° were said to be given by the interplay of electrical and thermal forces only, as expressed by the Boltzmann distribution law and Poisson s equation. 

A typical processive enzyme is terminal transferase. It adds on deoxynucleo-side monophosphates randomly to exposed 3 -hydroxyl termini so that the final products are formed in a statistical distribution. The distribution follows Poisson s law.5 Suppose that the enzyme adds on an average of x residues per chain. Then the probability of a particular chain having k residues added [i.e., p(k)] is given by... 

The statistical studies of Lienau cited above have amply supported the work of Martin and Gaudin. In general the probability of obtaining fi particles of diameter du n2 particles of diameter d2t etc., is given by the binomial law, but when the possible number of particles of any diameter is large and their probability P small, as is the case in crushing, the binomial distribution reduces to Poisson s law... 

Show that the distribution follows the law of large numbers (Poisson distribution). 

The volumetric charge density is of interest in the study of ionic solutions, in which one can calculate the charge density around a specific ion. This is done by using the Poisson equation, based on electrostatic electric fields or by Boltzman distribution law of classical statistic mechanics. For the simpler case of dilute solutions this approach yields the expression p =... 

Other distribution functions such as the Maxwell-Boltzman distribution, (%2) distribution, etc. are used as well [99], A discrete law of bubble size distribution (Poisson distribution) is presented in [10]... 

The Debye-Hiickel approach is an excellent example of electrochemical theory. Electrostatics is introduced into the problem in the form of Poisson s equation, and the chemistry is contained in the Boltzmann distribution law and the concept of true electrolytes (Section 3.2). The union of the electrostatic and chemical modes of... 

Recently, Infelta has elaborated a kinetic model160, 64) in which it was assumed that the solubilisate distribution over the micelles follows Poisson s law, i.e. 

Since all three Al—C bonds of the trialkyl alanes react equally quickly, the distribution of the alkyl groups in the product corresponds with Poisson s law (249) ... 

The binomial distribution law correctly expresses this probability, but it is common practice to use either the Poisson distribution or the normal Gaussian distribution fimctions since both approximate the first but are much simpler to use. If the average number of counts is high (above 100) the Gaussian function may be used with no appreciable error. The probability for observing a measured value of total count N is... 

The standard deviation of the mean is, as before, given by Equation 19.57. As the magnitude of /x (or its estimator x) increases, the portion of the Poisson distribution curve close to its mean becomes more symmetrical, and resembles more closely the normal distribution curve. Therefore, only for large values of x can one assume that the statistics of radioactive counting follow the normal distribution law, and then only as an approximation. 

The degree distribution P(k) is the probability that a node is linked to k other nodes. The P(k) of random networks exhibits a Poisson distribution, whereas that of scale-free networks approximates a power law of the form m An interesting suggestion is that most cellular networks approximate a scale-free topology" " with an exponent y between 2 and The... 

The potential distribution and width of space charge depend on the amount of charges transferred to the surface and the density of shallow donors in the material, Nx). Quantitative expressions for these relationships are indispensible in PEC research, and to understand where they come from, we derive them below. The geometry of the problem and the relevant parameters are schematically illustrated in Fig. 2.12. The starting point for the derivation is Poisson s law, which relates the potential to the net amount of charge ... 

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