Pareto distributionThe Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto, is a power-law probability distribution that is used in description of social, quality control, scientific, geophysical, actuarial, and many other types of observable phenomena; the principle originally applied to describing the distribution of wealth in a society, fitting the trend that a large portion of wealth is held by a small fraction of the population.
Exponential distributionIn probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts.
UraniumUranium is a chemical element with symbol U and atomic number 92. It is a silvery-grey metal in the actinide series of the periodic table. A uranium atom has 92 protons and 92 electrons, of which 6 are valence electrons. Uranium radioactively decays by emitting an alpha particle. The half-life of this decay varies between 159,200 and 4.5 billion years for different isotopes, making them useful for dating the age of the Earth.
Gamma distributionIn probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-squared distribution are special cases of the gamma distribution. There are two equivalent parameterizations in common use: With a shape parameter and a scale parameter . With a shape parameter and an inverse scale parameter , called a rate parameter. In each of these forms, both parameters are positive real numbers.
Nuclear fissionNuclear fission is a reaction in which the nucleus of an atom splits into two or more smaller nuclei. The fission process often produces gamma photons, and releases a very large amount of energy even by the energetic standards of radioactive decay. Nuclear fission was discovered on 19 December 1938 in Berlin by German chemists Otto Hahn and Fritz Strassmann. Physicists Lise Meitner and her nephew Otto Robert Frisch explained it theoretically in January 1939. Frisch named the process "fission" by analogy with biological fission of living cells.
Neutron temperatureThe neutron detection temperature, also called the neutron energy, indicates a free neutron's kinetic energy, usually given in electron volts. The term temperature is used, since hot, thermal and cold neutrons are moderated in a medium with a certain temperature. The neutron energy distribution is then adapted to the Maxwell distribution known for thermal motion. Qualitatively, the higher the temperature, the higher the kinetic energy of the free neutrons. The momentum and wavelength of the neutron are related through the de Broglie relation.
Normal distributionIn statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.
Beta distributionIn probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] or (0, 1) in terms of two positive parameters, denoted by alpha (α) and beta (β), that appear as exponents of the variable and its complement to 1, respectively, and control the shape of the distribution. The beta distribution has been applied to model the behavior of random variables limited to intervals of finite length in a wide variety of disciplines.
Continuous uniform distributionIn probability theory and statistics, the continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions. Such a distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. The bounds are defined by the parameters, and which are the minimum and maximum values. The interval can either be closed (i.e. ) or open (i.e. ). Therefore, the distribution is often abbreviated where stands for uniform distribution.
Poisson distributionIn probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. It is named after French mathematician Siméon Denis Poisson ('pwɑːsɒn; pwasɔ̃). The Poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume.
Uranium-236Uranium-236 (236U) is an isotope of uranium that is neither fissile with thermal neutrons, nor very good fertile material, but is generally considered a nuisance and long-lived radioactive waste. It is found in spent nuclear fuel and in the reprocessed uranium made from spent nuclear fuel. The fissile isotope uranium-235 fuels most nuclear reactors. When 235U absorbs a thermal neutron, one of two processes can occur. About 82% of the time, it will fission; about 18% of the time, it will not fission, instead emitting gamma radiation and yielding 236U.
Neutron cross sectionIn nuclear physics, the concept of a neutron cross section is used to express the likelihood of interaction between an incident neutron and a target nucleus. The neutron cross section σ can be defined as the area in cm2 for which the number of neutron-nuclei reactions taking place is equal to the product of the number of incident neutrons that would pass through the area and the number of target nuclei. In conjunction with the neutron flux, it enables the calculation of the reaction rate, for example to derive the thermal power of a nuclear power plant.
Boiling water reactorA boiling water reactor (BWR) is a type of light water nuclear reactor used for the generation of electrical power. It is the second most common type of electricity-generating nuclear reactor after the pressurized water reactor (PWR), which is also a type of light water nuclear reactor. The main difference between a BWR and PWR is that in a BWR, the reactor core heats water, which turns to steam and then drives a steam turbine. In a PWR, the reactor core heats water, which does not boil.
Nuclear reactorA nuclear reactor is a device used to initiate and control a fission nuclear chain reaction or nuclear fusion reactions. Nuclear reactors are used at nuclear power plants for electricity generation and in nuclear marine propulsion. Heat from nuclear fission is passed to a working fluid (water or gas), which in turn runs through steam turbines. These either drive a ship's propellers or turn electrical generators' shafts. Nuclear generated steam in principle can be used for industrial process heat or for district heating.
Uranium-234Uranium-234 (234U or U-234) is an isotope of uranium. In natural uranium and in uranium ore, 234U occurs as an indirect decay product of uranium-238, but it makes up only 0.0055% (55 parts per million) of the raw uranium because its half-life of just 245,500 years is only about 1/18,000 as long as that of 238U. Thus the ratio of 234U to 238U in a natural sample is equivalent to the ratio of their half-lives. The primary path of production of 234U via nuclear decay is as follows: uranium-238 nuclei emit an alpha particle to become thorium-234.
Relationships among probability distributionsIn probability theory and statistics, there are several relationships among probability distributions. These relations can be categorized in the following groups: One distribution is a special case of another with a broader parameter space Transforms (function of a random variable); Combinations (function of several variables); Approximation (limit) relationships; Compound relationships (useful for Bayesian inference); Duality; Conjugate priors. A binomial distribution with parameters n = 1 and p is a Bernoulli distribution with parameter p.
Plutonium-239Plutonium-239 (239Pu or Pu-239) is an isotope of plutonium. Plutonium-239 is the primary fissile isotope used for the production of nuclear weapons, although uranium-235 is also used for that purpose. Plutonium-239 is also one of the three main isotopes demonstrated usable as fuel in thermal spectrum nuclear reactors, along with uranium-235 and uranium-233. Plutonium-239 has a half-life of 24,110 years.
Fast-neutron reactorA fast-neutron reactor (FNR) or fast-spectrum reactor or simply a fast reactor is a category of nuclear reactor in which the fission chain reaction is sustained by fast neutrons (carrying energies above 1 MeV or greater, on average), as opposed to slow thermal neutrons used in thermal-neutron reactors. Such a fast reactor needs no neutron moderator, but requires fuel that is relatively rich in fissile material when compared to that required for a thermal-neutron reactor.
Chernobyl disasterThe Chernobyl disaster was a nuclear accident that occurred on 26 April 1986 at the No. 4 reactor in the Chernobyl Nuclear Power Plant, near the city of Pripyat in the north of the Ukrainian SSR in the Soviet Union. Called the world's worst-ever civil nuclear incident, it is one of only two nuclear energy accidents rated at seven—the maximum severity—on the International Nuclear Event Scale, the other being the 2011 Fukushima nuclear disaster in Japan.
Enriched uraniumEnriched uranium is a type of uranium in which the percent composition of uranium-235 (written 235U) has been increased through the process of isotope separation. Naturally occurring uranium is composed of three major isotopes: uranium-238 (238U with 99.2739–99.2752% natural abundance), uranium-235 (235U, 0.7198–0.7202%), and uranium-234 (234U, 0.0050–0.0059%). 235U is the only nuclide existing in nature (in any appreciable amount) that is fissile with thermal neutrons.
