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Viehland–Mason Theory
The Viehland–Mason theory is a two-temperature theory for charged and neutral atoms, which explains how trace ions can have a substantially different temperature than dilute gas atoms. It is one of any of a number of kinetic theories of the transport of trace amounts of molecular ions through neutral gases under the influence of a uniform electrostatic field. Larry Viehland and Edward A. Mason developed it in the late 1970s. They later extended this theory into a three-temperature theory that allowed for different ion temperatures parallel and perpendicular to the electric field. Current work for atomic ion-neutral systems uses a Gram–Charlier probability function as a zero-order approximation to the ion velocity distribution function. The Gram–Charlier theory has been remarkably successful in producing calculated mobilities and diffusion coefficients that are in excellent agreement with experimental results if the microscopic force between the ion and atom is accuratel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory
A theory is a systematic and rational form of abstract thinking about a phenomenon, or the conclusions derived from such thinking. It involves contemplative and logical reasoning, often supported by processes such as observation, experimentation, and research. Theories can be scientific, falling within the realm of empirical and testable knowledge, or they may belong to non-scientific disciplines, such as philosophy, art, or sociology. In some cases, theories may exist independently of any formal discipline. In modern science, the term "theory" refers to Scientific theory, scientific theories, a well-confirmed type of explanation of nature, made in a way Consistency, consistent with the scientific method, and fulfilling the Scientific theory#Characteristics of theories, criteria required by modern science. Such theories are described in such a way that scientific tests should be able to provide Empirical evidence, empirical support for it, or Empirical evidence, empirical contradi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gram–Charlier Theory
In probability theory, the Gram–Charlier A series (named in honor of Jørgen Pedersen Gram and Carl Charlier), and the Edgeworth series (named in honor of Francis Ysidro Edgeworth) are series that approximate a probability distribution over the real line (-\infty,\infty) in terms of its cumulants. The series are the same; but, the arrangement of terms (and thus the accuracy of truncating the series) differ. The key idea of these expansions is to write the characteristic function of the distribution whose probability density function is to be approximated in terms of the characteristic function of a distribution with known and suitable properties, and to recover through the inverse Fourier transform. Gram–Charlier A series We examine a continuous random variable. Let \hat be the characteristic function of its distribution whose density function is , and \kappa_r its cumulants. We expand in terms of a known distribution with probability density function , characteristic functi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
