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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] |
Kinetic Theories
The kinetic theory of gases is a simple classical model of the thermodynamic behavior of gases. Its introduction allowed many principal concepts of thermodynamics to be established. It treats a gas as composed of numerous particles, too small to be seen with a microscope, in constant, random motion. These particles are now known to be the atoms or molecules of the gas. The kinetic theory of gases uses their collisions with each other and with the walls of their container to explain the relationship between the macroscopic properties of gases, such as volume, pressure, and temperature, as well as transport properties such as viscosity, thermal conductivity and mass diffusivity. The basic version of the model describes an ideal gas. It treats the collisions as perfectly elastic and as the only interaction between the particles, which are additionally assumed to be much smaller than their average distance apart. Due to the time reversibility of microscopic dynamics (microscopic r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cross Section (geometry)
In geometry and science, a cross section is the non-empty intersection (set theory), intersection of a solid body in three-dimensional space with a Plane (geometry), plane, or the analog in higher-dimensional spaces. Cutting an object into slices creates many parallel cross-sections. The boundary of a cross-section in three-dimensional space that is parallel to two of the Cartesian coordinate system, axes, that is, parallel to the plane determined by these axes, is sometimes referred to as a contour line; for example, if a plane cuts through mountains of a raised-relief map parallel to the ground, the result is a contour line in two-dimensional space showing points on the surface of the mountains of equal elevation. In technical drawing a cross-section, being a Planar projection, projection of an object onto a plane that intersects it, is a common tool used to depict the internal arrangement of a 3-dimensional object in two dimensions. It is traditionally crosshatched with th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt to find approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences like economics, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics (predicting the motions of planets, stars and galaxies), numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum
In physics, a quantum (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization". This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum. For example, a photon is a single quantum of light of a specific frequency (or of any other form of electromagnetic radiation). Similarly, the energy of an electron bound within an atom is quantized and can exist only in certain discrete values. Atoms and matter in general are stable because electrons can exist only at discrete energy levels within an atom. Quantization is one of the foundations of the much broader physics of quantum mechanics. Quantization of energy and its influence on how energy and matter interact (quantum electrodynamics) is part of the fundamental framework for understanding and describing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degrees Of Freedom (physics And Chemistry)
In physics and chemistry, a degree of freedom is an independent physical parameter in the chosen parameterization of a physical system. More formally, given a parameterization of a physical system, the number of degrees of freedom is the smallest number n of parameters whose values need to be known in order to always be possible to determine the values of ''all'' parameters in the chosen parameterization. In this case, any set of n such parameters are called degrees of freedom. The location of a particle in three-dimensional space requires three Coordinate system, position coordinates. Similarly, the direction and speed at which a particle moves can be described in terms of three velocity components, each in reference to the three dimensions of space. So, if the time evolution of the system is Deterministic system, deterministic (where the state at one instant uniquely determines its past and future position and velocity as a function of time), such a system has six degrees of f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffusion
Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical potential. It is possible to diffuse "uphill" from a region of lower concentration to a region of higher concentration, as in spinodal decomposition. Diffusion is a stochastic process due to the inherent randomness of the diffusing entity and can be used to model many real-life stochastic scenarios. Therefore, diffusion and the corresponding mathematical models are used in several fields beyond physics, such as statistics, probability theory, information theory, neural networks, finance, and marketing. The concept of diffusion is widely used in many fields, including physics (Molecular diffusion, particle diffusion), chemistry, biology, sociology, economics, statistics, data science, and finance (diffusion of people, ideas, data and price v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ion Velocity
An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by convention. The net charge of an ion is not zero because its total number of electrons is unequal to its total number of protons. A cation is a positively charged ion with fewer electrons than protons (e.g. K+ (potassium ion)) while an anion is a negatively charged ion with more electrons than protons (e.g. Cl− (chloride ion) and OH− (hydroxide ion)). Opposite electric charges are pulled towards one another by electrostatic force, so cations and anions attract each other and readily form ionic compounds. Ions consisting of only a single atom are termed ''monatomic ions'', ''atomic ions'' or ''simple ions'', while ions consisting of two or more atoms are termed polyatomic ions or ''molecular ions''. If only a + or − is present, it indicates ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perpendicular
In geometry, two geometric objects are perpendicular if they intersect at right angles, i.e. at an angle of 90 degrees or π/2 radians. The condition of perpendicularity may be represented graphically using the '' perpendicular symbol'', ⟂. Perpendicular intersections can happen between two lines (or two line segments), between a line and a plane, and between two planes. ''Perpendicular'' is also used as a noun: a perpendicular is a line which is perpendicular to a given line or plane. Perpendicularity is one particular instance of the more general mathematical concept of '' orthogonality''; perpendicularity is the orthogonality of classical geometric objects. Thus, in advanced mathematics, the word "perpendicular" is sometimes used to describe much more complicated geometric orthogonality conditions, such as that between a surface and its '' normal vector''. A line is said to be perpendicular to another line if the two lines intersect at a right angle. Explicitly, a fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atoms
Atoms are the basic particles of the chemical elements. An atom consists of a nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished from each other by the number of protons that are in their atoms. For example, any atom that contains 11 protons is sodium, and any atom that contains 29 protons is copper. Atoms with the same number of protons but a different number of neutrons are called isotopes of the same element. Atoms are extremely small, typically around 100 picometers across. A human hair is about a million carbon atoms wide. Atoms are smaller than the shortest wavelength of visible light, which means humans cannot see atoms with conventional microscopes. They are so small that accurately predicting their behavior using classical physics is not possible due to quantum effects. More than 99.94% of an atom's mass is in the nucleus. Protons have a positive electric charge a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edward A
Edward is an English male name. It is derived from the Anglo-Saxon name ''Ēadweard'', composed of the elements '' ēad'' "wealth, fortunate; prosperous" and '' weard'' "guardian, protector”. History The name Edward was very popular in Anglo-Saxon England, but the rule of the Norman and Plantagenet dynasties had effectively ended its use amongst the upper classes. The popularity of the name was revived when Henry III named his firstborn son, the future Edward I, as part of his efforts to promote a cult around Edward the Confessor, for whom Henry had a deep admiration. Variant forms The name has been adopted in the Iberian peninsula since the 15th century, due to Edward, King of Portugal, whose mother was English. The Spanish/Portuguese forms of the name are Eduardo and Duarte. Other variant forms include French Édouard, Italian Edoardo and Odoardo, German, Dutch, Czech and Romanian Eduard and Scandinavian Edvard. Short forms include Ed, Eddy, Eddie, Ted, Teddy a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
