In physics, the cross section is a measure of the probability that a specific process will take place when some kind of radiant excitation intersects a localized phenomenon. For example, the Rutherford cross-section is a measure of probability that an alpha particle will be deflected by a given angle during an interaction with an atomic nucleus. Cross section is typically denoted σ (sigma) and is expressed in units of area, more specifically in barns. In a way, it can be thought of as the size of the object that the excitation must hit in order for the process to occur, but more exactly, it is a parameter of a stochastic process.
The Box–Muller transform, by George Edward Pelham Box and Mervin Edgar Muller, is a random number sampling method for generating pairs of independent, standard, normally distributed random numbers, given a source of uniformly distributed random numbers. The method was in fact first mentioned explicitly by Raymond E. A. C. Paley and Norbert Wiener in 1934.
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form
Linear elasticity is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mechanics.
In physics, the Rabi cycle is the cyclic behaviour of a two-level quantum system in the presence of an oscillatory driving field. A great variety of physical processes belonging to the areas of quantum computing, condensed matter, atomic and molecular physics, and nuclear and particle physics can be conveniently studied in terms of two-level quantum mechanical systems, and exhibit Rabi flopping when coupled to an optical driving field. The effect is important in quantum optics, magnetic resonance and quantum computing, and is named after Isidor Isaac Rabi.
In quantum physics, the scattering amplitude is the probability amplitude of the outgoing spherical wave relative to the incoming plane wave in a stationary-state scattering process. At large distances from the centrally symmetric scattering center, the plane wave is described by the wavefunction
Etendue or étendue is a property of light in an optical system, which characterizes how "spread out" the light is in area and angle. It corresponds to the beam parameter product (BPP) in Gaussian beam optics. Other names for etendue include acceptance, throughput, light grasp, light-gathering power, optical extent, and the AΩ product. Throughput and AΩ product are especially used in radiometry and radiative transfer where it is related to the view factor. It is a central concept in nonimaging optics.
In calculus, the Leibniz integral rule for differentiation under the integral sign states that for an integral of the form
In the mathematical description of general relativity, the Boyer–Lindquist coordinates are a generalization of the coordinates used for the metric of a Schwarzschild black hole that can be used to express the metric of a Kerr black hole.
A yield surface is a five-dimensional surface in the six-dimensional space of stresses. The yield surface is usually convex and the state of stress of inside the yield surface is elastic. When the stress state lies on the surface the material is said to have reached its yield point and the material is said to have become plastic. Further deformation of the material causes the stress state to remain on the yield surface, even though the shape and size of the surface may change as the plastic deformation evolves. This is because stress states that lie outside the yield surface are non-permissible in rate-independent plasticity, though not in some models of viscoplasticity.
In mathematics, a Scherk surface is an example of a minimal surface. Scherk described two complete embedded minimal surfaces in 1834; his first surface is a doubly periodic surface, his second surface is singly periodic. They were the third non-trivial examples of minimal surfaces. The two surfaces are conjugates of each other.
Lateral earth pressure is the pressure that soil exerts in the horizontal direction. The lateral earth pressure is important because it affects the consolidation behavior and strength of the soil and because it is considered in the design of geotechnical engineering structures such as retaining walls, basements, tunnels, deep foundations and braced excavations.
The scattering length in quantum mechanics describes low-energy scattering. For potentials that decay faster than as , it is defined as the following low-energy limit:
The Scherrer equation, in X-ray diffraction and crystallography, is a formula that relates the size of sub-micrometre crystallites in a solid to the broadening of a peak in a diffraction pattern. It is often referred to, incorrectly, as a formula for particle size measurement or analysis. It is named after Paul Scherrer. It is used in the determination of size of crystals in the form of powder.
The Flamant solution provides expressions for the stresses and displacements in a linear elastic wedge loaded by point forces at its sharp end. This solution was developed by A. Flamant in 1892 by modifying the three-dimensional solution of Boussinesq.
Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arch length.
In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when the diffraction pattern is viewed at a long distance from the diffracting object, and also when it is viewed at the focal plane of an imaging lens.
In physics, and especially scattering theory, the momentum-transfer cross section is an effective scattering cross section useful for describing the average momentum transferred from a particle when it collides with a target. Essentially, it contains all the information about a scattering process necessary for calculating average momentum transfers but ignores other details about the scattering angle.
Lode coordinates or Haigh–Westergaard coordinates. are a set of tensor invariants that span the space of real, symmetric, second-order, 3-dimensional tensors and are isomorphic with respect to principal stress space. This right-handed orthogonal coordinate system is named in honor of the German scientist Dr. Walter Lode because of his seminal paper written in 1926 describing the effect of the middle principal stress on metal plasticity. Other examples of sets of tensor invariants are the set of principal stresses or the set of kinematic invariants . The Lode coordinate system can be described as a cylindrical coordinate system within principal stress space with a coincident origin and the z-axis parallel to the vector .
Bearing pressure is a particular case of contact mechanics often occurring in cases where a convex surface contacts a concave surface. Excessive contact pressure can lead to a typical bearing failure such as a plastic deformation similar to peening. This problem is also referred to as bearing resistance.
