Numerical integrationIn analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.
Operator (physics)In physics, an operator is a function over a space of physical states onto another space of physical states. The simplest example of the utility of operators is the study of symmetry (which makes the concept of a group useful in this context). Because of this, they are useful tools in classical mechanics. Operators are even more important in quantum mechanics, where they form an intrinsic part of the formulation of the theory.
Magneto-inertial fusionMagneto-inertial fusion (MIF) describes a class of fusion devices which combine aspects of magnetic confinement fusion and inertial confinement fusion in an attempt to lower the cost of fusion devices. MIF uses magnetic fields to confine an initial warm, low-density plasma, then compresses that plasma to fusion conditions using an impulsive driver or "liner." Magneto-inertial fusion approaches differ in the degree of magnetic organization present in the initial target, as well as the nature and speed of the imploding liner.
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.
Nuclear fusionNuclear fusion is a reaction in which two or more atomic nuclei, usually deuterium and tritium (hydrogen variants), are combined to form one atomic nuclei and subatomic particles (neutrons or protons). The difference in mass between the reactants and products is manifested as either the release or absorption of energy. This difference in mass arises due to the difference in nuclear binding energy between the atomic nuclei before and after the reaction.
Momentum operatorIn quantum mechanics, the momentum operator is the operator associated with the linear momentum. The momentum operator is, in the position representation, an example of a differential operator. For the case of one particle in one spatial dimension, the definition is: where ħ is Planck's reduced constant, i the imaginary unit, x is the spatial coordinate, and a partial derivative (denoted by ) is used instead of a total derivative (d/dx) since the wave function is also a function of time. The "hat" indicates an operator.
Numerical methods for partial differential equationsNumerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.
Laplace operatorIn mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean space. It is usually denoted by the symbols , (where is the nabla operator), or . In a Cartesian coordinate system, the Laplacian is given by the sum of second partial derivatives of the function with respect to each independent variable. In other coordinate systems, such as cylindrical and spherical coordinates, the Laplacian also has a useful form.
Cauchy distributionThe Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution is the distribution of the x-intercept of a ray issuing from with a uniformly distributed angle. It is also the distribution of the ratio of two independent normally distributed random variables with mean zero.
Head-on collisionA head-on collision is a traffic collision where the front ends of two vehicles such as cars, trains, ships or planes hit each other when travelling in opposite directions, as opposed to a side collision or rear-end collision. With railways, a head-on collision occurs most often on a single line railway. This usually means that at least one of the trains has passed a signal at danger, or that a signalman has made a major error. Head-on collisions may also occur at junctions, for similar reasons.
