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.
Rate equationIn chemistry, the rate law or rate equation for a chemical reaction is a mathematical equation that links the rate of forward reaction with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial reaction orders). For many reactions, the initial rate is given by a power law such as where [\mathrm{A}] and [\mathrm{B}] express the concentration of the species \mathrm{A} and \mathrm{B}, usually in moles per liter (molarity, M).
Icosahedral symmetryIn mathematics, and especially in geometry, an object has icosahedral symmetry if it has the same symmetries as a regular icosahedron. Examples of other polyhedra with icosahedral symmetry include the regular dodecahedron (the dual of the icosahedron) and the rhombic triacontahedron. Every polyhedron with icosahedral symmetry has 60 rotational (or orientation-preserving) symmetries and 60 orientation-reversing symmetries (that combine a rotation and a reflection), for a total symmetry order of 120.
Rotational symmetryRotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation. Certain geometric objects are partially symmetrical when rotated at certain angles such as squares rotated 90°, however the only geometric objects that are fully rotationally symmetric at any angle are spheres, circles and other spheroids.
Heavy waterHeavy water (deuterium oxide, 2H2O, D2O) is a form of water whose hydrogen atoms are all deuterium (2H or D, also known as heavy hydrogen) rather than the common hydrogen-1 isotope (1H or H, also called protium) that makes up most of the hydrogen in normal water. The presence of the heavier hydrogen isotope gives the water different nuclear properties, and the increase in mass gives it slightly different physical and chemical properties when compared to normal water. Deuterium is a heavy hydrogen isotope.
Nuclear forceThe nuclear force (or nucleon–nucleon interaction, residual strong force, or, historically, strong nuclear force) is a force that acts between the protons and neutrons of atoms. Neutrons and protons, both nucleons, are affected by the nuclear force almost identically. Since protons have charge +1 e, they experience an electric force that tends to push them apart, but at short range the attractive nuclear force is strong enough to overcome the electromagnetic force. The nuclear force binds nucleons into atomic nuclei.
Self-ionization of waterThe self-ionization of water (also autoionization of water, and autodissociation of water) is an ionization reaction in pure water or in an aqueous solution, in which a water molecule, H2O, deprotonates (loses the nucleus of one of its hydrogen atoms) to become a hydroxide ion, OH−. The hydrogen nucleus, H+, immediately protonates another water molecule to form a hydronium cation, H3O+. It is an example of autoprotolysis, and exemplifies the amphoteric nature of water.
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.
Quantum yieldIn particle physics, the quantum yield (denoted Φ) of a radiation-induced process is the number of times a specific event occurs per photon absorbed by the system. The fluorescence quantum yield is defined as the ratio of the number of photons emitted to the number of photons absorbed. Fluorescence quantum yield is measured on a scale from 0 to 1.0, but is often represented as a percentage. A quantum yield of 1.0 (100%) describes a process where each photon absorbed results in a photon emitted.
Yukawa potentialIn particle, atomic and condensed matter physics, a Yukawa potential (also called a screened Coulomb potential) is a potential named after the Japanese physicist Hideki Yukawa. The potential is of the form: where is a magnitude scaling constant, i.e. is the amplitude of potential, m is the mass of the particle, r is the radial distance to the particle, and α is another scaling constant, so that is the approximate range. The potential is monotonically increasing in r and it is negative, implying the force is attractive.
