Dirichlet integralIn mathematics, there are several integrals known as the Dirichlet integral, after the German mathematician Peter Gustav Lejeune Dirichlet, one of which is the improper integral of the sinc function over the positive real line: This integral is not absolutely convergent, meaning is not Lebesgue-integrable, because the Dirichlet integral is infinite in the sense of Lebesgue integration. It is, however, finite in the sense of the improper Riemann integral or the generalized Riemann or Henstock–Kurzweil integral.
Navier–Stokes equationsThe Navier–Stokes equations (nævˈjeː_stəʊks ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842-1850 (Stokes). The Navier–Stokes equations mathematically express momentum balance and conservation of mass for Newtonian fluids.
Leibniz integral ruleIn calculus, the Leibniz integral rule for differentiation under the integral sign states that for an integral of the form where and the integrands are functions dependent on the derivative of this integral is expressible as where the partial derivative indicates that inside the integral, only the variation of with is considered in taking the derivative. It is named after Gottfried Leibniz.
Electron magnetic momentIn atomic physics, the electron magnetic moment, or more specifically the electron magnetic dipole moment, is the magnetic moment of an electron resulting from its intrinsic properties of spin and electric charge. The value of the electron magnetic moment (symbol μe) is In units of the Bohr magneton (μB), it is -1.00115965218059μB, a value that was measured with a relative accuracy of 1.3e-13. The electron is a charged particle with charge −e, where e is the unit of elementary charge.
Three-body problemIn physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation. The three-body problem is a special case of the n-body problem. Unlike two-body problems, no general closed-form solution exists, as the resulting dynamical system is chaotic for most initial conditions, and numerical methods are generally required.
Closed-form expressionIn mathematics, an expression is in closed form if it is formed with constants, variables and a finite set of basic functions connected by arithmetic operations (+, −, ×, ÷, and integer powers) and function composition. Commonly, the allowed functions are nth root, exponential function, logarithm, and trigonometric functions . However, the set of basic functions depends on the context.
Wave equationThe (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields - as they occur in classical physics - such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics. Single mechanical or electromagnetic waves propagating in a pre-defined direction can also be described with the first-order one-way wave equation, which is much easier to solve and also valid for inhomogeneous media.
Mesh generationMesh generation is the practice of creating a mesh, a subdivision of a continuous geometric space into discrete geometric and topological cells. Often these cells form a simplicial complex. Usually the cells partition the geometric input domain. Mesh cells are used as discrete local approximations of the larger domain. Meshes are created by computer algorithms, often with human guidance through a GUI , depending on the complexity of the domain and the type of mesh desired.
