Polar coordinate systemIn mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to the origin of a Cartesian coordinate system) is called the pole, and the ray from the pole in the reference direction is the polar axis. The distance from the pole is called the radial coordinate, radial distance or simply radius, and the angle is called the angular coordinate, polar angle, or azimuth.
Drilling fluidIn geotechnical engineering, drilling fluid, also known as drilling mud, is used to aid the drilling of boreholes into the earth. Often used while drilling oil and natural gas wells and on exploration drilling rigs, drilling fluids are also used for much simpler boreholes, such as water wells. The three main categories of drilling fluids are water-based muds (WBs), which can be dispersed and non-dispersed; non-aqueous muds, usually called oil-based muds (OBs); and gaseous drilling fluid, in which a wide range of gases can be used.
Classical electromagnetismClassical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model; It is, therefore, a classical field theory. The theory provides a description of electromagnetic phenomena whenever the relevant length scales and field strengths are large enough that quantum mechanical effects are negligible. For small distances and low field strengths, such interactions are better described by quantum electrodynamics, which is a quantum field theory.
Divergence (statistics)In information geometry, a divergence is a kind of statistical distance: a binary function which establishes the separation from one probability distribution to another on a statistical manifold. The simplest divergence is squared Euclidean distance (SED), and divergences can be viewed as generalizations of SED. The other most important divergence is relative entropy (also called Kullback–Leibler divergence), which is central to information theory.
Vector calculusVector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration. Vector calculus plays an important role in differential geometry and in the study of partial differential equations.
Stokes flowStokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion, is a type of fluid flow where advective inertial forces are small compared with viscous forces. The Reynolds number is low, i.e. . This is a typical situation in flows where the fluid velocities are very slow, the viscosities are very large, or the length-scales of the flow are very small. Creeping flow was first studied to understand lubrication. In nature, this type of flow occurs in the swimming of microorganisms and sperm.
Spherical coordinate systemIn mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin; its polar angle measured from a fixed polar axis or zenith direction; and the azimuthal angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the fixed axis, measured from another fixed reference direction on that plane.
Kullback–Leibler divergenceIn mathematical statistics, the Kullback–Leibler divergence (also called relative entropy and I-divergence), denoted , is a type of statistical distance: a measure of how one probability distribution P is different from a second, reference probability distribution Q. A simple interpretation of the KL divergence of P from Q is the expected excess surprise from using Q as a model when the actual distribution is P.
GradientIn vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) whose value at a point is the "direction and rate of fastest increase". If the gradient of a function is non-zero at a point , the direction of the gradient is the direction in which the function increases most quickly from , and the magnitude of the gradient is the rate of increase in that direction, the greatest absolute directional derivative.
Complex lamellar vector fieldIn vector calculus, a complex lamellar vector field is a vector field which is orthogonal to a family of surfaces. In the broader context of differential geometry, complex lamellar vector fields are more often called hypersurface-orthogonal vector fields. They can be characterized in a number of different ways, many of which involve the curl. A lamellar vector field is a special case given by vector fields with zero curl. The adjective "lamellar" derives from the noun "lamella", which means a thin layer.
Fluid mechanicsFluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical, and biomedical engineering, as well as geophysics, oceanography, meteorology, astrophysics, and biology. It can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion.
Gradient theoremThe gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the curve. The theorem is a generalization of the second fundamental theorem of calculus to any curve in a plane or space (generally n-dimensional) rather than just the real line. For φ : U ⊆ Rn → R as a differentiable function and γ as any continuous curve in U which starts at a point p and ends at a point q, then where ∇φ denotes the gradient vector field of φ.
