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60 relations: Boltzmann distribution, Cartesian coordinate system, Charge density, Complex number, Conservative vector field, Coulomb's law, Curl (mathematics), Debye–Hückel equation, Discrete Poisson equation, Divergence, Electric charge, Electric displacement field, Electric field, Electric potential, Electromagnetism, Electrostatics, Error function, Euclidean space, Euclidean vector, Faraday's law of induction, France, Function (mathematics), Fundamental solution, Gauge fixing, Gauss's law, Gaussian units, Gradient, Green's function, Helmholtz decomposition, Implicit function, Integral, International System of Units, Inverse problem, Laplace operator, Laplace's equation, Least squares, List of geometers, Magnetic potential, Manifold, Mathematician, Mathematics, Maxwell's equations, Mechanical engineering, Newton's law of universal gravitation, Normal (geometry), Normal distribution, Octree, Partial differential equation, Permittivity, Physicist, ..., PlanetMath, Point cloud, Poisson–Boltzmann equation, Polarization density, Real number, Relaxation (iterative method), Screened Poisson equation, Siméon Denis Poisson, Theoretical physics, Uniqueness theorem for Poisson's equation. Expand index (10 more) »
Boltzmann distribution
In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution Translated by J.B. Sykes and M.J. Kearsley. See section 28) is a probability distribution, probability measure, or frequency distribution of particles in a system over various possible states.
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Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
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Charge density
In electromagnetism, charge density is a measure of the amount of electric charge per unit length, surface area, or volume.
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Conservative vector field
In vector calculus, a conservative vector field is a vector field that is the gradient of some function, known in this context as a scalar potential.
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Coulomb's law
Coulomb's law, or Coulomb's inverse-square law, is a law of physics for quantifying the amount of force with which stationary electrically charged particles repel or attract each other.
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Curl (mathematics)
In vector calculus, the curl is a vector operator that describes the infinitesimal rotation of a vector field in three-dimensional Euclidean space.
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Debye–Hückel equation
The chemists Peter Debye and Erich Hückel noticed that solutions that contain ionic solutes do not behave ideally even at very low concentrations.
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Discrete Poisson equation
In mathematics, the discrete Poisson equation is the finite difference analog of the Poisson equation.
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Divergence
In vector calculus, divergence is a vector operator that produces a scalar field, giving the quantity of a vector field's source at each point.
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Electric charge
Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field.
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Electric displacement field
In physics, the electric displacement field, denoted by D, is a vector field that appears in Maxwell's equations.
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Electric field
An electric field is a vector field surrounding an electric charge that exerts force on other charges, attracting or repelling them.
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Electric potential
An electric potential (also called the electric field potential, potential drop or the electrostatic potential) is the amount of work needed to move a unit positive charge from a reference point to a specific point inside the field without producing any acceleration.
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Electromagnetism
Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles.
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Electrostatics
Electrostatics is a branch of physics that studies electric charges at rest.
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Error function
In mathematics, the error function (also called the Gauss error function) is a special function (non-elementary) of sigmoid shape that occurs in probability, statistics, and partial differential equations describing diffusion.
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Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
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Euclidean vector
In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.
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Faraday's law of induction
Faraday's law of induction is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF)—a phenomenon called electromagnetic induction.
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France
France, officially the French Republic (République française), is a sovereign state whose territory consists of metropolitan France in Western Europe, as well as several overseas regions and territories.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Fundamental solution
In mathematics, a fundamental solution for a linear partial differential operator is a formulation in the language of distribution theory of the older idea of a Green's function (although unlike Green's functions, fundamental solutions do not address boundary conditions).
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Gauge fixing
In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom in field variables.
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Gauss's law
In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field.
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Gaussian units
Gaussian units constitute a metric system of physical units.
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Gradient
In mathematics, the gradient is a multi-variable generalization of the derivative.
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Green's function
In mathematics, a Green's function is the impulse response of an inhomogeneous linear differential equation defined on a domain, with specified initial conditions or boundary conditions.
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Helmholtz decomposition
In physics and mathematics, in the area of vector calculus, Helmholtz's theorem, also known as the fundamental theorem of vector calculus, states that any sufficiently smooth, rapidly decaying vector field in three dimensions can be resolved into the sum of an irrotational (curl-free) vector field and a solenoidal (divergence-free) vector field; this is known as the Helmholtz decomposition or Helmholtz representation.
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Implicit function
In mathematics, an implicit equation is a relation of the form R(x_1,\ldots, x_n).
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Integral
In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.
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International System of Units
The International System of Units (SI, abbreviated from the French Système international (d'unités)) is the modern form of the metric system, and is the most widely used system of measurement.
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Inverse problem
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the density of the Earth from measurements of its gravity field.
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Laplace operator
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space.
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Laplace's equation
In mathematics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties.
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Least squares
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns.
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List of geometers
A geometer is a mathematician whose area of study is geometry.
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Magnetic potential
The term magnetic potential can be used for either of two quantities in classical electromagnetism: the magnetic vector potential, or simply vector potential, A; and the magnetic scalar potential ψ. Both quantities can be used in certain circumstances to calculate the magnetic field B. The more frequently used magnetic vector potential is defined so that its curl is equal to the magnetic field: curl A.
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
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Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.
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Mechanical engineering
Mechanical engineering is the discipline that applies engineering, physics, engineering mathematics, and materials science principles to design, analyze, manufacture, and maintain mechanical systems.
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Newton's law of universal gravitation
Newton's law of universal gravitation states that a particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
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Normal (geometry)
In geometry, a normal is an object such as a line or vector that is perpendicular to a given object.
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Normal distribution
In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.
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Octree
An octree is a tree data structure in which each internal node has exactly eight children.
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Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.
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Permittivity
In electromagnetism, absolute permittivity, often simply called permittivity, usually denoted by the Greek letter ε (epsilon), is the measure of resistance that is encountered when forming an electric field in a particular medium.
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Physicist
A physicist is a scientist who has specialized knowledge in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe.
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PlanetMath
PlanetMath is a free, collaborative, online mathematics encyclopedia.
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Point cloud
A point cloud is a set of data points in space.
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Poisson–Boltzmann equation
The Poisson–Boltzmann equation is a useful equation in many settings, whether it be to understand physiological interfaces, polymer science, electron interactions in a semiconductor, or more.
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Polarization density
In classical electromagnetism, polarization density (or electric polarization, or simply polarization) is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Relaxation (iterative method)
In numerical mathematics, relaxation methods are iterative methods for solving systems of equations, including nonlinear systems.
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Screened Poisson equation
In physics, the screened Poisson equation is a partial differential equation, which arises in (for example) the Klein–Gordon equation, electric field screening in plasmas, and nonlocal granular fluidity in granular flow.
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Siméon Denis Poisson
Baron Siméon Denis Poisson FRS FRSE (21 June 1781 – 25 April 1840) was a French mathematician, engineer, and physicist, who made several scientific advances.
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Theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena.
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Uniqueness theorem for Poisson's equation
The uniqueness theorem for Poisson's equation states that, for a large class of boundary conditions, the equation may have many solutions, but the gradient of every solution is the same.
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Poisson equation, Poisson problem, Poisson's Equation, Poisson's problem, Poisson’s equation.
References
[1] https://en.wikipedia.org/wiki/Poisson's_equation
