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Topics referred to by the same term
term potential function may refer to: A mathematical function, whose values are given by a scalar potential or vector potential The electric potential, in
Potential_function
Energy held by an object because of its position relative to other objects
certain scalar function, called a scalar potential. The potential energy is related to, and can be obtained from, this potential function. There are various
Potential_energy
Game class in game theory
potential game if the incentive of all players to change their strategy can be expressed using a single global function called the potential function
Potential_game
Model for the potential energy of a diatomic molecule
(Morse/Long-range) potential, the most popular potential energy function for fitting spectroscopic data. The Morse potential energy function is of the form
Morse_potential
Fundamental study of potential theory
gravitational potential satisfies Poisson's equation. See also Green's function for the three-variable Laplace equation and Newtonian potential. The integral
Gravitational_potential
Area of mathematics
be identified as the minimum of a smooth, well-defined potential function (Lyapunov function). Small changes in certain parameters of a nonlinear system
Catastrophe_theory
System in quantum mechanics
a particle with a step-like potential in one dimension. Typically, the potential is modeled as a Heaviside step function. The time-independent Schrödinger
Step_potential
Model of an energy potential in quantum mechanics
mechanics the delta potential is a potential well mathematically described by the Dirac delta function - a generalized function. Qualitatively, it corresponds
Delta_potential
Fractal sets in complex dynamics of mathematics
the outer Fatou domain, the potential function φ(z) is defined by φ(z) = log|z|. The equipotential lines for this function are concentric circles. As |f(z)|=|z|2
Julia_set
Method of analyzing the amortized complexity of a data structure
out the cost of infrequent but expensive operations. In the potential method, a function Φ is chosen that maps states of the data structure to non-negative
Potential_method
Model of intermolecular interactions
Lennard-Jones potential (also termed the LJ potential or 12-6 potential; named for John Lennard-Jones) is an intermolecular pair potential. Out of all the
Lennard-Jones_potential
of the state space. Then a potential function ϕ ( x ) {\displaystyle \phi (x)} is called a (feasible) navigation function if ϕ ( x ) = 0 ∀ x ∈ X g {\displaystyle
Navigation_function
Field of medical research
emerges. The term "gain of function" is sometimes applied more narrowly to refer to "research which could enable a pandemic-potential pathogen to replicate
Gain-of-function_research
Harmonic functions as solutions to Laplace's equation
mathematics and mathematical physics, potential theory is the study of harmonic functions. The term "potential theory" dates from 19th-century physics
Potential_theory
Functions for calculating potential energy
Interatomic potentials are mathematical functions to calculate the potential energy of a system of atoms with given positions in space. Interatomic potentials are
Interatomic_potential
Green's function for Laplacian
Newtonian potential, or Newton potential, is an operator in vector calculus that acts as the inverse to the negative Laplacian on functions that are smooth
Newtonian_potential
Topics referred to by the same term
a given vector field Potential function (disambiguation) Potential variable (Boolean differential calculus) Potential energy, the energy possessed by
Potential_(disambiguation)
Electrokinetic potential in colloidal dispersions
Zeta potential is the electrical potential at the slipping plane. This plane is the interface which separates mobile fluid from fluid that remains attached
Zeta_potential
Physical model of intermolecular interactions
that are not directly bonded as a function of the interatomic distance r {\displaystyle r} . The interatomic potential, Φ 12 ( r ) = A exp ( − B r ) −
Buckingham_potential
Line integral of the electric field
Practically, the electric potential is a continuous function in all space, because a spatial derivative of a discontinuous electric potential yields an electric
Electric_potential
Velocity field as the gradient of a scalar function
hypothesis. Potential flow describes the velocity field as the gradient of a scalar function: the velocity potential. As a result, a potential flow is characterized
Potential_flow
Generalization of the concept from statistical mechanics
and some sort of potential function or Hamiltonian H ( x 1 , x 2 , … ) {\displaystyle H(x_{1},x_{2},\dots )} , the partition function is defined as Z (
Partition function (mathematics)
Partition_function_(mathematics)
Thermodynamic potential used in statistical mechanics
open systems. The grand potential is the characteristic state function for the grand canonical ensemble. The grand potential is defined byΦG=defU−TS−μNwhere
Grand_potential
Process of energy transfer to an object via force application through displacement
(t_{2})).} The function U(x) is called the potential energy associated with the applied force. The force derived from such a potential function is said to
Work_(physics)
Potential energy of two interacting objects as a function of their distance
In physics, a pair potential is a function that describes the potential energy of two interacting objects solely as a function of the distance between
Pair_potential
Type of energy
electrostatic potential ϕ produced in the vacuum will be somewhat lower than the applied voltage, the difference depending on the work function of the material
Work_function
For a large class of boundary conditions, all solutions have the same gradient
this means that there is a unique electric field derived from a potential function satisfying Poisson's equation under the boundary conditions. The general
Uniqueness theorem for Poisson's equation
Uniqueness_theorem_for_Poisson's_equation
Class of games in game theory
congestion game is an exact potential game. Later, Monderer and Shapley proved a converse result: any game with an exact potential function is equivalent to some
Congestion_game
Elliptic partial differential equation
written as ∇2ϕ=f. In three-dimensional Cartesian coordinates, the potential function ϕ(x,y,z) satisfies ∂2ϕ∂x2+∂2ϕ∂y2+∂2ϕ∂z2=f(x,y,z). When f=0 identically
Poisson's_equation
Describes energy between atoms
energy between atoms and is a type of interatomic potential. The energy is a function of a sum of functions of the separation between an atom and its neighbors
Embedded_atom_model
Discovering chemical properties by physical simulations
der Waals}}\,} This function, referred to as a potential function, computes the molecular potential energy as a sum of energy terms that
Molecular_modelling
Function in thermodynamics and statistical physics
volume, and chemical potential. Other types of partition functions can be defined for different circumstances; see partition function (mathematics) for generalizations
Partition function (statistical mechanics)
Partition_function_(statistical_mechanics)
Tube attached to the intestine
Since the early 2000s, extensive work has been conducted regarding potential functions of the appendix (for example, serving as a reservoir for beneficial
Appendix_(anatomy)
When potential energy difference depends only on displacement
function of the Cartesian coordinates x, y, z. In some cases, mathematicians may use a positive sign in front of the gradient to define the potential
Scalar_potential
Region in space where every point is at the same potential
potential), although it can also be applied to vector potentials. An equipotential of a scalar potential function in n-dimensional space is typically an (n − 1)-dimensional
Equipotential
Space of vacuum states
refer to scalar fields whose potential energy function has continuous families of global minima. Such potential functions frequently occur in supersymmetric
Moduli_(physics)
Algorithm for supervised learning of binary classifiers
for supervised learning of binary classifiers. A binary classifier is a function that can decide whether or not an input, represented by a vector of numbers
Perceptron
Neuron communication by electric impulses
types of cells, their main function is to activate intracellular processes. In muscle cells, for example, an action potential is the first step in the chain
Action_potential
Effect in electrochemistry
mean that the electric potentials are equal. The electric potential outside each material is controlled by its work function, and so dissimilar metals
Volta_potential
Scalar physical quantities representing system states
of thermodynamic potentials is Pierre Duhem in an 1886 work. Josiah Willard Gibbs in his papers used the term fundamental functions. Effects of changes
Thermodynamic_potential
Concept on molecular modeling
parameters from one interatomic potential function can typically not be used together with another interatomic potential function. In some cases, modifications
Force_field_(chemistry)
Method of solution to differential equations
In mathematics, a Green's function (or Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with
Green's_function
Scalar potential used in fluid dynamics
{\displaystyle \phi } is known as a velocity potential for u. Velocity potentials are unique up to a constant and a function solely of the temporal variable. So
Velocity_potential
Any process that modulates the potential difference across a post-synaptic membrane
be confused with action potentials although their function is to initiate or inhibit action potentials. Postsynaptic potentials occur when the presynaptic
Postsynaptic_potential
Potential in mathematics
variable. If 0 < α < n, then the Riesz potential Iαf of a locally integrable function f on Rn is the function defined by where the constant is given by
Riesz_potential
Screened Coulomb potential which exponentially decays
potential (also called a screened Coulomb potential[citation needed]) is a potential named after the Japanese physicist Hideki Yukawa. The potential is
Yukawa_potential
Formulation of classical mechanics
smooth function L {\textstyle L} within that space called a Lagrangian. For many systems, L = T − V, where T and V are the kinetic and potential energy
Lagrangian_mechanics
Electrical potential evoked in the nervous system
An evoked potential or evoked response (EV) is an electrical potential in a specific pattern recorded from a specific part of the nervous system, especially
Evoked_potential
Formulation of classical mechanics using momenta
into the potential function produces a velocity dependent potential. Hence, the requirements are not satisfied when a dissipation function has effect
Hamiltonian_mechanics
Theoretical Physics. Vidybida, A.K. (1987). "Modification of the Potential Function of a Mechanical System Caused by Periodic Action". Soviet Physics
Nonlinear_frictiophoresis
Concept in quantum mechanics
imagined to tunnel through the walls of a potential well. The graph of a 2D potential energy function is a potential energy surface that can be imagined as
Potential_well
Functions in mathematics
proportional to the electrostatic potential due to these charge distributions. Each function above will yield another harmonic function when multiplied by a constant
Harmonic_function
Model in Quantum Physics
is a, the potential in the lattice will look something like this: The mathematical representation of the potential is a periodic function with a period
Particle in a one-dimensional lattice
Particle_in_a_one-dimensional_lattice
Quantum mechanical statistic
quantum potential, thus depends on the curvature of the amplitude of the wave function. In the limit ℏ → 0 {\displaystyle \hbar \to 0} , the function S {\displaystyle
Quantum_potential
Concept in mathematics
complex potential, where u is the potential function and v is the stream function. For example, consider the function u ( x , y ) = e x sin y . {\displaystyle
Harmonic_conjugate
Differential operator in mathematics
Laplace's equation Δf = 0 are called harmonic functions and represent the possible gravitational potentials in regions of vacuum. The Laplacian occurs in
Laplace_operator
Partial differential equations
Green's function for the three-variable Laplace operator, one can integrate the Poisson equation in order to determine the potential function. Green's
Green's function for the three-variable Laplace equation
Green's_function_for_the_three-variable_Laplace_equation
Change in the energies of a thermodynamic system with respect to particle number
as work function, however, work function varies from surface to surface even on a completely homogeneous material. Total chemical potential, on the other
Chemical_potential
Function describing the energy of a physical system in terms of certain parameters
define the energy as a function of one or more coordinates; if there is only one coordinate, the surface is called a potential energy curve or energy
Potential_energy_surface
Symmetry breaking through the vacuum state
and potential terms, It is in this potential term V ( ϕ ) {\displaystyle V(\phi )} that the symmetry breaking is triggered. An example of a potential, due
Spontaneous_symmetry_breaking
Class of mathematical functions
superharmonic functions are important classes of functions used extensively in partial differential equations, complex analysis and potential theory. Intuitively
Subharmonic_function
Potential after receptor activation
A receptor potential, also known as a generator potential, a type of graded potential, is the transmembrane potential difference produced by activation
Receptor_potential
Region of space in which a force acts
potential function: F = − ∇ ϕ {\displaystyle \mathbf {F} =-\nabla \phi } The work done is then simply the difference in the value of this potential in
Force_field_(physics)
pituitary use: autocrine/paracrine control of anterior pituitary cell function though the use of cytokines and growth factors, intrapituitary communication
Folliculostellate_cell
Model of the potential energy of a diatomic molecule
since been used on HF, HCl, HBr and HI. The Morse/Long-range potential energy function is of the form V(r)=𝔇e(1−u(r)u(re)e−β(r)ypreq(r))2 where for
Morse/Long-range_potential
Relativistic vector field
four-potential is a relativistic vector function from which the electromagnetic field can be derived. It combines both an electric scalar potential and
Electromagnetic four-potential
Electromagnetic_four-potential
Type of differential equation subject to a particular solution methodology
equation if there exists a continuously differentiable function F, called the potential function, so that ∂ F ∂ x = I {\displaystyle {\frac {\partial F}{\partial
Exact_differential_equation
printed in 1828). The name "potential" is due to Gauss (1840), and the distinction between potential and potential function to Clausius. With its development
History_of_calculus
Waxy substance found in the head cavities of sperm whales
Stephen M.; Otterstrom, Jason (2002). "The face that sank the Essex: potential function of the spermaceti organ in aggression" (PDF). Journal of Experimental
Spermaceti
model is a function for calculating the potential energy of covalent bonds and the interatomic force. In this model, the total potential energy of system
Reactive_empirical_bond_order
Signal boosting phenomenon using white noise
x}}+f(t)+\epsilon \cos(\omega t),} where U ( x ) {\displaystyle U(x)} is a potential function determining the system dynamics, f ( t ) {\displaystyle f(t)} is a
Stochastic_resonance
Description of a quantum-mechanical system
of the particle, and V ( x , t ) {\displaystyle V(x,t)} is the potential energy function that represents the environment in which the particle exists.
Schrödinger_equation
French mathematician and physicist (1781–1840)
equation ∇2ϕ=0 for potential ϕ. If ρ(x,y,z) is a continuous function and if for r→∞ (or if a point 'moves' to infinity) a function ϕ goes to 0 fast enough
Siméon_Denis_Poisson
Electric potential difference between interior and exterior of a biological cell
electrical potential across them, with the inside usually negative with respect to the outside. The membrane potential has two basic functions. First, it
Membrane_potential
Extension of the factorial function
The gamma function then is defined in the complex plane as the analytic continuation of this integral function: it is a meromorphic function which is holomorphic
Gamma_function
Mathematical potential
be more succinctly written in terms of a modified Bessel function, for which the potential gets its name: G s ( x ) = 1 2 ( s − 2 ) / 2 ( 2 π ) d / 2
Bessel_potential
Representation of a chemical process as a single energetic pathway
empirically based and potential energy is described as a function of component terms that correspond to individual potential functions such as torsion, stretches
Energy_profile_(chemistry)
Form of algorithmic art
landscape formed from the potential function on the domain outside the (usual) Mandelbrot set. However, as the potential function grows fast near the boundary
Fractal_art
Family of solutions to related differential equations
spherical coordinates. Bessel functions are therefore especially important for many problems of wave propagation and static potentials. In solving problems in
Bessel_function
Natural number
non-critical even unimodular lattices that do not interact with a Gaussian potential function of the form f α ( r ) = e − α r {\displaystyle f_{\alpha }(r)=e^{-\alpha
32_(number)
French polymath (1749–1827)
However, according to Rouse Ball, the term "potential function" was not actually used (to refer to a function V of the coordinates of space in Laplace's
Pierre-Simon_Laplace
Mathematical model in quantum mechanics
forces act upon the particle, which means that the potential V(x) vanishes and the part of the wave function inside the box oscillates through space and time
Particle_in_a_box
Category of positional games
find a function that assigns, to each winning-set, a potential based on the number of elements already taken from it by Maker/Breaker. The potential function
Maker-Breaker_game
Concept in mathematical physics
In mathematical physics, the Wu–Sprung potential, named after Hua Wu and Donald Sprung, is a potential function in one dimension inside a Hamiltonian H
Wu–Sprung_potential
Mathematical description of quantum state
Hamilton's principal function. For systems in time-independent potentials, the wave function can always be written as a function of the degrees of freedom
Wave_function
Property in physics
gravitational potential satisfies Poisson's equation. See also Green's function for the three-variable Laplace equation and Newtonian potential. The integral
Specific_potential_energy
Physical property when materials or objects return to original shape after deformation
material" models (for which stress can be derived from a scalar "elastic potential" function). A hypoelastic material can be rigorously defined as one that is
Elasticity_(physics)
In Euclidean space, a measure of that set's "size"
the conformal radius. The harmonic function u is called the capacity potential. It is called the Newtonian potential when n ≥ 3 {\displaystyle n\geq 3}
Capacity_of_a_set
Concept in fluid dynamics
body forces. Since a conservative body force is the gradient of some potential function, it has the same effect as a gradient in fluid pressure. It is often
Modified_pressure
Analytic function in mathematics
Riemann zeta function, or Euler–Riemann zeta function, denoted by the lowercase Greek letter ζ {\displaystyle \zeta } (zeta), is a function of a complex
Riemann_zeta_function
identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles but
List of trigonometric identities
List_of_trigonometric_identities
Measure of the tendency of a substance to gain or lose electrons
Redox potential (also known as oxidation / reduction potential, ORP, pe, Ered, or Eh) is a measure of the tendency of a chemical species to acquire electrons
Reduction_potential
Data structure that always preserves the previous version of itself when it is modified
potential function by one. (First, the node to be copied must be full and live, so it contributes to the potential function. The potential function will
Persistent_data_structure
Mathematical function conceived as a crude model
threshold potential), before being passed through a nonlinear function known as an activation function. Depending on the task, these functions could have
Artificial_neuron
Generalized function whose value is zero everywhere except at zero
Dirac delta function (or δ {\displaystyle {\boldsymbol {\delta }}} distribution), also known as the unit impulse, is a generalized function on the real
Dirac_delta_function
Solution method for linear differential equations
calculation in quantum mechanics in which the wave function is recast as an exponential function, semiclassically expanded, and then either the amplitude
WKB_approximation
Theorem of dynamical systems
{p} ^{2}}{2m}}-U(\mathbf {q} ^{2})} with U {\displaystyle U} some potential function. Defining the angular momentum L = p × q {\displaystyle \mathbf {L}
Liouville–Arnold_theorem
Second-order partial differential equation
equation is known as potential theory. The twice continuously differentiable solutions of Laplace's equation are the harmonic functions, which are important
Laplace's_equation
Multivalued function in mathematics
In mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse
Lambert_W_function
Quantum mechanical phenomenon
function into the barrier, without transmission on the other side, as a tunnelling effect, such as in tunnelling into the walls of a finite potential
Quantum_tunnelling
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