a time dependent vector field is a construction in vector calculus which generalizes the concept of vector fields. It can be thought of as a vector field...

In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space R n {\displaystyle...

one simple criterion is that the vector field F is compactly supported. In the case of time-dependent vector fields ⁠ F : R n × R → R n {\displaystyle...

the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area, per unit time) or power flow...

means that, for two vector spaces over a given field and with the same dimension, the properties that depend only on the vector-space structure are exactly...

deterministic flow along a time-dependent vector field, and the backward process is also a deterministic flow along the same vector field, but going backwards...

electric field between atoms is the force responsible for chemical bonding that result in molecules. The electric field is defined as a vector field that...

Vector field reconstruction is a method of creating a vector field from experimental or computer-generated data, usually with the goal of finding a differential...

electromagnetism, magnetic vector potential (often denoted A) is the vector quantity defined so that its curl is equal to the magnetic field, B: ∇ × A = B {\textstyle...

are time-dependent vector fields that in vacuum depend on a third vector field A ( r , t ) {\displaystyle \mathbf {A} (\mathbf {r} ,t)} (the vector potential)...

of multidimensional vectors or infinite-dimensional vectors. The input of a vector-valued function could be a scalar or a vector (that is, the dimension...

inversion is smooth. Let X ( t , x ) {\displaystyle X(t,x)} be a time dependent vector field on M {\displaystyle M} (in C ∞ ( R , X ( M ) ) {\displaystyle...

In physics, a gravitational field or gravitational acceleration field is a vector field used to explain the influences that a body extends into the space...

assigning a vector to each point of space, called a vector field (more precisely, a pseudovector field). In electromagnetics, the term magnetic field is used...

property. In vector calculus flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface...

Vector control, also called field-oriented control (FOC), is a variable-frequency drive (VFD) control method in which the stator currents of a three-phase...

point can be used. In classical electrostatics, the electrostatic field is a vector quantity expressed as the gradient of the electrostatic potential...

potential ϕ {\displaystyle \phi } and the vector potential A {\displaystyle \mathbf {A} } which are used to find the fields as is commonly done. Considering cases...

In special relativity, a four-vector (or 4-vector, sometimes Lorentz vector) is an object with four components, which transform in a specific way under...

σ {\displaystyle {\boldsymbol {\sigma }}} is the vector of Pauli matrices. Solving the time dependent Schrödinger equation H ψ = i ℏ ∂ t ψ {\displaystyle...

{\displaystyle \sigma (t):=1-2\lambda t} and integrating the time-dependent vector field X ( t ) := 1 σ ( t ) V {\displaystyle X(t):={\frac {1}{\sigma...

flows of a time-dependent vector field, i.e. of a smooth family { X t } t ∈ [ 0 , 1 ] {\displaystyle \{X_{t}\}_{t\in [0,1]}} of vector fields on M {\displaystyle...

physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude...

unit-length vector, and G ( d , t ) {\displaystyle G(d,t)} is a function that gives the field's value as dependent on only two real parameters: the time t {\displaystyle...

Bloch equations, which define the dynamics of the pseudo-spin vector in an electric field: u ˙ = − δ v , {\displaystyle {\dot {u}}=-\delta v,} v ˙ = δ...

H_{\text{S}}t/\hbar }|\psi (0)\rangle } be the time-dependent state vector in the Schrödinger picture. A state vector in the interaction picture, | ψ I ( t )...

macroscopic velocity is represented by the vector field u(x, t). The (total) derivative with respect to time of φ is expanded using the multivariate chain...

(x,t)} as used above can be written as the inner product of a time-dependent state vector | Ψ ( t ) ⟩ {\displaystyle |\Psi (t)\rangle } with unphysical...

in space and time for each electric and magnetic vector field component in Maxwell's curl equations. The descriptor "Finite-difference time-domain" and...

metric and a unit timelike vector field named the aether. The aether in this theory is "a Lorentz-violating vector field" unrelated to older luminiferous...