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searching for Laplace's equation 30 found (170 total)

Laplace equation for irrotational flow (428 words) [view diff] case mismatch in snippet view article find links to article

{v}}=0}, the scalar potential can be substituted back in to find Laplace's Equation for irrotational flow: ∇2ϕ=0{\displaystyle \nabla ^{2}\phi =0\,} Note

Separable partial differential equation (442 words) [view diff] exact match in snippet view article find links to article

multiplied by a product of functions of each individual coordinate. Laplace's equation on Rn{\displaystyle {\mathbb {R} }^{n}} is an example of a partial

Bäcklund transform (872 words) [view diff] exact match in snippet view article find links to article

above properties mean, more precisely, that Laplace's equation for u{\displaystyle u} and Laplace's equation for v{\displaystyle v} are the integrability

Hans Maass (406 words) [view diff] exact match in snippet view article find links to article

automorphic forms in the 1940s (Maaß waveforms). Instead of satisfying Laplace's equation (as analytic functions do), they are eigenfunctions of the invariant

Atmospheric tide (3,065 words) [view diff] no match in snippet view article find links to article

Atmospheric tides are global-scale periodic oscillations of the atmosphere. In many ways they are analogous to ocean tides. They can be excited by: The

Elliptic partial differential equation (1,278 words) [view diff] exact match in snippet view article find links to article

obtain Laplace's equation from the heat equation ut=Δu{\displaystyle u_{t}=\Delta u} by setting ut=0{\displaystyle u_{t}=0}. This means that Laplace's equation

Oblate spheroidal coordinates (3,046 words) [view diff] exact match in snippet view article find links to article

As is the case with spherical coordinates and spherical harmonics, Laplace's equation may be solved by the method of separation of variables to yield solutions

Electromagnetic shielding (2,497 words) [view diff] exact match in snippet view article find links to article

material, then we can define a magnetic scalar potential that satisfies Laplace's equation: H=−∇ΦM∇2ΦM=0{\displaystyle {\begin{aligned}\mathbf {H} &=-\nabla

Bouguer anomaly (707 words) [view diff] exact match in snippet view article find links to article

gravity field Potential theory – Harmonic functions as solutions to Laplace's equation Vertical deflection – Measure of the downward gravitational force's

Analytical regularization (542 words) [view diff] case mismatch in snippet view article find links to article

S. (5 January 2009). "Regularization of the Dirichlet Problem for Laplace's Equation: Surfaces of Revolution". Electromagnetics. 29 (1). Informa UK Limited:

Poisson kernel (1,395 words) [view diff] exact match in snippet view article find links to article

⋅)∗u](x){\displaystyle P[u](t,x)=[P(t,\cdot )*u](x)} is a solution of Laplace's equation in the upper half-plane. One can also show that as t → 0, P[u](t,x)

Ivan S. Sokolnikoff (1,126 words) [view diff] case mismatch in snippet view article find links to article

of Wisconsin-Madison. His doctoral dissertation On a Solution of Laplace's Equation with an Application to the Torsion Problem for a Polygon with Reentrant

Mixed boundary condition (744 words) [view diff] exact match in snippet view article find links to article

attention the following problem: to determine one function u satisfying Laplace's equation on a certain domain (D) being given, on a part (S) of its boundary

Prolate spheroidal coordinates (1,714 words) [view diff] exact match in snippet view article find links to article

orthogonal coordinates. As is the case with spherical coordinates, Laplace's equation may be solved by the method of separation of variables to yield solutions

Legendre wavelet (1,140 words) [view diff] exact match in snippet view article find links to article

of the spherical harmonics which are common to all separations of Laplace's equation in spherical polar coordinates. The radial part of the solution varies

Capacity of a set (1,616 words) [view diff] exact match in snippet view article find links to article

for Laplacian Potential theory – Harmonic functions as solutions to Laplace's equation Choquet theory – Area of functional analysis and convex analysis Brélot

Distorted Schwarzschild metric (1,358 words) [view diff] exact match in snippet view article find links to article

R=0{\displaystyle R=0} implies Eq(5.d). End derivation. Eq(5.a) is the linear Laplace's equation; that is to say, linear combinations of given solutions are still

Intracranial aneurysm (3,736 words) [view diff] exact match in snippet view article find links to article

ISBN 978-1-888799-97-2. Humphrey JD, Kyriacou SK (June 1996). "The use of Laplace's equation in aneurysm mechanics". Neurological Research. 18 (3): 204–08. doi:10

Roxbee Cox, Baron Kings Norton (1,453 words) [view diff] exact match in snippet view article find links to article

the age of 95. Cox, H. R. (1926). A reciprocal function solution of Laplace's equation in two dimensions : with an application to an aerofoil section (PhD

Quantitative susceptibility mapping (1,867 words) [view diff] exact match in snippet view article find links to article

The background field can also be directly computed by solving the Laplace's equation with simplified boundary values, as demonstrated in the Laplacian

Method of image charges (2,190 words) [view diff] exact match in snippet view article find links to article

Diagram illustrating the image method for Laplace's equation for a sphere of radius R. The green point is a charge q lying inside the sphere at a distance

Space charge (3,464 words) [view diff] exact match in snippet view article find links to article

electrons mobility and D {\displaystyle D} the diffusion coefficient. Laplace's equation gives for the field: d E d x = e n ε . {\displaystyle {\frac {dE}{dx}}=e{\frac

Fokas method (4,755 words) [view diff] exact match in snippet view article find links to article

Suppose that u{\displaystyle u} and v{\displaystyle v} both satisfy Laplace's equation in the interior of a convex bounded polygon Ω{\displaystyle \Omega

Hydrogeology (8,021 words) [view diff] case mismatch in snippet view article find links to article

equation is a solution to the steady state groundwater flow equation (Laplace's Equation) for flow to a well. Unless there are large sources of water nearby

Mermin–Wagner theorem (4,094 words) [view diff] exact match in snippet view article find links to article

)^{2}}}{\frac {e^{ik\cdot x}}{k^{2}+m^{2}}}.} For small m, G is a solution to Laplace's equation with a point source: ∇2G=δ(x).{\displaystyle \nabla ^{2}G=\delta (x)

Laplacian of the indicator (4,133 words) [view diff] exact match in snippet view article find links to article

membership Potential theory – Harmonic functions as solutions to Laplace's equation Dirac, Paul (1958), Principles of quantum mechanics (4th ed.), Oxford

Gradient vector flow (3,223 words) [view diff] exact match in snippet view article find links to article

is small, then the solution of each equation is guided entirely by Laplace's equation, for example ∇2u=0{\displaystyle \textstyle \nabla ^{2}u=0}, which

Spherical wave transformation (7,293 words) [view diff] exact match in snippet view article find links to article

Bateman, Harry (1912) [1910]. "Some geometrical theorems connected with Laplace's equation and the equation of wave motion". American Journal of Mathematics

History of Lorentz transformations (13,823 words) [view diff] exact match in snippet view article find links to article

Bateman, Harry (1912) [1910]. "Some geometrical theorems connected with Laplace's equation and the equation of wave motion". American Journal of Mathematics

Alexander Ramm (4,446 words) [view diff] exact match in snippet view article find links to article

developed for solving interior and exterior boundary value problems for Laplace's equation, analytic formulas for the S-matrix for acoustic and electromagnetic