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searching for Laplace's equation 29 found (171 total)

Laplace equation for irrotational flow (430 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: ∇ 2 ϕ = 0 {\displaystyle \nabla ^{2}\phi =0\

Separable partial differential equation (459 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 R n {\displaystyle {\mathbb {R} }^{n}} is an example of a partial

Bäcklund transform (916 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 (3,206 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 (1,558 words) [view diff] exact match in snippet view article find links to article

discontinuities have already been smoothed out. For instance, we can obtain Laplace's equation from the heat equation u t = Δ u {\displaystyle u_{t}=\Delta u} by

Oblate spheroidal coordinates (3,467 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 (2,542 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 = − ∇ Φ M ∇ 2 Φ M = 0 {\displaystyle {\begin{aligned}\mathbf {H}

Bouguer anomaly (739 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 (571 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 (1,481 words) [view diff] exact match in snippet view article find links to article

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 (1,127 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 (747 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

Legendre wavelet (1,206 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 (1,655 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

Prolate spheroidal coordinates (1,930 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

Distorted Schwarzschild metric (1,553 words) [view diff] exact match in snippet view article find links to article

{\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

Quantitative susceptibility mapping (1,871 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

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

Method of image charges (2,367 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 (5,052 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

Mermin–Wagner theorem (4,310 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: ∇ 2 G = δ ( x ) . {\displaystyle \nabla ^{2}G=\delta

Laplacian of the indicator (4,258 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 (3,232 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 ∇ 2 u = 0 {\displaystyle \textstyle \nabla ^{2}u=0}

Spherical wave transformation (7,653 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 (15,374 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 (4,450 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