This paper establishes important properties of the gradient, divergence, curl and Stokes operators in ℝ 3 . They are set in the weighted Sobolev spaces of Hanouzet with finite integer weights ranging from -∞ to +∞. Among the results that we prove are isomorphism properties of the gradient...
In any case, the function should warn if it’s returning junk that can’t be further processed. I spent far too much time debugging this when gene.relative.velocity.estimates could simply raise a warning telling me about $current containing all-NA cells and duplicate cells now, and that I ...
Although nonconservative, curl forces are notdissipative because volume in the position-velocity state space is preserved. When the force has rotational symmetry, for example when generated by a single optical vortex, particles spiral outwards and escape, even with an attractive gradient force, ...
摘要: We consider the marginal function of a vertically perturbed nonlinear mathematical program with equality and inequality constraints. Conditions are given to have this function locally Lipschitz and to obtain estimates for its generalized gradient....
The construction principle for multigrid smoothers for discrete Curl-Curl equations consists in the inclusion of an additional zero divergence constraint. ... M Clemens,S Feigh,T Weiland - 《IEEE Transactions on Magnetics》 被引量: 21发表: 2005年 Convergence of synchronous reinforcement learning with...
(combining right arrow above) = 0 if and only if A(combining right arrow above) = grad φ if A = grad φ, then the line integral does not depend on path; and if the line integral of a vector function is equal to zero for any closed path, then this vector is the gradient of a...
· B) (10)11.4 Vector Derivatives in Cartesian CoordinatesGradient:φφφφ= x+ y+ z (11)x y zDivergence:v v v·v = + + (12)x y zCurl:x y z ×v = x y z (13)vx vy vzLaplacian of a scalar:2φ ≡·φ (14)2 φ 2φ 2φ= + 2 + 2 (15)x2 y zLaplacian of a ...
Shashkov, Adjoint operators for the natural discretizations of the divergence, gradient and curl on logically rectangular grids, Applied Numerical Mathematics, ... JM Hyman,M Shashkov - 《Applied Numerical Mathematics》 被引量: 355发表: 1997年 Adaptive Multilevel Methods for Edge Element Discretizations...
It is shown that the most common methods of using divergence boundary conditions do not always work properly. Necessary and sufficient conditions for the equivalence of the formulations are given.关键词: BOUNDARY CONDITIONS DIVERGENCE BOUNDARY VALUE PROBLEMS HELMHOLTZ EQUATIONS COERCIVITY EQUIVALENCE CURL ...
Our analysis reveals that below about 1500 m there is a persistent baroclinic pressure gradient driving flow from the Pacific into the South China Sea through Luzon Strait. Applying hydraulic theory with assumptions of zero potential vorticity and flat bottom to the Luzon Strait yields a transport ...