[C]卷状物,螺旋状物; 鬈发hair that is round like a ring v.(动词) vt. & vi. (使)弯曲(cause to) twist into or form a curl or curls vt. & vi. 盘旋,缠绕go in a winding direction 英英释义 curl[ kə:l ] n. a round shape formed by a series of concentric circles (as formed ...
Why is the curl of a gradient zero geometrically? Calculate the indicated quantities. a) What is Curl F if F = <2 cos(2x)y + sin(5y), sin(2x)+5 cos(5y)x,1>? Let w=2xy-4yz, x=st, y=e^{st}, z=t^2. Compute \dfrac{\partial w}{\partial s}(-3,-1) \df...
Adjoint operators for the natural discretizations of the divergence, gradient and curl on logically rectangular grids The natural operators cannot be combined to construct discrete analogs of the second-order operators div grad , grad div , and curl curl because of in... JM Hyman,M Shashkov - ...
It is frequently employed in the numerical evaluatio... Rmer, Ulrich,Schps, Sebastian,T Weiland - 《Siam/asa Journal on Uncertainty Quantification》 被引量: 16发表: 2016年 Unified definition of divergence, curl, and gradient Tai C T. Unified Definition of Divergence, Curl, and Gradient [J]...
Conditions on Signed distance function and the norm of the gradient Given a closed curve inR2R2and its signed distance functionϕϕ(negative inside the curve, zero on the curve, and positive outside the curve), we know thatϕϕis differentiable ... ...
needs to be zero. Now I approached this problem using the product rules for divergence and curl and notices that the curl and divergence of the constant vector field is of course zero. This lead me to the conclusion that in both cases the gradient of the scalar field g must be ze...
In summary, the curl operator for time-varying vector fields is an extension of the traditional curl concept, which measures the rotation or circulation of a vector field at a given point. When applied to time-varying fields, the curl incorporates the effects of both spatial variation and ...
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(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...
In summary, the conversation discusses the topic of whether the field of an electric dipole is conservative. The speaker initially thought it would be, but after researching vector calculus, they discovered that the curl of the gradient of a function is equal to zero. This leads to a ...