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Jan
9
revised Determining the effective coefficient in a boundary value problem.
added relevant tags
Jan
8
asked Determining the effective coefficient in a boundary value problem.
Dec
11
asked What is the proper topological term for a region with a single hole?
Sep
23
awarded  Disciplined
Sep
23
awarded  Peer Pressure
Sep
15
comment Understanding the notation of the gradient of a vector function
Is the product in the notation $A\cdot B$ called a "tensor product" or a "tensor dot product"? Is there a special name for this product?
Sep
15
comment Understanding the notation of the gradient of a vector function
So then, $\nabla v$ is equivalent to the jacobian of v! That's cool!
Sep
15
comment Understanding the notation of the gradient of a vector function
Awesome! Thank you, @enzotib! :)
Sep
15
accepted Understanding the notation of the gradient of a vector function
Sep
15
comment Understanding the notation of the gradient of a vector function
According to the book, the final result $\sigma\cdot\nabla v^T$ is supposed to be a scalar quantity. Your final result seems to be a vector, if I'm not mistaken...
Sep
15
comment Understanding the notation of the gradient of a vector function
So the gradient of a vector is a matrix then, right?
Sep
15
revised Understanding the notation of the gradient of a vector function
emphasized output of gradient of a vector
Sep
15
asked Understanding the notation of the gradient of a vector function
Sep
15
comment Understanding tensor divergence notation in an integral
let us continue this discussion in chat
Sep
15
comment Understanding tensor divergence notation in an integral
Ok... and by the requirement that the tensor is smooth, can we conclude that $\sigma_{ij}$ is a smooth function!
Sep
14
accepted Understanding tensor divergence notation in an integral
Sep
14
comment Understanding tensor divergence notation in an integral
Oh... ok... So, at each point, a matrix is assigned. Could I also consider it as if $\sigma$ were a matrix whose elements are functions of variables in $R^2$?
Sep
14
comment Understanding tensor divergence notation in an integral
In the definition of $\sigma$, it maps a vector to a matrix. But in your notation of the right hand side, wouldn't $\sigma n$ be a vector? Isn't this a contradiction?
Sep
14
comment Understanding tensor divergence notation in an integral
So, you mean "the usual divergence theorem" for each column vector of $\sigma$?
Sep
14
accepted Accumulation points of sequences as limits of subsequences?