I am new user in Mathematica. I am working with liquid crystal theory, and one of the notation there is the tensor:
$ \Pi_{ij} = \frac {\partial {F_{el}}} { \partial ( \partial {n_i} / \partial { x_j})}$
Where numerator is scalar, denominator is tensor (matrix).
In order to calculate it in Mathematica, I introduce:
r={x,y,z}
nd[x_, y_, z_] = {n1[x, y], n2[x, y], 0}
Fel = ***Some expression (nd) ***
g = D[nd[x, y, z], {r}]
After that I need to take a derivative of Fel over a tensor g. But as long as I am restricted to a 2D space {x,y}, my tensor g looks like:
g= (n1^(1,0)(x,y) n1^(0,1)(x,y) 0
n2^(1,0)(x,y) n2^(0,1)(x,y) 0
0 0 0)
It is not allowed to differentiate over zero. Mathematically, zero values must be omitted (the corresponding term must be set to zero).
Thanks,