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Objective measure of anisotropy

If we know a function $f(\phi, \theta)$ in $\mathbb R^3$ only over a convex surface (which for simplicity let's assume a sphere of radius $r$), is there any measure for the degree of anisotropy over ...
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1answer
28 views

Isotropic systems and homogeneity

In isotropic systems, the atomic arrangement is homogeneous in all directions. In the case of glass, which has the atomic structure of a liquid and, therefore, a random atomic structure that is ...
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1answer
92 views

Best way to check for anisotropy given a metric tensor

Carroll gives the definition of isotropy at a point as given vector $V$ and $W$ in $T_{p}M$, there is some isometry that can push $V$ forward such that it ends up parallel to $W$. I understand what ...
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1answer
47 views

Definition of isotropy of radiation and its consequences

I have encountered different notions of isotropy of radiation and I would like to know if they are the same and what the exact definition of isotropy is, if one exists. Let's take black body ...
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1answer
531 views

Is the total angular momentum of the universe zero? [duplicate]

I know that having a net angular momentum will contradict isotropy of the universe by preferring a specific direction. But is there any experimental data on the total angular momentum of the universe ...
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1answer
365 views

How to use Legendre polynomials in order to determine the (an)isotropy of an on-lattice cluster aggregate?

I am currently testing various models of on-lattice (square lattice in two dimensions) cluster growth for anisotropy. I end up with a cluster, the boundary of which, in case of a truly isotropic ...