Asphericity: Difference between revisions
Carl McBride (talk | contribs) (Created page with "'''Asphericity''' is defined as <ref>[http://dx.doi.org/10.1088/0305-4470/19/4/004 Joseph Rudnick and George Gaspari "The aspherity of random walks", Journal of Physics A: Ma...") |
Carl McBride (talk | contribs) m (Added range) |
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where <math>R_1^2</math>, <math>R_2^2</math> and <math>R_3^2</math> are the three eigenvalues of the tensor. | where <math>R_1^2</math>, <math>R_2^2</math> and <math>R_3^2</math> are the three eigenvalues of the tensor. | ||
<math>\langle A \rangle </math> ranges from 0 for a spherical structure (or any of the platonic solid structures), to 1. | |||
==See also== | ==See also== | ||
*[[Random walk]] | *[[Random walk]] | ||
Revision as of 16:47, 18 March 2014
Asphericity is defined as [1] (Eq.5):
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \langle A \rangle = \frac{\langle \mathrm{Tr}^2 -3M \rangle }{\langle \mathrm{Tr}^2 \rangle}}
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{Tr}} is the trace of the moment of inertia tensor, given by (Eq. 3)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{Tr} = R_1^2 + R_2^2 + R_3^2}
and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M} is the sum of the three minors, given by
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M= R_1^2R_2^2 + R_1^2R_3^2 + R_2^2 R_3^2}
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_1^2} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_2^2} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_3^2} are the three eigenvalues of the tensor. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \langle A \rangle } ranges from 0 for a spherical structure (or any of the platonic solid structures), to 1.