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Commonly seen in physics(and statistics) are the concepts of moments of order zero(mass), one(center of mass), and two(moment of inertia). In statistics a third moment (referred to as skewness) also exists and is used. Actually, mathematically the moment can (of order n) be simplified to an operation in the form of:

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Once I look at this equation it begs the question: what if n is a ratio. What could be some physical applications of this fractional-order moment?

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    $\begingroup$ Fractal physics and phase transitions. $\endgroup$ – CuriousOne Aug 28 '14 at 4:45
  • $\begingroup$ by phase transitions can you elaborate a bit more $\endgroup$ – Skyler Aug 31 '14 at 4:39
  • $\begingroup$ You could take a peek at critical exponents: en.wikipedia.org/wiki/Critical_exponent. Near critical points, where systems undergo phase transitions, they exhibit a complex behavior that can be described by non-integer power laws as their scaling functions. $\endgroup$ – CuriousOne Aug 31 '14 at 19:55

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