Physics – Condensed Matter – Other Condensed Matter
Scientific paper
2010-04-14
Journal of Physics A: Mathematical and Theoretical Vol. 43 (2010)
Physics
Condensed Matter
Other Condensed Matter
12 pages, 1 figure
Scientific paper
By assuming a self-similar structure for Kelvin waves along vortex loops with successive smaller scale features, we model the fractal dimension of a superfluid vortex tangle in the zero temperature limit. Our model assumes that at each step the total energy of the vortices is conserved, but the total length can change. We obtain a relation between the fractal dimension and the exponent describing how the vortex energy per unit length changes with the length scale. This relation does not depend on the specific model, and shows that if smaller length scales make a decreasing relative contribution to the energy per unit length of vortex lines, the fractal dimension will be higher than unity. Finally, for the sake of more concrete illustration, we relate the fractal dimension of the tangle to the scaling exponents of amplitude and wavelength of a cascade of Kelvin waves.
Barenghi Carlo F.
Jou David
Mongiovi' Maria Stella
Sciacca Michele
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