TY - JOUR
T1 - Analytical Limit Distributions from Random Power-Law Interactions
AU - Zaid, Irwin
AU - Mizuno, Daisuke
PY - 2016/7/14
Y1 - 2016/7/14
N2 - Nature is full of power-law interactions, e.g., gravity, electrostatics, and hydrodynamics. When sources of such fields are randomly distributed in space, the superposed interaction, which is what we observe, is naively expected to follow a Gauss or Lévy distribution. Here, we present an analytic expression for the actual distributions that converge to novel limits that are in between these already-known limit distributions, depending on physical parameters, such as the concentration of field sources and the size of the probe used to measure the interactions. By comparing with numerical simulations, the origin of non-Gauss and non-Lévy distributions are theoretically articulated.
AB - Nature is full of power-law interactions, e.g., gravity, electrostatics, and hydrodynamics. When sources of such fields are randomly distributed in space, the superposed interaction, which is what we observe, is naively expected to follow a Gauss or Lévy distribution. Here, we present an analytic expression for the actual distributions that converge to novel limits that are in between these already-known limit distributions, depending on physical parameters, such as the concentration of field sources and the size of the probe used to measure the interactions. By comparing with numerical simulations, the origin of non-Gauss and non-Lévy distributions are theoretically articulated.
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U2 - 10.1103/PhysRevLett.117.030602
DO - 10.1103/PhysRevLett.117.030602
M3 - Article
AN - SCOPUS:84978706314
VL - 117
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 3
M1 - 030602
ER -