Abstract
In two-dimensional statistical mechanics, the Stochastic Loewner equation, introduced by Oded Schramm, provides a powerful technique to study and categorize critical random curves and interfaces. For the first time, a new type of stochastic Loewner equation entitled fractional stochastic Loewner evolution (FSLE) has been proposed. We introduce a wide class of fractal curves using the fractional time series as the driving function of the Loewner equation and local fractional integrodifferential operators. We suggest that, in addition to fractal dimension estimations, the Hurst index of the driving function leads significant differences in the FSLE curves. This modification introduces a new approach to categorize different types of scaling curves based on the Hurst index of the driving function. Such formalizations appear to be appropriate for studying a wide range of two-dimensional curves seen in statistical mechanics and natural phenomena.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Physica A: Statistical Mechanics and its Applications
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
