Multifractal modeling of the production of concentrated sugar syrup crystal

Abstract

High quality, concentrated sugar syrup crystal is produced in a critical step in cane sugar production: the clarification process. It is characterized by two variables: the color of the produced sugar and its clarity degree. We show that the temporal variations of these variables follow power-law distributions and can be well modeled by multiplicative cascade multifractal processes. These interesting properties suggest that the degradation in color and clarity degree has a systemwide cause. In particular, the cascade multifractal model suggests that the degradation in color and clarity degree can be equivalently accounted for by the initial "impurities" in the sugarcane. Hence, more effective cleaning of the sugarcane before the clarification stage may lead to substantial improvement in the effect of clarification.

Detection of meso-micro scale surface features based on microcanonical multifractal formalism

“…[2] Mathematically, multifractals are characterized by many or infinitely many power-law relations. [3] These relations are built by exponents. To describe the complex systems, we need a set of continuous exponents, which is a singular spectrum.…”