Hitting times in turbulent diffusion due to multiplicative noise

Area of Science:

• Physics
• Mathematics
• Stochastic Processes

Background:

• Turbulent diffusion is crucial in various physical phenomena.
• Multiplicative noise significantly impacts dynamical systems.
• Understanding first arrival times is key in diffusion processes.

Purpose of the Study:

• To investigate the distribution of first arrival times in turbulent diffusion systems with multiplicative noise.
• To analyze two distinct models exhibiting multiplicative noise: geometric Brownian motion and diffusion on a 2D comb.
• To characterize the statistical properties of first hitting times in these systems.

Main Methods:

• Studied a random process based on inhomogeneous diffusion (geometric Brownian motion).
• Analyzed random processes on a two-dimensional comb with inhomogeneous advection and diffusion.
• Characterized the distribution of first arrival times to absorbing targets.

Main Results:

• Turbulent diffusion in both models behaves as a one-dimensional random process.
• The distribution of particle arrivals follows a log-normal distribution.
• First hitting times to absorbing targets are characterized by the Lévy-Smirnov distribution.

Conclusions:

• Multiplicative noise in turbulent diffusion leads to predictable statistical distributions.
• The Lévy-Smirnov distribution accurately describes first hitting times in these complex systems.
• The findings provide insights into stochastic processes in physics and finance.