Hitting times in turbulent diffusion due to multiplicative noise
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Updated: Nov 29, 2025

Measurement of Particle Size Distribution in Turbid Solutions by Dynamic Light Scattering Microscopy
Published on: January 9, 2017
Trifce Sandev1,2,3, Alexander Iomin4, Ljupco Kocarev1,5
1Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov 2, 1000 Skopje, Macedonia.
Abstract:
We study a distribution of times of the first arrivals to absorbing targets in turbulent diffusion, which is due to a multiplicative noise. Two examples of dynamical systems with a multiplicative noise are studied. The first one is a random process according to inhomogeneous diffusion, which is also known as a geometric Brownian motion in the Black-Scholes model. The second model is due to a random processes on a two-dimensional comb, where inhomogeneous advection is possible only along the backbone, while Brownian diffusion takes place inside the branches. It is shown that in both cases turbulent diffusion takes place as the one-dimensional random process with the log-normal distribution in the presence of absorbing targets, which are characterized by the Lévy-Smirnov distribution for the first hitting times.
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