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Updated: Aug 24, 2025

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
A theoretical framework to analyse the flow of particles in a dynamical system with stochastic transition rates and
Aditi Jain1, Arun Kumar1, Arvind Kumar Gupta1
1Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, 140001 Punjab, India.
Abstract:
We study the stochasticity in a dynamical model: ribosome flow model with different site sizes that models the unidirectional movement of particles controlled by transition rates along a lattice having different site sizes. Our work models the parameters as random variables with known distributions and investigates the steady-state flow rate under this notion by using tools from the random matrix theory. Some closed-form theoretical results are derived for the steady-state flow rate under some restrictive assumptions such as random variables being independent and identically distributed. Furthermore, for arbitrary but bounded stochastic transition rates, stochastic site capacities, or both, we establish bounds for the steady-state flow rate. Our analysis can be generalized and applied to study the flow of particles in numerous transport systems in the stochastic environment.
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