Knowledge Flow Dynamics in Organizations: A Stochastic Multi-Scale Analysis of Learning Barriers

Organizations face fundamental challenges in managing knowledge flows across complex networks, yet existing frameworks often lack quantitative tools for optimization. We develop a novel stochastic multi-scale model introducing knowledge flow viscosity (KFV) to analyze organizational learning dynamics. This model quantifies resistance to knowledge transfer using a time-varying viscosity tensor, capturing both continuous learning processes and discrete knowledge acquisition events. Through renormalization group analysis, we establish the existence of critical thresholds in knowledge diffusion rates, characterizing phase transitions in organizational learning capacity. Numerical simulations demonstrate that targeted reductions in communication barriers near these thresholds can significantly enhance knowledge flow efficiency. The findings provide a mathematical foundation for understanding multi-level knowledge flow dynamics, suggesting precise conditions for effective interventions to optimize learning in complex organizational systems.