Discontinuous phase transition in chemotactic aggregation with density-dependent pressure

Abstract

Many small organisms such as bacteria can attract each other by depositing chemical attractants. At the same time, they exert repulsive force on each other when crowded, which can be modeled by effective pressure as an increasing function of the organisms' density. As the chemical attraction becomes strong compared to the effective pressure, the system will undergo a phase transition from homogeneous distribution to aggregation. In this work, we describe the interplay of organisms and chemicals on a two-dimensional disk with a set of partial differential equations of the Patlak-Keller-Segel type. By analyzing its Lyapunov functional, we show that the aggregation transition occurs discontinuously, forming an aggregate near the boundary of the disk. The result can be interpreted within a thermodynamic framework by identifying the Lyapunov functional with free energy.

arXiv comment11 pages, 3 figures

References in corpus (11)

• Scalar ${\varphi }^4$ field theory for active-particle phase separation
• Observation of PT phase transition in a simple mechanical system
• Percolation, Morphogenesis, and Burgers Dynamics in Blood Vessels Formation
• Towards a 'Thermodynamics' of Active Matter
• Active Model H: Scalar Active Matter in a Momentum-Conserving Fluid
• Nutrient transport driven by microbial active carpets
• Turing Instability and Pattern Formation in an Activator-Inhibitor System with Nonlinear Diffusion
• Universal entrainment mechanism governs contact times with motile cells
• A study of blow-ups in the Keller-Segel model of chemotaxis
• Non-equilibrium Lyapunov function and a fluctuation relation for stochastic systems: Poisson representation approach
• Free energy of a chemotactic model with nonlinear diffusion

Cited by in corpus (1)

• Agent-Based Simulation of the Two-Dimensional Patlak-Keller-Segel Model