Universal Laws Governing Autocatalytic Dynamics at Surfaces
Researchers have developed a theoretical framework explaining how autocatalytic processes—where replication is triggered at interfaces—behave across diverse systems from catalysis to viral infections. The work derives mathematical equations describing population dynamics when particles interact with surfaces where they can either disappear or reproduce. The findings provide quantitative predictions for when surface activity leads to extinction or explosive growth, with applications to catalysis, metabolism, and ecosystem persistence.
A new theoretical study presents a unified mathematical framework for understanding autocatalytic processes occurring at surfaces and interfaces. The research addresses systems where particles move through a bulk medium and interact with surface regions, including heterogeneous catalysis on solid substrates, enzyme activity at membranes, viral infections, biofilm growth, and spatially structured ecosystems. The authors derive a renewal-type nonlinear integral equation for the generating function of population size, providing access to the full probability distribution and statistical moments. They also establish an equivalent description using a Fokker-Planck equation with nonlinear Robin-type boundary conditions encoding surface reactions. The framework identifies distinct dynamical regimes and universal scaling laws, offering quantitative insights into catalytic efficiency, metabolic regulation, and population persistence in heterogeneous environments.
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- arXiv physicsCenter
Birth, Death, and Replication at Surfaces: Universal Laws of Autocatalytic Dynamics
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