Zero-Boundary Modeling of Environmental Pollutant Behavior Using Zero-Centric Arithmetic: A Mathematical Framework for Environmental Engineering

الملخص

Environmental engineering models extensively rely on algebraic ratio-based formulations to describe pollutant concentration, transport, partitioning, persistence, and exposure. These formulations implicitly assume that denominators such as environmental volume, concentration, reaction rate constants, or exposure duration remain strictly non-zero. However, many environmentally relevant boundary conditions involve zero or near-zero values, including non-detect concentrations, zero-emission states, vanishing reaction rates, and disappearing environmental compartments. Under classical arithmetic, such conditions generate undefined expressions that are frequently interpreted as physically meaningful infinities.
This paper introduces a Zero-Centric Arithmetic framework for modeling environmental pollutant behavior at zero boundaries. Within this framework, expressions involving division by zero are reinterpreted as non-operations, representing collapse points of mathematical models rather than extreme or infinite environmental states. By applying this reinterpretation to concentration equations, partition coefficients, atmospheric lifetime models, and exposure formulations, the proposed approach restores mathematical consistency and aligns environmental equations with physically observable behavior. The framework establishes clear operational domains for environmental models and provides a robust mathematical foundation for environmental simulation, risk assessment, and engineering decision-making.