  The problem of environmental monitoring using a wireless network of chemical
sensors with a limited energy supply is considered. Since the conventional
chemical sensors in active mode consume vast amounts of energy, an optimisation
problem arises in the context of a balance between the energy consumption and
the detection capabilities of such a network. A protocol based on "dynamic
sensor collaboration" is employed: in the absence of any pollutant, majority of
sensors are in the sleep (passive) mode; a sensor is invoked (activated) by
wake-up messages from its neighbors only when more information is required. The
paper proposes a mathematical model of a network of chemical sensors using this
protocol. The model provides valuable insights into the network behavior and
near optimal capacity design (energy consumption against detection). An
analytical model of the environment, using turbulent mixing to capture chaotic
fluctuations, intermittency and non-homogeneity of the pollutant distribution,
is employed in the study. A binary model of a chemical sensor is assumed (a
device with threshold detection). The outcome of the study is a set of simple
analytical tools for sensor network design, optimisation, and performance
analysis.
