A combined model of aggregation, fragmentation, and exchange processes: insights from analytical calculations

We introduce a mean-field framework for the study of systems of interacting particles sharing a conserved quantity. The work generalises and unites the existing fields of asset-exchange models, often applied to socio-economic systems, and aggregation-fragmentation models, typically used in modelling the dynamics of clusters. An initial model includes only two-body collisions, which is then extended to include many-body collisions and spontaneous fragmentation. We derive self-consistency equations for the steady-state distribution, which can be solved using a population dynamics algorithm, as well as a full solution for the time evolution of the moments, corroborated with numerical simulations. The generality of the model makes it applicable to many problems and allows for the study of systems exhibiting more complex interactions that those typically considered. The work is relevant to the modelling of barchan dune fields in which interactions between the bedforms and spontaneous fragmentation due to changes in the wind are thought to lead to size-selection. Our work could also be applied in finding wealth distributions when agents can both combine assets as well as split into multiple subsidiaries.Comment: 19 pages, 5 figures. To be published in Journal of Statistical Mechanics: Theory and Experiment (JSTAT

Low-cost electronic sensors for environmental research: pitfalls and opportunities

Repeat observations underpin our understanding of environmental processes, but financial constraints often limit scientists’ ability to deploy dense networks of conventional commercial instrumentation. Rapid growth in the Internet-Of-Things (IoT) and the maker movement is paving the way for low-cost electronic sensors to transform global environmental monitoring. Accessible and inexpensive sensor construction is also fostering exciting opportunities for citizen science and participatory research. Drawing on 6 years of developmental work with Arduino-based open-source hardware and software, extensive laboratory and field testing, and incor- poration of such technology into active research programmes, we outline a series of successes, failures and lessons learned in designing and deploying environmental sensors. Six case studies are presented: a water table depth probe, air and water quality sensors, multi-parameter weather stations, a time-sequencing lake sediment trap, and a sonic anemometer for monitoring sand transport. Schematics, code and purchasing guidance to reproduce our sensors are described in the paper, with detailed build instructions hosted on our King’s College London Geography Environmental Sensors Github repository and the FreeStation project website. We show in each case study that manual design and construction can produce research-grade scientific instrumentation (mean bias error for calibrated sensors –0.04 to 23%) for a fraction of the conventional cost, provided rigorous, sensor-specific calibration and field testing is conducted. In sharing our collective experiences with build-it- yourself environmental monitoring, we intend for this paper to act as a catalyst for physical geographers and the wider environmental science community to begin incorporating low-cost sensor development into their research activities. The capacity to deploy denser sensor networks should ultimately lead to superior envi- ronmental monitoring at the local to global scales