Building more reliable models of water flow at junctions in water distribution networks
In the dense, integrated societies that the majority of people now live, networked water distribution systems are essential. Maintaining the safety and security of water distribution networks from contamination, both accidental and intentional, is a key public safety challenge.
One tool used against this risk is real-time sensors, but in order to improve their efficacy, we need to better understand how a potential contaminant might flow through a complicated series of pipes, junctions and valves.
It is in this light that authors Gilbert et al. set out to use mathematics and modelling to approach this problem. In their paper the authors use computational fluid dynamics (CFD) and data from 3D CFD simulations to generate a generalised model of reduced dimensionality, which can complement existing transport models and allow real-time computation of the behaviour of contaminants in a complicated system.
Gilbert, I. Mortazavi, O. Piller and H. Ung (2017), Low dimensional modeling of Double T-junctions in water distribution networks using Kriging interpolation and Delaunay triangulation, Pacific Journal of Mathematics for Industry, 9:2, DOI 10.1186/s40736-016-0026-8
Modelling steel strip heating within an annealing furnace
Annealing is an important industrial heat treatment used to change the properties of metals such as steel. The simple process of heating steel and letting it cool very slowly can be used to increase the homogeneity and ductility of the metal and relieve internal stress. However, one of the problems with the industrial process of annealing steel strips in electric radiant furnaces is the production of wave-like defects near the edges of the strip, thought to be due to nonuniform heating.
Authors Taylor & Wang addressed the impracticality of physically measuring temperature inside an incredibly hot furnace by developing a model of temperature distribution across the steel strip surface, finding that damagingly high temperature gradients at the edges of the strip could be the result of the geometry of the strip and heating elements and the rate of conduction away from rough edges of the steel.
W. Taylor and S. Wang (2017), Modelling steel strip heating within an annealing furnace Pacific Journal of Mathematics for Industry, 9:5, DOI 10.1186/s40736-017-0030-7
Optimising the timing of harvesting farmed fish
Optimisation problems are a common theme in applied mathematics, and finding the optimal solution to an industrial process can make huge differences to the efficiency of a whole industry. Aquaculture is no exception to this, and finding the right time to begin the harvesting process at a fish farm has always been one of the most important decisions to get right.
To find a theoretical solution to a problem that fish farmers have long been trying to solve by trial and error, authors Yoshioka & Yaegashi developed a mathematical model of farmed fishery resources. They then applied their model to a particular example, finding the optimal time to begin the harvesting of farmed Ayu fish Plecoglossus altivelis, the main inland fishery resource in Japan.
Yoshioka and Y. Yaegashi (2016), Finding the optimal opening time of harvesting farmed fishery resources, Pacific Journal of Mathematics for Industry, 8:6, DOI 10.1186/s40736-016-0025-9
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