Concrush: Understanding fugitive dust production and potential emission at a recycled concrete manufacturing facility

The production and emission of fugitive dust is a topic ofconcern that Concrush brought to the MISG, 2020. Concrushis recycled concrete manufacturing company in the Hunterregion of New South Wales. Concrush's operations producefugitive dust, fine particles that can escape the site. Fugitive dust can travel long distances from the site ofemission, and can have negative health impacts includingrespiratory illnesses. Presently, concrete recyclingfacilities are managed by the Environmental ProtectionAgency using guidelines initially developed for the coalindustry. Concrush seeks to understand the appropriatenessof these guidelines, and how they can reduce and managefugitive dust on their Teralba site. Mathematical modellingof dust emission and transport, together with a review ofsimilar processes in the literature, identified a number ofpractical options for Concrush to reduce their dustemissions. In addition, opportunities for improved datacollection are identified

Infiltration in soils with a saturated surface

Key Points Analytic description of infiltration in soils Comparison of constant flux and saturated surface infiltration Linking infiltration to soil/water properties An earlier infiltration equation relied on curve fitting of infiltration data for the determination of one of the parameters, which limits its usefulness in practice. This handicap is removed here, and the parameter is now evaluated by linking it directly to soil-water properties. The new predictions of infiltration using this evaluation are quite accurate. Positions and shapes of soil-water profiles are also examined in detail and found to be predicted analytically with great precision

Infiltration from supply at constant water content: an integrable model

An integrable version of Richards’ equation for time-dependent unidimensional flow in unsaturated soil is subjected to boundary conditions of constant water content. The nonlinear boundary problem is transformed to a linear diffusion problem with modified Stefan boundary conditions. A formal series is developed, leading to successive approximations to the solution at early times. Each additional term of the series for the location of the free boundary in the transformed problem leads directly to another coefficient in the Philip infiltration series in the original problem.P. Broadbridge, D. Triadis and J. M. Hil

The self-thinning rule and plant population modelling with resource constraints

The Japan Agency for Marine-Earth Science and Technology contributed this challenge to the 2016 Mathematics-in-Industry New Zealand Study Group Workshop. It concerned implications of the self-thinning rule for modelling plant population characteristics via a partial differential equation governing the temporal evolution of the density distribution of plants of a particular size. The self-thinning rule is empirically observed for crowded populations under constrained resources. We investigate the theoretical consequences of a resource constraint on the partial differential equation of interest, and through numerical experiments reveal a surprisingly strong link between imposition of the resource constraint, and populations that evolve according to the self-thinning rule. The result is a simple condition between growth and mortality functions that implies self-thinning behaviour, and motivates further mathematical investigation

Infiltration from supply at constant water content: an integrable model

An integrable version of Richards’ equation for time-dependent unidimensional flow in unsaturated soil is subjected to boundary conditions of constant water content. The nonlinear boundary problem is transformed to a linear diffusion problem with modified Stefan boundary conditions. A formal series is developed, leading to successive approximations to the solution at early times. Each additional term of the series for the location of the free boundary in the transformed problem leads directly to another coefficient in the Philip infiltration series in the original problem

Nonclassical Symmetry Solutions for Fourth-Order Phase Field Reaction–Diffusion

Using the nonclassical symmetry of nonlinear reaction–diffusion equations, some exact multi-dimensional time-dependent solutions are constructed for a fourth-order Allen–Cahn–Hilliard equation. This models a phase field that gives a phenomenological description of a two-phase system near critical temperature. Solutions are given for the changing phase of cylindrical or spherical inclusion, allowing for a “mushy” zone with a mixed state that is controlled by imposing a pure state at the boundary. The diffusion coefficients for transport of one phase through the mixture depend on the phase field value, since the physical structure of the mixture depends on the relative proportions of the two phases. A source term promotes stability of both of the pure phases but this tendency may be controlled or even reversed through the boundary conditions