Towards an improved PEPT triangulation routine J Newling 1, AJ Morrison 1, N Fowkes 2, I Govender 1 and L Bbosa 1 1 University of Cape Town, Cape Town, South Africa 2 University of Western Australia, Perth, Australia

Tumbling Mills Minerals industry (gold, platinum, copper, etc …) Main aim is size reduction of extracted ore Very energy-intensive, however inefficient Aggressive environment, in situ measurement not feasible Models are empirical – Mill specific – Ore specific Mill diameter 0.3 – 5m Rotational speed 15 – 40 rpm

Positron Emission Particle Tracking

γ γ

Sources of false events True Pairing Scattered Pairing Random Pairing

Triangulation 75% - 90% of recorded events are discarded

Proposal 1: Minimum perpendicular distance method Method Find the midpoint of the perpendicular between successive lines of response Use the median of these midpoints to estimate the particle location in that time interval Motivation Avoid iteration by using the median to weight true pairs Shortcoming No guarantee that the closest approach is in the area of the tracer particle

Proposal 1: Minimum perpendicular distance method

Proposal 2: Density of lines Method Discretise the field of the view into a 3D grid. Use the number of intersections of the LoRs with each grid element to isolate the particle position Motivation Discriminate against random and scattered events Shortcoming Computationally expensive

Proposal 2: Density of lines Dino Giovannoni & Matthew Bickell (Physics Honours) From detected lines to line density… … to probability distributions… … to particle position.

Proposal 3: 2D triangulation Method Divide LoR into coplanar sets and use these to reduce the problem to a 2D one Motivation Simplify the 3D case into a 2D problem Shortcoming Drastically reduces the statistics Does not discriminate between true and false lines.

Proposal 4: Distance distribution Method Use the current iterative method to calculate the centroid Use the distribution of LoR distances from the centroid to dynamically determine the fraction to discard Recalculate the centroid and repeat until some convergence criteria is met. Motivation Avoid having to calibrate the routine for each experiment Shortcoming Does not reduce the computational expense

Proposal 4: Distance distribution Frequency of events Distance from centroid /mm

Conclusion