Steven Psaltis

Comparing Charge Transport Predictions for a Ternary Electrolyte Using the Maxwell–Stefan and Nernst–Planck Equations

In this work, we investigate and compare the Maxwell–Stefan and Nernst–Planck equations for modeling multicomponent charge transport in liquid electrolytes. Specifically, we consider charge transport in the Li+/I−/I3−/ACN ternary electrolyte originally found in dye-sensitized solar cells. We employ molecular dynamics simulations to obtain the Maxwell–Stefan diffusivities for this electrolyte. These simulated diffusion coefficients are used in a multicomponent charge transport model based on the Maxwell– Stefan equations, and this is compared to a Nernst–Planck based model which employs binary diffusion coefficients sourced from the literature. We show that significant differences between the electrolyte concentrations at electrode interfaces, as predicted by the Maxwell–Stefan and Nernst–Planck models, can occur. We find that these differences are driven by a pressure term that appears in the Maxwell–Stefan equations. We also investigate what effects the Maxwell–Stefan diffusivities have on the simulated charge transport. By incorporating binary diffusivities found in the literature into the Maxwell–Stefan framework, we show that the simulated transient concentration profiles depend on the diffusivities; however, the simulated equilibrium profiles remain unaffected.

Sampling methods for exploring between-subject variability in cardiac electrophysiology experiments

Between-subject and within-subject variability is ubiquitous in biology and physiology, and understanding and dealing with this is one of the biggest challenges in medicine. At the same time, it is difficult to investigate this variability by experiments alone. A recent modelling and simulation approach, known as population of models (POM), allows this exploration to take place by building a mathematical model consisting of multiple parameter sets calibrated against experimental data. However, finding such sets within a high-dimensional parameter space of complex electrophysiological models is computationally challenging. By placing the POM approach within a statistical framework, we develop a novel and efficient algorithm based on sequential Monte Carlo (SMC). We compare the SMC approach with Latin hypercube sampling (LHS), a method commonly adopted in the literature for obtaining the POM, in terms of efficiency and output variability in the presence of a drug block through an in-depth investigation via the Beeler–Reuter cardiac electrophysiological model. We show improved efficiency for SMC that produces similar responses to LHS when making out-of-sample predictions in the presence of a simulated drug block. Finally, we show the performance of our approach on a complex atrial electrophysiological model, namely the Courtemanche–Ramirez–Nattel model.

Nonlinear Porous Diffusion Modeling of Hydrophilic Ionic Agrochemicals in Astomatous Plant Cuticle Aqueous Pores: A Mechanistic Approach

The agricultural industry requires improved efficacy of sprays being applied to crops and weeds in order to reduce their environmental impact and deliver improved financial returns. Enhanced foliar uptake is one means of improving efficacy. The plant leaf cuticle is known to be the main barrier to diffusion of agrochemicals within the leaf. The usefulness of a mathematical model to simulate uptake of agrochemicals in plant cuticles has been noted previously in the literature, as the results of each uptake experiment are specific to each formulation of active ingredient, plant species and environmental conditions. In this work we develop a mathematical model and numerical simulation for the uptake of hydrophilic ionic agrochemicals through aqueous pores in plant cuticles. We propose a novel, nonlinear, porous diffusion model for ionic agrochemicals in isolated cuticles, which extends simple diffusion through the incorporation of parameters capable of simulating: plant species variations, evaporation of surface droplet solutions, ion binding effects on the cuticle surface and swelling of the aqueous pores with water. We validate our theoretical results against appropriate experimental data, discuss the key sensitivities in the model and relate theoretical predictions to appropriate physical mechanisms. Major influencing factors have been found to be cuticle structure, including tortuosity and density of the aqueous pores, and to a lesser extent humidity and cuticle surface ion binding effects.

Three-dimensional virtual reconstruction of timber billets from rotary peeling

Abstract Accurately determining the timber properties for products prior to cutting the tree is difficult. In this work we discuss a method for reconstructing a timber billet virtually, including internal features, after it has been peeled into a full veneer (ribbon). This reconstruction process is the first stage in developing a mathematical model for the variation in timber properties within a given tree. The reconstruction of internal timber features is typically achieved through the use of computed tomography (CT) scanning. However, this requires the use of equipment that may be cost-prohibitive. Here we discuss an approach that utilises more readily available equipment for timber processors, including a spindleless lathe and digital SLR camera. In comparison to conventional scanning methods, this reconstruction method based on a destructive process has the key advantage of delivering high-resolution colour images. This reconstruction serves two purposes. Firstly, we are able to generate three-dimensional visualisations of the timber billet, to uncover internal structures such as knots, defects, insect or fungi attack, discoloration, resin, etc. Secondly, the reconstruction allows us to map timber properties measured on the veneer to their original location within the billet. This allows us to locally inform the mapping with wood properties and subsequently derive their distribution throughout the billet. From this information it is then possible to extract any part of the billet and obtain the appearance and wood properties of any processed products. To validate our reconstruction process we show that we can obtain reasonable agreement between our predicted billet modulus of elasticity and that measured on the original billet.

A Mathematical Model of the Ripening of Cheddar Cheese

Cheddar cheese undergoes a number of biochemical changes during ripening. These processes were modelled with differential equations in a project at MISG2013 (the 2013 mathematics-in-industry study group) at Queensland University of Technology, Australia. Models could aid in the prediction of cheese quality from initial measurements. The model is presented and the effect of small changes in initial conditions is explored.