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Item Open Access A mathematical model for nutrient–limited uniaxial growth of a compressible tissue(Elsevier BV, 2023) Li, K.; Gallo, A.J.; Binder, B.J.; Green, J.E.F.We consider the uniaxial growth of a tissue or colony of cells, where a nutrient (or some other chemical) required for cell proliferation is supplied at one end, and is consumed by the cells. An example would be the growth of a cylindrical yeast colony in the experiments described by Vulin et al. (2014). We develop a reaction– diffusion model of this scenario which couples nutrient concentration and cell density on a growing domain. A novel element of our model is that the tissue is assumed to be compressible. We define replicative regions, where cells have sufficient nutrient to proliferate, and quiescent regions, where the nutrient level is insufficient for this to occur. We also define pathlines, which allow us to track individual cell paths within the tissue. We begin our investigation of the model by considering an incompressible tissue where cell density is constant before exploring the solution space of the full compressible model. In a large part of the parameter space, the incompressible and compressible models give qualitatively similar results for both the nutrient concentration and cell pathlines, with the key distinction being the variation in density in the compressible case. In particular, the replicative region is located at the base of the tissue, where nutrient is supplied, and nutrient concentration decreases monotonically with distance from the nutrient source. However, for a highly-compressible tissue with small nutrient consumption rate, we observe a counter-intuitive scenario where the nutrient concentration is not necessarily monotonically decreasing, and there can be two replicative regions. For parameter values given in the paper by Vulin et al. (2014), the incompressible model slightly overestimates the colony length compared to experimental observations; this suggests the colony may be somewhat compressible. Both incompressible and compressible models predict that, for these parameter values, cell proliferation is ultimately confined to a small region close to the colony base.Item Metadata only An Equation Free algorithm accurately simulates macroscale shocks arising from heterogeneous microscale systems(Institute of Electrical and Electronics Engineers, 2021) Maclean, J.; Bunder, J.E.; Kevrekidis, I.G.; Roberts, A.J.Scientists and engineers often create accurate, trustworthy, computational simulation schemes—but all too often these are too computationally expensive to execute over the time or spatial domain of interest. The equation-free approach is to marry such trusted simulations to a framework for numerical macroscale reduction—the patch dynamics scheme. This article extends the patch scheme to scenarios in which the trusted simulation resolves abrupt state changes on the microscale that appear as shocks on the macroscale. Accurate simulation for problems in these scenarios requires capturing the shock within a novel patch, and also modifying the patch coupling rules in the vicinity in order to maintain accuracy. With these two extensions to the patch scheme, straightforward arguments derive consistency conditions that match the usual order of accuracy for patch schemes. The new scheme is successfully tested to simulate a heterogeneous microscale partial differential equation.This technique willempower scientists and engineers to accurately and efficiently simulate, over large spatial domains, multiscale multiphysics systems that have rapid transition layers on the microscale.Item Metadata only A tale of two vortices: How numerical ergodic theory and transfer operators reveal fundamental changes to coherent structures in non-autonomous dynamical systems(American Institute of Mathematical Sciences (AIMS), 2020) Blachut, C.; González-Tokman, C.Coherent structures are spatially varying regions which disperse minimally over time and organise motion in non-autonomous systems. This work develops and implements algorithms providing multilayered descriptions of time-dependent systems which are not only useful for locating coherent structures, but also for detecting time windows within which these structures undergo fundamental structural changes, such as merging and splitting events. These algorithms rely on singular value decompositions associated to Ulam type discretisations of transfer operators induced by dynamical systems, and build on recent developments in multiplicative ergodic theory. Furthermore, they allow us to investigate various connections between the evolution of relevant singular value decompositions and dynamical features of the system. The approach is tested on models of periodically and quasi-periodically driven systems, as well as on a geophysical dataset corresponding to the splitting of the Southern Polar Vortex.Item Open Access Geometry and holonomy of indecomposable cones(EMS Press - European Mathematical Society, 2023) Alekseevsky, D.; Cortés, V.; Leistner, T.We study the geometry and holonomy of semi-Riemannian, time-like metric cones that are indecomposable, i.e., which do not admit a local decomposition into a semi-Riemannian product. This includes irreducible cones, for which the holonomy can be classified, as well as non-irreducible cones. The latter admit a parallel distribution of null k-planes, and we study the cases k = 1 in detail. We give structure theorems about the base manifold and in the case when the base manifold is Lorentzian, we derive a description of the cone holonomy. This result is obtained by a computation of certain cocycles of indecomposable subalgebras in so(1,n - 1).Item Metadata only Parametric analysis of a two-body floating-point absorber wave energy converter(AIP Publishing, 2023) Xu, Q.; Li, Y.; Bennetts, L.G.; Wang, S.; Zhang, L.; Xu, H.; Narasimalu, S.In the evolution of floating-point absorber wave energy conversion systems, multiple-body systems are gaining more attention than singlebody systems. Meanwhile, the design and operation factors affecting the performance of multiple-body systems are much greater than those of single-body systems. However, no systematic study has yet been presented. In this article, a theoretical model is proposed by using a coupled oscillator system consisting of a damper-spring system to represent a two-body system (the floating body and the reacting body). Dimensionless expressions for the motion response and wave power absorption efficiency are derived. With the newly developed model, we prove that an appropriately tuned two-body system can obtain a limiting power absorption width of L=2p (L is the incident wavelength) as much as a single-body system. The generic case of a two-body system is presented with numerical simulations as an example. The results show that increasing the damping coefficient can reduce the wave frequency at which the peak of power absorption efficiency occurs. Increasing stiffness can make the wave frequencies for high power absorption efficiency move to a higher frequency region and can also make the spectrum bandwidth for high power absorption efficiency become narrower. Further, we show that the two-body system can absorb more wave energy at low wave frequencies than the single-body system.Item Open Access Covalent Protein Immobilization on 3D-Printed Microfiber Meshes for Guided Cartilage Regeneration(Wiley, 2023) Ainsworth, M.J.; Lotz, O.; Gilmour, A.; Zhang, A.; Chen, M.J.; McKenzie, D.R.; Bilek, M.M.M.; Malda, J.; Akhavan, B.; Castilho, M.Current biomaterial-based strategies explored to treat articular cartilage defects have failed to provide adequate physico-chemical cues in order to guide functional tissue regeneration. Here, it is hypothesized that atmospheric-pressure plasma (APPJ) treatment and melt electrowriting (MEW) will produce microfiber support structures with covalently-immobilized transforming growth factor beta-1 (TGFβ1) that can stimulate the generation of functional cartilage tissue. The effect of APPJ operational speeds to activate MEW polycaprolactone meshes for immobilization of TGFβ1 is first investigated and chondrogenic differentiation and neo-cartilage production are assessed in vitro. All APPJ speeds test enhanced hydrophilicity of the meshes, with the slow treatment speed having significantly less CC/CH and more COOH than the untreated meshes. APPJ treatment increases TGFβ1 loading efficiency. Additionally, in vitro experiments highlight that APPJ-based TGFβ1 attachment to the scaffolds is more advantageous than direct supplementation within the medium. After 28 days of culture, the group with immobilized TGFβ1 has significantly increased compressive modulus (more than threefold) and higher glycosaminoglycan production (more than fivefold) than when TGFβ1 is supplied through the medium. These results demonstrate that APPJ activation allows reagent-free, covalent immobilization of TGFβ1 on microfiber meshes and, importantly, that the biofunctionalized meshes can stimulate neo-cartilage matrix formation. This opens new perspectives for guided tissue regeneration.Item Open Access A Patch in Time Saves Nine: Methods for the Identification of Localised Dynamical Behaviour and Lifespans of Coherent Structures(Springer Verlag, 2023) Blachut, C.; Gonzalez-Tokman, C.; Hernandez-Duenas, G.We develop a transfer operator-based method for the detection of coherent structures and their associated lifespans. Characterising the lifespan of coherent structures allows us to identify dynamically meaningful time windows, which may be associated with transient coherent structures in the localised phase space, as well as with time intervals within which these structures experience fundamental changes, such as merging or separation events. The localised transfer operator approach we pursue allows one to explore the fundamental properties of a dynamical system without full knowledge of the dynamics. The algorithms we develop prove useful not only in the simple case of a periodically driven double well potential model, but also in more complex cases generated using the rotating Boussinesq equations.Item Metadata only Substructural fixed-point theorems and the diagonal argument: theme and variations(Compositionality Journal, 2023) Roberts, D.M.This article re-examines Lawvere's abstract, category-theoretic proof of the fixed-point theorem whose contrapositive is a `universal' diagonal argument. The main result is that the necessary axioms for both the fixed-point theorem and the diagonal argument can be stripped back further, to a semantic analogue of a weak substructural logic lacking weakening or exchange.Item Metadata only A note on the Nielsen realization problem for K3 surfaces(American Mathematical Society, 2023) Baraglia, D.; Konno, H.We will show the following three theorems on the diffeomorphism and homeomorphism groups of a K3 surface. The first theorem is that the natural map π₀ (Diff(K3)) → Aut(H²(K3;Z)) has a section over its image. The second is that there exists a subgroup G of π₀ (Diff(K3)) of order two over which there is no splitting of the map (Diff(K3) → π₀ (Diff(K3)), but there is a splitting of Homeo(K3) → π₀(Homeo(K3)) over the image of G in π₀(Homeo(K3)), which is non-trivial. The third is that the map π₁(Diff(K3)) → π₁(Homeo(K3)) is not surjective. Our proof of these results is based on Seiberg-Witten theory and the global Torelli theorem for K3 surfaces.Item Open Access Tautological classes of definite 4-manifolds(Mathematical Sciences Publishers, 2023) Baraglia, D.We prove a diagonalisation theorem for the tautological, or generalised Miller–Morita– Mumford, classes of compact, smooth, simply connected, definite 4–manifolds. Our result can be thought of as a families version of Donaldson’s diagonalisation theorem. We prove our result using a families version of the Bauer–Furuta cohomotopy refinement of Seiberg–Witten theory. We use our main result to deduce various results concerning the tautological classes of such 4–manifolds. In particular, we completely determine the tautological rings of CP2 and CP2 # CP2 . We also derive a series of linear relations in the tautological ring which are universal in the sense that they hold for all compact, smooth, simply connected definite 4–manifolds.Item Open Access Almost Robinson geometries(Springer Science and Business Media LLC, 2023) Fino, A.; Leistner, T.; Taghavi-Chabert, A.We investigate the geometry of almost Robinson manifolds, Lorentzian analogues of almost Hermitian manifolds, defined by Nurowski and Trautman as Lorentzian manifolds of even dimension equipped with a totally null complex distribution of maximal rank. Associated to such a structure, there is a congruence of null curves, which, in dimension four, is geodesic and non-shearing if and only if the complex distribution is involutive. Under suitable conditions, the distribution gives rise to an almost Cauchy–Riemann structure on the leaf space of the congruence. We give a comprehensive classification of such manifolds on the basis of their intrinsic torsion. This includes an investigation of the relation between an almost Robinson structure and the geometric properties of the leaf space of its congruence. We also obtain conformally invariant properties of such a structure, and we finally study an analogue of so-called generalised optical geometries as introduced by Robinson and Trautman.Item Open Access Attractor-driven matter(AIP Publishing, 2023) Valani, R.N.; Paganin, D.M.The state of a classical point-particle system may often be specified by giving the position and momentum for each constituent particle. For non-pointlike particles, the center-of-mass position may be augmented by an additional coordinate that specifies the internal state of each particle. The internal state space is typically topologically simple, in the sense that the particle’s internal coordinate belongs to a suitable symmetry group. In this paper, we explore the idea of giving internal complexity to the particles, by attributing to each particle an internal state space that is represented by a point on a strange (or otherwise) attracting set. It is, of course, very well known that strange attractors arise in a variety of nonlinear dynamical systems. However, rather than considering strange attractors as emerging from complex dynamics, we may employ strange attractors to drive such dynamics. In particular, by using an attractor (strange or otherwise) to model each particle’s internal state space, we present a class of matter coined “attractor-driven matter.” We outline the general formalism for attractor-driven matter and explore several specific examples, some of which are reminiscent of active matter. Beyond the examples studied in this paper, our formalism for attractor-driven dynamics may be applicable more broadly, to model complex dynamical and emergent behaviors in a variety of contexts.Item Open Access The dark web trades wildlife, but mostly for use as drugs(Wiley, 2023) Stringham, O.C.; Maher, J.; Lassaline, C.R.; Wood, L.; Moncayo, S.; Toomes, A.; Heinrich, S.; Watters, F.; Drake, C.; Chekunov, S.; Hill, K.G.W.; Decary‐Hetu, D.; Mitchell, L.; Ross, J.V.; Cassey, P.1. Contemporary wildlife trade is massively facilitated by the Internet. By design, the dark web is one layer of the Internet that is difficult to monitor and continues to lack thorough investigation. 2. Here, we accessed a comprehensive database of dark web marketplaces to search across c. 2 million dark web advertisements over 5 years using c. 7 k wildlife trade-related search terms. 3. We found 153 species traded in 3332 advertisements (c. 600 advertisements per year). We characterized a highly specialized wildlife trade market, where c. 90% of dark-web wildlife advertisements were for recreational drugs. 4. We verified that 68 species contained chemicals with drug properties. Species advertised as drugs mostly comprised of plant species, however, fungi and animals were also traded as drugs. Most species with drug properties were psychedelics (45 species), including one genera of fungi, Psilocybe, with 19 species traded on the dark web. The native distribution of plants with drug properties were clustered in Central and South America. A smaller proportion of trade was for purported medicinal properties of wildlife, clothing, decoration, and as pets. 5. Synthesis and applications. Our results greatly expand on what wildlife species are currently traded on the dark web and provide a baseline to track future changes. Given the low number of advertisements, we assume current conservation and biosecurity risks of the dark web are low. While wildlife trade is rampant on other layers of the Internet, particularly on e-commerce and social media sites, trade on the dark web may still increase if these popular platforms are rendered less accessible to traders (e.g., via an increase in enforcement). We recommend focussing on surveillance of e-commerce and social media sites, but we encourage continued monitoring of the dark web periodically to evaluate potential shifts in wildlife trade across this more occluded layer of the Internet.Item Metadata only Viscous effects on the added mass and damping forces during free heave decay of a floating cylinder with a hemispherical bottom(Elsevier BV, 2023) Chen, H.; Xu, Q.; Zheng, X.; Bennetts, L.G.; Xie, B.; Lin, Z.; Lin, Z.; Li, Y.This paper presents an analysis of viscous effects on the added mass and damping forces during free heave decay of a cylinder with a hemispherical bottom. Results from unsteady Reynolds-averaged Navier–Stokes (URANS) simulations and linear potential-flow solutions are compared. Expressions for the cycle-averaged viscous added mass and damping coefficients are derived based on first-order Fourier analysis of the URANS results. Viscous effects are extracted by comparing the URANS results and linear potential-flow solutions, as nonlinear potential-flow effects in this case are demonstrated to be negligible. It is observed that viscous effects on the added mass coefficient are minor during heave decay, such that the linear potential-flow model can predict the value of the added mass coefficient to within 5% deviations. In contrast, the viscous damping coefficient exhibits strong cycledependent variations. A parametric study of the effects of initial displacement, cylinder diameter and draft shows that viscous damping forces can play an important role when the cylinder has a relatively small diameter and large draft. Further, the damping coefficient is transformed to the nondimensional drag force coefficient, and its dependence on the Reynolds number Re is investigated, for Keulegan– Carpenter numbers in the range KC = 1.5–2.5. It is found that the drag force coefficient is likely to be unrelated to Re and KC during the first cycle. From the second cycle to the fourth cycle, the drag force coefficient rapidly decreases with increasing Re, up to Re ≈ 3 × 10⁵.Item Open Access Gender-specific effects of COVID-19 lockdowns on scientific publishing productivity: Impact and resilience(Elsevier, 2023) Ryan, M.; Tuke, J.; Hutchinson, M.R.; Spencer, S.J.Rationale: The SARS-CoV2 pandemic led to drastic social restrictions globally. Early data suggest that women in science have been more adversely affected by these lockdowns than men, with relatively fewer scientific articles authored by women. However, these observations test broad populations with many potential causes of disparity. Australia presents a natural experimental condition where several states of similar demographics and disease impact had differing approaches in their social isolation strategies. The state of Victoria experienced 280 days of lockdowns from 2020 to 2021, whereas the comparable state of New South Wales experienced 107 days, most of these in 2021, and other states even fewer restrictions. Objective and methods: To assess how the gender balance changed in Australian biomedical publishing with the lockdowns, we created a custom workflow to analyse PubMed data from more than 120,000 published articles submitted in 2019–2021 from Australian authors. Results: Broadly, Australian women have been incredibly resilient to the challenges faced by the lockdowns. There was an increase in the number of published articles submitted in 2020 that was equally due to women as men, including from Victoria. On the other hand, articles specifically addressing COVID-19 were significantly less likely to be authored by women than those on other topics, a finding not likely due to particular gender imbalance in virology or viral epidemiology, since publications on HIV followed similar patterns to previous years. By 2021, this imbalance had reversed, with more COVID-19-related papers authored by women than men. Conclusions: These data suggest women from Victoria were less able to rapidly transition to new research early in the pandemic but had accommodated to the new conditions by 2021. This work indicates we need strategies to support women in science as the pandemic continues and to continue to monitor the situation for its impact on vulnerable groups.Item Open Access The effect of bottleneck size on evolution in nested Darwinian populations.(Elsevier, 2023) Nitschke, M.C.; Black, A.J.; Bourrat, P.; Rainey, P.B.Previous work has shown how a minimal ecological structure consisting of patchily distributed resources and recurrent dispersal between patches can scaffold Darwinian properties onto collections of cells. When the timescale of dispersal is long compared with the time to consume resources, patch fitness increases but comes at a cost to cell growth rates. This creates conditions that initiate evolutionary transitions in individuality. A key feature of the scaffold is a bottleneck created during dispersal, causing patches to be founded by single cells. The bottleneck decreases competition within patches and, hence, creates a strong hereditary link at the level of patches. Here, we construct a fully stochastic model to investigate the effect of bottleneck size on the evolutionary dynamics of both cells and collectives. We show that larger bottlenecks simply slow the dynamics, but, at some point, which depends on the parameters of the within-patch model, the direction of evolution towards the equilibrium reverses. Introduction of random fluctuations in bottleneck sizes with some positive probability of smaller sizes counteracts this, even when the probability of smaller bottlenecks is minimal.Item Metadata only Simpler foundations for the hyperbolic plane(De Gruyter, 2023) Bamberg, J.; Penttila, T.H. L. Skala (1992) gave the first elegant first-order axiom system for hyperbolic geometry by replacing Menger’s axiom involving projectivities with the theorems of Pappus and Desargues for the hyperbolic plane. In so doing, Skala showed that hyperbolic geometry is incidence geometry. We improve upon Skala’s formulation by doing away with Pappus and Desargues altogether, by substituting for them two simpler axioms.Item Metadata only Pseudolaminar chaos from on-off intermittency(American Physical Society (APS), 2003) Müller-Bender, D.; Valani, R.N.; Radons, G.In finite-dimensional, chaotic, Lorenz-like wave-particle dynamical systems one can find diffusive trajectories, which share their appearance with that of laminar chaotic diffusion [Phys. Rev. Lett. 128, 074101 (2022)] known from delay systems with lag-time modulation. Applying, however, to such systems a test for laminar chaos, as proposed in [Phys. Rev. E 101, 032213 (2020)], these signals fail such a test, thus leading to the notion of pseudolaminar chaos. The latter can be interpreted as integrated periodically driven on-off intermittency. We demonstrate that, on a signal level, true laminar and pseudolaminar chaos are hardly distinguishable in systems with and without dynamical noise. However, very pronounced differences become apparent when correlations of signals and increments are considered. We compare and contrast these properties of pseudolaminar chaos with true laminar chaos.Item Metadata only Drone-as-a-Service Composition Under Uncertainty(Institute of Electrical and Electronics Engineers (IEEE), 2021) Ali, A.; Salim, F.D.; Kim, D.Y.; Ghari Neiat, A.; Bouguettaya, A.We propose an uncertainty-aware service approach to provide drone-based delivery services called Drone-as-a-Service (DaaS) effectively. Specifically, we propose a service model of DaaS based on the dynamic spatiotemporal features of drones and their in-flight contexts. The proposed DaaS service approach consists of three components: scheduling, route-planning, and composition. First, we develop a DaaS scheduling model to generate DaaS itineraries through a Skyway network. Second, we propose an uncertainty-aware DaaS route-planning algorithm that selects the optimal Skyways under weather uncertainties. Third, we develop two DaaS composition techniques to select an optimal DaaS composition at each station of the planned route. A spatiotemporal DaaS composer first selects the optimal DaaSs based on their spatiotemporal availability and drone capabilities. A predictive DaaS composer then utilises the outcome of the first composer to enable fast and accurate DaaS composition using several Machine Learning classification methods. We train the classifiers using a new set of spatiotemporal features which are in addition to other DaaS QoS properties. Our experiments results show the effectiveness and efficiency of the proposed approach.Item Open Access Bifurcations and Dynamics in Inertial Focusing of Particles in Curved Rectangular Ducts(Society for Industrial & Applied Mathematics (SIAM), 2022) Valani, R.N.; Harding, B.; Stokes, Y.M.Particles suspended in fluid flow through a curved duct focus to stable equilibrium positions in the duct cross-section due to the balance of two dominant forces: (i) inertial lift force, arising from the inertia of the fluid, and (ii) secondary drag force, resulting from cross-sectional vortices induced by the curvature of the duct. Such particle focusing is exploited in various medical and industrial technologies aimed at separating particles by size. Using the theoretical model developed by Harding, Stokes, and Bertozzi [J. Fluid Mech., 875 (2019), pp. 1–43], we numerically investigate the dynamics of neutrally buoyant particles in fluid flow through curved ducts with rectangular cross-sections at low flow rates. We explore the rich bifurcations that take place in the particle equilibria as a function of three system parameters—particle size, duct bend radius, and aspect ratio of the cross-section. We also explore the transient dynamics of particles as they focus to their equilibria by delineating the effects of these three parameters, as well as the initial location of the particle inside the cross-section, on the focusing dynamics.