Canards in advection-reaction-diffusion systems in one spatial dimension

This thesis contains a mathematical investigation of the existence of travelling wave solutions to singularly perturbed advection-reaction-diffusion models of biological processes. An enhanced mathematical understanding of these solutions and models is gained via the identification of canards (special solutions of fast/slow dynamical systems) and their role in the existence of the most biologically relevant, shock-like solutions. The analysis focuses on two existing models. A new proof of existence of a whole family of travelling waves is provided for a model describing malignant tumour invasion, while new solutions are identified for a model describing wound healing angiogenesis.

In-plane graphene/boron-nitride heterostructure as efficient metal-free electrocatalyst for the oxygen reduction reaction

Exploiting metal-free catalysts for the oxygen reduction reaction (ORR) and understanding their catalytic mechanisms are vital for the development of fuel cells (FCs). Our study has demonstrated that in-plane heterostructures of graphene and boron nitride (G/BN) can serve as an efficient metal-free catalyst for the ORR, in which the C-N interfaces of G/BN heterostructures act as reactive sites. The formation of water at the heterointerface is both energetically and kinetically favorable via a fourelectron pathway. Moreover, the water formed can be easily released from the heterointerface, and the catalytically active sites can be regenerated for the next reaction. Since G/BN heterostructures with controlled domain sizes have been successfully synthesized in recent reports (e.g. Nat. Nanotechnol., 2013, 8, 119), our results highlight the great potential of such heterostructures as a promising metal-free catalyst for ORR in FCs.

The chain reaction

Synopsis and review of the Australian feature film The Chain Reaction, directed by Ian Barry.

A Crank--Nicolson ADI spectral method for a two-dimensional riesz space fractional nonlinear reaction-diffusion equation

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank--Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived method is stable and convergent of order $2$ in time. An optimal error estimate in space is also obtained by introducing a new orthogonal projector. The present method is extended to solve the fractional FitzHugh--Nagumo model. Numerical results are provided to verify the theoretical analysis.

Charge mediated semiconducting-to-metallic phase transition in molybdenum disulphide monolayer and hydrogen evolution reaction in New 1T’ phase

The phase transition of single layer molybdenum disulphide (MoS2) from semi-conducting 2H to metallic 1T and then to 1T' phases, and the effect of the phase transition on hydrogen evolution reaction (HER) are investigated within this work by density functional theory. Experimentally, 2H-MoS2 has been widely used as an excellent electrode for HER and can get charged easily. Here we find that the negative charge has a significant impact on the structural phase transition in a MoS2 monolayer. The thermodynamic stability of 1T-MoS2 increases with the negative charge state, comparing with the 2H-MoS2 structure before phase transition and the kinetic energy barrier for a phase transition from 2H to 1T decreases from 1.59 eV to 0.27 eV when 4 e- are injected per MoS2 unit. Additionally, 1T phase is found to transform into the distorted structure (1T' phase) spontaneously. On their activity toward hydrogen evolution reaction, 1T'-MoS2 structure hydrogen coverage shows comparable hydrogen evolution reaction activity to the 2H-MoS2 structure. If the charge transfer kinetics is taken into account, the catalytic activity of 1T'-MoS2 is superior to that of 2H-MoS2. Our finding provides a possible novel method for phase transition of MoS2, and enriches understanding of the catalytic properties of MoS2 for HER.

Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model

A two-dimensional variable-order fractional nonlinear reaction-diffusion model is considered. A second-order spatial accurate semi-implicit alternating direction method for a two-dimensional variable-order fractional nonlinear reaction-diffusion model is proposed. Stability and convergence of the semi-implicit alternating direct method are established. Finally, some numerical examples are given to support our theoretical analysis. These numerical techniques can be used to simulate a two-dimensional variable order fractional FitzHugh-Nagumo model in a rectangular domain. This type of model can be used to describe how electrical currents flow through the heart, controlling its contractions, and are used to ascertain the effects of certain drugs designed to treat arrhythmia.

Charge mediated semiconducting-to-metallic phase transition in molybdenum disulfide monolayer and hydrogen evolution reaction in new 1T′ phase

The phase transition of single layer molybdenum disulfide (MoS2) from semiconducting 2H to metallic 1T and then to 1T′ phases, and the effect of the phase transition on hydrogen evolution reaction (HER) are investigated within this work by density functional theory. Experimentally, 2H-MoS2 has been widely used as an excellent electrode for HER and can get charged easily. Here we find that the negative charge has a significant impact on the structural phase transition in a MoS2 monolayer. The thermodynamic stability of 1T-MoS2 increases with the negative charge state, comparing with the 2H-MoS2 structure before phase transition and the kinetic energy barrier for a phase transition from 2H to 1T decreases from 1.59 to 0.27 eV when 4e– are injected per MoS2 unit. Additionally, 1T phase is found to transform into the distorted structure (1T′ phase) spontaneously. On their activity toward hydrogen evolution reaction, 1T′-MoS2 structure shows comparable hydrogen evolution reaction activity to the 2H-MoS2 structure. If the charge transfer kinetics is taken into account, the catalytic activity of 1T′-MoS2 is superior to that of 2H-MoS2. Our finding provides a possible novel method for phase transition of MoS2 and enriches understanding of the catalytic properties of MoS2 for HER.

A preconditioned numerical solver for stiff nonlinear reaction-diffusion equations with fractional Laplacians that avoids dense matrices

The numerical solution of fractional partial differential equations poses significant computational challenges in regard to efficiency as a result of the spatial nonlocality of the fractional differential operators. The dense coefficient matrices that arise from spatial discretisation of these operators mean that even one-dimensional problems can be difficult to solve using standard methods on grids comprising thousands of nodes or more. In this work we address this issue of efficiency for one-dimensional, nonlinear space-fractional reaction–diffusion equations with fractional Laplacian operators. We apply variable-order, variable-stepsize backward differentiation formulas in a Jacobian-free Newton–Krylov framework to advance the solution in time. A key advantage of this approach is the elimination of any requirement to form the dense matrix representation of the fractional Laplacian operator. We show how a banded approximation to this matrix, which can be formed and factorised efficiently, can be used as part of an effective preconditioner that accelerates convergence of the Krylov subspace iterative solver. Our approach also captures the full contribution from the nonlinear reaction term in the preconditioner, which is crucial for problems that exhibit stiff reactions. Numerical examples are presented to illustrate the overall effectiveness of the solver.

On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process

Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration.

A polymerase chain reaction-based method for isolating clones from a complimentary DNA library in sheep

The sheep (Ovis aries) is favored by many musculoskeletal tissue engineering groups as a large animal model because of its docile temperament and ease of husbandry. The size and weight of sheep are comparable to humans, which allows for the use of implants and fixation devices used in human clinical practice. The construction of a complimentary DNA (cDNA) library can capture the expression of genes in both a tissue- and time-specific manner. cDNA libraries have been a consistent source of gene discovery ever since the technology became commonplace more than three decades ago. Here, we describe the construction of a cDNA library using cells derived from sheep bones based on the pBluescript cDNA kit. Thirty clones were picked at random and sequenced. This led to the identification of a novel gene, C12orf29, which our initial experiments indicate is involved in skeletal biology. We also describe a polymerase chain reaction-based cDNA clone isolation method that allows the isolation of genes of interest from a cDNA library pool. The techniques outlined here can be applied in-house by smaller tissue engineering groups to generate tools for biomolecular research for large preclinical animal studies and highlights the power of standard cDNA library protocols to uncover novel genes.

Fourier spectral methods for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains ofRn. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.

Double diffusive Marangoni convection flow of electrically conducting fluid in a square cavity with chemical reaction

Double diffusive Marangoni convection flow of viscous incompressible electrically conducting fluid in a square cavity is studied in this paper by taking into consideration of the effect of applied magnetic field in arbitrary direction and the chemical reaction. The governing equations are solved numerically by using alternate direct implicit (ADI) method together with the successive over relaxation (SOR) technique. The flow pattern with the effect of governing parameters, namely the buoyancy ratio W, diffusocapillary ratio w, and the Hartmann number Ha, is investigated. It is revealed from the numerical simulations that the average Nusselt number decreases; whereas the average Sherwood number increases as the orientation of magnetic field is shifted from horizontal to vertical. Moreover, the effect of buoyancy due to species concentration on the flow is stronger than the one due to thermal buoyancy. The increase in diffusocapillary parameter, w caus

Directional synthesis of tin oxide@graphene nanocomposites via a one-step up-scalable wet-mechanochemical route for lithium ion batteries

Directional synthesis of SnO2@graphene nanocomposites via a one-step, low-cost, and up-scalable wetmechanochemical method is achieved using graphene oxide and SnCl2 as precursors. The graphene oxides are reduced to graphene while the SnCl2 is oxidized to SnO2 nanoparticles that are in situ anchored onto the graphene sheets evenly and densely, resulting in uniform SnO2@graphene nanocomposites. The prepared nanocomposites possess excellent electrochemical performance and outstanding cycling in Li-ion batteries.

Unimolecular reaction chemistry of a charge-tagged beta-hydroxyperoxyl radical

β-Hydroxyperoxyl radicals are formed during atmospheric oxidation of unsaturated volatile organic compounds such as isoprene. They are intermediates in the combustion of alcohols. In these environments the unimolecular isomerization and decomposition of β-hydroxyperoxyl radicals may be of importance, either through chemical or thermal activation. We have used ion-trap mass spectrometry to generate the distonic charge-tagged β-hydroxyalkyl radical anion, ˙CH2C(OH)(CH3)CH2C(O)O−, and investigated its subsequent reaction with O2 in the gas phase under conditions that are devoid of complicating radical–radical reactions. Quantum chemical calculations and master equation/RRKM theory modeling are used to rationalize the results and discern a reaction mechanism. Reaction is found to proceed via initial hydrogen abstraction from the γ-methylene group and from the β-hydroxyl group, with both reaction channels eventually forming isobaric product ions due to loss of either ˙OH + HCHO or ˙OH + CO2. Isotope labeling studies confirm that a 1,5-hydrogen shift from the β-hydroxyl functionality results in a hydroperoxyalkoxyl radical intermediate that can undergo further unimolecular dissociations. Furthermore, this study confirms that the facile decomposition of β-hydroxyperoxyl radicals can yield ˙OH in the gas phase.

SnO2 decorated graphene nanocomposite anode materials prepared via an up-scalable wet-mechanochemical process for sodium ion batteries

A facile and up-scalable wet-mechanochemical process is designed for fabricating ultra-fine SnO2 nanoparticles anchored on graphene networks for use as anode materials for sodium ion batteries. A hierarchical structure of the SnO2@graphene composite is obtained from the process. The resultant rechargeable SIBs achieved high rate capability and good cycling stability.