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OPTIMAL LOCATION OF AN UNDERGROUND CONNECTOR USING DISCOUNTED STEINER TREE THEORY ANZIAM J. (IF 0.581) Pub Date : 2021-01-18 K. G. SIRINANDA; M. BRAZIL; P. A. GROSSMAN; J. H. RUBINSTEIN; D. A. THOMAS
The objective of this paper is to demonstrate that the gradient-constrained discounted Steiner point algorithm (GCDSPA) described in an earlier paper by the authors is applicable to a class of real mine planning problems, by using the algorithm to design a part of the underground access in the Rubicon gold mine near Kalgoorlie in Western Australia. The algorithm is used to design a decline connecting
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CONFORMAL IMAGE REGISTRATION BASED ON CONSTRAINED OPTIMIZATION ANZIAM J. (IF 0.581) Pub Date : 2021-01-12 S. MARSLAND; R. I. MCLACHLAN; M. Y. TUFAIL
Image registration is the process of finding an alignment between two or more images so that their appearances match. It has been widely studied and applied to several fields, including medical imaging and biology, where it is related to morphometrics. In this paper, we present a construction of conformal diffeomorphisms which is based on constrained optimization. We consider a set of different penalty
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LINEARLY IMPLICIT ENERGY-PRESERVING FOURIER PSEUDOSPECTRAL SCHEMES FOR THE COMPLEX MODIFIED KORTEWEG–DE VRIES EQUATION ANZIAM J. (IF 0.581) Pub Date : 2021-01-12 J. L. YAN; L. H. ZHENG; L. ZHU; F. Q. LU
We propose two linearly implicit energy-preserving schemes for the complex modified Korteweg–de Vries equation, based on the invariant energy quadratization method. First, a new variable is introduced and a new Hamiltonian system is constructed for this equation. Then the Fourier pseudospectral method is used for the space discretization and the Crank–Nicolson leap-frog schemes for the time discretization
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POINTWISE RESIDUAL METHOD FOR SOLVING PRIMAL AND DUAL ILL-POSED LINEAR PROGRAMMING PROBLEMS WITH APPROXIMATE DATA ANZIAM J. (IF 0.581) Pub Date : 2021-01-12 A. Y. IVANITSKIY; V. V. EJOV; F. P. VASILYEV
We propose a variation of the pointwise residual method for solving primal and dual ill-posed linear programming with approximate data, sensitive to small perturbations. The method leads to an auxiliary problem, which is also a linear programming problem. Theorems of existence and convergence of approximate solutions are established and optimal estimates of approximation of initial problem solutions
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AN OPTIMAL LINEAR FILTER FOR ESTIMATION OF RANDOM FUNCTIONS IN HILBERT SPACE ANZIAM J. (IF 0.581) Pub Date : 2021-01-07 PHIL HOWLETT; ANATOLI TOROKHTI
Let $\boldsymbol{f}$ be a square-integrable, zero-mean, random vector with observable realizations in a Hilbert space H, and let $\boldsymbol{g}$ be an associated square-integrable, zero-mean, random vector with realizations which are not observable in a Hilbert space K. We seek an optimal filter in the form of a closed linear operator X acting on the observable realizations of a proximate vector
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DRAPING WOVEN SHEETS ANZIAM J. (IF 0.581) Pub Date : 2021-01-07 P. D. HOWELL; H. OCKENDON; J. R. OCKENDON
Motivated by the manufacture of carbon fibre components, this paper considers the smooth draping of loosely woven fabric over rigid obstacles, both smooth and nonsmooth. The draped fabric is modelled as the continuum limit of a Chebyshev net of two families of short rigid rods that are freely pivoted at their joints. This approach results in a system of nonlinear hyperbolic partial differential equations
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IMPLEMENTATION OF HIGH-ORDER, DISCONTINUOUS GALERKIN TIME STEPPING FOR FRACTIONAL DIFFUSION PROBLEMS ANZIAM J. (IF 0.581) Pub Date : 2020-11-06 WILLIAM MCLEAN
The discontinuous Galerkin (DG) method provides a robust and flexible technique for the time integration of fractional diffusion problems. However, a practical implementation uses coefficients defined by integrals that are not easily evaluated. We describe specialized quadrature techniques that efficiently maintain the overall accuracy of the DG method. In addition, we observe in numerical experiments
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EVOLUTIONARY DYNAMICS IN DISCRETE TIME FOR THE PERTURBED POSITIVE DEFINITE REPLICATOR EQUATION ANZIAM J. (IF 0.581) Pub Date : 2020-12-09 AMIE ALBRECHT; KONSTANTIN AVRACHENKOV; PHIL HOWLETT; GEETIKA VERMA
The population dynamics for the replicator equation has been well studied in continuous time, but there is less work that explicitly considers the evolution in discrete time. The discrete-time dynamics can often be justified indirectly by establishing the relevant evolutionary dynamics for the corresponding continuous-time system, and then appealing to an appropriate approximation property. In this
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ASYMPTOTIC BEHAVIOUR OF THE STOCHASTIC MAKI–THOMPSON MODEL WITH A FORGETTING MECHANISM ON OPEN POPULATIONS ANZIAM J. (IF 0.581) Pub Date : 2020-11-06 HAIJIAO LI; KUAN YANG
Rumours have become part of our daily lives, and their spread has a negative impact on a variety of human affairs. Therefore, how to control the spread of rumours is an important topic. In this paper, we extend the classic Maki–Thompson model from a deterministic framework to a stochastic framework with a forgetting mechanism, because real-world person-to-person communications are inevitably affected
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MEAN–VARIANCE EQUILIBRIUM ASSET-LIABILITY MANAGEMENT STRATEGY WITH COINTEGRATED ASSETS ANZIAM J. (IF 0.581) Pub Date : 2020-11-06 MEI CHOI CHIU
This paper investigates asset-liability management problems in a continuous-time economy. When the financial market consists of cointegrated risky assets, institutional investors attempt to make profit from the cointegration feature on the one hand, while on the other hand they need to maintain a stable surplus level, that is, the company’s wealth less its liability. Challenges occur when the liability
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MODELLING HUMAN CARRYING CAPACITY AS A FUNCTION OF FOOD AVAILABILITY ANZIAM J. (IF 0.581) Pub Date : 2020-12-18 DINY ZULKARNAEN; MARIANITO R. RODRIGO
We assume that human carrying capacity is determined by food availability. We propose three classes of human population dynamical models of logistic type, where the carrying capacity is a function of the food production index. We also employ an integration-based parameter estimation technique to derive explicit formulas for the model parameters. Using actual population and food production index data
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CRITICAL LENGTH FOR THE SPREADING–VANISHING DICHOTOMY IN HIGHER DIMENSIONS ANZIAM J. (IF 0.581) Pub Date : 2020-06-19 MATTHEW J. SIMPSON
We consider an extension of the classical Fisher–Kolmogorov equation, called the “Fisher–Stefan” model, which is a moving boundary problem on $0L_{\text{c}}$ will eventually spread as $t\rightarrow \infty$ , whereas solutions where $L(t)\ngtr L_{\text{c}}$ will vanish as $t\rightarrow \infty$ . In one dimension it is well known that the critical length is $L_{\text{c}}=\unicode[STIX]{x1D70B}/2$ . In
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STREAMLINED SOLUTIONS TO MULTILEVEL SPARSE MATRIX PROBLEMS ANZIAM J. (IF 0.581) Pub Date : 2020-06-01 TUI H. NOLAN; MATT P. WAND
We define and solve classes of sparse matrix problems that arise in multilevel modelling and data analysis. The classes are indexed by the number of nested units, with two-level problems corresponding to the common situation, in which data on level-1 units are grouped within a two-level structure. We provide full solutions for two-level and three-level problems, and their derivations provide blueprints
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GAME MODEL FOR ONLINE AND OFFLINE RETAILERS UNDER BUY-ONLINE AND PICK-UP-IN-STORE MODE WITH DELIVERY COST AND RANDOM DEMAND ANZIAM J. (IF 0.581) Pub Date : 2020-07-03 YING OUYANG; ZHAOMAN WAN; ZHONG WAN
Online retailers are increasingly adding buy-online and pick-up-in-store (BOPS) modes to order fulfilment. In this paper, we study a system of BOPS by developing a stochastic Nash equilibrium model with incentive compatibility constraints, where the online retailer seeks optimal online sale prices and an optimal delivery schedule in an order cycle, and the offline retailer pursues a maximal rate of
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STRATEGIC CUSTOMERS IN MARKOVIAN QUEUES WITH VACATIONS AND SYNCHRONIZED ABANDONMENT ANZIAM J. (IF 0.581) Pub Date : 2020-07-03 GOPINATH PANDA; VEENA GOSWAMI
We study impatient customers’ joining strategies in a single-server Markovian queue with synchronized abandonment and multiple vacations. Customers receive the system information upon arrival, and decide whether to join or balk, based on a linear reward-cost structure under the acquired information. Waiting customers are served in a first-come-first-serve discipline, and no service is rendered during
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THE MAGNETIC FIELD ABOUT A THREE-DIMENSIONAL BLOCK NEODYMIUM MAGNET ANZIAM J. (IF 0.581) Pub Date : 2020-06-22 GRAHAM WEIR; GEORGE CHISHOLM; JEROME LEVENEUR
Neodymium magnets were independently discovered in 1984 by General Motors and Sumitomo. Today, they are the strongest type of permanent magnets commercially available. They are the most widely used industrial magnets with many applications, including in hard disk drives, cordless tools and magnetic fasteners. We use a vector potential approach, rather than the more usual magnetic potential approach
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THE PARADOX OF ENRICHMENT, SPATIAL HETEROGENEITY, COMMUNITY EFFECTS AND THE PHENOMENON OF APPARENT DISAPPEARANCE IN THE MARINE BACTERIOPHAGE DYNAMICS ANZIAM J. (IF 0.581) Pub Date : 2020-06-22 ANDREI KOROBEINIKOV; ELENA SHCHEPAKINA; VLADIMIR SOBOLEV
In aquatic microbial systems, high-magnitude variations in abundance, such as sudden blooms alternating with comparatively long periods of very low abundance (“apparent disappearance”), are relatively common. We suggest that in order for this to occur, such variations in abundance in microbial systems and, in particular, the apparent disappearance of species do not require seasonal or periodic forcing
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A MODIFIED IMMERSED FINITE VOLUME ELEMENT METHOD FOR ELLIPTIC INTERFACE PROBLEMS ANZIAM J. (IF 0.581) Pub Date : 2020-05-13 Q. WANG; Z. ZHANG
This paper presents a new immersed finite volume element method for solving second-order elliptic problems with discontinuous diffusion coefficient on a Cartesian mesh. The new method possesses the local conservation property of classic finite volume element method, and it can overcome the oscillating behaviour of the classic immersed finite volume element method. The idea of this method is to reconstruct
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THE ALTERNATIVE KIRCHHOFF APPROXIMATION IN ELASTODYNAMICS WITH APPLICATIONS IN ULTRASONIC NONDESTRUCTIVE TESTING ANZIAM J. (IF 0.581) Pub Date : 2020-04-23 L. J. FRADKIN; A. K. DJAKOU; C. PRIOR; M. DARMON; S. CHATILLON; P.-F. CALMON
The Kirchhoff approximation is widely used to describe the scatter of elastodynamic waves. It simulates the scattered field as the convolution of the free-space Green’s tensor with the geometrical elastodynamics approximation to the total field on the scatterer surface and, therefore, cannot be used to describe nongeometrical phenomena, such as head waves. The aim of this paper is to demonstrate that
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ONE-DIMENSIONAL CHAOTIC LAMINAR FLOW WITH COMPETITIVE EXOTHERMIC AND ENDOTHERMIC REACTIONS ANZIAM J. (IF 0.581) Pub Date : 2020-04-15 S. D. WATT; Z. HUANG; H. S. SIDHU; A. C. MCINTOSH; J. BRINDLEY
We consider the numerical solution of competitive exothermic and endothermic reactions in the presence of a chaotic advection flow. The resulting behaviour is characterized by a strong dependence on the competitive reaction history. The burnt temperature is not immediately connected to simple enthalpy calculations, so there is a subtlety in the interplay between the major parameters, notably the Damköhler
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THE VALUE OF COMMUNICATION AND COOPERATION WHEN SERVERS ARE STRATEGIC ANZIAM J. (IF 0.581) Pub Date : 2020-04-06 M. FACKRELL; C. LI; P. G. TAYLOR; J. WANG
In 2015, Guglielmi and Badia discussed optimal strategies in a particular type of service system with two strategic servers. In their setup, each server can be either active or inactive and an active server can be requested to transmit a sequence of packets. The servers have varying probabilities of successfully transmitting when they are active, and both servers receive a unit reward if the sequence
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APPROXIMATION OF AND BY COMPLETELY MONOTONE FUNCTIONS ANZIAM J. (IF 0.581) Pub Date : 2020-03-06 R. J. LOY; R. S. ANDERSSEN
We investigate convergence in the cone of completely monotone functions. Particular attention is paid to the approximation of and by exponentials and stretched exponentials. The need for such an analysis is a consequence of the fact that although stretched exponentials can be approximated by sums of exponentials, exponentials cannot in general be approximated by sums of stretched exponentials.
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A SEMI-ANALYTICAL PRICING FORMULA FOR EUROPEAN OPTIONS UNDER THE ROUGH HESTON-CIR MODEL ANZIAM J. (IF 0.581) Pub Date : 2020-03-06 XIN-JIANG HE; SHA LIN
We combine the rough Heston model and the CIR (Cox–Ingersoll–Ross) interest rate together to form a rough Heston-CIR model, so that both the rough behaviour of the volatility and the stochastic nature of the interest rate can be captured. Despite the convoluted structure and non-Markovian property of this model, it still admits a semi-analytical pricing formula for European options, the implementation
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ASYMPTOTICS OF A GAUSS HYPERGEOMETRIC FUNCTION WITH TWO LARGE PARAMETERS: A NEW CASE ANZIAM J. (IF 0.581) Pub Date : 2019-12-10 J. F. HARPER
Asymptotic expansions of the Gauss hypergeometric function with large parameters, $F(\unicode[STIX]{x1D6FC}+\unicode[STIX]{x1D716}_{1}\unicode[STIX]{x1D70F},\unicode[STIX]{x1D6FD}+\unicode[STIX]{x1D716}_{2}\unicode[STIX]{x1D70F};\unicode[STIX]{x1D6FE}+\unicode[STIX]{x1D716}_{3}\unicode[STIX]{x1D70F};z)$ as $|\unicode[STIX]{x1D70F}|\rightarrow \infty$ , are known for many special cases, but not for
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NUMERICAL ENTROPY PRODUCTION AS SMOOTHNESS INDICATOR FOR SHALLOW WATER EQUATIONS ANZIAM J. (IF 0.581) Pub Date : 2019-11-28 SUDI MUNGKASI; STEPHEN GWYN ROBERTS
The numerical entropy production (NEP) for shallow water equations (SWE) is discussed and implemented as a smoothness indicator. We consider SWE in three different dimensions, namely, one-dimensional, one-and-a-half-dimensional, and two-dimensional SWE. An existing numerical entropy scheme is reviewed and an alternative scheme is provided. We prove the properties of these two numerical entropy schemes
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PRICING HOLDER-EXTENDABLE CALL OPTIONS WITH MEAN-REVERTING STOCHASTIC VOLATILITY ANZIAM J. (IF 0.581) Pub Date : 2019-10-14 S. N. I. IBRAHIM; A. DÍAZ-HERNÁNDEZ; J. G. O’HARA; N. CONSTANTINOU
Options with extendable features have many applications in finance and these provide the motivation for this study. The pricing of extendable options when the underlying asset follows a geometric Brownian motion with constant volatility has appeared in the literature. In this paper, we consider holder-extendable call options when the underlying asset follows a mean-reverting stochastic volatility.
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A MULTIPHASE MULTISCALE MODEL FOR NUTRIENT-LIMITED TISSUE GROWTH, PART II: A SIMPLIFIED DESCRIPTION ANZIAM J. (IF 0.581) Pub Date : 2019-09-18 E. C. HOLDEN; S. J. CHAPMAN; B. S. BROOK; R. D. O’DEA
In this paper, we revisit our previous work in which we derive an effective macroscale description suitable to describe the growth of biological tissue within a porous tissue-engineering scaffold. The underlying tissue dynamics is described as a multiphase mixture, thereby naturally accommodating features such as interstitial growth and active cell motion. Via a linearization of the underlying multiphase
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