ORCID Profile
0000-0001-7302-0369
Current Organisation
University of South Australia
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In Research Link Australia (RLA), "Research Topics" refer to ANZSRC FOR and SEO codes. These topics are either sourced from ANZSRC FOR and SEO codes listed in researchers' related grants or generated by a large language model (LLM) based on their publications.
Optimisation | Applied Mathematics | Operations Research | Calculus of Variations, Systems Theory and Control Theory | Applied Statistics | Numerical and Computational Mathematics | Stochastic Analysis and Modelling | Numerical Computation | Applied Mathematics not elsewhere classified
Energy Conservation and Efficiency in Transport | Expanding Knowledge in the Mathematical Sciences | Energy Systems Analysis |
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 22-03-2018
Publisher: Elsevier BV
Date: 09-2023
Publisher: Cambridge University Press (CUP)
Date: 04-2020
DOI: 10.1017/S1446181120000140
Abstract: 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 paper we study the discrete-time system directly, and establish basic stability results for the evolution of a population defined by a positive definite system matrix, where the population is disrupted by random perturbations to the genotype distribution either through migration or mutation, in each successive generation.
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 13-01-2021
DOI: 10.21914/ANZIAMJ.V62.14843
Abstract: 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 paper we study the discrete-time system directly, and establish basic stability results for the evolution of a population defined by a positive definite system matrix, where the population is disrupted by random perturbations to the genotype distribution either through migration or mutation, in each successive generation. doi: 10.1017/S1446181120000140
Publisher: Elsevier BV
Date: 08-2019
Publisher: Elsevier BV
Date: 05-2018
Publisher: Elsevier BV
Date: 06-2020
Publisher: IEEE
Date: 07-2015
Publisher: Informa UK Limited
Date: 06-2012
Publisher: Informa UK Limited
Date: 12-04-2018
Publisher: Elsevier BV
Date: 10-2013
Publisher: IEEE
Date: 10-2014
Publisher: Informa UK Limited
Date: 02-2013
DOI: 10.1057/JORS.2012.42
Publisher: Cambridge University Press (CUP)
Date: 21-12-2018
DOI: 10.1017/S1446788718000411
Abstract: We consider a linear operator pencil with complex parameter mapping one Hilbert space onto another. It is known that the resolvent is analytic in an open annular region of the complex plane centred at the origin if and only if the coefficients of the Laurent series satisfy a doubly-infinite set of left and right fundamental equations and are suitably bounded. If the resolvent has an isolated singularity at the origin we propose a recursive orthogonal decomposition of the domain and range spaces that enables us to construct the key nonorthogonal projections that separate the singular and regular components of the resolvent and subsequently allows us to find a formula for the basic solution to the fundamental equations. We show that each Laurent series coefficient in the singular part of the resolvent can be approximated by a weakly convergent sequence of finite-dimensional matrix operators and we show how our analysis can be extended to find a global expression for the resolvent of a linear pencil in the case where the resolvent has only a finite number of isolated singularities.
Publisher: Elsevier BV
Date: 06-2010
Publisher: Elsevier BV
Date: 11-2015
Publisher: Elsevier BV
Date: 06-2020
Publisher: Poincare Publishers
Date: 30-12-2018
Publisher: Elsevier BV
Date: 12-2016
Publisher: Institute for Operations Research and the Management Sciences (INFORMS)
Date: 03-2023
Abstract: We propose an analytic solution to the problem of finding optimal driving strategies that minimize total tractive energy consumption for a fleet of trains traveling on the same track in the same direction subject to clearance-time equality constraints that ensure safe separation and compress the headway timespan. We assume the track is ided into sections by a set of trackside signals at fixed positions. For each intermediate signal there is an associated signal segment consisting of the two adjacent sections. Successive trains are safely separated only if the leading train leaves the signal segment before the following train enters. Although the fleet can be safely separated by a complete set of clearance times and associated clearance-time inequality constraints the problem of finding optimal schedules with safe separation rapidly becomes intractable as the number of trains and signals increases. The main difficulty is in distinguishing between active equality constraints and inactive inequality constraints. The curse of dimensionality means it is not feasible to check every different combination of active constraints, find the optimal strategies for each train, optimize the corresponding prescribed times and calculate the cost. Nevertheless we can formulate and solve an alternative problem with active clearance-time equality constraints for successive trains defined at selected signals. We show that this problem can be formulated as an unconstrained convex optimization and propose a solution algorithm that finds the optimal schedule and the associated optimal strategies for each train. Finally we find optimal schedules for a case study using realistic parameters on a busy metropolitan line.
Publisher: Elsevier BV
Date: 05-2014
Publisher: Informa UK Limited
Date: 03-2010
Publisher: Elsevier BV
Date: 12-2016
Publisher: Informa UK Limited
Date: 27-08-2015
Publisher: Elsevier BV
Date: 11-2011
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 27-08-2016
Publisher: Elsevier BV
Date: 03-2013
Publisher: SAGE Publications
Date: 09-2013
Abstract: In Australia, and elsewhere, the movement of trains on long-haul rail networks is usually planned in advance. Typically, a train plan is developed to confirm that the required train movements and track maintenance activities can occur. The plan specifies when track segments will be occupied by particular trains and maintenance activities. On the day of operation, a train controller monitors and controls the movement of trains and maintenance crews, and updates the train plan in response to unplanned disruptions. It can be difficult to predict how good a plan will be in practice. The main performance indicator for a train service should be reliability – the proportion of trains running the service that complete at or before the scheduled time. We define the robustness of a planned train service to be the expected reliability. The robustness of in idual train services and for a train plan as a whole can be estimated by simulating the train plan many times with random, but realistic, perturbations to train departure times and segment durations, and then analysing the distributions of arrival times. This process can also be used to set arrival times that will achieve a desired level of robustness for each train service.
Publisher: Cambridge University Press (CUP)
Date: 07-2016
DOI: 10.1017/S1446181116000092
Abstract: In this paper, we show that the cost of an optimal train journey on level track over a fixed distance is a strictly decreasing and strictly convex function of journey time. The precise structure of the cost–time curves for in idual trains is an important consideration in the design of energy-efficient timetables on complex rail networks. The development of optimal timetables for busy metropolitan lines can be considered as a two-stage process. The first stage seeks to find optimal transit times for each in idual journey segment subject to the usual trip-time, dwell-time, headway and connection constraints in such a way that the total energy consumption over all proposed journeys is minimized. The second stage adjusts the arrival and departure times for each journey while preserving the in idual segment times and the overall journey times, in order to best synchronize the collective movement of trains through the network and thereby maximize recovery of energy from regenerative braking. The precise nature of the cost–time curve is a critical component in the first stage of the optimization.
Publisher: Elsevier BV
Date: 06-2018
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 2022
Start Date: 04-2016
End Date: 08-2019
Amount: $388,294.00
Funder: Australian Research Council
View Funded ActivityStart Date: 12-2015
End Date: 12-2018
Amount: $430,000.00
Funder: Australian Research Council
View Funded ActivityStart Date: 11-2011
End Date: 06-2016
Amount: $540,000.00
Funder: Australian Research Council
View Funded ActivityStart Date: 07-2021
End Date: 06-2024
Amount: $285,638.00
Funder: Australian Research Council
View Funded Activity