ANZIAM Journal最新文献

{"title":"Asymmetrical suction and injection in laminar channels with porous walls: a fixed point approach","authors":"David Bee Olmedo","doi":"10.21914/anziamj.v64.17975","DOIUrl":"https://doi.org/10.21914/anziamj.v64.17975","url":null,"abstract":"\u0000\u0000\u0000The problem of laminar flow in a rectangular channel with a pair of porous walls is considered. The porous walls allow fluid to be injected into or sucked out of the channel at constant velocities normal to the walls; the velocities at each wall are not necessarily of equal magnitude nor symmetrical in direction. In this article, a unique solution to this problem is shown to exist for sufficiently low Reynolds numbers through the application of Banach's fixed point theorem. This serves to further the discussion about the uniqueness of solutions for this problem, whilst also demonstrating the suitability of a fixed point approach to this family of fluid dynamics problems.\u0000References\u0000\u0000S. S. Almuthaybiri and C. C. Tisdell. Laminar flow in channels with porous walls: Advancing the existence, uniqueness and approximation of solutions via fixed point approaches. J. Fixed Point Theory Appl. 24.3, 55 (2022). doi: 10.1007/s11784-022-00971-8\u0000A. S. Berman. Laminar flow in channels with porous walls. J. Appl. Phys. 24.9 (1953), pp. 1232–1235. doi: 10.1063/1.1721476\u0000H. Guo, C. Gui, P. Lin, and M. Zhao. Multiple solutions and their asymptotics for laminar flows through a porous channel with different permeabilities. IMA J. Appl. Math. 85.2 (2020), pp. 280–308. doi: 10.1093/imamat/hxaa006\u0000A. J. Jerri. Introduction to Integral Equations with Applications. New York: Dekker Inc., 1985, p. 254\u0000R. M. Terrill and G. M. Shrestha. Laminar flow through parallel and uniformly porous walls of different permeability. Z. Angew. Math. Phys. 16.4 (1965), pp. 470–482. doi: 10.1007/BF01593923\u0000F. M. White, B. F. Barfield, and M. J. Goglia. Laminar flow in a uniformly porous channel. J. Appl. Mech. 25.4 (1958), pp. 613–617. doi: 10.1115/1.4011881\u0000\u0000\u0000\u0000","PeriodicalId":50745,"journal":{"name":"ANZIAM Journal","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141806228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical analysis of the axisymmetric lattice Boltzmann method for steady and oscillatory flows in periodic geometries","authors":"Samuel Stephen, Barbara Johnston, Peter Johnston","doi":"10.21914/anziamj.v64.17949","DOIUrl":"https://doi.org/10.21914/anziamj.v64.17949","url":null,"abstract":"Compared to more typical computational fluid dynamics techniques, the lattice Boltzmann method (LBM) is relatively new and unexplored. In recent years, axisymmetric LBM formulations, which can simulate flow in rotationally symmetric 3D geometries, have been published. Here we verify a novel axisymmetric LBM implementation using numerical criteria. Hagen–Poiseuille and Womersley flow are considered within a straight tube where analytic solutions are available. With this, we establish sufficient accuracy of the approximated flow and study the effects of changing simulation parameters (e.g. Reynolds number, Womersley number) and spatial/temporal parameters (e.g. relaxation time, mesh nodes, time steps). Furthermore, steady and oscillatory flows within a periodically-varying, longitudinally asymmetric geometry are considered. Analytic solutions are not available in these cases; however, the validity of the axisymmetric LBM for curved boundaries is ensured through convergence, mesh independence and qualitative observations. Guaranteeing reasonable flow field determination for the aformentioned geometry is relevant to a larger problem where particulate suspension is pumped back and forth through a membrane of axisymmetric micropores. In these circumstances, experiments have induced directed particle transport even though there is no net flow of the carrier fluid. Hence, our work aims to improve current numerical simulations of these flow problems to better understand the factors that facilitate particle transport.\u0000References\u0000\u0000R. D. Astumian and P. Hänggi. Brownian motors. Phys. Today 55.11 (2002), pp. 33–39. doi: 10.1063/1.1535005. (Cit. on p. C214).\u0000W. R. Bowen and F. Jenner. Theoretical descriptions of membrane filtration of colloids and fine particles: An assessment and review. Adv. Colloid Interface Sci. 56 (1995), pp. 141–200. doi: 10.1016/0001-8686(94)00232-2\u0000N. Islam. Fluid flow and particle transport through periodic capillaries. Bull. Aust. Math. Soc. 96.3 (2017), pp. 521–522. doi: 10.1017/S0004972717000739\u0000C. Kettner, P. Reimann, P. Hänggi, and F. Müller. Drift ratchet. Phys. Rev. E 61.1 (2000), pp. 312–323. doi: 10.1103/PhysRevE.61.312 S. H. Kim and H. Pitsch. A generalized periodic boundary condition for lattice Boltzmann method simulation of a pressure driven flow in a periodic geometry. Phys. Fluids 19.10, 108101 (2007). doi: 10.1063/1.2780194\u0000T. Krüger, H. Kusumaatmaja, A. Kuzmin, O. Shardt, G. Silva, and E. M. Viggen. The lattice Boltzmann method: Principles and practice. Vol. 10. Graduate Texts in Physics. Springer, 2017, pp. 978–3. doi: 10.1007/978-3-319-44649-3\u0000S. Matthias and F. Müller. Asymmetric pores in a silicon membrane acting as massively parallel brownian ratchets. Nature 424 (2003), pp. 53–57. doi: 10.1038/nature01736\u0000S. J. Stephen, B. M. Johnston, and P. R. Johnston. Comparing lattice Boltzmann simulations of periodic fluid flow in repeated micropore structures with longitudinal symmetry and asymmetry. Proceedings of the 15","PeriodicalId":50745,"journal":{"name":"ANZIAM Journal","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141660689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Minimum volume covering ellipsoids","authors":"Elizabeth Harris","doi":"10.21914/anziamj.v64.17956","DOIUrl":"https://doi.org/10.21914/anziamj.v64.17956","url":null,"abstract":"We present a new initialisation of an adaptive batch strategy to compute the ε-approximate minimum volume covering ellipsoid (MVCE) for a set of n points. We focus on moderately sized datasets (up to dimension d = 100 and n = 1 000 000). The adaptive batch strategy works in an optimisation-deletion-adaptation cycle: we solve the MVCE problem using a smaller number of points, we delete points from consideration that are guaranteed to not lie on the boundary of the MVCE, and then carefully select a new batch of points. We propose a new initialisation, which involves selecting the points corresponding to some highest leverage scores. We show using numerical examples that this new initialisation tends to improve computation time as well as reduce the total number of cycles, as compared with initialising with a random selection of points.\u0000References\u0000\u0000C. L. Atwood. Sequences converging to D-optimal designs of experiments. Ann. Statist. 1.2 (1973), pp. 342–352. doi: 10.1214/aos/1176342371\u0000Y.-J. Chen, M.-Y. Ju, and K.-S. Hwang. A virtual torque-based approach to kinematic control of redundant manipulators. IEEE Trans. Indust. Elec. 64.2 (2017), pp. 1728–1736. doi: 10.1109/TIE.2016.2548439\u0000F. L. Chernousko. Ellipsoidal state estimation for dynamical systems. Nonlin. Anal. 63.5-7 (2005), pp. 872–879. doi: 10.1016/j.na.2005.01.009\u0000D. Eberly. 3D game engine design: A practical approach to real-time computer graphics. CRC Press, 2007. doi: 10.1201/b18212\u0000M. Frank and P. Wolfe. An algorithm for quadratic programming. Naval Res. Log. Quart. 3.1-2 (1956), pp. 95–110. doi: 10.1002/nav.3800030109\u0000R. Harman, L. Filová, and P. Richtárik. A randomized exchange algorithm for computing optimal approximate designs of experiments. J. Am. Stat. Ass. 115.529 (2020), pp. 348–361. doi: 10.1080/01621459.2018.1546588\u0000R. Harman and L. Pronzato. Improvements on removing nonoptimal support points in D-optimum design algorithms. Stat. Prob. Lett. 77.1 (2007), pp. 90–94. doi: 10.1016/j.spl.2006.05.014\u0000F. John. Extremum problems with inequalities as subsidiary conditions. Traces and emergence of nonlinear programming. Springer Basel, 2014, pp. 197–215. doi: 10.1007/978-3-0348-0439-4_9\u0000L. Källberg and D. Andrén. Active set strategies for the computation of minimum-volume enclosing ellipsoids. Tech. rep. Mälardalen University, 2019. url: http://www.es.mdu.se/publications/5680-\u0000L. G. Khachiyan. Rounding of polytopes in the real number model of computation. Math. Op. Res. 21.2 (1996), pp. 307–320. doi: 10.1287/moor.21.2.307\u0000J. Kudela. Minimum-volume covering ellipsoids: Improving the efficiency of the Wolfe–Atwood algorithm for large-scale instances by pooling and batching. MENDEL 25.2 (2019), pp. 19–26. doi: 10.13164/mendel.2019.2.019\u0000P. Kumar and E. A. Yildirim. Minimum-volume enclosing ellipsoids and core sets. J. Op. Theor. Appl. 126.1 (2005), pp. 1–21. doi: 10.1007/s10957-005-2653-6\u0000S. Rosa and R. Harman. Computing minimum-volume enclosing ellipsoids for large datasets. Comput. Sta","PeriodicalId":50745,"journal":{"name":"ANZIAM Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141013734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A reduced concurrent memory access method to accelerate the computation of the lineal path function on large microstructures","authors":"Edward Bissaker, B. Lamichhane, David Jenkins","doi":"10.21914/anziamj.v64.17973","DOIUrl":"https://doi.org/10.21914/anziamj.v64.17973","url":null,"abstract":"The Concurrent Reduced Memory Access method (CRMA) is a scalable memory-efficient Monte Carlo method for computing the lineal path function. It addresses an inherent memory bottleneck of lineal path function algorithms by utilising known properties of the two-point correlation function to reduce the number of voxels where the phase value must be evaluated. The CRMA method reduces the computation time and improves the scalability characteristics of the traditional lineal path function Monte Carlo methods. CRMA also provides additional information useful for analysing microstructures since the two-point correlation function is computed as part of the method. The CRMA method offers an efficient, scalable and extendable solution for computing the lineal path function.\u0000References\u0000\u0000A. A. Agra, A. Nicolodi, B. D. Flores, I. V. Flores, G. L. R. da Silva, A. C. F. Vilela, and E. Osório. Automated procedure for coke microstructural characterization in imagej software aiming industrial application. Fuel 304, 121374 (2021). doi: 10.1016/j.fuel.2021.121374\u0000J. Baruchel, P. Bleuet, A. Bravin, P. Coan, E. Lima, A. Madsen, W. Ludwig, P. Pernot, and J. Susini. Advances in synchrotron hard X-ray based imaging. Comptes Rendus Physique 9.5-6 (2008), pp. 624–641. doi: 10.1016/j.crhy.2007.08.003\u0000J. E. Bresenham. Algorithm for computer control of a digital plotter. IBM Sys. J. 4.1 (1965), pp. 25–30. doi: 10.1147/sj.41.0025\u0000D. T. Fullwood, S. R. Kalidindi, S. R. Niezgoda, A. Fast, and N. Hampson. Gradient-based microstructure reconstructions from distributions using fast Fourier transforms. Mat. Sci. Eng.: A 494.1-2 (2008), pp. 68–72. doi: 10.1016/j.msea.2007.10.087\u0000J. Gajdošík, J. Zeman, and M. Šejnoha. Qualitative analysis of fiber composite microstructure: Influence of boundary conditions. Prob. Eng. Mech. 21.4 (2006), pp. 317–329. doi: 10.1016/j.probengmech.2005.11.006\u0000E. Y. Guo, N. Chawla, T. Jing, S. Torquato, and Y. Jiao. Accurate modeling and reconstruction of three-dimensional percolating filamentary microstructures from two-dimensional micrographs via dilation-erosion method. Mat. Character. 89 (2014), pp. 33–42. doi: 10.1016/j.matchar.2013.12.011\u0000J. Havelka, A. Kučerová, and J. Sýkora. Compression and reconstruction of random microstructures using accelerated lineal path function. Comput. Mat. Sci. 122 (2016), pp. 102–117. doi: 10.1016/j.commatsci.2016.04.044\u0000J. H. Kinney and M. C. Nichols. X-ray tomographic microscopy (XTM) using synchrotron radiation. Ann. Rev. Mat. Sci. 22.1 (1992), pp. 121–152. doi: 10.1146/annurev.ms.22.080192.001005\u0000D. Kirk and W.-m. W. Hwu. Programming massively parallel processors: A hands-on approach. Morgan Kaufmann, 2016. url: https://shop.elsevier.com/books/programming-massively-parallel-processors/kirk/978-0-12-811986-0\u0000J. Kováčik. Correlation between Young’s modulus and porosity in porous materials. J. Matt. Sci. Lett. 18.13 (1999), pp. 1007–1010. doi: 10.1023/A:1006669914946\u0000J. Kukunas. Power and performance: Software analysis a","PeriodicalId":50745,"journal":{"name":"ANZIAM Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141013963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Evaluation of component interface quality in 3D micro-CT images of metallurgical coke","authors":"David Jenkins, Ai Wang","doi":"10.21914/anziamj.v64.17972","DOIUrl":"https://doi.org/10.21914/anziamj.v64.17972","url":null,"abstract":"Metallurgical coke is a crucial component in the production of steel worldwide. It is a porous composite material, created by conversion of metallurgical coal in a coke oven. A key property of metallurgical coke is its strength, and there is evidence that poor interface quality between the two key components of coke can have deleterious effect on coke strength. Here we create small samples of coke and image them using high resolution 3D micro-CT, with pixel size of approximately (8,mu)m. We use a Gabor filter, combined with morphology techniques to isolate the different components in the samples. We then develop a measure, called excess porosity to quantify the quality of the interfaces between components. This measure enables us to highlight problem interactions between components.\u0000References\u0000\u0000R. Barranco, J. Patrick, C. Snape, and A. Thompson. Impact of low-cost filler material on coke quality. Fuel 86.14 (2007), pp. 2179–2185. doi: 10.1016/j.fuel.2007.03.013\u0000C. Barriocanal, S. Hanson, J. W. Patrick, and A. Walker. Reactive-inert interfaces in metallurgical cokes: Effect of added inerts. Fuel 75.2 (1996), pp. 243–245. doi: 10.1016/0016-2361(95)00233-2\u0000C. Barriocanal, S. Hanson, J. W. Patrick, and A. Walker. The characterization of interfaces between textural components in metallurgical cokes. Fuel 73.12 (1994), pp. 1842–1847. doi: 10.1016/0016-2361(94)90209-7\u0000C. Barriocanal, S. Hanson, J. W. Patrick, and A. Walker. The quality of interfaces in metallurgical cokes containing petroleum coke. Fuel Proces. Tech. 45 (1995), pp. 1–10. doi: 10.1016/0378-3820(95)00003-P\u0000P. Bennett, F. Shi, and N. Andriopoulos. Determination of a theoretically based coke strength index or indices based on drum tests. ACARP Project C20009 (2013). url: https://www.acarp.com.au/abstracts.aspx?repId=C20009\u0000M. Haghighat, S. Zonouz, and M. Abdel-Mottaleb. CloudID: Trustworthy cloud-based and cross-enterprise biometric identification. Expert Sys. Appl. 42 (2015), pp. 7905–7916. doi: 10.1016/j.eswa.2015.06.025\u0000T. Kanai, Y. Yamazaki, X. Zhang, A. Uchida, Y. Saito, M. Shoji, H. Aoki, S. Nomura, Y. Kubota, H. Hayashizaki, and S. Miyashita. Quantification of the existence ratio of non-adhesion grain boundaries and factors governing the strength of coke containing low-quality coal. J. Therm. Sci. Tech. 7.2 (2012), pp. 351–363. doi: 10.1299/jtst.7.351\u0000Y. Kubota, S. Nomura, T. Arima, and K. Kato. Effects of coal inertinite size on coke strength. ISIJ Int. 48.5 (2008), pp. 563–571. doi: 10.2355/isijinternational.48.563\u0000R. Li, D. R. Jenkins, and R. Pearce. Texture-based identification of inert-maceral derived components in metallurgical coke. MODSIM (2015). url: https://www.mssanz.org.au/modsim2015/A1/li_r.pdf\u0000H. Lomas, D. R. Jenkins, M. R. Mahoney, R. Pearce, R. Roest, K. Steel, and S. Mayo. Examining mechanisms of metallurgical coke fracture using micro-CT imaging and analysis. Fuel Proc. Tech. 155 (2017), pp. 183–190. doi: 10.1016/j.fuproc.2016.05.039\u0000N. Otsu. A threshold selection m","PeriodicalId":50745,"journal":{"name":"ANZIAM Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140721749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal Hessian recovery using a biorthogonal system with an application to adaptive refinement","authors":"Jordan A. Shaw-Carmody, B. Lamichhane","doi":"10.21914/anziamj.v64.17971","DOIUrl":"https://doi.org/10.21914/anziamj.v64.17971","url":null,"abstract":"We present a method for recovering the Hessian from a linear finite element approach to achieve a higher rate of convergence. This method uses an (L^{2})-based projection as well as boundary modification to achieve and improve the convergence rate. The projection uses a biorthogonal system to make the computation more numerically efficient. We present numerical examples to illustrate the efficiency and optimality of our approach on different meshes. The performance of our approach on adaptively refined meshes is briefly explored.\u0000References\u0000\u0000R. E. Bank, A. H. Sherman, and A. Weiser. Some refinement algorithms and data structures for regular local mesh refinement. Scientific computing: Applications of mathematics and computing to the physical sciences. Ed. by R. S. Stepleman. North-Holland Publishing, 1983, pp. 3–17\u0000R. E. Bank and J. Xu. Asymptotically exact a posteriori error estimators, Part I: Grids with superconvergence. SIAM J. Numer. Anal. 41 (2003), pp. 2294–2312. doi: 10.1137/S003614290139874X\u0000J. H. Bramble and A. H. Schatz. Higher order local accuracy by averaging in the finite element method. Math. Comput. 31.137 (1977), pp. 94–111. doi: 10.2307/2005782.\u0000S. A. Funken and A. Schmidt. Adaptive mesh refinement in 2D—An efficient implementation in Matlab. Comput. Meth. Appl. Math. 20.3 (2020), pp. 459–479. doi: doi:10.1515/cmam-2018-0220.\u0000H. Guo, Z. Zhang, and R. Zhao. Hessian recovery for finite element methods. Math. Comput. 86.306 (2017), pp. 1671–1692. url: https://www.jstor.org/stable/90004689\u0000B.-O. Heimsund, X.-C. Tai, and J. Wang. Superconvergence for the gradient of finite element approximations by L2 projections. SIAM J. Numer. Anal. 40.4 (2002), pp. 1263–1280. doi: 10.1137/S003614290037410X.\u0000Y. Huang and N. Yi. The superconvergent cluster recovery method. J. Sci. Comput. 44 (2010), pp. 301–322. doi: 10.1007/s10915-010-9379-9 \u0000M. Ilyas, B. P. Lamichhane, and M. H. Meylan. A gradient recovery method based on an oblique projection and boundary modification. Proceedings of the 18th Biennial Computational Techniques and Applications Conference, CTAC-2016. Ed. by J. Droniou,\u0000M. Page, and S. Clarke. Vol. 58. ANZIAM J. Aug. 2017, pp. C34–C45. doi: 10.21914/anziamj.v58i0.11730 L. Kamenski and W. Huang. How A nonconvergent recovered Hessian works in mesh adaptation. SIAM J. Numer. Anal. 52.4 (2014), pp. 1692–1708. url: http://www.jstor.org/stable/24512164\u0000M. Krízek and P. Neittaanmäki. Superconvergence phenomenon in the finite element method arising from averaging gradients. Numer. Math. 45 (1984), pp. 105–116. doi: 10.1007/BF01379664\u0000B. P. Lamichhane and J. Shaw-Carmody. A gradient recovery approach for nonconforming finite element methods with boundary modification. Proceedings of the 19th Biennial Computational Techniques and Applications Conference, CTAC-2020. Ed. by\u0000W. McLean, S. Macnamara, and J. Bunder. Vol. 62. ANZIAM J. Feb. 2022, pp. C163–C175. doi: 10.21914/anziamj.v62.16032 \u0000A. Naga and Z. Zhang. A posteriori error estimates base","PeriodicalId":50745,"journal":{"name":"ANZIAM Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140235457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Data-informed uncertainty quantification for wave scattering by heterogeneous media","authors":"M. Ganesh, S. C. Hawkins, N. Kordzakhia, Linda Stals","doi":"10.21914/anziamj.v64.17965","DOIUrl":"https://doi.org/10.21914/anziamj.v64.17965","url":null,"abstract":"We present an efficient data-driven offline/online Bayesian algorithm for uncertainty quantification (UQ) in the induced scattered field when a time-harmonic incident wave interacts with an uncertain heterogeneous medium. The incident wave of interest need not be known in advance, and the uncertainty is informed by noisy scattering data obtained from other incident waves impinging on the medium. Our UQ algorithm is accelerated by a novel stochastic reduced order model (ROM) based on the T-matrix, and the ROM is independent of both the incident wave, and other incident waves used to generate the data. This important property allows the model to be set up offline. References M. Bachmayr and A. Djurdjevac. Multilevel representations of isotropic Gaussian random fields on the sphere. IMA J. Numer. Anal. 43.4 (2023), pp. 1970–2000. doi: 10.1093/imanum/drac034 C. Borges and G. Biros. Reconstruction of a compactly supported sound profile in the presence of a random background medium. Inv. Prob. 34, 115007 (2018). doi: 10.1088/1361-6420/aadbc5 on p. C101). Y. Chen. Inv. Prob. 13 (1997), pp. 253–282. doi: 10.1088/0266-5611/13/2/005 D. Colton and R. Kress. Inverse Acoustic and Electromagnetic Scattering Theory. 4th. Springer, 2019. doi: 10.1007/978-3-030-30351-8 M. Ganesh and S. C. Hawkins. A far-field based T-matrix method for two dimensional obstacle scattering. Proceedings of the 9th Biennial Engineering Mathematics and Applications Conference, EMAC-2009. Ed. by P. Howlett, M. Nelson, and A. J. Roberts. Vol. 51. ANZIAM J. 2010, pp. C215–C230. doi: 10.21914/anziamj.v51i0.2581 M. Ganesh and S. C. Hawkins. A numerically stable T-matrix method for acoustic scattering by nonspherical particles with large aspect ratios and size parameters. J. Acoust. Soc. Am. 151 (2022), pp. 1978–1988. doi: 10.1121/10.0009679 M. Ganesh and S. C. Hawkins. Algorithm 975: TMATROM–A T-matrix reduced order model software. ACM Trans. Math. Softw. 44, 9 (2017), pp. 1–8. doi: 10.1145/3054945 M. Ganesh, S. C. Hawkins, and R. Hiptmair. Convergence analysis with parameter estimates for a reduced basis acoustic scattering T-matrix method. IMA J. Numer. Anal. 32 (2012), pp. 1348–1374. doi: 10.1093/imanum/drr041 M. Ganesh, S. C. Hawkins, A. M. Tartakovsky, and R. Tipireddy. A stochastic domain decomposition and post-processing algorithm for epistemic uncertainty quantification. Int. J. Uncertain. Quant. 13 (2023), pp. 1–22. doi: 10.1615/Int.J.UncertaintyQuantification.2023045687 S. C. Hawkins. Algorithm 1009: MieSolver–An object-oriented Mie series software for wave scattering by cylinders. ACM Trans. Math. Softw. 46, 19 (2020), pp. 1–28. doi: 10.1145/3381537 on p. C109). S. C. Hawkins. Noisy far-field data. Published online 12th August 2023. doi: 10.5281/zenodo.8240111 T. Hohage. On the numerical solution of a three-dimensional inverse medium scattering problem. Inv. Prob. 17 (2001), pp. 1743–1763. doi: 10.1088/0266-5611/17/6/314 A. Kirsch and P. Monk. An analysis of the coupling of fini","PeriodicalId":50745,"journal":{"name":"ANZIAM Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139233225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"THE METRIC OPERATORS FOR PSEUDO-HERMITIAN HAMILTONIAN","authors":"WEN-HUA WANG, ZHENG-LI CHEN, WEI LI","doi":"10.1017/s1446181123000184","DOIUrl":"https://doi.org/10.1017/s1446181123000184","url":null,"abstract":"Abstract The Hamiltonian of a conventional quantum system is Hermitian, which ensures real spectra of the Hamiltonian and unitary evolution of the system. However, real spectra are just the necessary conditions for a Hamiltonian to be Hermitian. In this paper, we discuss the metric operators for pseudo-Hermitian Hamiltonian which is similar to its adjoint. We first present some properties of the metric operators for pseudo-Hermitian Hamiltonians and obtain a sufficient and necessary condition for an invertible operator to be a metric operator for a given pseudo-Hermitian Hamiltonian. When the pseudo-Hermitian Hamiltonian has real spectra, we provide a new method such that any given metric operator can be transformed into the same positive-definite one and the new inner product with respect to the positive-definite metric operator is well defined. Finally, we illustrate the results obtained with an example.","PeriodicalId":50745,"journal":{"name":"ANZIAM Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135406077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"NUMERICAL ANALYSIS OF APPARATUS-INDUCED DISPERSION FOR DENSITY-DEPENDENT SOLUTE TRANSPORT IN POROUS MEDIA","authors":"H. ZHANG, D. A. BARRY, B. SEYMOUR, G. HOCKING","doi":"10.1017/s1446181123000135","DOIUrl":"https://doi.org/10.1017/s1446181123000135","url":null,"abstract":"Abstract The effects of apparatus-induced dispersion on nonuniform, density-dependent flow in a cylindrical soil column were investigated using a finite-element model. To validate the model, the results with an analytical solution and laboratory column test data were analysed. The model simulations confirmed that flow nonuniformities induced by the apparatus are dissipated within the column when the distance to the apparatus outlet exceeds $3R/2$ , where R represents the radius of the cylindrical column. Furthermore, the simulations revealed that convergent flow in the vicinity of the outlet introduces additional hydrodynamic dispersion in the soil column apparatus. However, this effect is minimal in the region where the column height exceeds $3R/2$ . Additionally, it is found that an increase in the solution density gradient during the solute breakthrough period led to a decrease in flow velocity, which stabilized the flow and ultimately reduced dispersive mixing. Overall, this study provides insights into the behaviour of apparatus-induced dispersion in nonuniform, density-dependent flow within a cylindrical soil column, shedding light on the dynamics and mitigation of flow nonuniformities and dispersive mixing phenomena.","PeriodicalId":50745,"journal":{"name":"ANZIAM Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135443190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ANZ VOLUME 65 ISSUE 1-2 COVER AND BACK MATTER","authors":"","doi":"10.1017/s1446181122000165","DOIUrl":"https://doi.org/10.1017/s1446181122000165","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.","PeriodicalId":50745,"journal":{"name":"ANZIAM Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135750275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}