ANZIAM Journal最新文献

{"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":"82 1","pages":""},"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":"14 6","pages":"0"},"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":"139 1","pages":"0"},"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":"59 1","pages":"0"},"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}

{"title":"ANZ VOLUME 65 ISSUE 1-2 COVER AND FRONT MATTER","authors":"","doi":"10.1017/s1446181122000153","DOIUrl":"https://doi.org/10.1017/s1446181122000153","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":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135750627","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}