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Injective linear transformations with equal gap and defect
No full texthttp://dx.doi.org/10.1017/S000497271200033
Coarse reduced model selection for nonlinear state estimation
Get PDFState estimation is the task of approximately reconstructing a solu- tion u of a parametric partial differential equation when the parameter vector y is unknown and the only information is m linear measurements of u. Cohen et al. [arXiv:2009.02687, Nov. 2020] proposed a method to use a family of linear reduced spaces as a generalised nonlinear reduced model for state estimation. A computable surrogate distance is used to evaluate which linear estimate lies closest to a true solution of the pde problem. In this article we propose a strategy of coarse computation of the surrogate distance while maintaining a fine mesh reduced model, as the computational cost of the surrogate distance is large relative to the reduced modelling task. We demonstrate numerically that the error induced by the coarse distance is dominated by other approximation errors.
References
P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova, and P. Wojtaszczyk. Convergence rates for geedy algorithms in reduced basis methods. SIAM J. Math. Anal. 43.3 (2011), pp. 1457–1472. doi: 10.1137/100795772.
P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova, and P. Wojtaszczyk. Data assimilation in reduced modeling. SIAM/ASA J. Uncert. Quant. 5.1 (2017), pp. 1–29. doi: 10.1137/15M1025384
A. Cohen, W. Dahmen, O. Mula, and J. Nichols. Nonlinear reduced models for state and parameter estimation. arXiv:2009.02687 [cs, math] (2020). url: http://arxiv.org/abs/2009.02687 (visited on 01/07/2021)
A. Cohen, D. Wolfgang, R. DeVore, and J. Nichols. Reduced basis greedy selection using random training sets. ESAIM: Math. Model. Num. Anal. 54 (2020), pp. 1509–1524. doi: 10.1051/m2an/2020004.
J. S. Hesthaven, G. Rozza, and B. Stamm. Certified reduced basis methods for parametrized partial differential equations. SpringerBriefs in Mathematics. Springer, 2016. doi: 10.1007/978-3-319-22470-1.
Y. Maday, A. T. Patera, J. D. Penn, and M. Yano. A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics. Int. J. Num. Meth. Eng. 102.5 (2015), pp. 933–965. doi: 10.1002/nme.4747
Parametric study of E. coli incidence with reference to the New Zealand freshwater standards and the Manawatū–Whanganui region
Get PDFThe New Zealand National Policy Statement for Freshwater Management 2020 sets several targets for freshwater quality, six of which are measurements of rivers; others relate to lakes. Each regional council is required to monitor freshwater quality and to respond as prescribed in order to meet the targets. One target of particular public interest is based on four criteria determined from recent E. coli readings, and concerns the health risk of swimming in a river. However, the inherent variability of the data makes it difficult to determine the water quality state and trend reliably, particularly using traditional methods based on percentiles. Therefore, in this study we return to the parametric lognormal model of E. coli distribution, from which the official criteria were developed. We interpret the classification system in terms of the parametric model and show that the parametric model can reduce uncertainty and can incorporate more useful information, especially from very high E. coli readings, and is suitable for censored data. We apply the parametric model for state and trend to 135 sites in the Manawatū–Whanganui region
Comparing lattice Boltzmann simulations of periodic fluid flow in repeated micropore structures with longitudinal symmetry and asymmetry
Get PDFPumping of a particulate suspension back and forth through a membrane of periodic axisymmetric pores results in no net flow of the fluid; however, the particles are transported along the pores from one side of the membrane to the other. The movement of the particles is dependent on the geometry of the pore walls. Current simulations for this problem utilise standard computational fluid dynamics techniques (e.g. finite element method, boundary element method). However, there are difficulties associated with applying these techniques to this problem, such as the requirement of many spatial periods. The lattice Boltzmann method overcomes these disadvantages by utilising periodic boundary conditions, which are straightforward to implement. Flow simulations in longitudinally symmetric and asymmetric pores with various Reynolds numbers are compared. The importance of pore shape and viscous effects is showcased through streamline plots.
References
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T. 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 International Publishing, 2017, pp. 978–3. doi: 10.1007/978-3-319-44649-3.
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M. Sakthivel and K. Anupindi. An off-lattice Boltzmann method for blood flow simulation through a model irregular arterial stenosis: The effects of amplitude and frequency of the irregularity. Phys. Fluids 33.3 (2021), p. 031912. doi: 10.1063/5.0044948
T. Sikdar, N. J. Pinky, A. Roy, S. S. Hossain, and N. Islam. Oscillating flow of viscous incompressible fluid through sinusoidal periodic tube at low Reynolds number. Int. J. Fluid Mech. Therm. Sci. 6.1 (2020), pp. 9–18. doi: 10.11648/j.ijfmts.20200601.12
J. G. Zhou. Axisymmetric lattice Boltzmann method revised. Phys. Rev. E 84.3 (2011), p. 036704. doi: 10.1103/PhysRevE.84.03670
A proof of Merca's conjectures on sums of odd divisor functions
No full texthttp://dx.doi.org/10.1017/S000497271200033
On the strong metric dimension of a total graph of nonzero annihilating ideals
No full text
http://dx.doi.org/10.1017/S000497271200033