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Projective character values on real and rational elements
No full texthttp://dx.doi.org/10.1017/S000497271200033
Approximation of irrational numbers by pairs of integers from a large set
No full texthttp://dx.doi.org/10.1017/S000497271200033
Characterisation of primes dividing the index of a class of polynomials and its applications
No full texthttp://dx.doi.org/10.1017/S000497271200033
Divisibility of sums of partition numbers by multiples of 2 and 3
No full texthttp://dx.doi.org/10.1017/S000497271200033
On the cumulative distribution function of the variance-gamma distribution
No full texthttp://dx.doi.org/10.1017/S000497271200033
Cuntz-Krieger algebras associated to self-similar groupoids
No full texthttp://dx.doi.org/10.1017/S000497271200033
Numerical analysis of the axisymmetric lattice Boltzmann method for steady and oscillatory flows in periodic geometries
Get PDFCompared 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.
References
R. D. Astumian and P. Hänggi. Brownian motors. Phys. Today 55.11 (2002), pp. 33–39. doi: 10.1063/1.1535005. (Cit. on p. C214).
W. 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
N. Islam. Fluid flow and particle transport through periodic capillaries. Bull. Aust. Math. Soc. 96.3 (2017), pp. 521–522. doi: 10.1017/S0004972717000739
C. 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
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, 2017, pp. 978–3. doi: 10.1007/978-3-319-44649-3
S. 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
S. 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 15th Biennial Engineering Mathematics and Applications Conference, EMAC-2021. Ed. by A. Clark, Z. Jovanoski, and J. Bunder. Vol. 63. ANZIAM J. 2022, pp. C69–C83. doi: 10.21914/anziamj.v63.17158
W. Wang and J. Zhou. Enhanced Lattice Boltzmann modelling of axisymmetric flows. Proceedings of the Institution of Civil Engineers—Engineering and Computational Mechanics 167.4 (2014), pp. 156–166. doi: 10.1680/eacm.14.00005
J. G. Zhou. Axisymmetric lattice Boltzmann method revised. Phys. Rev. E 84.3, 036704 (2011). doi: 10.1103/PhysRevE.84.03670
Minimum volume covering ellipsoids
Get PDFWe 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.
References
C. L. Atwood. Sequences converging to D-optimal designs of experiments. Ann. Statist. 1.2 (1973), pp. 342–352. doi: 10.1214/aos/1176342371
Y.-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
F. 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
D. Eberly. 3D game engine design: A practical approach to real-time computer graphics. CRC Press, 2007. doi: 10.1201/b18212
M. 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
R. 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
R. 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
F. 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
L. 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-
L. 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
J. 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
P. 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
S. Rosa and R. Harman. Computing minimum-volume enclosing ellipsoids for large datasets. Comput. Stat. Data Anal. 171, 107452 (2022). doi: 10.1016/j.csda.2022.107452
J. B. Rosen. Pattern separation by convex programming. J. Math. Anal. Appl. 10.1 (1965), pp. 123–134. doi: 10.1016/0022-247X(65)90150-2
P. J. Rousseeuw and M. Hubert. Robust statistics for outlier detection. WIREs: Data mining and knowledge discovery 1.1 (2011), pp. 73–79. doi: 10.1002/widm.2
F. Schweppe. Recursive state estimation: Unknown but bounded errors and system inputs. IEEE Trans. Auto. Control 13.1 (1968), pp. 22–28. doi: 10.1109/TAC.1968.1098790
R. Sibson. Discussion of Dr Wynn’s and of Dr Laycock’s papers. J. Roy. Stat. Soc. B 34.2 (1972), pp. 181–183. doi: 10.1111/j.2517-6161.1972.tb00898.x
S. D. Silvey. Optimal design: An introduction to the theory for parameter estimation. Ettore Majorana International Science Series. London, Chapman and Hall, 1980. doi: 10.1007/978-94-009-5912-5
P. Sun and R. M. Freund. Computation of minimum-volume covering ellipsoids. Op. Res. 52.5 (2004), pp. 690–706. doi: 10.1287/opre.1040.0115
D. M. Titterington. Estimation of correlation coefficients by ellipsoidal trimming. J. Roy. Stat. Soc.: C 27.3 (1978), pp. 227–234. doi: 10.2307/2347157
D. M. Titterington. Optimal design: Some geometrical aspects of D-optimality. Biometrika 62.2 (1975), pp. 313–320. doi: 10.2307/2335366
M. J. Todd. Minimum-volume ellipsoids: Theory and algorithms. MOS-SIAM Series on Optimization. SIAM, 2016. doi: 10.1137/1.9781611974386
P. Wolfe. Convergence theory in nonlinear programming. ed. by J. Abadie. Integer and Nonlinear Programming. North Holland, Amsterdam, 1970, pp. 1–36. doi: 10.1007/BF0093285
Conditions for recurrence and transience for time-inhomogeneous birth-and-death processes
No full texthttp://dx.doi.org/10.1017/S000497271200033