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The number of cyclic subgroups of finite abelian groups and Menon's identity
No full textDOI:
10.1017/S000497271900060
Intersections of subgroups in virtually free groups and virtually free products
No full textDOI:
10.1017/S000497271900076
The mechanism of vortex instability in electromagnetically driven flow in an annular thin layer of electrolyte
Get PDFA circumferential flow of a conducting fluid in an annular channel can be created by the action of a Lorentz force arising as a result of the interaction between an applied vertical magnetic field and a radial electric current flowing through the electrolyte. Quite unexpectedly, experiments revealed that a robust vortex system appears near the outer cylindrical wall in such flows. McCloughan and Suslov (J. Fluid Mech. 887:A23, 2020) (McCS) reported comprehensive linear stability results of such a flow for variable Lorentz forcing. Here we complement that study by investigating the flow structure as a function of the channel aspect ratio. Remarkably, despite the completely different physical nature of parametric dependences, dynamic in McCS and purely geometric here, we show that in both scenarios vortices appear on a background of a steady axisymmetric flow at the boundary between two counter-rotating toroidal structures and have a similar energy distributions. The two studies demonstrate the robustness of the mechanism responsible for the vortex formation: Rayleigh's inviscid centrifugal instability aided by radial shear in the boundary layer near the outer cylindrical wall.
References
P. A. Davidson. An introduction to magnetohydrodynamics. Cambridge University Press, 2nd edition, 2017. doi:10.1017/CBO9780511626333.
J. McCloughan and S. A. Suslov. Linear stability and saddle–node bifurcation of electromagnetically driven electrolyte flow in an annular layer. J. Fluid Mech., 887:A23.1–30, 2020. doi:10.1017/jfm.2020.29.
J. Perez-Barrera, J. E. Perez-Espinoza, A. Ortiz, E. Ramos, and S. Cuevas. Instability of electrolyte flow driven by an azimuthal Lorentz force. Magnetohydrodynamics, 51(2):203–213, 2015. http://mhd.sal.lv/contents/2015/2/MG.51.2.4.R.html.
S. A. Suslov, J. Perez-Barrera, and S. Cuevas. Electromagnetically driven flow of electrolyte in a thin annular layer: Axisymmetric solutions. J. Fluid Mech., 828: 573–600, 2017. doi:10.1017/jfm.2017.551
A comparison of triangular and quadrilateral finite element meshes for Bragg edge neutron transmission strain tomography
Get PDFA wavelength resolved measurement technique used in neutron imaging applications is known as energy-resolved neutron transmission imaging. This technique of reconstructing residual strain maps provides high spatial resolution measurements of strain distribution in polycrystalline materials from sets of Bragg edge measurement images. Strain field reconstructions obtained from both triangular and quadrilateral finite element meshes are compared. The reconstruction is approached via a least square method and relies on the inversion of the longitudinal ray transform, which has uniqueness issues.
References
B. Abbey, S. Y. Zhang, W. J. J. Vorster, and A. M. Korsunsky. Feasibility study of neutron strain tomography. Proc. Eng., 1:185–188, 2009. doi:10.1016/j.proeng.2009.06.043.
R. Aggarwal, M. H. Meylan, B. P. Lamichhane, and C. M. Wensrich. Energy resolved neutron imaging for strain reconstruction using the finite element method. J. Imag., 6(3):13, 2020a. doi:10.3390/jimaging6030013.
R. Aggarwal, M. H. Meylan, C. M. Wensrich, and B. P. Lamichhane. Finite element approach to Bragg edge neutron strain tomography. In B. Lamichhane, T. Tran, and J. Bunder, editors, Proceedings of the 18th Biennial Computational Techniques and Applications Conference, CTAC-2018, volume 60 of ANZIAM J., pages C279–C294, June 2020b. doi:10.21914/anziamj.v60i0.14054.
M. E. Fitzpatrick and A. Lodini. Analysis of residual stress by diffraction using neutron and synchrotron radiation. CRC Press, 2003. URL https://www.routledge.com/Analysis-of-Residual-Stress-by-Diffraction-using-Neutron-and-Synchrotron/Fitzpatrick-Lodini/p/book/9780367446802.
A. W. T. Gregg, J. N. Hendriks, C. M. Wensrich, A. Wills, A. S. Tremsin, V. Luzin, T. Shinohara, O. Kirstein, M. H. Meylan, and E. H. Kisi. Tomographic reconstruction of two-dimensional residual strain fields from Bragg-edge neutron imaging. Phys. Rev. Appl., 10:064034, Dec 2018. doi:10.1103/PhysRevApplied.10.064034.
J. N. Hendriks, A. W. T. Gregg, C. M. Wensrich, A. S. Tremsin, T. Shinohara, M. Meylan, E. H. Kisi, V. Luzin, and O. Kirsten. Bragg-edge elastic strain tomography for in situ systems from energy-resolved neutron transmission imaging. Phys. Rev. Mat., 1:053802, 2017. doi:10.1103/PhysRevMaterials.1.053802.
E. H. Kisi and C. J. Howard. Applications of neutron powder diffraction, volume 15 of Neutron Scattering in Condensed Matter. Oxford University Press, 2012. URL https://global.oup.com/academic/product/applications-of-neutron-powder-diffraction-9780199657421.
W. R. B. Lionheart and P. J. Withers. Diffraction tomography of strain. Inv. Prob., 31:045005, 2015. doi:10.1088/0266-5611/31/4/045005.
C. C. Paige and M. A. Saunders. LSQR: An algorithm for sparse linear equations and sparse least squares. ACM Trans. Math. Software, 8:43–71, 1982. doi:10.1145/355984.355989.
J. R. Santisteban, L. Edwards, M. E. Fitzpatrick, A. Steuwer, P. J. Withers, M. R. Daymond, M. W. Johnson, N. Rhodes, and E. M. Schooneveld. Strain imaging by Bragg edge neutron transmission. Nucl. Inst. Meth. Phys. Res., 481:765–768, 2002. doi:10.1016/S0168-9002(01)01256-6.
T. Shinohara and T. Kai. Commissioning start of energy-resolved neutron imaging system, RADEN in J-PARC. Neut. News, 26(2):11–14, 2015. doi:10.1080/10448632.2015.1028271.
T. Shinohara, T. Kai, K. Oikawa, M. Segawa, M. Harada, T. Nakatani, M. Ooi, K. Aizawa, H. Sato, T. Kamiyama, H. Yokota, T. Sera, K. Mochiki, and Y. Kiyanagi. Final design of the energy-resolved neutron imaging system RADEN at J-PARC. J. Phys., 746, 2016. doi:10.1088/1742-6596/746/1/012007.
A. S. Tremsin, J. B. McPhate, W. Kockelmann, J. V. Vallerga, O. H. W. Siegmund, and W. B. Feller. High resolution Bragg edge transmission spectroscopy at pulsed neutron sources: proof of principle experiments with a neutron counting MCP detector. Nucl. Inst. Meth. Phys. Res., 633:S235–S238, 2011. doi:10.1016/j.nima.2010.06.176.
R. Woracek, J. Santisteban, A. Fedrigo, and M. Strobl. Diffraction in neutron imaging—A review. Nucl. Inst. Meth. Phys. Res., 878:141–158, 2018. doi:10.1016/j.nima.2017.07.040
Number theory problems related to the spectrum of Cantor-type measures with consecutive digits
No full texthttp://dx.doi.org/10.1017/S000497271200033
New super congruences involving products of two binomial coefficients
No full textDOI:
10.1017/S000497271900091