James Thomas Beale

James Thomas (J. Thomas "Tom") Beale (born 1947) is an American mathematician, specializing in fluid dynamics, partial differential equations, and numerical analysis.^[1]

J. Thomas Beale grew up in Savannah, Georgia.^[2] In 1967 he graduated from California Institute of Technology (Caltech) with a B.S. in mathematics.^[3] In 1973 he received his PhD in mathematics from Stanford University. His PhD thesis Purely imaginary scattering frequencies for exterior domains.^[4] was written under the supervision of Ralph S. Phillips.^[5] Soon after receiving his PhD Beale became a faculty member at Tulane University. In 1983 he resigned from Tulane University and became a professor at Duke University, where he retired as professor emeritus in 2016.^[6]

His 1984 article with Tosio Kato and Andrew Majda, Remarks on the breakdown of smooth solutions for the 3-D Euler equations (Comm. Math. Phys. 94 (1984), no. 1, 61–66) has been a very influential result in the study of singularities in fluid flows — one of the remaining open problems in the Clay Institute's Millennium problems. He has more than 50 scientific publications with many collaborators and covering areas including water waves, vortex methods, quasi-geostrophic models of the atmosphere and oceans, numerical splitting methods, and recent work in computational methods for nearly singular integrals.^[1]

In 1994 Beale was an invited speaker with talk Analytical and numerical aspects of fluid interfaces at the International Congress of Mathematicians in Zurich.^[7]

His research has centered on mathematical models of basic scientific problems, usually described by partial differential equations, such as fluid flow with moving interfaces. He has been interested in using mathematical analysis to understand the accuracy of numerical methods with the aim to improve their design, especially for those methods where solutions are represented by singular integrals.^[6]

From June 28 to 30, 2010, the mathematics department of Duke University held a conference in his honor.^[1]

Selected publications

• Beale, J. Thomas (1976). "Spectral Properties of an Acoustic Boundary Condition". Indiana University Mathematics Journal. 25 (9): 895–917. doi:10.1512/iumj.1976.25.25071. JSTOR 24891055.
• Beale, J. Thomas (1977). "Acoustic Scattering from Locally Reacting Surfaces". Indiana University Mathematics Journal. 26 (2): 199–222. Bibcode:1977IUMJ...26..199B. doi:10.1512/iumj.1977.26.26015. JSTOR 24891336.
• Beale, J. Thomas; Majda, Andrew (1981). "Rates of convergence for viscous splitting of the Navier-Stokes equations". Mathematics of Computation. 37 (156): 243. doi:10.1090/S0025-5718-1981-0628693-0.
• Beale, J. Thomas; Majda, Andrew (1982). "Vortex methods. I. Convergence in three dimensions". Mathematics of Computation. 39 (159): 1. doi:10.1090/S0025-5718-1982-0658212-5.
• Beale, J. Thomas; Majda, Andrew (1982). "Vortex methods. II. Higher order accuracy in two and three dimensions". Mathematics of Computation. 39 (159): 29. doi:10.1090/S0025-5718-1982-0658213-7.
• Beale, J. T.; Kato, T.; Majda, A. (1984). "Remarks on the breakdown of smooth solutions for the ${\displaystyle 3}$ –${\displaystyle D}$  Euler equations". Communications in Mathematical Physics. 94 (1): 61–66. Bibcode:1984CMaPh..94...61B. doi:10.1007/BF01212349. S2CID 120560503. (over 1600 citations)
• Beale, J. Thomas; Nishida, Takaaki (1985). Large-Time Behavior of Viscous Surface Waves. University of Wisconsin-Madison Mathematics Research Center, MRC Technical Summary Report # 2809, Accession Number AD-A154 805. Defense Technical Information Center. from the original on August 3, 2021.
• Beale, J.T.; Majda, A. (1985). "High order accurate vortex methods with explicit velocity kernels". Journal of Computational Physics. 58 (2): 188–208. Bibcode:1985JCoPh..58..188B. doi:10.1016/0021-9991(85)90176-7.
• Beale, J. Thomas (1985). "Large-time behavior of the Broadwell model of a discrete velocity gas". Communications in Mathematical Physics. 102 (2): 217–235. Bibcode:1985CMaPh.102..217B. doi:10.1007/BF01229378. S2CID 121412754. (The Broadwell model was introduced in 1964 by James Eugene Broadwell.^[8])
• Beale, J. Thomas (1986). "A convergent ${\displaystyle 3}$ -D vortex method with grid-free stretching". Mathematics of Computation. 46 (174): 401. Bibcode:1986MaCom..46..401B. doi:10.1090/S0025-5718-1986-0829616-6.
• Beale, J. Thomas (1986). "Large-time behavior of discrete velocity Boltzmann equations". Communications in Mathematical Physics. 106 (4): 659–678. Bibcode:1986CMaPh.106..659B. doi:10.1007/BF01463401. S2CID 122431829.
• Beale, J. Thomas (1988). "On the Accuracy of Vortex Methods at Large Times". Computational Fluid Dynamics and Reacting Gas Flows. The IMA Volumes in Mathematics and Its Applications. Vol. 12. pp. 19–32. doi:10.1007/978-1-4612-3882-9_2. ISBN 978-1-4612-8388-1.
• Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John S. (1993). "Growth rates for the linearized motion of fluid interfaces away from equilibrium". Communications on Pure and Applied Mathematics. 46 (9): 1269–1301. doi:10.1002/cpa.3160460903.
• Beale, J. Thomas; Greengard, Claude (1994). "Convergence of Euler-Stokes splitting of the Navier-Stokes equations". Communications on Pure and Applied Mathematics. 47 (8): 1083–1115. doi:10.1002/cpa.3160470805.
• Bourgeois, Alfred J.; Beale, J. Thomas (1994). "Validity of the Quasigeostrophic Model for Large-Scale Flow in the Atmosphere and Ocean". SIAM Journal on Mathematical Analysis. 25 (4): 1023–1068. doi:10.1137/S0036141092234980.
• Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John (1996). "Convergence of a Boundary Integral Method for Water Waves". SIAM Journal on Numerical Analysis. 33 (5): 1797–1843. doi:10.1137/S0036142993245750.
• Beale, J. Thomas; Lai, Ming-Chih (2001). "A Method for Computing Nearly Singular Integrals". SIAM Journal on Numerical Analysis. 38 (6): 1902–1925. doi:10.1137/S0036142999362845.
• Beale, J. Thomas (2004). "A Grid-Based Boundary Integral Method for Elliptic Problems in Three Dimensions". SIAM Journal on Numerical Analysis. 42 (2): 599–620. doi:10.1137/S0036142903420959.
• Baker, Gregory R.; Beale, J.Thomas (2004). "Vortex blob methods applied to interfacial motion". Journal of Computational Physics. 196 (1): 233–258. Bibcode:2004JCoPh.196..233B. doi:10.1016/j.jcp.2003.10.023.
• Beale, J. Thomas; Strain, John (2008). "Locally corrected semi-Lagrangian methods for Stokes flow with moving elastic interfaces". Journal of Computational Physics. 227 (8): 3896–3920. Bibcode:2008JCoPh.227.3896B. doi:10.1016/j.jcp.2007.11.047. hdl:10161/6958.
• Beale, J. Thomas; Layton, Anita T. (2009). "A velocity decomposition approach for moving interfaces in viscous fluids". Journal of Computational Physics. 228 (9): 3358–3367. Bibcode:2009JCoPh.228.3358B. CiteSeerX 10.1.1.218.9623. doi:10.1016/j.jcp.2009.01.023. ISSN 0021-9991.
• Beale, J. Thomas (2009). "Smoothing Properties of Implicit Finite Difference Methods for a Diffusion Equation in Maximum Norm". SIAM Journal on Numerical Analysis. 47 (4): 2476–2495. doi:10.1137/080731645.
• Tlupova, Svetlana; Beale, J. Thomas (2013). "Nearly Singular Integrals in 3D Stokes Flow". Communications in Computational Physics. 14 (5): 1207–1227. Bibcode:2013CCoPh..14.1207T. doi:10.4208/cicp.020812.080213a.
• Beale, J. Thomas; Ying, Wenjun; Wilson, Jason R. (2016). "A Simple Method for Computing Singular or Nearly Singular Integrals on Closed Surfaces". Communications in Computational Physics. 20 (3): 733–753. arXiv:1508.00265. Bibcode:2016CCoPh..20..733B. doi:10.4208/cicp.030815.240216a. S2CID 41606464.

References

1. "Fluid dynamics, Analysis, and Numerics 2010: A conference in honor of J. Thomas Beale". Department of Mathematica, Duke University. June 2020.
2. "Lillian Neidlinger Beale". Savannah Morning News. October 8, 2004.
3. Seventy-Third Annual Commencement (PDF). California Institute of Technology. June 9, 1967.
4. Beale, James Thomas (1973). Purely Imaginary Scattering Frequencies for Exterior Domains.
5. James Thomas Beale at the Mathematics Genealogy Project
6. "Professor J. Thomas Beale Retires". Department of Mathematics, Duke University. May 20, 2016.
7. Beale, J. Thomas (1995). "Analytical and Numerical Aspects of Fluid Interfaces". Proceedings of the International Congress of Mathematicians, 1994, Zürich. Basel: Birkhäuser. pp. 1055–1064. doi:10.1007/978-3-0348-9078-6_98. ISBN 978-3-0348-9897-3.
8. Broadwell, James E. (1964). "Shock Structure in a Simple Discrete Velocity Gas". Physics of Fluids. 7 (8): 1243–1247. Bibcode:1964PhFl....7.1243B. doi:10.1063/1.1711368. ISSN 0031-9171.