詹姆斯·托馬斯·比爾

詹姆斯·托馬斯·比爾（英語：James Thomas Beale，1947年—）是一位美國數學家，專長於流體動力學、偏微分方程和數值分析。^[1]

詹姆斯·托馬斯·比爾 James Thomas Beale
出生	1947年
國籍	美國
母校	加州理工學院、史丹福大學
科學生涯
研究領域	數學
機構	杜蘭大學（至1983年） 杜克大學（1983年至2016年）

詹姆斯·比爾在佐治亞州薩凡納長大。^[2]在1967年，他畢業於加州理工學院，獲得數學理學學士士學位。^[3]在1973年，他獲得史丹福大學數學博士學位。他的博士論文《外部域的純虛散射頻率》（Purely imaginary scattering frequencies for exterior domains）^[4]是在拉爾夫·索爾·菲利普斯的監督下編寫的。^[5]獲得博士學位後不久，比爾就成為杜蘭大學的一名教員。在1983年，他從杜蘭大學辭職，成為杜克大學教授，並於2016年以名譽教授身份退休。^[6]

他於1984年與加藤敏夫和安德魯·馬伊達（英語：Andrew Majda）合作的文章Remarks on the Breakdown of smooth Solutions for the 3-D Eulerequations（《數學物理通訊（英語：Communications in Mathematical Physics）》 94 (1984), no. 1, 61–66）在流體流動奇點研究中（克雷研究所千禧年難題中剩餘懸而未決的問題之一）是非常有影響力的成果。他與許多合作者發表了50多篇科學出版物，涵蓋的領域包括水波、渦旋方法、大氣和海洋的准地轉方程、數值分裂方法以及近奇異積分計算方法的最新工作。^[1]

在1994年，比爾受邀在蘇黎世國際數學家大會上發表流體界面的分析和數值方面的演講。^[7]

他的研究集中在基礎科學問題的數學模型上，這些問題通常是偏微分方程，例如具有移動界面的流體流動。他一直對使用數學分析來了解數值方法的準確性感興趣，目的是改進其設計，特別是對於那些用奇異積分表示解的方法。^[6]

在2010年6月28日至30日，杜克大學數學係為他舉行了一次會議。^[1]

精選出版物

• Beale, J. Thomas. Spectral Properties of an Acoustic Boundary Condition. Indiana University Mathematics Journal. 1976, 25 (9): 895–917. JSTOR 24891055. doi:10.1512/iumj.1976.25.25071 .
• Beale, J. Thomas. Acoustic Scattering from Locally Reacting Surfaces. Indiana University Mathematics Journal. 1977, 26 (2): 199–222. Bibcode:1977IUMJ...26..199B. JSTOR 24891336. doi:10.1512/iumj.1977.26.26015 .
• Beale, J. Thomas; Majda, Andrew. Rates of convergence for viscous splitting of the Navier-Stokes equations. Mathematics of Computation. 1981, 37 (156): 243. doi:10.1090/S0025-5718-1981-0628693-0 .
• Beale, J. Thomas; Majda, Andrew. Vortex methods. I. Convergence in three dimensions. Mathematics of Computation. 1982, 39 (159): 1. doi:10.1090/S0025-5718-1982-0658212-5 .
• Beale, J. Thomas; Majda, Andrew. Vortex methods. II. Higher order accuracy in two and three dimensions. Mathematics of Computation. 1982, 39 (159): 29. doi:10.1090/S0025-5718-1982-0658213-7 .
• Beale, J. T.; Kato, T.; Majda, A. Remarks on the breakdown of smooth solutions for the ${\displaystyle 3}$–${\displaystyle D}$ Euler equations. Communications in Mathematical Physics. 1984, 94 (1): 61–66 [2023-06-30]. Bibcode:1984CMaPh..94...61B. S2CID 120560503. doi:10.1007/BF01212349. （原始內容存檔於2020-08-07）. (over 1600 citations)
• Beale, J. Thomas; Nishida, Takaaki. 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. 1985. （原始內容存檔於August 3, 2021）.
• Beale, J.T.; Majda, A. High order accurate vortex methods with explicit velocity kernels. Journal of Computational Physics. 1985, 58 (2): 188–208. Bibcode:1985JCoPh..58..188B. doi:10.1016/0021-9991(85)90176-7.
• Beale, J. Thomas. Large-time behavior of the Broadwell model of a discrete velocity gas. Communications in Mathematical Physics. 1985, 102 (2): 217–235 [2023-06-30]. Bibcode:1985CMaPh.102..217B. S2CID 121412754. doi:10.1007/BF01229378. （原始內容存檔於2020-06-06）. (The Broadwell model was introduced in 1964 by James Eugene Broadwell.^[8])
• Beale, J. Thomas. A convergent ${\displaystyle 3}$-D vortex method with grid-free stretching. Mathematics of Computation. 1986, 46 (174): 401. Bibcode:1986MaCom..46..401B. doi:10.1090/S0025-5718-1986-0829616-6 .
• Beale, J. Thomas. Large-time behavior of discrete velocity Boltzmann equations. Communications in Mathematical Physics. 1986, 106 (4): 659–678 [2023-06-30]. Bibcode:1986CMaPh.106..659B. S2CID 122431829. doi:10.1007/BF01463401. （原始內容存檔於2020-06-12）.
• Beale, J. Thomas. On the Accuracy of Vortex Methods at Large Times. Computational Fluid Dynamics and Reacting Gas Flows. The IMA Volumes in Mathematics and Its Applications 12. 1988: 19–32. ISBN 978-1-4612-8388-1. doi:10.1007/978-1-4612-3882-9_2.
• Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John S. Growth rates for the linearized motion of fluid interfaces away from equilibrium. Communications on Pure and Applied Mathematics. 1993, 46 (9): 1269–1301. doi:10.1002/cpa.3160460903.
• Beale, J. Thomas; Greengard, Claude. Convergence of Euler-Stokes splitting of the Navier-Stokes equations. Communications on Pure and Applied Mathematics. 1994, 47 (8): 1083–1115. doi:10.1002/cpa.3160470805.
• Bourgeois, Alfred J.; Beale, J. Thomas. Validity of the Quasigeostrophic Model for Large-Scale Flow in the Atmosphere and Ocean. SIAM Journal on Mathematical Analysis. 1994, 25 (4): 1023–1068. doi:10.1137/S0036141092234980.
• Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John. Convergence of a Boundary Integral Method for Water Waves. SIAM Journal on Numerical Analysis. 1996, 33 (5): 1797–1843 [2023-06-30]. doi:10.1137/S0036142993245750. （原始內容存檔於2023-06-30）.
• Beale, J. Thomas; Lai, Ming-Chih. A Method for Computing Nearly Singular Integrals. SIAM Journal on Numerical Analysis. 2001, 38 (6): 1902–1925. doi:10.1137/S0036142999362845.
• Beale, J. Thomas. A Grid-Based Boundary Integral Method for Elliptic Problems in Three Dimensions. SIAM Journal on Numerical Analysis. 2004, 42 (2): 599–620. doi:10.1137/S0036142903420959.
• Baker, Gregory R.; Beale, J.Thomas. Vortex blob methods applied to interfacial motion. Journal of Computational Physics. 2004, 196 (1): 233–258. Bibcode:2004JCoPh.196..233B. doi:10.1016/j.jcp.2003.10.023.
• Beale, J. Thomas; Strain, John. Locally corrected semi-Lagrangian methods for Stokes flow with moving elastic interfaces. Journal of Computational Physics. 2008, 227 (8): 3896–3920. Bibcode:2008JCoPh.227.3896B. doi:10.1016/j.jcp.2007.11.047.
• Beale, J. Thomas; Layton, Anita T. A velocity decomposition approach for moving interfaces in viscous fluids. Journal of Computational Physics. 2009, 228 (9): 3358–3367. Bibcode:2009JCoPh.228.3358B. ISSN 0021-9991. doi:10.1016/j.jcp.2009.01.023.
• Beale, J. Thomas. Smoothing Properties of Implicit Finite Difference Methods for a Diffusion Equation in Maximum Norm. SIAM Journal on Numerical Analysis. 2009, 47 (4): 2476–2495. doi:10.1137/080731645.
• Tlupova, Svetlana; Beale, J. Thomas. Nearly Singular Integrals in 3D Stokes Flow. Communications in Computational Physics. 2013, 14 (5): 1207–1227. Bibcode:2013CCoPh..14.1207T. doi:10.4208/cicp.020812.080213a.
• Beale, J. Thomas; Ying, Wenjun; Wilson, Jason R. A Simple Method for Computing Singular or Nearly Singular Integrals on Closed Surfaces. Communications in Computational Physics. 2016, 20 (3): 733–753. Bibcode:2016CCoPh..20..733B. S2CID 41606464. arXiv:1508.00265 . doi:10.4208/cicp.030815.240216a.

參考資料

1. Fluid dynamics, Analysis, and Numerics 2010: A conference in honor of J. Thomas Beale. Department of Mathematica, Duke University. June 2020 [2023-06-30]. （原始內容存檔於2022-07-03）.
2. Lillian Neidlinger Beale. Savannah Morning News. October 8, 2004 [2023-06-30]. （原始內容存檔於2023-06-30）.
3. Seventy-Third Annual Commencement (PDF). California Institute of Technology. June 9, 1967 [2023-06-30]. （原始內容存檔 (PDF)於2023-06-30）.
4. Beale, James Thomas. Purely Imaginary Scattering Frequencies for Exterior Domains. 1973 [2023-06-30]. （原始內容存檔於2023-06-30）.
5. 詹姆斯·托馬斯·比爾在數學譜系計劃的資料。
6. Professor J. Thomas Beale Retires. Department of Mathematics, Duke University. May 20, 2016 [2023-06-30]. （原始內容存檔於2023-06-30）.
7. Beale, J. Thomas. Analytical and Numerical Aspects of Fluid Interfaces. Proceedings of the International Congress of Mathematicians, 1994, Zürich. Basel: Birkhäuser. 1995: 1055–1064. ISBN 978-3-0348-9897-3. doi:10.1007/978-3-0348-9078-6_98.
8. Broadwell, James E. Shock Structure in a Simple Discrete Velocity Gas. Physics of Fluids. 1964, 7 (8): 1243. Bibcode:1964PhFl....7.1243B. ISSN 0031-9171. doi:10.1063/1.1711368.