Willard Miller

8.7k total citations · 3 hit papers
153 papers, 5.8k citations indexed

About

Willard Miller is a scholar working on Statistical and Nonlinear Physics, Atomic and Molecular Physics, and Optics and Applied Mathematics. According to data from OpenAlex, Willard Miller has authored 153 papers receiving a total of 5.8k indexed citations (citations by other indexed papers that have themselves been cited), including 80 papers in Statistical and Nonlinear Physics, 75 papers in Atomic and Molecular Physics, and Optics and 39 papers in Applied Mathematics. Recurrent topics in Willard Miller's work include Quantum Mechanics and Non-Hermitian Physics (66 papers), Nonlinear Waves and Solitons (53 papers) and Quantum chaos and dynamical systems (29 papers). Willard Miller is often cited by papers focused on Quantum Mechanics and Non-Hermitian Physics (66 papers), Nonlinear Waves and Solitons (53 papers) and Quantum chaos and dynamical systems (29 papers). Willard Miller collaborates with scholars based in United States, New Zealand and Mexico. Willard Miller's co-authors include Л.В. Овсянников, E. G. Kalnins, J. M. Kress, H. S. Valk, G. S. Pogosyan, E. G. Kalnins, Charles P. Boyer, P. Winternitz, Gareth Williams and J. Patera and has published in prestigious journals such as Physics Today, Mathematics of Computation and Communications in Mathematical Physics.

In The Last Decade

Willard Miller

152 papers receiving 5.2k citations

Hit Papers

Group Analysis of Differential Equations. 1972 2026 1990 2008 1985 1984 1972 500 1000 1.5k
What are hit papers?

Hit papers significantly outperform the citation benchmark for their cohort. A paper qualifies if it has ≥500 total citations, achieves ≥1.5× the top-1% citation threshold for papers in the same subfield and year (this is the minimum needed to enter the top 1%, not the average within it), or reaches the top citation threshold in at least one of its specific research topics.

  1. Group Analysis of Differential Equations.
    1985 1.9k citations Willard Miller et al. profile →
  2. Symmetry and Separation of Variables
    1984 465 citations Willard Miller profile →
  3. Symmetry groups and their applications
    1972 335 citations Willard Miller CERN Document Server (European Organization for Nuclear Research) profile →

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name h Career Trend Papers Cites
Willard Miller United States 33 3.5k 2.1k 938 903 727 153 5.8k
F. Calogero Italy 37 5.2k 1.5× 3.1k 1.5× 538 0.6× 2.0k 2.2× 642 0.9× 364 7.9k
Wilhelm Magnus United States 20 1.4k 0.4× 2.4k 1.1× 1.2k 1.2× 1.8k 1.9× 504 0.7× 42 8.0k
V. I. Arnold Russia 2 2.8k 0.8× 1000 0.5× 418 0.4× 843 0.9× 576 0.8× 3 5.6k
F. W. J. Olver United States 26 1.3k 0.4× 1.8k 0.9× 2.1k 2.3× 458 0.5× 988 1.4× 85 7.4k
E. T. Whittaker United States 10 1.5k 0.4× 978 0.5× 813 0.9× 731 0.8× 248 0.3× 25 5.0k
H. Bateman 9 1.8k 0.5× 2.2k 1.1× 3.1k 3.3× 794 0.9× 884 1.2× 10 9.2k
Arthur Erdélyi United States 5 1.6k 0.4× 1.9k 0.9× 2.7k 2.8× 697 0.8× 763 1.0× 7 8.0k
Percy Deift United States 43 3.3k 0.9× 1.0k 0.5× 2.1k 2.3× 1.1k 1.2× 598 0.8× 110 7.9k
Harvey Segur United States 33 9.8k 2.8× 2.9k 1.4× 343 0.4× 1.8k 2.0× 1.1k 1.6× 70 11.5k
N. N. Bogolyubov Ukraine 18 1.7k 0.5× 1.8k 0.9× 524 0.6× 233 0.3× 455 0.6× 113 5.6k

Countries citing papers authored by Willard Miller

Since Specialization
Citations

This map shows the geographic impact of Willard Miller's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Willard Miller with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Willard Miller more than expected).

Fields of papers citing papers by Willard Miller

Since Specialization
Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Willard Miller. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Willard Miller. The network helps show where Willard Miller may publish in the future.

Co-authorship network of co-authors of Willard Miller

This figure shows the co-authorship network connecting the top 25 collaborators of Willard Miller. A scholar is included among the top collaborators of Willard Miller based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Willard Miller. Willard Miller is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

20 of 20 papers shown
1.
Linares, Román, et al.. (2021). Classical n-body system in geometrical and volume variables: I. Three-body case. International Journal of Modern Physics A. 36(18). 2150140–2150140. 3 indexed citations
2.
Turbiner, Alexander V., et al.. (2020). From two-dimensional (super-integrable) quantum dynamics to (super-integrable) three-body dynamics. Journal of Physics A Mathematical and Theoretical. 54(1). 15204–15204. 3 indexed citations
3.
Kalnins, E. G., et al.. (2017). Bôcher and Abstract Contractions of 2nd Order Quadratic Algebras. Symmetry Integrability and Geometry Methods and Applications. 3 indexed citations
4.
Kalnins, E. G., et al.. (2016). 2D 2nd order Laplace superintegrable systems, Heun equations, QES and Bocher contractions. arXiv (Cornell University). 1 indexed citations
5.
Kalnins, E. G., et al.. (2016). Bôcher Contractions of Conformally Superintegrable Laplace Equations. Symmetry Integrability and Geometry Methods and Applications. 6 indexed citations
6.
Chen, Yuxuan, et al.. (2015). Examples of Complete Solvability of 2D Classical Superintegrable Systems. Symmetry Integrability and Geometry Methods and Applications. 3 indexed citations
7.
Kalnins, E. G., J. M. Kress, Willard Miller, & Sarah Post. (2010). Laplace-type equations as conformal superintegrable systems. Advances in Applied Mathematics. 46(1-4). 396–416. 8 indexed citations
8.
Kalnins, E. G. & Willard Miller. (1996). A note on tensor products of q-algebra representations and orthogonal polynomials. Journal of Computational and Applied Mathematics. 68(1-2). 197–207. 8 indexed citations
9.
Kalnins, E. G., Willard Miller, & Gareth Williams. (1992). Recent advances in the use of separation of variables methods in general relativity. Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences. 340(1658). 337–352. 17 indexed citations
10.
Kalnins, E. G., Willard Miller, & Gareth Williams. (1989). Teukolsky–Starobinsky identities for arbitrary spin. Journal of Mathematical Physics. 30(12). 2925–2929. 11 indexed citations
11.
Kalnins, E. G., Willard Miller, & Gareth Williams. (1986). Electromagnetic waves in Kerr geometry. Proceedings of the Royal Society of London A Mathematical and Physical Sciences. 408(1834). 23–30. 2 indexed citations
12.
Kalnins, E. G. & Willard Miller. (1985). Generalized Stäckel matrices. Journal of Mathematical Physics. 26(9). 2168–2173. 24 indexed citations
13.
Kalnins, E. G., et al.. (1984). Separation of variables for complex Riemannian spaces of constant curvature - I. Orthogonal separable coordinates for S n c and E n c. Proceedings of the Royal Society of London A Mathematical and Physical Sciences. 394(1806). 183–206. 22 indexed citations
14.
Kalnins, E. G. & Willard Miller. (1984). The theory of orthogonal R-separation for Helmholtz equations. Advances in Mathematics. 51(1). 91–106. 17 indexed citations
15.
Kalnins, E. G. & Willard Miller. (1983). Conformal Killing Tensors and Variable Separation for Hamilton–Jacobi Equations. SIAM Journal on Mathematical Analysis. 14(1). 126–137. 17 indexed citations
16.
Miller, Willard, J. Patera, & P. Winternitz. (1981). Subgroups of Lie groups and separation of variables. Journal of Mathematical Physics. 22(2). 251–260. 28 indexed citations
17.
Miller, Willard. (1972). Lie theory and difference equations. II. Journal of Mathematical Analysis and Applications. 39(2). 406–422. 1 indexed citations
18.
Miller, Willard. (1972). Symmetry groups and their applications. CERN Document Server (European Organization for Nuclear Research). 335 indexed citations breakdown →
19.
Miller, Willard. (1969). Lie theory and difference equations. I. Journal of Mathematical Analysis and Applications. 28(2). 383–399. 27 indexed citations
20.
Miller, Willard. (1965). On a generalization of bessel functions. Communications on Pure and Applied Mathematics. 18(3). 493–499. 9 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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