Peter W. Bates

6.8k total citations · 2 hit papers
98 papers, 4.7k citations indexed

About

Peter W. Bates is a scholar working on Computational Theory and Mathematics, Applied Mathematics and Control and Systems Engineering. According to data from OpenAlex, Peter W. Bates has authored 98 papers receiving a total of 4.7k indexed citations (citations by other indexed papers that have themselves been cited), including 39 papers in Computational Theory and Mathematics, 32 papers in Applied Mathematics and 28 papers in Control and Systems Engineering. Recurrent topics in Peter W. Bates's work include Advanced Mathematical Modeling in Engineering (38 papers), Stability and Controllability of Differential Equations (27 papers) and Solidification and crystal growth phenomena (21 papers). Peter W. Bates is often cited by papers focused on Advanced Mathematical Modeling in Engineering (38 papers), Stability and Controllability of Differential Equations (27 papers) and Solidification and crystal growth phenomena (21 papers). Peter W. Bates collaborates with scholars based in United States, China and Greece. Peter W. Bates's co-authors include Kening Lu, Bixiang Wang, Paul C. Fife, Adam Chmaj, Nicholas D. Alikakos, Xinfu Chen, Xiaofeng Ren, Giorgio Fusco, Xuefeng Wang and Hannelore Lisei and has published in prestigious journals such as The Journal of Chemical Physics, SHILAP Revista de lepidopterología and Proceedings of the Royal Society B Biological Sciences.

In The Last Decade

Peter W. Bates

96 papers receiving 4.2k citations

Hit Papers

align trajectories

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.

Traveling Waves in a Convolution Model for Phase Transitions

1997 413 citations Peter W. Bates et al. Archive for Rational Mechanics and Analysis profile →
Random attractors for stochastic reaction–diffusion equations on unbounded domains

2008 321 citations Peter W. Bates, Kening Lu et al. Journal of Differential Equations profile →

Peers — A (Enhanced Table)

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

Name	h						Papers	Cites
Peter W. Bates United States	36	2.1k	1.6k	1.4k	993	851	98	4.7k
Daniel Henry France	27	1.7k 0.8×	2.2k 1.4×	1.9k 1.3×	1.1k 1.1×	1.3k 1.5×	161	7.2k
Marshall Slemrod United States	33	1.1k 0.5×	1.5k 0.9×	1.4k 1.0×	644 0.6×	990 1.2×	118	5.0k
Konstantin Mischaikow United States	38	1.5k 0.7×	313 0.2×	400 0.3×	612 0.6×	1.1k 1.3×	138	4.9k
Hiroshi Matano Japan	27	930 0.4×	763 0.5×	1.2k 0.8×	302 0.3×	522 0.6×	72	2.3k
D. H. Sattinger United States	28	1.0k 0.5×	1.2k 0.7×	1.5k 1.0×	553 0.6×	1.5k 1.8×	74	4.7k
Kening Lu United States	36	2.1k 1.0×	2.7k 1.7×	731 0.5×	1.1k 1.1×	997 1.2×	105	3.8k
Shui-Nee Chow United States	31	878 0.4×	1.2k 0.7×	1.1k 0.8×	1.4k 1.4×	848 1.0×	91	4.9k
John Mallet‐Paret United States	36	1.1k 0.5×	1.3k 0.8×	999 0.7×	1.7k 1.7×	666 0.8×	75	4.6k
D. G. Aronson United States	25	1.4k 0.7×	559 0.3×	1.9k 1.3×	1.2k 1.2×	1.2k 1.4×	70	5.0k
Herbert Amann Switzerland	42	3.8k 1.9×	1.8k 1.1×	5.2k 3.6×	285 0.3×	2.3k 2.6×	117	8.1k

Countries citing papers authored by Peter W. Bates

Since Specialization

Citations

This map shows the geographic impact of Peter W. Bates'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 Peter W. Bates with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Peter W. Bates more than expected).

Fields of papers citing papers by Peter W. Bates

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Peter W. Bates. 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 Peter W. Bates. The network helps show where Peter W. Bates may publish in the future.

Co-authorship network of co-authors of Peter W. Bates

This figure shows the co-authorship network connecting the top 25 collaborators of Peter W. Bates. A scholar is included among the top collaborators of Peter W. Bates 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 Peter W. Bates. Peter W. Bates is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

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20 of 20 papers shown

Bates, Peter W., et al.. (2022). Is bisphosphonate use a risk factor for atypical periprosthetic/peri-implant fractures? – A metanalysis of retrospective cohort studies and systematic review of the current evidence. Orthopaedics & Traumatology Surgery & Research. 109(2). 103475–103475. 5 indexed citations

Wen, Zhenshu, Peter W. Bates, & Mingji Zhang. (2021). Effects on I – V relations from small permanent charge and channel geometry via classical Poisson–Nernst–Planck equations with multiple cations. Nonlinearity. 34(6). 4464–4502. 15 indexed citations

Bates, Peter W., Giorgio Fusco, & Georgia Karali. (2018). Gradient Dynamics: Motion Near a Manifold of Quasi-Equilibria. SIAM Journal on Applied Dynamical Systems. 17(3). 2106–2145. 2 indexed citations

Bates, Peter W., et al.. (2017). Multiphase Solutions to the Vector Allen–Cahn Equation: Crystalline and Other Complex Symmetric Structures. Archive for Rational Mechanics and Analysis. 225(2). 685–715. 6 indexed citations

Lu, H. Peter, Peter W. Bates, Wenping Chen, & Mingji Zhang. (2017). The spectral collocation method for efficiently solving PDEs with fractional Laplacian. Advances in Computational Mathematics. 44(3). 861–878. 5 indexed citations

Bates, Peter W., et al.. (2013). Entire Solutions with Six-fold Junctions to Elliptic Gradient Systems with Triangle Symmetry. Advanced Nonlinear Studies. 13(1). 1–11. 5 indexed citations

Bates, Peter W., Kening Lu, & Bixiang Wang. (2008). Random attractors for stochastic reaction–diffusion equations on unbounded domains. Journal of Differential Equations. 246(2). 845–869. 321 indexed citations breakdown →

Bates, Peter W. & Xing‐Bin Pan. (2008). Nucleation of Instability of the Meissner State of 3-Dimensional Superconductors. Communications in Mathematical Physics. 283(3). 861–861. 7 indexed citations

Bates, Peter W., Gang Wei, & Shan Zhao. (2007). Minimal molecular surfaces and their applications. Journal of Computational Chemistry. 29(3). 380–391. 102 indexed citations

10.

Bates, Peter W. & Guangyu Zhao. (2006). Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal. Journal of Mathematical Analysis and Applications. 332(1). 428–440. 144 indexed citations

11.

Bates, Peter W. & Jianlong Han. (2005). The Neumann boundary problem for a nonlocal Cahn–Hilliard equation. Journal of Differential Equations. 212(2). 235–277. 81 indexed citations

12.

Bates, Peter W. & Jianlong Han. (2005). The Dirichlet boundary problem for a nonlocal Cahn–Hilliard equation. Journal of Mathematical Analysis and Applications. 311(1). 289–312. 48 indexed citations

13.

Bates, Peter W. & Fengxin Chen. (2002). Spectral analysis and multidimensional stability of traveling waves for nonlocal Allen–Cahn equation. Journal of Mathematical Analysis and Applications. 273(1). 45–57. 37 indexed citations

14.

Bates, Peter W., Xinfu Chen, & Adam Chmaj. (2000). Equilibria and Traveling Waves for Bistable Equations with Non-Local and Discrete Dissipation (Nonlinear Diffusive Systems--Dynamics and Asymptotics). Kyoto University Research Information Repository (Kyoto University). 1178(1178). 48–71. 2 indexed citations

15.

Bates, Peter W. & Fengxin Chen. (1999). Periodic traveling waves for a nonlocal integro-differential model. SHILAP Revista de lepidopterología. 28 indexed citations

16.

Bates, Peter W., et al.. (1995). A numerical scheme for the two phase Mullins-Sekerka problem.. Electronic Journal of Differential Equations. 1995(11). 1–27. 20 indexed citations

17.

Alikakos, Nicholas D., Peter W. Bates, & Giorgio Fusco. (1991). Slow motion for the Cahn-Hilliard equation in one space dimension. Journal of Differential Equations. 90(1). 81–135. 145 indexed citations

18.

Alikakos, Nicholas D. & Peter W. Bates. (1988). Stabilization of solutions for a class of degenerate equations in divergence form in one space dimension. Journal of Differential Equations. 73(2). 363–393. 10 indexed citations

19.

Bates, Peter W.. (1982). Reduction theorems for a class of semilinear equations at resonance. Proceedings of the American Mathematical Society. 84(1). 73–78. 4 indexed citations

20.

Bates, Peter W.. (1982). Reduction Theorems for a Class of Semilinear Equations at Resonance. Proceedings of the American Mathematical Society. 84(1). 73–73. 2 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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