World's Best Scientists 2026 revealed!

D-Index & Metrics

Mathematics

D-Index
42
Citations
8617
World Ranking
1772
National Ranking
762

Peter W. Bates publication distribution in Mathematics in 2026

The chart shows the distribution of publications by all Research.com ranked scientists in the field of Mathematics in 2026. The highlighted bar marks where Peter W. Bates sits on this spectrum.

42–46 publications: 3 scientists 47–51 publications: 5 scientists 52–56 publications: 7 scientists 57–61 publications: 20 scientists 62–66 publications: 14 scientists 67–71 publications: 25 scientists 72–76 publications: 19 scientists 77–81 publications: 35 scientists 82–86 publications: 50 scientists 87–91 publications: 60 scientists 92–96 publications: 86 scientists 97–101 publications: 84 scientists 102–106 publications: 83 scientists 107–111 publications: 90 scientists 112–116 publications: 99 scientists 117–121 publications: 90 scientists 122–126 publications: 91 scientists 127–131 publications: 109 scientists 132–136 publications: 110 scientists 137–141 publications: 98 scientists 142–146 publications: 112 scientists 147–151 publications: 102 scientists 152–156 publications: 88 scientists 157–161 publications: 106 scientists 162–166 publications: 83 scientists 167–171 publications: 102 scientists 172–176 publications: 77 scientists 177–181 publications: 81 scientists 182–186 publications: 78 scientists 187–191 publications: 71 scientists 192–196 publications: 92 scientists 197–201 publications: 64 scientists 202–206 publications: 69 scientists 207–211 publications: 64 scientists 212–216 publications: 62 scientists 217–221 publications: 58 scientists 222–226 publications: 53 scientists 227–231 publications: 50 scientists 232–236 publications: 46 scientists 237–241 publications: 46 scientists 242–246 publications: 46 scientists 247–251 publications: 43 scientists 252–256 publications: 29 scientists 257–261 publications: 45 scientists 262–266 publications: 30 scientists 267–271 publications: 33 scientists 272–276 publications: 34 scientists 277–281 publications: 30 scientists 282–286 publications: 31 scientists 287–291 publications: 21 scientists 292–296 publications: 34 scientists 297–301 publications: 26 scientists 302–306 publications: 10 scientists 307–311 publications: 17 scientists 312–316 publications: 23 scientists 317–321 publications: 13 scientists 322–326 publications: 16 scientists 327–331 publications: 26 scientists 332–336 publications: 13 scientists 337–341 publications: 13 scientists 342–346 publications: 16 scientists 347–351 publications: 17 scientists 352–356 publications: 12 scientists 357–361 publications: 18 scientists 362–366 publications: 18 scientists 367–371 publications: 9 scientists 372–376 publications: 11 scientists 377–381 publications: 8 scientists 382–386 publications: 8 scientists 387–391 publications: 9 scientists 392–396 publications: 9 scientists 397–401 publications: 8 scientists 402–406 publications: 11 scientists 407–411 publications: 6 scientists 412–416 publications: 6 scientists 417–421 publications: 9 scientists 422–426 publications: 8 scientists 427–431 publications: 5 scientists 432–436 publications: 8 scientists 437–441 publications: 8 scientists 442–446 publications: 4 scientists 447–451 publications: 4 scientists 452–456 publications: 4 scientists 457–461 publications: 2 scientists 462–466 publications: 2 scientists 467–471 publications: 4 scientists 472–476 publications: 3 scientists 477–481 publications: 3 scientists 482–486 publications: 6 scientists 487–491 publications: 3 scientists 492–496 publications: 5 scientists 497–501 publications: 5 scientists 502–506 publications: 1 scientists 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientists 522–526 publications: 3 scientists 527–531 publications: 1 scientists 532–536 publications: 4 scientists 537+ publications: 100 scientists
42 publications 537+

This scientist: 113 publications — 17th percentile

17% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 537 publications or more.

Peter W. Bates D-index placement in Mathematics in 2026

The chart shows the D-index (discipline H-index) distribution of Mathematics scientists ranked by Research.com in 2026. The highlighted bar marks where Peter W. Bates sits on this spectrum.

30 D-Index: 174 scientists 31 D-Index: 151 scientists 32 D-Index: 174 scientists 33 D-Index: 117 scientists 34 D-Index: 136 scientists 35 D-Index: 127 scientists 36 D-Index: 145 scientists 37 D-Index: 153 scientists 38 D-Index: 150 scientists 39 D-Index: 150 scientists 40 D-Index: 138 scientists 41 D-Index: 136 scientists 42 D-Index: 93 scientists 43 D-Index: 108 scientists 44 D-Index: 115 scientists 45 D-Index: 112 scientists 46 D-Index: 103 scientists 47 D-Index: 75 scientists 48 D-Index: 59 scientists 49 D-Index: 67 scientists 50 D-Index: 60 scientists 51 D-Index: 57 scientists 52 D-Index: 59 scientists 53 D-Index: 62 scientists 54 D-Index: 60 scientists 55 D-Index: 50 scientists 56 D-Index: 42 scientists 57 D-Index: 54 scientists 58 D-Index: 50 scientists 59 D-Index: 42 scientists 60 D-Index: 41 scientists 61 D-Index: 35 scientists 62 D-Index: 40 scientists 63 D-Index: 21 scientists 64 D-Index: 31 scientists 65 D-Index: 27 scientists 66 D-Index: 29 scientists 67 D-Index: 19 scientists 68 D-Index: 25 scientists 69 D-Index: 17 scientists 70 D-Index: 18 scientists 71 D-Index: 12 scientists 72 D-Index: 14 scientists 73 D-Index: 13 scientists 74 D-Index: 18 scientists 75 D-Index: 9 scientists 76 D-Index: 11 scientists 77 D-Index: 10 scientists 78 D-Index: 9 scientists 79 D-Index: 16 scientists 80 D-Index: 12 scientists 81 D-Index: 10 scientists 82 D-Index: 5 scientists 83 D-Index: 5 scientists 84 D-Index: 13 scientists 85 D-Index: 6 scientists 86+ D-Index: 99 scientists
30 D-Index 86+

This scientist: 42 D-Index — 51st percentile

51% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 86 D-Index or more.

Research.com Recognitions

  • 2013 - Fellow of the American Mathematical Society

Overview

Peter W. Bates is affiliated with Michigan State University in the United States. The researcher's work spans several fields including Engineering and Medicine, with particular focus on subfields such as Biomedical Engineering, Surgery, Molecular Biology, Oral Surgery, and Statistical and Nonlinear Physics.

Their recent publications address topics related to nanopore and nanochannel transport, ion channel regulation, orthopaedic implants, dental implant techniques, microfluidic applications, stochastic dynamics, and the thermal properties of materials.

Notable recent papers include:

  • Small Permanent Charge Effects on Individual Fluxes via Poisson-Nernst-Planck Models with Multiple Cations, 2021, Journal of Nonlinear Science
  • Dynamics of ionic flows via Poisson-Nernst-Planck systems with local hard-sphere potentials: Competition between cations, 2020, Mathematical Biosciences & Engineering
  • Effects on I - V relations from small permanent charge and channel geometry via classical Poisson-Nernst-Planck equations with multiple cations, 2021, Nonlinearity
  • 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, 2022, Orthopaedics & Traumatology Surgery & Research
  • L'utilisation de bisphosphonates est-elle un facteur de risque de fractures périprothétiques atypiques? Méta-analyse d'études de cohorte rétrospectives et revue systématique de la littérature actuelle, 2023, Revue de Chirurgie Orthopédique et Traumatologique

Frequent coauthors who have collaborated on multiple occasions with this researcher include:

  • Zhenshu Wen
  • Mingji Zhang
  • Pedro Ferreira
  • Ahmed Daoub
  • Debashis Dass

Key publication venues for this researcher's work are:

  • Journal of Nonlinear Science
  • Mathematical Biosciences & Engineering
  • Nonlinearity
  • Orthopaedics & Traumatology Surgery & Research
  • Revue de Chirurgie Orthopédique et Traumatologique

Their research covers main topics such as:

  • Nanopore and Nanochannel Transport Studies
  • Ion channel regulation and function
  • Orthopaedic implants and arthroplasty
  • Dental Implant Techniques and Outcomes
  • Microfluidic and Capillary Electrophoresis Applications
  • Stochastic dynamics and bifurcation
  • Thermal properties of materials

Peter W. Bates was recognized as a Fellow of the American Mathematical Society in 2013.

Best Publications

  • Traveling Waves in a Convolution Model for Phase Transitions

    Peter W. Bates;Paul C. Fife;Xiaofeng Ren;Xuefeng Wang

  • Convergence of the Cahn-Hilliard equation to the Hele-Shaw model

    Nicholas D. Alikakos;Nicholas D. Alikakos;Nicholas D. Alikakos;Peter W. Bates;Peter W. Bates;Peter W. Bates;Xinfu Chen;Xinfu Chen;Xinfu Chen

  • Random attractors for stochastic reaction–diffusion equations on unbounded domains

    Peter W. Bates;Kening Lu;Bixiang Wang

  • Invariant Manifolds for Semilinear Partial Differential Equations

    Peter W. Bates;Christopher K. R. T. Jones

  • ATTRACTORS FOR STOCHASTIC LATTICE DYNAMICAL SYSTEMS

    Peter W. Bates;Hannelore Lisei;Kening Lu

  • ATTRACTORS FOR LATTICE DYNAMICAL SYSTEMS

    Peter W. Bates;Kening Lu;Bixiang Wang

  • Slow motion for the Cahn-Hilliard equation in one space dimension

    Nicholas Alikakos;Peter W. Bates;Giorgio Fusco

  • A Discrete Convolution Model¶for Phase Transitions

    Peter W. Bates;Adam Chmaj

  • An integrodifferential model for phase transitions: Stationary solutions in higher space dimensions

    Peter W. Bates;Adam Chmaj

  • Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal

    Peter W. Bates;Guangyu Zhao

  • The dynamics of nucleation for the Cahn-Hilliard equation

    Peter W. Bates;Paul C. Fife

  • Existence and Persistence of Invariant Manifolds for Semiflows in Banach Space

    Peter W. Bates;Kening Lu;Chongchun Zeng

  • The Neumann boundary problem for a nonlocal Cahn–Hilliard equation

    Peter W. Bates;Jianlong Han

  • Traveling Waves of Bistable Dynamics on a Lattice

    Peter W. Bates;Xinfu Chen;Adam J. J. Chmaj

  • Best practice framework for Patient and Public Involvement (PPI) in collaborative data analysis of qualitative mental health research: methodology development and refinement

    Helen Jennings;Mike Slade;Peter Bates;Emma Munday

  • ON SOME NONLOCAL EVOLUTION EQUATIONS ARISING IN MATERIALS SCIENCE

    Unknown

  • Attractors of non-autonomous stochastic lattice systems in weighted spaces

    Peter W. Bates;Kening Lu;Bixiang Wang

  • Periodic traveling waves and locating oscillating patterns in multidimensional domains

    Nicholas D. Alikakos;Nicholas D. Alikakos;Peter W. Bates;Xinfu Chen

  • Equilibria with Many Nuclei for the Cahn–Hilliard Equation

    Peter W. Bates;Giorgio Fusco

  • Minimal molecular surfaces and their applications.

    Peter W. Bates;Guo-Wei Wei;Shan Zhao

  • Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability

    Peter W. Bates;E. Norman Dancer;Junping Shi

Frequent Co-Authors

Kening Lu
Kening Lu Brigham Young University
Xinfu Chen
Xinfu Chen University of Pittsburgh
Christopher K. R. T. Jones
Christopher K. R. T. Jones University of North Carolina at Chapel Hill
Mike Slade
Mike Slade University of Nottingham
Paul C. Fife
Paul C. Fife University of Utah
Birgit Völlm
Birgit Völlm University of Rostock
Guo-Wei Wei
Guo-Wei Wei Michigan State University
Bixiang Wang
Bixiang Wang New Mexico Institute of Mining and Technology
Shan Zhao
Shan Zhao University of Alabama
Justine Schneider
Justine Schneider University of Nottingham

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