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Subfield · Physics and Astronomy

Statistical and Nonlinear Physics research

Statistical and Nonlinear Physics is a subfield of Physics and Astronomy. Science Explorer counts 460k research works in it since 1950. 19.2% of them reached the world's top 10% most cited for their field and year.

In short: branch of physics.

Research works
460k
fractional, since 1950
In the world top 10%
88k
per year above
Top-10% rate
19.2%
share of its works in the world top 10%
Topics
16
Growth, 2013–17 → 2018–22
+12%
the tick is no change

What is Statistical and Nonlinear Physics research about, and what is growing?

By the world's output in 2019–23, its most used keywords are Network Dynamics, Social Influence, Community Structure, Scale-Free Networks, Nonlinear Equations, Rogue Waves. Gaining share since 2009–13: Deep Learning, Partial Differential Equations, Chaotic Dynamics, Inertial Electrostatic Confinement Fusion, Community Structure. Losing share: Optics, Spectroscopy, Quantum Mechanics, Complex Systems.

▲ gaining share of this field◆ holding its share▼ losing share

Size is the world's fractional works in 2019–23 in the topics tagged with each word; colour compares the word's share of this field with 2009–13. Each links to the topic it comes from most.

All 38 words, with their numbers
  1. Network Dynamics22k◆ 1.10×2 topics
  2. Social Influence22k◆ 1.10×2 topics
  3. Community Structure14k◆ 1.15×1 topic
  4. Scale-Free Networks14k◆ 1.15×1 topic
  5. Nonlinear Equations9,085◆ 1.12×1 topic
  6. Rogue Waves9,085◆ 1.12×1 topic
  7. Fluctuation Theorems8,962◆ 0.99×1 topic
  8. Stochastic Thermodynamics8,962◆ 0.99×1 topic
  9. Bounded Confidence7,624◆ 1.03×1 topic
  10. Opinion Dynamics7,624◆ 1.03×1 topic
  11. Quantum Gravity6,419◆ 0.94×2 topics
  12. Deep Learning6,238▲ 2.2×1 topic
  13. Partial Differential Equations6,238▲ 2.2×1 topic
  14. Nonlinear Photonic Systems6,090◆ 1.15×1 topic
  15. Solitons6,090◆ 1.15×1 topic
  16. Lagrangian Coherent Structures5,537▼ 0.75×1 topic
  17. Quantum Chaos5,537▼ 0.75×1 topic
  18. Complex Systems4,477▼ 0.70×2 topics
  19. Nonlinear Dynamics4,477▼ 0.70×2 topics
  20. Chaos4,293▼ 0.70×1 topic
  21. Synchronization4,293▼ 0.70×1 topic
  22. Lorentz Violation4,248▼ 0.86×1 topic
  23. Noncommutative Field Theory4,248▼ 0.86×1 topic
  24. Brownian Motors4,010▼ 0.86×1 topic
  25. Stochastic Resonance4,010▼ 0.86×1 topic
  26. Experimental Tools3,580◆ 0.95×1 topic
  27. Smartphones3,580◆ 0.95×1 topic
  28. Quantum Mechanics3,036▼ 0.63×2 topics
  29. Long-Range Interactions2,605◆ 0.89×1 topic
  30. Nonextensive Statistical Mechanics2,605◆ 0.89×1 topic
  31. Optics2,229▼ 0.52×1 topic
  32. Spectroscopy2,229▼ 0.52×1 topic
  33. Cantorian-Fractal2,171◆ 1.13×1 topic
  34. E-Infinity Theory2,171◆ 1.13×1 topic
  35. Chaotic Dynamics807▲ 1.57×1 topic
  36. Inertial Electrostatic Confinement Fusion807▲ 1.57×1 topic
  37. Meta-Structures184▼ 0.78×1 topic
  38. Self-Organization184▼ 0.78×1 topic

Which countries lead Statistical and Nonlinear Physics research?

On research quality in 2022–2025, China, the United States and the United Kingdom rank highest in Statistical and Nonlinear Physics. By volume, China and the United States publish the most (17k and 9k works in 2022–2025).

By research quality, 2022–2025

  1. 1 China · #2 all time 20.6% top 10% · 17k works
  2. 2 United States · #1 all time 17.8% top 10% · 9k works
  3. 3 United Kingdom · #4 all time 20.6% top 10% · 2.2k works
  4. 4 India · #9 all time 15.8% top 10% · 4k works
  5. 5 Germany · #3 all time 18.2% top 10% · 2.7k works
  6. 6 Italy · #6 all time 19.8% top 10% · 2.3k works
  7. 7 France · #5 all time 15.7% top 10% · 2.3k works
  8. 8 Saudi Arabia · #20 all time 27.9% top 10% · 1k works
  9. 9 Spain · #10 all time 18.8% top 10% · 1.3k works
  10. 10 Pakistan · #29 all time 30.8% top 10% · 757 works

The track on each row is that row’s top-10% rate. The ranking itself is the composite score, which the rate is only one part of.

Of 47 countries ranked in Statistical and Nonlinear Physics. Composite of field-normalised excellence (50%), output (30%) and citations (20%); the bracket is the all-time rank.

All countries ranked in Statistical and Nonlinear Physics

By volume, 2022–2025

  1. 1 China 17k works
  2. 2 United States 9k works
  3. 3 India 4k works
  4. 4 Russia 2.8k works
  5. 5 Germany 2.7k works
  6. 6 France 2.3k works
  7. 7 Italy 2.3k works
  8. 8 United Kingdom 2.2k works
  9. 9 Japan 2k works
  10. 10 Brazil 1.4k works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 37.7%United States: 19.5%India: 8.7%Russia: 6.0%6 others listed: 28.1%38%largest
China17k · 37.7%United States9,015 · 19.5%India4,014 · 8.7%Russia2,791 · 6.0%6 others listed13k · 28.1%

Shares of the rows listed above, not of the whole node.

Which institutions lead Statistical and Nonlinear Physics research?

Henan Polytechnic University (China) ranks first in Statistical and Nonlinear Physics on research quality in 2022–2025, followed by Northwestern Polytechnical University and University of Delhi.

By research quality, 2022–2025

  1. 1 Henan Polytechnic University China · Jiaozuo 58.3% top 10% · 106 works
  2. 2 Northwestern Polytechnical University China · Xi'an · #87 all time 27.9% top 10% · 190 works
  3. 3 University of Delhi India · New Delhi 41.2% top 10% · 102 works
  4. 4 Stanford University United States · Stanford · #3 all time 35.7% top 10% · 118 works
  5. 5 Beijing University of Posts and Telecommunications China · Beijing · #50 all time 24.1% top 10% · 192 works
  6. 6 Tsinghua University China · Beijing · #22 all time 24.3% top 10% · 228 works
  7. 7 Massachusetts Institute of Technology United States · Cambridge · #1 all time 29.0% top 10% · 138 works
  8. 8 Centre National de la Recherche Scientifique France · Paris · #12 all time 18.3% top 10% · 338 works
  9. 9 University of Oxford United Kingdom · Oxford · #15 all time 27.8% top 10% · 130 works
  10. 10 Jiangsu University China · Zhenjiang 28.9% top 10% · 149 works

The track on each row is that row’s top-10% rate. The ranking itself is the composite score, which the rate is only one part of.

Of 172 institutions above the floor of 40 fractional works in Statistical and Nonlinear Physics.

Top 100 Statistical and Nonlinear Physics institutions

By volume, 2022–2025

  1. 1 Centre National de la Recherche Scientifique France 338 works
  2. 2 Tsinghua University China 228 works
  3. 3 Shanghai Jiao Tong University China 227 works
  4. 4 Harbin Institute of Technology China 208 works
  5. 5 The University of Tokyo Japan 198 works
  6. 6 Beihang University China 196 works
  7. 7 Beijing University of Posts and Telecommunications China 192 works
  8. 8 Northwestern Polytechnical University China 191 works
  9. 9 National University of Defense Technology China 189 works
  10. 10 Lomonosov Moscow State University Russia 186 works

Who are the leading researchers in Statistical and Nonlinear Physics?

Among the most productive authors in Statistical and Nonlinear Physics, Yoshua Bengio, Stanley Osher and Edward Witten rank highest on the composite score.

  1. 1 Yoshua Bengio Canada · #4 worldwide 17k citations · 298 works
  2. 2 Stanley Osher United States · #48 worldwide 8k citations · 207 works
  3. 3 Edward Witten United States · #88 worldwide 7.2k citations · 151 works
  4. 4 Alex Pentland United States · #100 worldwide 6k citations · 219 works
  5. 5 David N. Spergel United States · #104 worldwide 7.9k citations · 198 works
  6. 6 Steven Weinberg United States · #121 worldwide 5.1k citations · 151 works
  7. 7 Heng Fan China · #132 worldwide 5.5k citations · 146 works
  8. 8 George Em Karniadakis United States · #151 worldwide 6.3k citations · 268 works
  9. 9 E. P. Wigner United States · #214 worldwide 2.8k citations · 203 works
  10. 10 Jure Leskovec United States · #252 worldwide 4.3k citations · 142 works

Re-ranked on the composite score from the 5,358 highest-output authors in Statistical and Nonlinear Physics. Identities come from OpenAlex author disambiguation, which occasionally merges or splits people.

Top 100 Statistical and Nonlinear Physics researchers

Where is Statistical and Nonlinear Physics research done?

The largest centres of Statistical and Nonlinear Physics research in 2022–2025 are Beijing (China), Moscow (Russia), Shanghai (China) and Nanjing (China). Among places with at least 20 works in it, it is an unusually large share of all research in Zeytinburnu, Āmol and Pābna.

Largest cities, 2022–2025

  1. 1 Beijing China 2.8k works
  2. 2 Moscow Russia 1.3k works
  3. 3 Shanghai China 1.3k works
  4. 4 Nanjing China 922 works
  5. 5 Xi'an China 852 works
  6. 6 Paris France 847 works
  7. 7 Wuhan China 714 works
  8. 8 Tokyo Japan 685 works
  9. 9 Guangzhou China 634 works
  10. 10 Chengdu China 634 works

Where it is the local speciality

  1. ZeytinburnuTR · 76.3 works23×
  2. ĀmolIR · 22.3 works22×
  3. PābnaBD · 28.5 works15×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Statistical and Nonlinear Physics than the world average.

See Statistical and Nonlinear Physics on the map

Statistical and Nonlinear Physics research by country

The best places for Statistical and Nonlinear Physics research inside each country, with that country's researchers and world standing.

Where is the best place to study Statistical and Nonlinear Physics?

Among universities, judged by research, Taibah University, University of Gujrat and El Shorouk Academy score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%25%50%mean 41.43%fractional works in this node (log) →share in the world top 10% →Taibah University: 98, 38.2%University of Gujrat: 45, 59.1%El Shorouk Academy: 37, 47.9%Henan Polytechnic University: 106, 58.3%Biruni University: 76, 34.3%COMSATS University Islamabad: 83, 32.7%Scuola Internazionale Superiore di Studi Avanzati: 61, 35.5%Higher Institute of Engineering: 38, 45.7%Zhejiang Normal University: 175, 25.2%Lebanese American University: 51, 37.4%University of GujratHenan Polytechnic Un…El Shorouk AcademyTaibah University
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1Taibah University Saudi Arabia 72.938.2%9.8×98 +399.0%
2University of Gujrat Pakistan 60.959.1%8.1×45 —
3El Shorouk Academy Egypt 58.447.9%48.2×37 —
4Henan Polytechnic University China 57.758.3%5.7×106 +23.6%
5Biruni University Türkiye 57.634.3%23.2×76 —
6COMSATS University Islamabad Pakistan 57.332.7%5.5×83 +333.6%
7Scuola Internazionale Superiore di Studi Avanzati Italy 56.935.5%22.5×61 +29.7%
8Higher Institute of Engineering Egypt 55.745.7%9.0×38 —
9Zhejiang Normal University China 52.825.2%9.4×175 -30.0%
10Lebanese American University Lebanon 52.737.4%7.1×51 —

Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.

Is Statistical and Nonlinear Physics research growing?

Output in 2018–2022 was 12% higher than in 2013–2017, peaking in 2025. The fastest-growing topics are Complex Network Analysis Techniques, Opinion Dynamics and Social Influence and Model Reduction and Neural Networks.

19801990200020102020
grewheldshrank

The same series as a ribbon — one cell per year, darker for more. The line above answers how much; this answers when.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

  1. Complex Network Analysis Techniques+175%
  2. Opinion Dynamics and Social Influence+141%
  3. Model Reduction and Neural Networks+70%
  4. Fusion and Plasma Physics Studies+51%
  5. Advanced Thermodynamics and Statistical Mechanics+39%
  6. Experimental and Theoretical Physics Studies+39%
  7. Chaos control and synchronization-2%
  8. Quantum chaos and dynamical systems-6%
  9. Scientific Research and Discoveries-13%
← shrinkingno changegrowing →

Growth in output from 2005–09 to 2015–19. Every topic is a page of its own.

What does Statistical and Nonlinear Physics include?

Advanced Thermodynamics …61kAdvanced Thermodynamics and Statistical Mechanics: 61k fractional worksComplex Network Analysis…51kComplex Network Analysis Techniques: 51k fractional worksQuantum chaos and dynamical systems: 47k fractional worksNonlinear Waves and Solitons: 46k fractional worksOpinion Dynamics and Social Influence: 32k fractional worksNonlinear Photonic Systems: 31k fractional worksScientific Research and Discoveries: 28k fractional worksChaos control and synchronization: 27k fractional worksExperimental and Theoretical Physics Studies: 27k fractional worksNoncommutative and Quantum Gravity Theories: 26k fractional worksModel Reduction and Neural Networks: 25k fractional worksstochastic dynamics and bifurcation: 23k fractional works

Area is fractional works in that topic. Every name below is a page of its own.