## Monaghan, Joseph J.

Compute Distance To:
 Author ID: monaghan.joseph-j Published as: Monaghan, J. J.; Monaghan, Joseph J.; Monaghan, Joe J.; Monaghan, Joe; Monaghan, J.
 Documents Indexed: 62 Publications since 1964 Co-Authors: 32 Co-Authors with 38 Joint Publications 325 Co-Co-Authors
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### Co-Authors

 22 single-authored 5 Kajtar, J. B. 4 Gingold, R. A. 4 Huppert, Herbert E. 4 Valizadeh, Alireza 2 Kos, A. M. 2 Lattanzio, J. C. 2 Mansour, John 2 Mériaux, Catherine A. 2 Pongracic, H. 1 Antuono, Matteo 1 Cally, Paul S. 1 Cas, R. A. F. 1 Cleary, Paul W. 1 Colagrossi, Andrea 1 Gray, Joshua P. 1 Hallworth, Mark A. 1 Humble, R. J. 1 Kwon, Jihoe 1 le Touzé, David 1 Mériaux, Catherine 1 Monaghan, J. M. 1 Morris, Joseph P. 1 Nash, P. E. 1 Pan, Wenxiao 1 Pattle, R. E. 1 Phillips, G. J. 1 Rafiee, Ashkan 1 Robinson, Martin 1 Swift, R. P. 1 Tartakovsky, Alexandre M. 1 Worster, M. Grae 1 Yan, Rui
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### Serials

 19 Journal of Computational Physics 11 European Journal of Mechanics. B. Fluids 5 Monthly Notices of the Royal Astronomical Society 3 Computer Physics Communications 3 International Journal for Numerical Methods in Fluids 3 Journal of Fluid Mechanics 2 SIAM Journal on Scientific and Statistical Computing 2 Physics of Fluids 1 Astronomy and Astrophysics 1 Computers and Fluids 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Mathematical Physics 1 Quarterly Journal of Mechanics and Applied Mathematics 1 Physica D 1 Applied Numerical Mathematics 1 Journal of Turbulence
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### Fields

 57 Fluid mechanics (76-XX) 7 Astronomy and astrophysics (85-XX) 6 Numerical analysis (65-XX) 4 Geophysics (86-XX) 3 Mechanics of particles and systems (70-XX) 2 Mechanics of deformable solids (74-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 History and biography (01-XX) 1 Approximations and expansions (41-XX) 1 Probability theory and stochastic processes (60-XX) 1 Relativity and gravitational theory (83-XX) 1 Biology and other natural sciences (92-XX)

### Citations contained in zbMATH Open

51 Publications have been cited 3,093 times in 1,531 Documents Cited by Year
Smoothed particle hydrodynamics: theory and application to non-spherical stars. Zbl 0421.76032
Gingold, R. A.; Monaghan, J. J.
1977
Simulating free surface flows with SPH. Zbl 0794.76073
Monaghan, J. J.
1994
An introduction to SPH. Zbl 0673.76089
Monaghan, J. J.
1988
SPH without a tensile stability. Zbl 0980.76065
Monaghan, J. J.
2000
Shock simulation by the particle method SPH. Zbl 0572.76059
Monaghan, J. J.; Gingold, R. A.
1983
Smoothed particle hydrodynamics and its diverse applications. Zbl 1361.76019
Monaghan, J. J.
2012
Theory and applications of smoothed particle hydrodynamics. Zbl 1160.76399
Monaghan, Joseph J.
2005
On the problem of penetration in particle methods. Zbl 0665.76124
Monaghan, J. J.
1989
A refined particle method for astrophysical problems. Zbl 0622.76054
Monaghan, J. J.; Lattanzio, J. C.
1985
SPH elastic dynamics. Zbl 1021.74050
Gray, J. P.; Monaghan, J. J.; Swift, R. P.
2001
Conduction modelling using smoothed particle hydrodynamics. Zbl 0930.76069
Cleary, Paul W.; Monaghan, Joseph J.
1999
Why particle methods work. Zbl 0498.76010
Monaghan, J. J.
1982
SHP simulation of multi-phase flow. Zbl 0923.76195
Monaghan, J. J.; Kocharyan, A.
1995
Kernel estimates as a basis for general particle methods in hydrodynamics. Zbl 0487.76010
Gingold, R. A.; Monaghan, J. J.
1982
SPH particle boundary forces for arbitrary boundaries. Zbl 1197.76104
Monaghan, J. J.; Kajtar, J. B.
2009
Extrapolating B splines for interpolation. Zbl 0588.41005
Monaghan, J. J.
1985
SPH and Riemann solvers. Zbl 0893.76069
Monaghan, J. J.
1997
A switch to reduce SPH viscosity. Zbl 0889.76065
Morris, J. P.; Monaghan, J. J.
1997
A simple SPH algorithm for multi-fluid flow with high density ratios. Zbl 1430.76400
Monaghan, J. J.; Rafiee, Ashkan
2013
Gravity currents descending a ramp in a stratified tank. Zbl 0938.76506
Monaghan, J. J.; Cas, R. A. F.; Kos, A. M.; Hallworth, M.
1999
SPH simulations of swimming linked bodies. Zbl 1196.76026
Kajtar, J.; Monaghan, J. J.
2008
Implicit SPH drag and dusty gas dynamics. Zbl 0947.76066
Monaghan, J. J.
1997
A turbulence model for smoothed particle hydrodynamics. Zbl 1258.76124
Monaghan, J. J.
2011
Scott Russell’s wave generator. Zbl 1149.76485
Monaghan, J. J.; Kos, A.
2000
A study of solid wall models for weakly compressible SPH. Zbl 1349.76743
2015
Artificial viscosity for particle methods. Zbl 0607.76069
Monaghan, J. J.; Pongracic, H.
1985
SPH simulation of 2D turbulence driven by a cylindrical stirrer. Zbl 1408.76284
2015
Solidification using smoothed particle hydrodynamics. Zbl 1121.76373
Monaghan, Joseph J.; Huppert, Herbert E.; Worster, M. Grae
2005
Smoothed particle hydrodynamics non-Newtonian model for ice-sheet and ice-shelf dynamics. Zbl 1426.76611
Pan, W.; Tartakovsky, A. M.; Monaghan, J. J.
2013
Ultrarelativistic SPH. Zbl 0887.76046
Chow, E.; Monaghan, J. J.
1997
Gravity currents and solitary waves. Zbl 0899.76099
Monaghan, J. J.
1996
Direct numerical simulation of decaying two-dimensional turbulence in a no-slip square box using smoothed particle hydrodynamics. Zbl 1253.76049
Robinson, Martin; Monaghan, Joseph J.
2012
Gravity current interaction with interfaces. Zbl 1296.76013
Monaghan, J. J.
2007
On the dynamics of swimming linked bodies. Zbl 1196.76030
Kajtar, J. B.; Monaghan, J. J.
2010
SPH-$$\epsilon$$ simulation of 2D turbulence driven by a moving cylinder. Zbl 1408.76322
Monaghan, J. J.
2017
On the swimming of fish like bodies near free and fixed boundaries. Zbl 1258.76222
Kajtar, J. B.; Monaghan, J. J.
2012
A numerical method for three-dimensional simulations of collapsing, isothermal, magnetic gas clouds. Zbl 0572.76113
Phillips, G. J.; Monaghan, J. J.
1985
Controlling penetration. Zbl 0624.76084
Lattanzio, J. C.; Monaghan, J. J.; Pongracic, H.; Schwarz, M. P.
1986
Particulate gravity currents along V-shaped valleys. Zbl 1181.76009
Monaghan, Joe J.; Mériaux, Catherine; Huppert, Herbert E.; Mansour, John
2009
A novel SPH method for sedimentation in a turbulent fluid. Zbl 1349.76702
Kwon, Jihoe; Monaghan, J. J.
2015
High Reynolds number gravity currents along V-shaped valleys. Zbl 1176.76005
Monaghan, J. J.; Mériaux, C. A.; Huppert, H. E.; Monaghan, J. M.
2009
A study of energy spectra calculated with disordered particles. Zbl 1390.76092
2015
An SPH study of driven turbulence near a free surface in a tank under gravity. Zbl 1408.76323
Monaghan, J. J.; Mériaux, Catherine A.
2018
On the integration of the SPH equations for a dusty fluid with high drag. Zbl 1473.76069
Monaghan, J. J.
2020
Smoothed particle hydrodynamics simulations of turbulence in fixed and rotating boxes in two dimensions with no-slip boundaries. Zbl 1410.76385
2012
Statistical mechanics and the gravothermal catastrophe. Zbl 0483.76091
Cally, P.; Monaghan, J. J.
1981
SPH simulation of skipping stones. Zbl 1408.76057
Yan, Rui; Monaghan, J. J.
2017
New developments in smoothed particle hydrodynamics. Zbl 1090.76568
Monaghan, Joseph J.
2002
Fluctuating hydrodynamics and the thermodynamics of self-gravitating systems. Zbl 0395.76046
Monaghan, J. J.
1978
Energy transfer in a particle $$\alpha$$ model. Zbl 1083.76528
Monaghan, J. J.
2004
On the integration of the SPH equations for a highly viscous fluid. Zbl 1452.76179
Monaghan, J. J.
2019
On the integration of the SPH equations for a dusty fluid with high drag. Zbl 1473.76069
Monaghan, J. J.
2020
On the integration of the SPH equations for a highly viscous fluid. Zbl 1452.76179
Monaghan, J. J.
2019
An SPH study of driven turbulence near a free surface in a tank under gravity. Zbl 1408.76323
Monaghan, J. J.; Mériaux, Catherine A.
2018
SPH-$$\epsilon$$ simulation of 2D turbulence driven by a moving cylinder. Zbl 1408.76322
Monaghan, J. J.
2017
SPH simulation of skipping stones. Zbl 1408.76057
Yan, Rui; Monaghan, J. J.
2017
A study of solid wall models for weakly compressible SPH. Zbl 1349.76743
2015
SPH simulation of 2D turbulence driven by a cylindrical stirrer. Zbl 1408.76284
2015
A novel SPH method for sedimentation in a turbulent fluid. Zbl 1349.76702
Kwon, Jihoe; Monaghan, J. J.
2015
A study of energy spectra calculated with disordered particles. Zbl 1390.76092
2015
A simple SPH algorithm for multi-fluid flow with high density ratios. Zbl 1430.76400
Monaghan, J. J.; Rafiee, Ashkan
2013
Smoothed particle hydrodynamics non-Newtonian model for ice-sheet and ice-shelf dynamics. Zbl 1426.76611
Pan, W.; Tartakovsky, A. M.; Monaghan, J. J.
2013
Smoothed particle hydrodynamics and its diverse applications. Zbl 1361.76019
Monaghan, J. J.
2012
Direct numerical simulation of decaying two-dimensional turbulence in a no-slip square box using smoothed particle hydrodynamics. Zbl 1253.76049
Robinson, Martin; Monaghan, Joseph J.
2012
On the swimming of fish like bodies near free and fixed boundaries. Zbl 1258.76222
Kajtar, J. B.; Monaghan, J. J.
2012
Smoothed particle hydrodynamics simulations of turbulence in fixed and rotating boxes in two dimensions with no-slip boundaries. Zbl 1410.76385
2012
A turbulence model for smoothed particle hydrodynamics. Zbl 1258.76124
Monaghan, J. J.
2011
On the dynamics of swimming linked bodies. Zbl 1196.76030
Kajtar, J. B.; Monaghan, J. J.
2010
SPH particle boundary forces for arbitrary boundaries. Zbl 1197.76104
Monaghan, J. J.; Kajtar, J. B.
2009
Particulate gravity currents along V-shaped valleys. Zbl 1181.76009
Monaghan, Joe J.; Mériaux, Catherine; Huppert, Herbert E.; Mansour, John
2009
High Reynolds number gravity currents along V-shaped valleys. Zbl 1176.76005
Monaghan, J. J.; Mériaux, C. A.; Huppert, H. E.; Monaghan, J. M.
2009
SPH simulations of swimming linked bodies. Zbl 1196.76026
Kajtar, J.; Monaghan, J. J.
2008
Gravity current interaction with interfaces. Zbl 1296.76013
Monaghan, J. J.
2007
Theory and applications of smoothed particle hydrodynamics. Zbl 1160.76399
Monaghan, Joseph J.
2005
Solidification using smoothed particle hydrodynamics. Zbl 1121.76373
Monaghan, Joseph J.; Huppert, Herbert E.; Worster, M. Grae
2005
Energy transfer in a particle $$\alpha$$ model. Zbl 1083.76528
Monaghan, J. J.
2004
New developments in smoothed particle hydrodynamics. Zbl 1090.76568
Monaghan, Joseph J.
2002
SPH elastic dynamics. Zbl 1021.74050
Gray, J. P.; Monaghan, J. J.; Swift, R. P.
2001
SPH without a tensile stability. Zbl 0980.76065
Monaghan, J. J.
2000
Scott Russell’s wave generator. Zbl 1149.76485
Monaghan, J. J.; Kos, A.
2000
Conduction modelling using smoothed particle hydrodynamics. Zbl 0930.76069
Cleary, Paul W.; Monaghan, Joseph J.
1999
Gravity currents descending a ramp in a stratified tank. Zbl 0938.76506
Monaghan, J. J.; Cas, R. A. F.; Kos, A. M.; Hallworth, M.
1999
SPH and Riemann solvers. Zbl 0893.76069
Monaghan, J. J.
1997
A switch to reduce SPH viscosity. Zbl 0889.76065
Morris, J. P.; Monaghan, J. J.
1997
Implicit SPH drag and dusty gas dynamics. Zbl 0947.76066
Monaghan, J. J.
1997
Ultrarelativistic SPH. Zbl 0887.76046
Chow, E.; Monaghan, J. J.
1997
Gravity currents and solitary waves. Zbl 0899.76099
Monaghan, J. J.
1996
SHP simulation of multi-phase flow. Zbl 0923.76195
Monaghan, J. J.; Kocharyan, A.
1995
Simulating free surface flows with SPH. Zbl 0794.76073
Monaghan, J. J.
1994
On the problem of penetration in particle methods. Zbl 0665.76124
Monaghan, J. J.
1989
An introduction to SPH. Zbl 0673.76089
Monaghan, J. J.
1988
Controlling penetration. Zbl 0624.76084
Lattanzio, J. C.; Monaghan, J. J.; Pongracic, H.; Schwarz, M. P.
1986
A refined particle method for astrophysical problems. Zbl 0622.76054
Monaghan, J. J.; Lattanzio, J. C.
1985
Extrapolating B splines for interpolation. Zbl 0588.41005
Monaghan, J. J.
1985
Artificial viscosity for particle methods. Zbl 0607.76069
Monaghan, J. J.; Pongracic, H.
1985
A numerical method for three-dimensional simulations of collapsing, isothermal, magnetic gas clouds. Zbl 0572.76113
Phillips, G. J.; Monaghan, J. J.
1985
Shock simulation by the particle method SPH. Zbl 0572.76059
Monaghan, J. J.; Gingold, R. A.
1983
Why particle methods work. Zbl 0498.76010
Monaghan, J. J.
1982
Kernel estimates as a basis for general particle methods in hydrodynamics. Zbl 0487.76010
Gingold, R. A.; Monaghan, J. J.
1982
Statistical mechanics and the gravothermal catastrophe. Zbl 0483.76091
Cally, P.; Monaghan, J. J.
1981
Fluctuating hydrodynamics and the thermodynamics of self-gravitating systems. Zbl 0395.76046
Monaghan, J. J.
1978
Smoothed particle hydrodynamics: theory and application to non-spherical stars. Zbl 0421.76032
Gingold, R. A.; Monaghan, J. J.
1977
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### Cited by 2,543 Authors

 40 Liu, Gui-Rong 25 Monaghan, Joseph J. 24 Belytschko, Ted Bohdan 23 Liew, Kim Meow 19 Liu, Moubin 19 Liu, Wing Kam 17 Zhang, Aman 16 Ming, Furen 16 Zhang, Lu-Wen 15 Belinha, Jorge 15 Cleary, Paul W. 14 Adams, Nikolaus A. 14 Bonet, Javier 14 Colagrossi, Andrea 14 Idelsohn, Sergio Rodolfo 14 Marrone, Salvatore 14 Oñate Ibáñez de Navarra, Eugenio 14 Rogers, Benedict D. 13 Dumbser, Michael 13 Koshizuka, Seiichi 13 Quinlan, Nathan J. 13 Rabczuk, Timon 13 Stansby, Peter K. 12 Francomano, Elisa 12 Gotoh, Hitoshi 12 Khayyer, Abbas 12 Tartakovsky, Alexandre M. 11 Afshar, Mohammad Hadi 11 Natal Jorge, Renato Manuel 11 Negrut, Dan 10 Koumoutsakos, Petros D. 10 le Touzé, David 10 Ouyang, Jie 10 Shadloo, Mostafa Safdari 10 Violeau, Damien 10 Zhang, Chi 9 Chen, Jiun-Shyan 9 Cheng, Rongjun 9 Dinis, Lúcia M. J. S. 9 Gu, Yuantong 9 Li, Shaofan 9 Oger, Guillaume 9 Ren, Jinlian 9 Sun, Pengnan 9 Vacondio, Renato 8 Antuono, Matteo 8 Chatelain, Philippe 8 Kulasegaram, Sivakumar 8 Shakibaeinia, Ahmad 8 Walther, Jens Honoré 7 Asai, Mitsuteru 7 Duan, Guangtao 7 Hu, Xiangyu 7 Jin, Yee-Chung 7 Lam, Khin-Yong 7 Li, Hua 7 Lind, Steven J. 7 Meakin, Paul 7 Salehi, Rezvan 7 Wriggers, Peter 7 Zhang, Shuai 6 Ala, Guido 6 Aly, Abdelraheem Mahmoud 6 Dehghan Takht Fooladi, Mehdi 6 Domínguez, José M. 6 Fatehi, Rouhollah 6 Hu, Wei 6 Jun, Sukky 6 Li, Guangyao 6 Nieken, Ulrich 6 Pan, Wenxiao 6 Pazouki, Arman 6 Rakhsha, Milad 6 Rezavand, Massoud 6 Shimizu, Yuma 6 Tiwari, Sudarshan 6 Tofighi, Nima 6 Tortorici, Adele 6 Toscano, Elena 6 Wang, Pingping 6 Xiao, Shaoping 6 Xu, Xiaoyang 6 Zhang, Xiong 6 Zong, Zhi 5 Basa, Mihai 5 Børve, Steinar 5 Chen, Shenshen 5 Colominas, Ignasi 5 Combescure, Alain 5 Dai, Kaiyu 5 Di G. Sigalotti, Leonardo 5 Djidjeli, K. 5 Ellero, Marco 5 Gimenez, Juan M. 5 Han, Xu 5 Heydari, Mohammad Hossien 5 Hu, Dean 5 Kajtar, J. B. 5 Klar, Axel 5 Krongauz, Yury ...and 2,443 more Authors
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### Cited in 149 Serials

 226 Journal of Computational Physics 188 Computer Methods in Applied Mechanics and Engineering 152 Engineering Analysis with Boundary Elements 114 Computers and Fluids 100 International Journal for Numerical Methods in Engineering 69 International Journal of Computational Methods 57 Computational Mechanics 57 Applied Mathematical Modelling 49 International Journal for Numerical Methods in Fluids 32 Computers & Mathematics with Applications 32 Applied Mathematics and Computation 31 European Journal of Mechanics. B. Fluids 29 Mathematical Problems in Engineering 24 Journal of Fluid Mechanics 20 Computer Physics Communications 16 International Journal of Computational Fluid Dynamics 13 Journal of Computational and Applied Mathematics 11 Applied Numerical Mathematics 9 International Journal of Numerical Methods for Heat & Fluid Flow 9 Acta Mechanica Sinica 8 Archives of Computational Methods in Engineering 7 Acta Mechanica 7 SIAM Journal on Scientific Computing 7 Communications in Numerical Methods in Engineering 6 International Journal for Numerical and Analytical Methods in Geomechanics 6 Journal of Engineering Mathematics 6 Mathematics and Computers in Simulation 6 Journal of Scientific Computing 6 European Journal of Mechanics. A. Solids 6 Computational Geosciences 6 Engineering Computations 5 International Journal of Heat and Mass Transfer 5 Shock Waves 5 Meccanica 5 Applied Mathematics and Mechanics. (English Edition) 5 Numerical Algorithms 5 Physics of Fluids 4 Numerische Mathematik 4 Japan Journal of Industrial and Applied Mathematics 4 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 4 Communications in Computational Physics 3 Astrophysics and Space Science 3 Journal of the Mechanics and Physics of Solids 3 Wave Motion 3 Numerical Methods for Partial Differential Equations 3 SIAM Journal on Mathematical Analysis 3 Computational and Applied Mathematics 3 Advances in Computational Mathematics 3 Journal of Applied Mechanics and Technical Physics 3 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 Living Reviews in Relativity 3 Journal of Applied Mathematics 3 Sādhanā 3 Multiscale Modeling & Simulation 3 Structural and Multidisciplinary Optimization 3 Journal of Shanghai Jiaotong University (Science) 3 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 Astronomische Nachrichten 2 International Journal of Solids and Structures 2 Journal of Statistical Physics 2 Physica A 2 Physics Reports 2 Mathematics of Computation 2 Bulletin of Mathematical Biology 2 Applied Mathematics Letters 2 Journal of Non-Newtonian Fluid Mechanics 2 Archive of Applied Mechanics 2 Multibody System Dynamics 2 International Journal of Modern Physics C 2 Journal of Cosmology and Astroparticle Physics 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 International Journal for Computational Methods in Engineering Science and Mechanics 2 Science China. Technological Sciences 2 International Journal for Numerical Methods in Biomedical Engineering 2 Symmetry 2 AMM. Applied Mathematics and Mechanics. (English Edition) 1 International Journal of Modern Physics B 1 Artificial Intelligence 1 Archive for Rational Mechanics and Analysis 1 Classical and Quantum Gravity 1 Communications on Pure and Applied Mathematics 1 Fluid Dynamics 1 International Journal of Engineering Science 1 Mathematical Methods in the Applied Sciences 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Chaos, Solitons and Fractals 1 BIT 1 Calcolo 1 Computing 1 Journal of Optimization Theory and Applications 1 Mechanics Research Communications 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Numerical Functional Analysis and Optimization 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 SIAM Journal on Numerical Analysis 1 Acta Applicandae Mathematicae 1 Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik 1 Computer Aided Geometric Design 1 Physica D 1 Acta Mathematicae Applicatae Sinica. English Series ...and 49 more Serials
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### Cited in 35 Fields

 996 Fluid mechanics (76-XX) 658 Numerical analysis (65-XX) 516 Mechanics of deformable solids (74-XX) 127 Partial differential equations (35-XX) 50 Classical thermodynamics, heat transfer (80-XX) 50 Geophysics (86-XX) 37 Biology and other natural sciences (92-XX) 35 Statistical mechanics, structure of matter (82-XX) 19 Optics, electromagnetic theory (78-XX) 19 Astronomy and astrophysics (85-XX) 15 Computer science (68-XX) 15 Mechanics of particles and systems (70-XX) 11 Approximations and expansions (41-XX) 10 Relativity and gravitational theory (83-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 6 Probability theory and stochastic processes (60-XX) 6 Statistics (62-XX) 5 Real functions (26-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Operations research, mathematical programming (90-XX) 4 Integral equations (45-XX) 3 Ordinary differential equations (34-XX) 3 Operator theory (47-XX) 3 Systems theory; control (93-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Quantum theory (81-XX) 2 Information and communication theory, circuits (94-XX) 1 Combinatorics (05-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)