Edit Profile (opens in new tab) Holmes, Mark H. Co-Author Distance Author ID: holmes.mark-h Published as: Holmes, Mark H.; Holmes, M. H.; Holmes, Mark more...less Documents Indexed: 62 Publications since 1930, including 8 Books and 3 Additional arXiv Preprints 2 Contributions as Editor · 1 Further Contribution Co-Authors: 10 Co-Authors with 17 Joint Publications 211 Co-Co-Authors all top 5 Co-Authors 21 single-authored 5 Bell, Jonathan 5 Kleptsyn, Victor A. 4 Haider, Mansoor A. 3 Beaton, Nicholas R. 3 Hirsch, Christian 3 Kious, Daniel 2 Angel, Omer 2 Fessel, Kimberly 2 Grimmett, Geoffrey R. 1 Allen, Jont B. 1 Barry, Steven Ian 1 Brydges, David C. 1 Chadwick, Richard S. 1 Cole, Julian David 1 Collevecchio, Andrea 1 Cook, L. Pamela 1 Croydon, David A. 1 Dandy, G. C. 1 Fralix, Brian H. 1 Gibbs, M. S. 1 Helmuth, Tyler 1 Heydenreich, Markus 1 Holroyd, Alexander E. 1 Huang, Xin 1 Leonard, D. G. B. 1 Löpker, Andreas H. 1 Maier, Holger R. 1 Mailler, Cécile 1 Mohylevskyy, Yevhen 1 Morgan, Neal 1 Newman, Charles Michael 1 Nixon, J. B. 1 Pavliotis, Grigorios A. 1 Rabbitt, Richard D. 1 Rogers, Lisa 1 Rubenfeld, Lester A. 1 Sailor, W. 1 Spilker, Robert L. 1 Stein, F. Max 1 Suh, J.-K. 1 Taylor, Peter Gerrard all top 5 Serials 6 Texts in Applied Mathematics 5 SIAM Journal on Applied Mathematics 3 Journal of the Acoustical Society of America 2 Journal of Mathematical Biology 2 Mathematical Biosciences 2 Journal of Applied Probability 2 Mathematical and Computer Modelling 1 American Mathematical Monthly 1 Communications in Mathematical Physics 1 Communications on Pure and Applied Mathematics 1 IMA Journal of Applied Mathematics 1 Journal of Computational Physics 1 Journal of Engineering Mathematics 1 Journal of Fluid Mechanics 1 Journal of the Mechanics and Physics of Solids 1 Journal of Statistical Physics 1 Nonlinearity 1 Quarterly Journal of Mechanics and Applied Mathematics 1 The Annals of Probability 1 International Journal for Numerical Methods in Engineering 1 Journal of Differential Equations 1 Mechanics Research Communications 1 Portugaliae Mathematica 1 Quarterly of Applied Mathematics 1 Statistics & Probability Letters 1 IMA Journal of Mathematics Applied in Medicine and Biology 1 Computational Mechanics 1 The Annals of Applied Probability 1 The Electronic Journal of Combinatorics 1 Electronic Journal of Probability 1 Nova Journal of Mathematics, Game Theory, and Algebra 1 Mathematical Physics, Analysis and Geometry 1 Chaos 1 Stochastic Models 1 Mathematical Biosciences and Engineering 1 Oberwolfach Reports 1 Lecture Notes in Biomathematics 1 Texts in Computational Science and Engineering 1 Journal of Physics A: Mathematical and Theoretical all top 5 Fields 21 Probability theory and stochastic processes (60-XX) 20 Mechanics of deformable solids (74-XX) 14 Biology and other natural sciences (92-XX) 12 Fluid mechanics (76-XX) 8 Partial differential equations (35-XX) 7 Numerical analysis (65-XX) 6 Ordinary differential equations (34-XX) 5 Combinatorics (05-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 General and overarching topics; collections (00-XX) 2 Statistics (62-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Computer science (68-XX) 1 Optics, electromagnetic theory (78-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 38 Publications have been cited 317 times in 306 Documents Cited by ▼ Year ▼ Introduction to perturbation methods. Zbl 0830.34001 Holmes, Mark H. 151 1995 Introduction to perturbation methods. 2nd ed. Zbl 1270.34002 Holmes, Mark H. 56 2013 Introduction to numerical methods in differential equations. Zbl 1110.65001 Holmes, Mark H. 18 2007 A penalty finite element analysis for nonlinear mechanics of biphasic hydrated soft tissue under large deformation. Zbl 0763.73057 Suh, J.-K.; Spilker, R. L.; Holmes, M. H. 17 1991 Asymptotic behaviour of thin poroelastic layers. Zbl 0971.74030 Barry, S. I.; Holmes, M. 14 2001 Introduction to perturbation methods. 2nd corrected printing. Zbl 0980.34052 Holmes, Mark H. 11 1998 Microscale reduction error indicators and estimators for a periodic heterogeneous medium. Zbl 0806.73003 Fish, J.; Nayak, P.; Holmes, M. H. 10 1994 Introduction to the foundations of applied mathematics. Zbl 1250.74002 Holmes, Mark H. 9 2009 Proof of the WARM whisker conjecture for neuronal connections. Zbl 1387.60143 Holmes, Mark; Kleptsyn, Victor 8 2017 Model of the dynamics of receptor potential in a mechanoreceptor. Zbl 0761.92011 Bell, Jonathan; Holmes, Mark 7 1992 Absence of warm percolation in the very strong reinforcement regime. Zbl 1479.60196 Hirsch, Christian; Holmes, Mark; Kleptsyn, Victor 7 2021 Comparison theorems and similarity solution approximations for a nonlinear diffusion equation arising in the study of soft tissue. Zbl 0598.76009 Holmes, Mark H. 6 1984 Cochlear mechanics: Analysis for a pure tone. Zbl 0543.73126 Holmes, Mark H.; Cole, Julian D. 5 1984 Nonlinear ionic diffusion through charged polymeric gels. Zbl 0715.35004 Holmes, Mark H. 5 1990 The continuous-time lace expansion. Zbl 07433689 Brydges, David; Helmuth, Tyler; Holmes, Mark 5 2021 On the speed of once-reinforced biased random walk on trees. Zbl 1417.60085 Collevecchio, Andrea; Holmes, Mark; Kious, Daniel 5 2018 A nonlinear diffusion equation arising in the study of soft tissue. Zbl 0562.76125 Holmes, Mark H. 4 1983 A comprehensive arithmetic and mensuration. For advanced division central and secondary schools. JFM 56.0079.05 Holmes 4 1930 Backbone scaling for critical lattice trees in high dimensions. Zbl 1368.82005 Holmes, Mark 4 2016 A model of a sensory mechanoreceptor derived from homogenization. Zbl 0686.92008 Holmes, Mark H.; Bell, Jonathan 3 1990 Infinite WARM graphs III: strong reinforcement regime. Zbl 1523.60167 Hirsch, Christian; Holmes, Mark; Kleptsyn, Victor 3 2023 A mathematical model of the dynamics of the inner ear. Zbl 0499.76071 Holmes, Mark H. 2 1982 A spectral problem in hydroelasticity. Zbl 0404.35078 Holmes, Mark H. 2 1979 Study of the transient motion in the cochlea. Zbl 0457.73087 Holmes, Mark H. 2 1981 Introduction to scientific computing and data analysis. Zbl 1368.65002 Holmes, Mark H. 2 2016 A model for the nonlinear mechanism responsible for cochlear amplification. Zbl 1333.92011 Fessel, Kimberly; Holmes, Mark H. 2 2014 Waves and dispersion relations for hydroelastic systems. Zbl 0479.73038 Cook, L. Pamela; Holmes, Mark 1 1981 A perturbation-based numerical method for solving a three-dimensional axisymmetric indentation problem. Zbl 1036.74040 Pavliotis, Grigorios A.; Holmes, Mark H. 1 2002 Behaviour of a model for the synapse of an auditory receptor cell. Zbl 0609.92007 Bell, Jonathan; Holmes, Mark H. 1 1986 Auditory transduction: A model for the role of intracellular calcium in short-term adaptation. Zbl 0754.92006 Holmes, Mark H.; Bell, Jonathan 1 1991 Indentation of a thin compressible elastic layer: Approximate analytic and numerical solutions for rigid flat indenters. Zbl 0918.73095 Haider, Mansoor A.; Holmes, Mark H. 1 1995 Note on the spectrum and normal modes of a general hydroelastic system. Zbl 0367.76020 Holmes, Mark 1 1977 Low frequency asymptotics for a hydroelastic model of the cochlea. Zbl 0447.76065 Holmes, Mark H. 1 1980 A Markovian arrival stream approach to stochastic gene expression in cells. Zbl 1515.92035 Fralix, Brian; Holmes, Mark; Löpker, Andreas 1 2023 Letter to the editor (Kemeny’s constant for infinite DTMCs is infinite). Zbl 1448.60153 Angel, Omer; Holmes, Mark 1 2019 A monotonicity property for once reinforced biased random walk on \(\mathbb{Z}^d\). Zbl 1446.82030 Holmes, Mark; Kious, Daniel 1 2019 Biased random walk on the trace of biased random walk on the trace of \(\dots\). Zbl 1440.60085 Croydon, David; Holmes, Mark 1 2020 Alignment percolation. Zbl 1456.60249 Beaton, Nicholas R.; Grimmett, Geoffrey R.; Holmes, Mark 1 2021 Infinite WARM graphs III: strong reinforcement regime. Zbl 1523.60167 Hirsch, Christian; Holmes, Mark; Kleptsyn, Victor 3 2023 A Markovian arrival stream approach to stochastic gene expression in cells. Zbl 1515.92035 Fralix, Brian; Holmes, Mark; Löpker, Andreas 1 2023 Absence of warm percolation in the very strong reinforcement regime. Zbl 1479.60196 Hirsch, Christian; Holmes, Mark; Kleptsyn, Victor 7 2021 The continuous-time lace expansion. Zbl 07433689 Brydges, David; Helmuth, Tyler; Holmes, Mark 5 2021 Alignment percolation. Zbl 1456.60249 Beaton, Nicholas R.; Grimmett, Geoffrey R.; Holmes, Mark 1 2021 Biased random walk on the trace of biased random walk on the trace of \(\dots\). Zbl 1440.60085 Croydon, David; Holmes, Mark 1 2020 Letter to the editor (Kemeny’s constant for infinite DTMCs is infinite). Zbl 1448.60153 Angel, Omer; Holmes, Mark 1 2019 A monotonicity property for once reinforced biased random walk on \(\mathbb{Z}^d\). Zbl 1446.82030 Holmes, Mark; Kious, Daniel 1 2019 On the speed of once-reinforced biased random walk on trees. Zbl 1417.60085 Collevecchio, Andrea; Holmes, Mark; Kious, Daniel 5 2018 Proof of the WARM whisker conjecture for neuronal connections. Zbl 1387.60143 Holmes, Mark; Kleptsyn, Victor 8 2017 Backbone scaling for critical lattice trees in high dimensions. Zbl 1368.82005 Holmes, Mark 4 2016 Introduction to scientific computing and data analysis. Zbl 1368.65002 Holmes, Mark H. 2 2016 A model for the nonlinear mechanism responsible for cochlear amplification. Zbl 1333.92011 Fessel, Kimberly; Holmes, Mark H. 2 2014 Introduction to perturbation methods. 2nd ed. Zbl 1270.34002 Holmes, Mark H. 56 2013 Introduction to the foundations of applied mathematics. Zbl 1250.74002 Holmes, Mark H. 9 2009 Introduction to numerical methods in differential equations. Zbl 1110.65001 Holmes, Mark H. 18 2007 A perturbation-based numerical method for solving a three-dimensional axisymmetric indentation problem. Zbl 1036.74040 Pavliotis, Grigorios A.; Holmes, Mark H. 1 2002 Asymptotic behaviour of thin poroelastic layers. Zbl 0971.74030 Barry, S. I.; Holmes, M. 14 2001 Introduction to perturbation methods. 2nd corrected printing. Zbl 0980.34052 Holmes, Mark H. 11 1998 Introduction to perturbation methods. Zbl 0830.34001 Holmes, Mark H. 151 1995 Indentation of a thin compressible elastic layer: Approximate analytic and numerical solutions for rigid flat indenters. Zbl 0918.73095 Haider, Mansoor A.; Holmes, Mark H. 1 1995 Microscale reduction error indicators and estimators for a periodic heterogeneous medium. Zbl 0806.73003 Fish, J.; Nayak, P.; Holmes, M. H. 10 1994 Model of the dynamics of receptor potential in a mechanoreceptor. Zbl 0761.92011 Bell, Jonathan; Holmes, Mark 7 1992 A penalty finite element analysis for nonlinear mechanics of biphasic hydrated soft tissue under large deformation. Zbl 0763.73057 Suh, J.-K.; Spilker, R. L.; Holmes, M. H. 17 1991 Auditory transduction: A model for the role of intracellular calcium in short-term adaptation. Zbl 0754.92006 Holmes, Mark H.; Bell, Jonathan 1 1991 Nonlinear ionic diffusion through charged polymeric gels. Zbl 0715.35004 Holmes, Mark H. 5 1990 A model of a sensory mechanoreceptor derived from homogenization. Zbl 0686.92008 Holmes, Mark H.; Bell, Jonathan 3 1990 Behaviour of a model for the synapse of an auditory receptor cell. Zbl 0609.92007 Bell, Jonathan; Holmes, Mark H. 1 1986 Comparison theorems and similarity solution approximations for a nonlinear diffusion equation arising in the study of soft tissue. Zbl 0598.76009 Holmes, Mark H. 6 1984 Cochlear mechanics: Analysis for a pure tone. Zbl 0543.73126 Holmes, Mark H.; Cole, Julian D. 5 1984 A nonlinear diffusion equation arising in the study of soft tissue. Zbl 0562.76125 Holmes, Mark H. 4 1983 A mathematical model of the dynamics of the inner ear. Zbl 0499.76071 Holmes, Mark H. 2 1982 Study of the transient motion in the cochlea. Zbl 0457.73087 Holmes, Mark H. 2 1981 Waves and dispersion relations for hydroelastic systems. Zbl 0479.73038 Cook, L. Pamela; Holmes, Mark 1 1981 Low frequency asymptotics for a hydroelastic model of the cochlea. Zbl 0447.76065 Holmes, Mark H. 1 1980 A spectral problem in hydroelasticity. Zbl 0404.35078 Holmes, Mark H. 2 1979 Note on the spectrum and normal modes of a general hydroelastic system. Zbl 0367.76020 Holmes, Mark 1 1977 A comprehensive arithmetic and mensuration. For advanced division central and secondary schools. JFM 56.0079.05 Holmes 4 1930 all cited Publications top 5 cited Publications all top 5 Cited by 607 Authors 9 Penta, Raimondo 8 Fish, Jacob 7 Holmes, Mark H. 7 Jung, Changyeol 5 Bell, Jonathan 5 Filobello-Nino, Uriel A. 5 Merodio, Jose 5 Powell, James A. 5 Ramírez-Torres, Ariel 5 Vázquez-Leal, Héctor 4 Anderson, Daniel M. 4 Huerta-Chua, Jesus 4 Kadalbajoo, Mohan K. 4 Kovács, Endre 4 Kumar, Manoj 4 Rodríguez-Ramos, Reinaldo 3 Atzberger, Paul J. 3 Demiralp, Metin 3 Garlick, Martha J. 3 Gie, Gung-Min 3 Hooten, Mevin B. 3 Jimenez-Fernandez, Victor Manuel 3 Negulescu, Claudia 3 Patidar, Kailash C. 3 Sarmiento-Reyes, Arturo 3 Schoof, Christian 3 Tuna, Süha 3 Yurk, Brian P. 2 Ai, Wen-Yuan 2 Barry, Steven Ian 2 Calvo, Begoña 2 Carr, Elliot Joseph 2 Castañeda-Sheissa, Roberto 2 Cervantes-Perez, J. 2 Champneys, Alan R. 2 Chen, Wenhui 2 Cheng, Lei 2 Dai, Hui-Hui 2 Del Palomar, A. Pérez 2 Doblaré, Manuel 2 Fan, Xiaoting 2 Feng, Xinlong 2 Fessel, Kimberly 2 Gerisch, Alf 2 Ghayesh, Mergen H. 2 Gonzalez-Lee, M. 2 Grillo, Alfio 2 Grosh, Karl 2 Ironi, Liliana 2 Kelley, Walter G. 2 King, John Robert 2 Lee, Hoyeon 2 Li, Wenlei 2 Liu, Weishi 2 Martínez, Miguel Ángel 2 McLaughlin, Richard M. 2 Miller, Cass T. 2 Morales-Mendoza, L. J. 2 Nagy, Adam 2 Neupane, Ram C. 2 Nguyen, Thien Binh 2 Panzeri, Luigi 2 Parul 2 Peña, Estefanía 2 Pereyra-Díaz, Domitilo 2 Pérez-Sesma, A. 2 Plahte, Erik 2 Potomkin, Mykhailo 2 Poznanski, Roman R. 2 Prasad, Hari Shankar 2 Ranjan, Rakesh 2 Ricarte, Gleydson Chaves 2 Roul, Pradip 2 Saleh, Mahmoud 2 Schäfer, Tobias 2 Schmuck, Markus 2 Schnell, Santiago 2 Shek, Kamlun 2 Shephard, Mark S. 2 Shi, Shaoyun 2 Siddique, Javed I. 2 Spilker, Robert L. 2 Strogatz, Steven Henry 2 Temam, Roger Meyer 2 Turner, Ian William 2 Van de Ven, Alphons Adrianus Francisca 2 van Horssen, Wilhem Teunis 2 Wang, Jing 2 Wang, Xiaoming 2 Xie, Feng 1 Aghamohammadi, Amir 1 Ahmed, Aftab 1 Akhmatskaya, Elena 1 Akhmedov, Odiljon S. 1 Akhtar, Rizwan 1 Al-Shibani, Faoziya 1 Aldis, Geoffrey K. 1 Allahviranloo, Tofigh 1 Allez, Romain 1 Almeida, Edgard S. ...and 507 more Authors all top 5 Cited in 141 Serials 19 Computer Methods in Applied Mechanics and Engineering 13 Applied Mathematics and Computation 13 Physica D 11 Mathematical Biosciences 7 Journal of Fluid Mechanics 7 Bulletin of Mathematical Biology 6 Journal of Computational Physics 6 Applied Mathematical Modelling 6 Journal of Theoretical Biology 5 Journal of Scientific Computing 5 SIAM Journal on Applied Mathematics 5 Nonlinear Analysis. Real World Applications 4 Journal of Mathematical Analysis and Applications 4 Journal of Mathematical Biology 4 International Journal for Numerical Methods in Engineering 4 Journal of Computational and Applied Mathematics 4 Journal of Differential Equations 4 Numerical Methods for Partial Differential Equations 4 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 3 Journal of Engineering Mathematics 3 Physics Letters. A 3 Mathematics and Computers in Simulation 3 Mathematical and Computer Modelling 3 International Journal of Computer Mathematics 3 Physics of Fluids 3 Journal of Mathematical Chemistry 3 Nonlinear Dynamics 3 Discrete Dynamics in Nature and Society 3 Natural Resource Modeling 3 Communications in Nonlinear Science and Numerical Simulation 2 Acta Mechanica 2 Computers & Mathematics with Applications 2 International Journal of Solids and Structures 2 Journal of Mathematical Physics 2 Journal of Statistical Physics 2 Mathematical Methods in the Applied Sciences 2 Wave Motion 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Applied Numerical Mathematics 2 Journal of Economic Dynamics & Control 2 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 2 SIAM Review 2 Journal of Dynamics and Differential Equations 2 Continuum Mechanics and Thermodynamics 2 Journal of Difference Equations and Applications 2 Mathematical Problems in Engineering 2 Computing and Visualization in Science 2 Chaos 2 European Journal of Mechanics. A. Solids 2 Journal of High Energy Physics 2 SIAM Journal on Applied Dynamical Systems 2 Multiscale Modeling & Simulation 2 International Journal of Computational Methods 2 Mathematical Biosciences and Engineering 2 Journal of Biological Dynamics 2 Advances in Applied Mathematics and Mechanics 1 Modern Physics Letters A 1 Archive for Rational Mechanics and Analysis 1 Classical and Quantum Gravity 1 Computers and Fluids 1 Computer Physics Communications 1 Communications on Pure and Applied Mathematics 1 European Journal of Physics 1 General Relativity and Gravitation 1 International Journal of Engineering Science 1 International Journal for Numerical Methods in Fluids 1 Journal of the Mechanics and Physics of Solids 1 Moscow University Mechanics Bulletin 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Reviews in Mathematical Physics 1 Chaos, Solitons and Fractals 1 Calcolo 1 Fuzzy Sets and Systems 1 International Statistical Review 1 Journal of Economic Theory 1 Journal of Econometrics 1 Journal of Statistical Planning and Inference 1 Meccanica 1 Numerische Mathematik 1 Quarterly of Applied Mathematics 1 SIAM Journal on Control and Optimization 1 Studies in Applied Mathematics 1 Synthese 1 Ergodic Theory and Dynamical Systems 1 Acta Mathematicae Applicatae Sinica 1 Circuits, Systems, and Signal Processing 1 Stochastic Analysis and Applications 1 Acta Applicandae Mathematicae 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Probability Theory and Related Fields 1 Revista Matemática Iberoamericana 1 Computational Mechanics 1 Applied Mathematics Letters 1 SIAM Journal on Matrix Analysis and Applications 1 European Journal of Operational Research 1 Journal of Elasticity 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Celestial Mechanics and Dynamical Astronomy 1 Archive of Applied Mechanics ...and 41 more Serials all top 5 Cited in 33 Fields 82 Partial differential equations (35-XX) 77 Biology and other natural sciences (92-XX) 74 Numerical analysis (65-XX) 68 Mechanics of deformable solids (74-XX) 64 Fluid mechanics (76-XX) 58 Ordinary differential equations (34-XX) 12 Probability theory and stochastic processes (60-XX) 10 Dynamical systems and ergodic theory (37-XX) 10 Statistical mechanics, structure of matter (82-XX) 9 Classical thermodynamics, heat transfer (80-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Difference and functional equations (39-XX) 7 Mechanics of particles and systems (70-XX) 6 Quantum theory (81-XX) 6 Relativity and gravitational theory (83-XX) 6 Systems theory; control (93-XX) 5 Integral equations (45-XX) 5 Optics, electromagnetic theory (78-XX) 5 Geophysics (86-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Statistics (62-XX) 4 Computer science (68-XX) 3 Operator theory (47-XX) 3 Astronomy and astrophysics (85-XX) 2 General and overarching topics; collections (00-XX) 2 Mathematical logic and foundations (03-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Approximations and expansions (41-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Operations research, mathematical programming (90-XX) 2 Information and communication theory, circuits (94-XX) 1 Combinatorics (05-XX) 1 Potential theory (31-XX) Citations by Year