My formal education is in applied mathematics (Ph.D, Brown 2001), theoretical and applied mechanics (MS, Cornell 1996), and mechanical engineering (B.Tech, IIT Kharagpur, 1994). This was followed by temporary appointments at the Max Planck Institute for Mathematics in the Sciences, Leipzig, and the University of Wisconsin, Madison. I returned to Brown as an Assistant Professor in July, 2004 and have been at Brown since.
|Li, Xingjie, Williams, Matthew O, Kevrekidis, Ioannis G, Menon, Govind Coarse graining, dynamic renormalization and the kinetic theory of shock clustering. nonlinearity. 2016; 29 (3) : 947-961.|
|Russell, Emily R., Menon, Govind Energy Landscapes for the Self-Assembly of Supramolecular Polyhedra. Journal of Nonlinear Science. 2016; 26 (3) : 663-681.|
|Menon, Govind, Trogdon, Thomas, Deift, Percy A. On the condition number of the critically-scaled Laguerre Unitary Ensemble. Discrete and Continuous Dynamical Systems. 2016; 36 (8) : 4287-4347.|
|Govind Menon The Airy function is a Fredholm determinant. Journal of Dynamics and Differential Equations. 2016; 28 : 1031-1038.|
|Johnson-Chyzhykov, Daniel, Menon, Govind The Building Game: From Enumerative Combinatorics to Conformational Diffusion. Journal of Nonlinear Science. 2016; 26 (4) : 815-845.|
|Kaplan, Ryan, Klobušický, Joseph, Pandey, Shivendra, Gracias, David H., Menon, Govind Building Polyhedra by Self-Assembly: Theory and Experiment. Artificial Life. 2014; 20 (4) : 409-439.|
|Pandey, Shivendra, Johnson, Daniel, Kaplan, Ryan, Klobusicky, Joseph, Menon, Govind, Gracias, David H. Self-Assembly of Mesoscale Isomers: The Role of Pathways and Degrees of Freedom. PLoS ONE. 2014; 9 (10) : e108960.|
|Deift, P. A., Menon, G., Olver, S., Trogdon, T. Universality in numerical computations with random data. Proceedings of the National Academy of Sciences. 2014; 111 (42) : 14973-14978.|
|Li, Xingjie Helen, Menon, Govind Numerical Solution of Dyson Brownian Motion and a Sampling Scheme for Invariant Matrix Ensembles. Journal of Statistical Physics. 2013; 153 (5) : 801-812.|
|Sageman-Furnas, A. O., Goswami, P., Menon, G., Russell, S. J. The Sphereprint: An approach to quantifying the conformability of flexible materials. Textile Research Journal. 2013; 84 (8) : 793-807.|
|Hadžić, Mahir, Menon, Govind Gradient flow structure for domain relaxation in Langmuir films. Quarterly of Applied Mathematics. 2012; 70 (4) : 659-664.|
|Menon, Govind Lesser known miracles of Burgers equation. Acta Mathematica Scientia. 2012; 32 (1) : 281-294.|
|Menon, Govind Complete Integrability of Shock Clustering and Burgers Turbulence. Arch Rational Mech Anal. 2011; 203 (3) : 853-882.|
|Menon, Govind, Niethammer, Barbara, Pego, Robert L. Dynamics and self-similarity in min-driven clustering. Trans. Amer. Math. Soc.. 2010; 362 (12) : 6591-6591.|
|Menon, Govind, Srinivasan, Ravi Kinetic Theory and Lax Equations for Shock Clustering and Burgers Turbulence. Journal of Statistical Physics. 2010; 140 (6) : 1195-1223.|
|Menon, Govind Mathematical approaches to dynamic scaling. Journal of Non-Newtonian Fluid Mechanics. 2008; 152 (1-3) : 113-119.|
|Menon, Govind, Pego, Robert L. Scaling dynamics for solvable coagulation equations with dust and gel. Proc. Appl. Math. Mech.. 2007; 7 (1) : 1042901-1042902.|
|Menon, Govind, Pego, Robert L. The Scaling Attractor and Ultimate Dynamics for Smoluchowski’s Coagulation Equations. Journal of Nonlinear Science. 2007; 18 (2) : 143-190.|
|Menon, Govind, Pego, Robert L. Universality Classes in Burgers Turbulence. Commun. Math. Phys.. 2007; 273 (1) : 177-202.|
|Menon, Govind, Otto, Felix Diffusive slowdown in miscible viscous fingering. Communications in Mathematical Sciences. 2006; 4 (1) : 267-273.|
|Menon, Govind, Pego, Robert L. Dynamical Scaling in Smoluchowski’s Coagulation Equations: Uniform Convergence. SIAM Rev.. 2006; 48 (4) : 745-768.|
|Menon, G., Otto, F. Dynamic Scaling in Miscible Viscous Fingering. Commun. Math. Phys.. 2005; 257 (2) : 303-317.|
|Menon, Govind, Pego, Robert L. Dynamical Scaling in Smoluchowski's Coagulation Equations: Uniform Convergence. SIAM Journal on Mathematical Analysis. 2005; 36 (5) : 1629-1651.|
|Menon, Govind, Pego, Robert L. Approach to self-similarity in Smoluchowski's coagulation equations. Communications on Pure and Applied Mathematics. 2004; 57 (9) : 1197-1232.|
I view myself as a problem solver, rather than a specialist in any particular technique. My work spans a wide range and includes pure mathematics (analysis, dynamical systems, partial differential equations), applied mathematics (computational methods, asymptotics, modelling), and active collaboration with experimentalists in the sciences (self-assembly, textiles, soft condensed matter).
My recent work focuses on the formation and propagation of disorder in physical models and numerical algorithms. I hope to use integrable systems to explain some tantalizing links between random matrix theory, Burgers-KPZ turbulence, and number theory that have come to light in the past fifteen years. I am also strongly interested in the development of a mathematical theory for biological and synthetic self-assembly.
National Science Foundation, DMS 14-11278, (2014-2017), PI for Proposal in Applied Mathematics: Turbulence and integrability.
Research grants (completed):
National Science Foundation, DMS 07-48482, 2008-2013, PI for Proposal in Applied Mathematics: CAREER: Scaling and self-similarity in Nonlinear Science education and research.
National Science Foundation, EFRI 10-22638, PI for Proposal: BECS: Collaborative Research: Engineering complex self-assembling systems composed of interacting patterned polyhedra: theory and experiments.
National Science Foundation, DMS 06-05006, 2006-2009, PI for Proposal in Applied Mathematics: Scaling and Infinite Divisibility in Models of Coarsening and Other Dynamic Selection Problems.
National Science Foundation, DMS 03-05985, 2003-2006, Proposal in Applied Mathematics: Dynamic scaling, coarsening and stability in physical systems. Subcontract of an award to PI R.L.Pego.
S. Pandey, D. Johnson, R. Kaplan, J. Klobusicky, G. Menon, D.H. Gracias, Self-assembly of mesoscale isomers: The role of pathways and degrees of freedom. PLoS One (2014).
P. Deift, G. Menon, S.Olver and T. Trogdon, Universality in numerical computations with random data. Case studies. PNAS (2014).
R. Kaplan, J. Klobusicky, S. Pandey, D.H. Gracias and G. Menon, Building polyhedra by self-assembly: theory and experiment, Artificial Life (2014).
A. Sageman-Furnas, P. Goswami, G. Menon and S.J. Russell, The sphereprint: an approach to quantifying the conformability of flexible materials, Textile Research Journal (2013), doi:10.1177/0040517513512402
X. Li and G. Menon, Numerical solution of Dyson Brownian motion and a sampling scheme for invariant matrix ensembles, J. Stat. Phys. (2013), Vol. 153,doi/10.1007/s10955-013-0858-x
C.W. Pfrang, P. Deift and G. Menon, How long does it take to compute the eigenvalues of a random symmetric matrix, MSRI Publications (to appear in a forthcoming volume on Random Matrix Theory).
G. Menon, Lesser known miracles of Burgers equation, Acta Mathematica Scientia (2012), Vol 32B.
G. Menon, Complete integrability of shock clustering and Burgers turbulence, Arch. Rat. Mech. Analysis (2012), Vol. 203, doi/10.1007/s00205-011-0461-8
S. Pandey, M. Ewing, A. Kunas, N. Nguyen, D.H. Gracias and G. Menon, Algorithmic design of self-folding polyhedra, PNAS (2011), doi/10.1073/pnas.1110857108
G. Menon and R. Srinivasan, Kinetic theory and Lax equations for shock clustering and Burgers turbulence, J. Stat. Phys. (2010), doi/10.1007/s10955-010-0028-3
G. Menon and R.L. Pego, Universality classes in Burgers turbulence, Comm. Math. Phys (2007), Vol. 273, doi/10.1007/s00220-007-0251-1
G. Menon and R.L.Pego, Dynamic scaling in Smoluchowski's coagulation equation: uniform convergence, SIAM Review (2006), Vol. 48, No.4, pp. 745-768.
Dynamic scaling in miscible viscous fingering , with Felix Otto , Comm. Math. Phys. (2005), Vol. 257, p. 303-317
Approach to self-similarity in Smoluchowski's coagulation equations , with R.L. Pego , Comm. Pure. App. Math. (2004), Vol. 57, pp.1197-1232.
Gradient systems with wiggly energies and related averaging problems , Arch. Rat. Mech. Analysis, Vol. 162, (2002), 193-246.
|1994||BT||Indian Institute of Technology|
NSF Career award, 2008-2013.
Clay Mathematics Institute Emissary, August 2000.
Applied Mathematics Letters (Associate Editor, 2011-- present)
Journal of Nonlinear Science (Associate Editor, 2011--present)
Quarterly of Applied Mathematics (Associate Editor, 2015--present)
SIAM Journal of Mathematical Analysis (Associate Editor, 2010--present)
American Mathematical Society (AMS)
Society for Industrial and Applied Mathematics (SIAM)
I teach classes in dynamical systems and partial differential equations. These include the core undergraduate and graduate sequences in these areas, as well as several specialized topics (random matrix theory, mathematical problems in materials science, kinetic theory).
|APMA 1710 - Information Theory|
|APMA 1940V - Topics in Coding Theory|
|APMA 2200 - Nonlinear Dynamical Systems: Theory and Applications|
|APMA 2811O - Dynamics and Stochastics|
|APMA 2821X - Statistical Theories of Turbulence|