Main projects:

Nystrom-type numerical methods for boundary integral equations.

Hydrodynamic transport and diffusion of rigid and flexible particles.

Sequence-dependent models for DNA structure prediction.

Global curvature and optimal packing of curves with finite thickness.

Structure-preserving numerical methods in classical and continuum mechanics.

Books

O. Gonzalez, Topics in Applied Mathematics and Modeling: Concise Theory with Case Studies, Pure and Applied Undergraduate Texts, Volume 59, American Mathematical Society (2023). Print ISBN 978-1-4704-6991-7, Electronic ISBN 978-1-4704-7217-7. 210 pages, 300+ exercises, 180+ illustrations.

O. Gonzalez & A. Stuart, A First Course in Continuum Mechanics, Cambridge Texts in Applied Mathematics, Cambridge University Press (2008). ISBN 978-0-521-88680-2 hardback, ISBN 978-0-521-71424-2 paperback. 416 pages, 170+ exercises.

O. Gonzalez & A. Stuart, A First Course in Continuum Mechanics: Complete Solutions Manual, Cambridge University Press (2008). 119 pages.

Articles

O. Gonzalez, Theorems on the stokesian hydrodynamics of a rigid filament in the limit of vanishing radius, SIAM Journal on Applied Mathematics, 81 (2021) 551-573. Supplementary material: PDF file. [This article was originally submitted Aug 2019, then shortened by request and re-submitted Oct 2019, then accepted Jan 2021, and published electronically Apr 2021.]

A. Mauney, J. Tokuda, L. Gloss, O. Gonzalez & L. Pollack, Local DNA sequence controls the cooperativity and asymmetry of DNA unwrapping from nucleosome core particles, Biophysical Journal, 115 (2018) 773-781. [This work was recognized in a dedicated commentary article.]

O. Gonzalez, Bounds on the average velocity of a rigid body in a Stokes fluid, SIAM Journal on Applied Mathematics, 77 (2017) 1904-1920.

O. Gonzalez, M. Pasi, D. Petkeviciute, J. Glowacki & J.H. Maddocks, Absolute versus relative entropy parameter estimation in a coarse-grain model of DNA, SIAM Multiscale Modeling and Simulation, 15 (2017) 1073-1107. Supplementary website: http://lcvmwww.epfl.ch/cgDNA. cgDNAweb (a web-based viewer for the cgDNA model): http://cgdnaweb.epfl.ch.

O. Gonzalez, A theorem on the surface traction field in potential representations of Stokes flow, SIAM Journal on Applied Mathematics, 75 (2015) 1578-1598.

O. Gonzalez & J. Li, A convergence theorem for a class of Nystrom methods for weakly singular integral equations on surfaces in R^3, Mathematics of Computation, 84 (2015) 675-714.

D. Petkeviciute, M. Pasi, O. Gonzalez & J.H. Maddocks, cgDNA: a software package for the prediction of sequence-dependent coarse-grain free energies of B-form DNA, Nucleic Acids Research, 42 (2014) e153: 1-9. Supplementary material: PDF file. Supplementary website: http://lcvmwww.epfl.ch/cgDNA. cgDNAweb (a web-based viewer for the cgDNA model): http://cgdnaweb.epfl.ch.

J. Li & O. Gonzalez, Convergence and conditioning of a Nystrom method for Stokes flow in exterior three-dimensional domains, Advances in Computational Mathematics, 39 (2013) 143-174.

O. Gonzalez, D. Petkeviciute & J.H. Maddocks, A sequence-dependent rigid-base model of DNA, Journal of Chemical Physics, 138 (2013) 055102: 1-28. Supplementary material: PDF file. Supplementary website: http://lcvmwww.epfl.ch/cgDNA. cgDNAweb (a web-based viewer for the cgDNA model): http://cgdnaweb.epfl.ch. [This article was selected for the 2013 JCP Editors' Choice Collection.]

O. Gonzalez & J. Li, On the hydrodynamic diffusion of rigid particles of arbitrary shape with application to DNA, SIAM Journal on Applied Mathematics, 70 (2010) 2627-2651.

J. Walter, O. Gonzalez & J.H. Maddocks, On the stochastic modeling of rigid body systems with application to polymer dynamics, SIAM Multiscale Modeling and Simulation, 8 (2010) 1018-1053.

F. Lankas, O. Gonzalez, L.M. Heffler, G. Stoll, M. Moakher & J.H. Maddocks, On the parameterization of rigid base and basepair models of DNA from molecular dynamics simulations, Physical Chemistry Chemical Physics, 11 (2009) 10565-10588.

O. Gonzalez, On stable, complete and singularity-free boundary integral formulations of exterior Stokes flow, SIAM Journal on Applied Mathematics 69 (2009) 933-958.

O. Gonzalez & J. Li, Modeling the sequence-dependent diffusion coefficients of short DNA sequences, Journal of Chemical Physics 129 (2008) 165105: 1-12.

O. Gonzalez, A.B.A. Graf & J.H. Maddocks, Dynamics of a rigid body in a Stokes fluid, Journal of Fluid Mechanics 519 (2004) 133-160.

O. Gonzalez & R. de la Llave, Existence of ideal knots, Journal of Knot Theory and Its Ramifications 12 (2003) 123-133.

J.R. Banavar, O. Gonzalez, J.H. Maddocks & A. Maritan, Self-interactions of strands and sheets, Journal of Statistical Physics 110 (2003) 35-50.

O. Gonzalez, J.H. Maddocks & J. Smutny, Curves, circles and spheres, Contemporary Mathematics 304 (2002) 195-215.

O. Gonzalez, J.H. Maddocks, F. Schuricht & H. von der Mosel, Global curvature and self-contact of nonlinearly elastic curves and rods, Calculus of Variations and Partial Differential Equations 14 (2002) 29-68.

O. Gonzalez & J.H. Maddocks, Extracting parameters for base-pair level models of DNA from molecular dynamics simulations, Theoretical Chemistry Accounts 106 (2001) 76-82.

O. Gonzalez, J.H. Maddocks & R.L. Pego, Multi-multiplier ambient space formulations of constrained dynamical systems, with an application to elastodynamics, Archive for Rational Mechanics and Analysis 157 (2001) 285-323.

O. Gonzalez, Exact energy-momentum conserving algorithms for general models in nonlinear elasticity, Computer Methods in Applied Mechanics and Engineering 190 (2000) 1763-1783.

O. Gonzalez & J.H. Maddocks, Global curvature, thickness and the ideal shapes of knots, The Proceedings of the National Academy of Sciences, USA 96 (1999) 4769-4773.

O. Gonzalez, Mechanical systems subject to holonomic constraints: differential-algebraic formulations and conservative integration, Physica D 132 (1999) 165-174.

O. Gonzalez, D.J. Higham & A.M. Stuart, Qualitative properties of modified equations, IMA Journal of Numerical Analysis 19 (1999) 169-190.

A. Stasiak, J. Dubochet, P. Furrer, O. Gonzalez & J. Maddocks, DNA: uncooked, al dente, or scotti?, Science 283 (1999) 1641.

O. Gonzalez & A.M. Stuart, On the qualitative properties of modified equations, in Foundations of Computational Mathematics, edited by F. Cucker & M. Shub, Springer Verlag, Berlin (1997) 169-179.

O. Gonzalez, Time integration and discrete hamiltonian systems, Journal of Nonlinear Science 6 (1996) 449-467.

O. Gonzalez & J.C. Simo, On the stability of symplectic and energy-momentum algorithms for nonlinear hamiltonian systems with symmetry, Computer Methods in Applied Mechanics and Engineering 134 (1996) 197-222.

J.C. Simo & O. Gonzalez, Recent results on the numerical integration of infinite-dimensional hamiltonian systems, in Recent Developments in Finite Element Analysis, edited by T.J.R. Hughes, E. Onate, and O.C. Zienkiewicz, International Center for Numerical Methods in Engineering, Barcelona, Spain (1994) 255-271.

J.C. Simo & O. Gonzalez, Assessment of energy-momentum and symplectic schemes for stiff dynamical systems, American Society of Mechanical Engineers, proceedings of the ASME Winter Annual Meeting, New Orleans, Louisiana (1993) 1-12.

NSF Grant DMS-0706951, (PI, $166,898) 2010-2007.

NSF Grant DMS-0405955, (PI, $141,999) 2007-2004.

University Summer Research Award, (PI, $15,778) 2004.

NSF Grant DMS-0322962, (Co-PI, $111,553) 2004-2003.

College of Natural Sciences Teaching Excellence Award, 2003.

NSF Grant DMS-0102476, (PI, $102,000) 2004-2001.

NSF Mathematical Sciences Postdoctoral Fellowship, 2000-1997.

NSF Graduate Fellowship, Stanford University, 1995-1992.

Stanford Graduate Fellowship, Stanford University, 1991.