Oscar Gonzalez
- Professor
- Mathematics
Affiliated Faculty, Oden Institute
Contact Information
Biography
Oscar Gonzalez is a professor in the Department of Mathematics at The University of Texas at Austin. He earned his Ph.D. in applied mechanics from Stanford University in 1996.
Gonzalez's research interests encompass computational and applied mathematics, focusing on modeling, numerical analysis, differential equations, integral equations, and the geometry of curves and surfaces. His main projects include:
- Developing Nystrom-type numerical methods for boundary integral equations.
- Investigating hydrodynamic transport and diffusion of rigid and flexible particles.
- Creating sequence-dependent models for DNA structure prediction.
- Studying global curvature and optimal packing of curves with finite thickness.
- Designing structure-preserving numerical methods in classical and continuum mechanics.
Throughout his career, Gonzalez has received several grants and awards, including multiple National Science Foundation grants and the College of Natural Sciences Teaching Excellence Award in 2003. He has also co-authored books such as "A First Course in Continuum Mechanics" and "Topics in Applied Mathematics and Modeling: Concise Theory with Case Studies."
Research
Area: computational and applied mathematics.
Interests: modeling, numerical analysis, differential equations, integral equations, geometry of curves and surfaces.
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.
Research Areas
- Mathematics
Fields of Interest
- Applied and Computational Mathematics
Education
- Ph.D., Stanford University (1996)
Publications
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.
Awards
- 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.