|
Department of Mathematics University of Texas 1 University Station C1200 Austin, Texas 78712-0257 Office: 512 471 1138 ..... Fax: 512 471 9038 E-Mail: og@math.utexas.edu |
| Research Interests | My general interests are in computational and applied mathematics with an emphasis on classical continuum mechanics. My current efforts are focussed on modeling the mechanical properties of DNA at various length scales. Keywords: modeling, numerical analysis, differential equations, integral equations, geometry of curves and surfaces. |
| Education |
Doctor of Philosophy in Applied Mechanics Stanford University, June 1996 Advisors: Juan C. Simo and Andrew M. Stuart Thesis Title: Design and analysis of conserving integrators for nonlinear hamiltonian systems with symmetry Master of Science in Scientific Computing and Computational Mathematics Stanford University, June 1996 Master of Science in Applied Mechanics Stanford University, June 1992 Bachelor of Science in Mechanical Engineering University of Texas at Austin, May 1991 with Highest Honors |
| Grants & 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 All-American Scholar, 1991 National Collegiate Engineering Award, 1991 Engineering Scholar, University of Texas at Austin, 1991-1988 Texas Achievement Award, University of Texas at Austin, 1989-1986 Texas Valedictorian Tuition Award, University of Texas at Austin, 1986 |
| Academic Positions |
present - 2013 Professor, Department of Mathematics, University of Texas, Austin. 2013 - 2006 Associate Professor, Department of Mathematics, University of Texas, Austin. 2006 - 2000 Assistant Professor, Department of Mathematics, University of Texas, Austin. August 1999 - June 1999 Lecturer, Scientific Computing and Computational Mathematics Program, Department of Computer Science, Stanford University. August 2000 - October 1997 NSF Postdoctoral Fellow, Department of Mathematics, Swiss Federal Institute of Technology, Lausanne. December 1997 - April 1996 Postdoctoral Research Associate, Institute for Physical Science and Technology, University of Maryland, College Park. |
| Teaching Experience |
Fall 2006, 2004, 2003 Numerical Treatment of Differential Equations, a first-year graduate course on the approximation of differential equations by numerical methods. The main methods considered are one-step and multi-step methods for systems of ordinary differential equations, and finite difference and finite element methods for elliptic, parabolic and hyperbolic partial differential equations. An analysis of consistency, stability and convergence is given for various classic methods applied to standard model problems. Spring 2006, 2002 Computational Modeling, a graduate course on the mathematical modeling of rigid bodies and elastic filaments in fluids with applications to DNA. Topics include coordinates and kinematics on the three-dimensional rotation group, rigid body equations, elastic filament equations, Stokes equations, hydrodynamic diffusion equations on the six-dimensional Euclidean group, and the Stokes diffusion tensors. Attention is focussed on modeling various experimental methods for probing the structure of DNA and other molecules in solution at diffusive time scales. Fall 2021, 2020, 2019, 2018, 2017 Spring 2024, 2023, 2022, 2021, 2020, 2019, 2018, 2017, 2016, 2015, 2009, 2008, 2007, 2005, 2003 Mathematical Modeling in Science and Engineering, a course for advanced undergraduates interested in mathematical modeling and analysis. The goals are to develop tools for studying differential equation models that arise in applications, and to illustrate how the derivation and analysis of models can be used to gain insight and make predictions about physical systems. Topics include: dimensional analysis, scaling, dynamical systems, stability and bifurcation, perturbation methods, and calculus of variations. Spring 2014, 2013, 2012, 2011, 2010 Numerical Methods for Applications, a second undergraduate course in the theory and application of numerical methods and computer programming. The main topics include iterative methods for systems of linear and nonlinear equations, least squares approximation and orthogonal polynomials, approximation of eigenvalues, and finite-difference and finite-element methods for ordinary and partial differential equations. Spring 2011, 2009, 2004 Scientific Computation in Numerical Analysis, a first undergraduate course in the theory and application of numerical methods and computer programming. The main topics include nonlinear algebraic equations, polynomial interpolation, numerical differentiation and integration, initial-value problems for ordinary differential equations, and direct methods for systems of linear algebraic equations. Fall 2002 Applied Linear Algebra, a course for advanced undergraduates with an interest in linear algebra and its applications to dynamical systems and data analysis. The main topics include vector spaces, linear operators, eigenvalues, diagonalization, normal mode expansions, inner products, orthogonality and Fourier series. Fall 2005 Linear Algebra and Matrix Theory, an undergraduate course for math majors which covers a variety of topics in the theory of vectors and matrices and provides an introduction to proofs and abstract mathematics. The main topics include vectors and matrices, systems of linear equations, determinants and eigenvalues, vector spaces, linear transformations and orthogonality. Spring 2001 Advanced Calculus for Applications I, an undergraduate course on the theory of ordinary differential equations. The main topics include initial value problems, exact and approximate solution techniques, basic existence and uniqueness theorems, fundamental sets of solutions and linear independence, series expansions, Laplace transforms, boundary value problems, Fourier series and an introduction to partial differential equations. Spring 2023, 2021, 2020, 2019, 2017, 2016, 2015, 2014, 2013, 2012, 2010, 2008, 2007, 2006, 2005, 2004, 2003 Differential and Integral Calculus II, a second course in calculus that focuses on the concepts of infinite series, vectors and multivariable functions. The main topics include L'Hospital's rules for limits, infinite sequences and sums, power and Taylor series, polar coordinates and parametric equations for plane curves, algebra and calculus of vectors, and partial derivatives, gradients, optimization and integration of multivariable functions. Fall 2024, 2023, 2022, 2021, 2017, 2016, 2015, 2014, 2013, 2012, 2011, 2010, 2009, 2008, 2007, 2006, 2005, 2004, 2003, 2002, 2001, 2000 Differential and Integral Calculus I, a first course in calculus that focuses on the elementary theory of functions of one variable. The main topics include limits, continuity, derivatives and their applications, integrals and their applications, the fundamental theorems of calculus, and trigonometric, exponential and logarithmic functions. Spring 2000, Fall 1999 (Assistant) Analysis III and IV, a year-long advanced undergraduate course on multivariable calculus and vector analysis, Fourier series and transforms, and complex analysis. Summer 1999 Introduction to Scientific Computing, an undergraduate course on the theory and application of numerical methods. The main topics include nonlinear algebraic equations, polynomial interpolation, numerical differentiation and integration, initial-value problems for ordinary differential equations, and methods for systems of linear algebraic equations. Spring 1999, Fall 1998 (Assistant) Mathematical Modeling of DNA, an advanced undergraduate course in mathematical modeling. The main topics include the theory of elastic rods; calculus of variations; DNA structure and topology; link, twist and writhe of framed curves; polymer physics. Spring 1997 Multivariable and Vector Calculus, a third-semester calculus course. The main topics include the algebra and calculus of vectors; partial derivatives, gradients, optimization and integration of multivariable functions; line and surface integrals; classic theorems of vector calculus. Fall 1996 (Assistant) Methods and Models in Applied Mathematics, a first-year graduate course in methods of applied mathematics. The main topics include dimensional analysis and scaling; regular and singular perturbation methods; boundary layers and matched asymptotic expansions; Floquet theory and parametric resonance; calculus of variations. Fall 1995 (Assistant) Introduction to Continuum Mechanics, a first-year graduate course in the basic principles of continuum mechanics. The main topics include tensor analysis in three-dimensional Euclidean space; continuum mass and force distributions; deformation and strain; balance laws of mass, momentum, energy and entropy; the principle of material frame-indifference; ideal, compressible and viscous fluids; linear and nonlinear elastic solids; thermo-mechanical theories of fluids and solids. |
| Invited Presentations |
Conference on Mathematical Modeling of Filaments,
January 2018, Lausanne, Switzerland Society for Mathematical Biology Annual Meeting, July 2012, Knoxville, TN Mathematical Physics Seminar, University of Texas, January 2012, Austin, TX International Congress on Industrial and Applied Mathematics, July 2011, Vancouver, British Columbia Applied Math RTG Seminar, University of Texas, April 2009, Austin, TX Blackwell-Tapia Conference, Statistical and Applied Mathematical Sciences Institute, November 2008, Research Triangle Park, NC Workshop on Multiscale Modeling and Analysis, University of Texas, August 2008, Austin, TX AMS Southeastern Section Meeting, Louisiana State University, March 2008, Baton Rouge, LA Introduction to Research Seminar, Department of Mathematics, University of Texas, March 2007, Austin, TX Summer Math Institute, Cornell University, July 2006, Ithaca, NY Mathematics of Biomolecules Conference, University of Warwick, January 2006, Coventry, England Math Majors Seminar, Trinity University, October 2005, San Antonio, TX Keynote Address: MAA Sectional Meeting, University of Kansas, March 2005, Lawrence, KS Bioscience Initiative Lecture, University of Kansas, March 2005, Lawrence, KS Theoretical Chemistry Seminar, University of Texas, February 2005, Austin, TX SIAM Conference on Analysis of PDEs, December 2004, Houston, TX SACNAS National Conference, October 2004, Austin, TX Math in Science Lecture, University of Texas, February 2004, Austin, TX Mathematical Physics Seminar, University of Texas, February 2004, Austin, TX SIAM-AMS-MAA Joint Meeting, January 2004, Phoenix, AZ Introduction to Research Seminar, Institute for Computational Engineering and Science, University of Texas, September 2003, Austin, TX Workshop on Knots, Random Walks and Biomolecules, July 2003, Les Diableretes, Switzerland SIAM Conference on Applications of Dynamical Systems, May 2003, Snowbird, UT AMS Western Section Meeting, San Francisco State University, May 2003, San Francisco, CA AMS Central Section Meeting, University of Wisconsin, October 2002, Madison, WI Workshop on Topology in Condensed Matter Physics, Max Planck Institute for the Physics of Complex Systems, July 2002, Dresden, Germany Introduction to Research Seminar, Department of Mathematics, University of Texas, April 2002, Austin, TX Applied Math Colloquium, University of Arizona, March 2002, Tucson, AZ Math GADGET Seminar, University of Texas, November 2001, Austin, TX Math TACG Seminar, University of Texas, October 2001, Austin, TX Workshop on Long Molecules and Thin Films, July 2001, Ascona, Switzerland Applied Analysis Seminar, Swiss Federal Institute of Technology, June 2001, Lausanne, Switzerland Workshop on Computational SDEs, University of Warwick, March 2001, Coventry, England Math TACG Seminar, University of Texas, December 2000, Austin, TX Geometry Seminar, University of Texas, November 2000, Austin, TX Mathematical Physics Seminar, University of Texas, September 2000, Austin, TX Applied Math Seminar, Duke University, February 2000, Durham, NC Applied Math Seminar, University of California, February 2000, Los Angeles, CA Applied Math Seminar, University of Wisconsin, February 2000, Madison, WI Applied Math Seminar, Georgia Institute of Technology, February 2000, Atlanta, GA Applied Math Seminar, University of Texas, February 2000, Austin, TX Applied Math Seminar, University of California, February 2000, Davis, CA Applied Math Seminar, University of Maryland, January 2000, Baltimore County, MD Applied Math Seminar, University of Michigan, January 2000, Ann Arbor, MI Numerical Analysis Seminar, University of Michigan, January 2000, Ann Arbor, MI Numerical Analysis Seminar, University of Geneva, February 1999, Geneva, Switzerland Applied Analysis Seminar, Swiss Federal Institute of Technology, May 1998, Lausanne, Switzerland Applied Analysis Seminar, Swiss Federal Institute of Technology, December 1997, Lausanne, Switzerland Meeting on Numerical Dynamics and Elasticity, University of Kansas, July 1996, Lawrence, KS SIAM Annual Meeting, July 1996, Kansas City, MO Computational Mechanics Seminar, University of California, February 1996, Berkeley, CA Numerical Analysis Seminar, University of Kansas, February 1996, Lawrence, KS Numerical Analysis Seminar, University of Maryland, February 1996, College Park, MD SciCADE Conference, Stanford University, March 1995, Stanford, CA SIAM Conference on Applications of Dynamical Systems, May 1995, Snowbird, UT Conference in honor of Robert L. Taylor, September 1994, Palo Alto, CA Meeting on Geometric Mechanics and Nonholonomic Systems, University of California, August 1994, Berkeley, CA |
| 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, Building a better bridge between models and experimental data for DNA, Biophysical Journal, (2024) submitted. 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. 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. |
| Students |
Jun Li (PhD, Computational and Applied Mathematics, UT-Austin,
May 2010) Joshua Fisher (MS, Mathematics, UT-Austin, May 2006) Mathias Carlen (MS/Diplome, Physics, EPFL, Switzerland, Feb 2005) Changsub Lee (MS, Mathematics, UT-Austin, May 2004) Shubing Wang (MS, Mathematics, UT-Austin, Dec 2003) Michele Renehan (MS, Mathematics, UT-Austin, Aug 2003) Monica Shaw (MS, Computational and Applied Mathematics, UT-Austin, Aug 2003) Cecilia Diniz (MS, Mathematics, UT-Austin, May 2002) |
| Service |
Preliminary Exam Committees, Applied Math and CSEM (regular participation) Mathematics Instructional Faculty Chair's Committee (present-2019) Mathematics Teaching Faculty Committee (2018 co-chair, 2017 co-chair) Mathematics NTT Faculty Review Committee (2018-2016, 2013) Mathematics Teaching Evaluation Committee (2018) Mathematics Hiring Committee (2015 chair, 2014, 2013) Mathematics Admissions Committee (2021, 2019, 2017, 2014-2012) Mathematics Undergraduate Studies Committee (2013, 2012) CSEM Graduate Studies Sub-Committee (GSSC) (2018-2010, 2003) CSEM Admissions Committee (2016, 2013, 2011 chair, 2010 chair, 2003, 2002) External Review Committee, Applied Math Program, University of Arizona, Tucson (2010) NSF Review Panel (2010, 2008, 2003) CNS Diversity and Inclusion Committee (2018, 2017) University Faculty Grievance Committee (2015-2013) University Parking and Traffic Appeals Committee (2015-2013, 2005-2001) University Admissions and Registration Committee (2007, 2006) University Recruitment and Retention Committee (2007-2005) University Faculty Council, elected member (2007-2005) Peer reviewer for : Professional memberships: AMS, MAA, SIAM. |