NICHOLAS D. BRUBAKER

Transcription

1 NICHOLAS D. BRUBAKER Department of Mathematics The University of Arizona, Tucson, AZ math.arizona.edu/~nbrubaker/ EMPLOYMENT & EDUCATION NSF Postdoctoral Fellow, Dept. of Mathematics, The University of Arizona Project: Math. modeling of capillary and electro-capillary origami Mentor: J. Lega present Ph.D. in Applied Mathematics, University of Delaware 05/2013 Dissertation: Mathematical Theory of Electro-Capillary Surfaces Advisor: J. A. Pelesko M.Sc. in Applied Mathematics, University of Delaware 05/2010 B.Sc. in Mathematics with Honors, Millersville University 05/2008 Honors Thesis: Numerical Approximations of Center Manifolds Advisor: Z. Shao AWARDS & HONORS NSF Postdoctoral Research Fellowship, The University of Arizona 2013 NSF Graduate Research Fellowship, University of Delaware Winter Research Review Travel Award, University of Delaware 2012 VIGRE Summer Program on Math Modeling, The University of Arizona 2007 Edna H. Myers Mathematics Scholarship, Millersville University Millar Kraybill Academic Scholarship, Millersville University RESEARCH INTERESTS Modeling nonlinear phenomena, especially those occurring in micro-scale systems coupling fluids, electrostatics and elasticity Free boundary problems, often for interfaces and thin sheets Capillary surfaces coupled with external forces Variational methods involving geometric quantities Micro-electromechanical systems PUBLICATIONS & PREPRINTS [1] N. D. Brubaker, Two-Dimensional Capillary Origami with inextensibility and a free contact line, preprint, (2015). [2] N. D. Brubaker and J. Lega, Two-dimensional capillary origami, submitted to Phys. Lett. A, (2015). [3] N. D. Brubaker and J. Lega, Two-dimensional capillary origami with pinned contact line, SIAM J. Appl. Math., 75:3 (2015),

2 [4] N. D. Brubaker, J. I. Siddique, E. Sabo, R. Deaton, and J. A. Pelesko, Refinements to the study of electrostatic deflections: Theory and experiment, European J. Appl. Math., 24:3 (2013), [5] N. D. Brubaker and A. E. Lindsay, The onset of multi-valued solutions of a prescribed mean curvature equation with singular non-linearity, European J. Appl. Math., 24:5 (2013), [6] N. D. Brubaker and J. A. Pelesko, Analysis of a one-dimensional prescribed mean curvature equation with singular nonlinearity, Nonlinear Anal., 75:13 (2012), [7] N. D. Brubaker and J. A. Pelesko, Non-Linear Effects on Canonical MEMS Models, European J. Appl. Math., 22:5 (2011), [8] N. D. Brubaker, S. Carter, S. M. Evans, D. E. Kravatz Jr., S. Linn, S. W. Peurifoy, and R. Walker, Double Bubble Experiments in the Three-Torus, Math Horizons, 15:4 (2008), PRESENTATIONS Invited Conference and Seminar Talks 1. Elasto-capillary systems and Capillary Origami, Minisymposium on Patterns in Complex Systems, Annual Meeting of SIAM Central States Section, Rolla, MO (Apr , 2015). 2. Capillary origami, Analysis, Dynamics, and Applications Seminar, The University of Arizona (Sept. 23, 2014). 3. Modeling capillary origami, Minisymposium on Analysis and Applications of Pattern-Forming Systems, SIAM Conference on Nonlinear Waves and Coherent Structures, Cambridge, UK (Aug. 13, 2014). 4. Capillary Origami, ACMS Colloquium, University of Notre Dame (Mar. 31, 2014). 5. Electro-capillary surfaces, Analysis and Its Applications Seminar, The University of Arizona (Oct. 08, 2013). 6. On a prescribed mean curvature equation in modeling MEMS, Minisymposium on Self- Organized Behavior of Nonlinear Elliptic Equations and Pattern Formation of Strongly Interacting Systems, 9th AIMS DSDEA Conference, Orlando, FL (July 3, 2012). 7. Electrostatic Deflections in Microelectromechanical Systems, Analysis and Its Applications Seminar, University of Arizona (Apr. 3, 2012). 8. Mathematical Modeling of MEMS, Millersville University and F&M College Joint Math Colloquium, Millersville (Oct. 6, 2011). Contributed Talks 1. Capillary Origami, Frontiers in Applied and Computational Mathematics, Newark, NJ (June 5 6, 2015). Poster. 2. Electro-capillary problems motivated by microelectromechanical systems, Workshop on Geometry of Interfaces and Capillarity, University of Granada, Spain (June 25, 2012). 2

3 3. Bifurcations of a Prescribed Mean Curvature Equation, 2012 Graduate Student Winter Research Symposium, University of Delaware (Feb. 10, 2011). Poster. 4. The Study of Electrostatic Deflections, 7th International Congress on Industrial and Applied Mathematics, Vancouver (July 19, 2011). 5. Refinements to Pull-in Voltage Predictions, 2011 Graduate Student Winter Research Symposium, University of Delaware (Feb. 11, 2011). 6. Electrostatic Deflections of an Elastic Membrane, SIAM Annual Meeting, Pittsburgh (July 13, 2010). Poster. 7. A Corrected Model for Electrostatic Deflections of an Elastic Membrane, SIAM/MMA Mid- Atlantic Regional Applied Mathematics Student Conference (Mar. 20, 2010). 8. Double Bubble Experiments in the 3-Torus, The 22nd Annual Student Mathematics Conference, Moravian College (Feb. 16, 2008). Talk. Expository Lectures 1. Equilibrium Capillary Surfaces, Undergraduate Brown Bag Seminar, The University of Arizona (Nov. 07, 2013). 2. Bifurcations due the Mean Curvature Operator, Hallenbeck Grad Student Seminar, University of Delaware (Oct. 6, 2011). 3. Nonlinear Elastic Effects on MEMS Models, Hallenbeck Grad Student Seminar, University of Delaware (Dec. 1, 2010). 4. Modeling Electrostatic Deflections of an Elastic Membrane, Brown-bag Lunch Seminar, University of Delaware (July 29, 2009). Talk. 5. Formation and Dynamics of Sand Dunes, VIGRE Summer Program, The University of Arizona (July 26, 2007). OUTREACH Organizer, Math Circle on fractals, University of Delaware, Spring SERVICE TO THE PROFESSION Co-organizer, with K. Lin, Modeling, Computation, Nonlinearity, Randomness, and Waves Seminar, Program in Applied Mathematics, The University of Arizona, Spring Vice President, University of Delaware Student Chapter of SIAM, Speaker and panelist, EPaDel Careers in Math Conference. Millersville University, Fall Reviewer, European J. Applied Mathematics, ZAMP, Comptes rendus Mathematique, Discrete and Continuous Dynamical Systems, Boundary Value Problems, Proceedings of the Edinburgh Mathematical Society. 3

4 SERVICE TO THE UNIVERSITY The University of Arizona Member, Graduate admissions committee, Program in Applied Mathematics, The University of Arizona, Speaker, NSF GRFP Application Strategies Workshop, Graduate College, The University of Arizona, Fall University of Delaware Application reviewer, NSF GRFP workshop, Department of Mathematical Sciences, University of Delaware, Fall Speaker, NSF GRFP application information session, Office of Graduate and Professional Education, University of Delaware, PROFESSIONAL ORGANIZATIONS Member, Society for Industrial and Applied Mathematics (SIAM). Member, American Mathematical Society (AMS). Vice President, University of Delaware Student Chapter of SIAM, 2010 Member, University of Delaware Student Chapter of SIAM, TEACHING EXPERIENCE Courses Taught Math 454: ODE and Stability Theory, The University of Arizona Dynamical systems course for upper level mathematics majors Math 322: Mathematical Analysis for Engineers, The University of Arizona Mathematical methods course for upper level STEM majors Fall 2015 Spring 2015 Math 129: Calculus II, The University of Arizona Fall 2014 Math 115: Pre-Calculus, University of Delaware A pre-calculus course for non-science majors Math 113: Contemporary Mathematics, University of Delaware An alternative introductory mathematics course for liberal arts majors Summer 2013 Winter

5 Mentoring Co-organizer, with A. Gillette, D. Glickenstein and J. Lega, Research Tutorial Groups on Optimization, geometry, and numerical analysis. Discussions to introduce graduate students to mathematical research at the end of the first year and beginning of the second year. Teaching Assist., Math 512: Contemporary App. of Math, University of Delaware A capstone course for STEM majors. Held lab/office hours and assisted in guiding research projects, which included modeling the diffusion of ink, the oscillations of charged particles, the behavior cell rafts and the deflating of soap bubbles. Mentor, Groups Exploring Mathematical Sciences, University of Delaware A summer program for undergraduate research experience. Served as a mathematical guide, directing five projects on interspecies competition, self-assembly, electrostatics, math curricula and freezing drops. Spring 2015 Fall 2009 Summer 2009 Other Teaching Experience Teaching Assist., Advanced Calculus Prep. Session, University of Delaware Advanced calculus preparation session for incoming graduate students. Assisted in problem solving and held review sessions. Summer 2010 Teaching Assist., Calculus I, University of Delaware Spring 2010 Teaching Assist., Business Calculus I, University of Delaware Fall 2008 EARLY RESEARCH EXPERIENCE Groups Exploring the Mathematical Sciences, University of Delaware Modeled electrostatic induced deflections of a membrane under the direction of Professor John A. Pelesko. Undergraduate Honors Research, Millersville University Developed an algorithm for approximating center manifolds under the direction of Professor Zhoude Shao VIGRE Summer Program on Mathematical Modeling, University of Arizona Modeled the formation and dynamics of sand dunes under the direction of Dr. Predrag Punosevac and Professor Joceline Lega Undergraduate Research, Millersville University Studied the double bubble conjecture in the three torus under the direction of Professors Ron Umble and Frank Morgan Summer 2009 Spring 2008 Summer 2007 Spring 2007 Last updated: August 13,