N. Benjamin Murphy
nbmurphy@math.uci.edu
(949) 824-5503 (department)
(801) 688-1767 (mobile)
(949) 824-7993 (fax)
www.math.uci.edu/~nbmurphy/
University of California, Irvine
Department of Mathematics
340 Rowland Hall
Irvine, CA
92697-3875
USA
Education
2004
2005
2006
2012
University of Utah, B.S., Mathematics
University of Utah, B.S., Physics
University of Utah, M.S., Mathematics
University of Utah, Ph.D., Mathematics
Thesis: “Phase Transitions in Random Media”
Research Interests
Homogenization for multiscale composite materials. Effective diffusivity for advection enhanced
diffusion by time-dependent chaotic flows. Transport of electrical current, heat, and
electromagnetic waves in composite materials. Methods include: scientific computing, statistical
mechanics, percolation theory, inverse problems, functional analysis, random matrix theory,
complex analysis, dynamical systems theory, and stochastic processes.
Professional Experience
2006—2009
2009—2012
2012—2013
2013—2015
Spring 2015
Summer 2015—present
Research in Mathematical Biology, University of Utah
Department of Mathematics
Mentor: Paul Bressloff
Doctoral Dissertation Research, University of Utah
Department of Mathematics
Mentor: Ken Golden
Postdoctoral Research, University of Utah
Department of Mathematics
Mentors: Jingyi Zhu and Ken Golden
Postdoctoral Research, University of California, Irvine
Department of Mathematics
Mentor: Jack Xin
Postdoctoral Research, University of Utah
Department of Mathematics
Mentors: Elena Cherkaev and Ken Golden
Postdoctoral Research, University of California at Irvine
Department of Mathematics
Mentor: Jack Xin
Publications
1. K. M. Golden, N. B. Murphy, and E. Cherkaev. Spectral Analysis and Connectivity of Porous
Microstructures in Bone. J. Biomech., 44:337-344, 2011.
2. N. B. Murphy and K. M. Golden. The Ising Model and Critical Behavior of Transport in
Binary Composite Media. J. Math. Phys., 53, 063506, 25 pp., 2012.
3. N. B. Murphy, E. Cherkaev, C. Hohenegger, and K. M. Golden. Spectral Measure
Computations for Composite Materials. Comm. Math. Sci., 13(4):825-862, 2015.
4. N. B. Murphy, E. Cherkaev, and K. M. Golden. Random Matrix Universality for Classical
Transport in Composite Materials. 6 pp. Submitted, 2016.
5. N. B. Murphy, E. Cherkaev, J. Zhu, J. Xin, and K. M. Golden. Spectral Analysis and
Computation of Effective Diffusivities for Steady Random Flows. 40 pp. Submitted, 2016.
6. N. B. Murphy, E. Cherkaev, J. Xin, J. Zhu, and K. M. Golden. Spectral Analysis and
Computation of Effective Diffusivities in Space-Time Periodic Incompressible Flows. 50 pp.
Submitted, 2016.
7. N. B. Murphy, E. Cherkaev, and K. M. Golden. Analytic Continuation and Integral
Representations for the Effective Transport Properties of Polycrystalline Media. In revision
before submission, 2016.
8. N. B. Murphy, P. Sheng, and K. M. Golden. Statistical Mechanics of Homogenization for
Composite Materials. In revision before submission, 2016.
9. N. B. Murphy, J. Lin, P. Sheng, and K. M. Golden. On the Existence of a Phase Transition in
Electrorheological Fluids. In preparation, 2016.
Teaching Experience
University of Utah, Department of Mathematics
2004 Assistant for Math 2250, Ordinary Differential Equations and Linear Algebra, Fall
2005 Assistant for Math 2250, Ordinary Differential Equations and Linear Algebra, Spring
2007 Teacher for Math 1030, Introduction to Quantitative Reasoning, Fall
2009 Assistant for Math 1210, Calculus I, Fall
2010 Assistant for Math 2250, Ordinary Differential Equations and Linear Algebra, Spring
2010 Assistant for Math 6710, Linear Operators and Spectral Theory, Fall
2011 Assistant for Math 1220, Calculus II, Spring
University of California, Department of Mathematics
2014 Teacher and Undergraduate Mentor for the Interdisciplinary Computational and Applied
Mathematics Program (iCAMP), Stochastic Time Series Group, Summer
Awards
2012
Conference Presentation Prize for “Random Matrix Theory for Composites”,
Electrical, Transport, and Optical Properties of Inhomogeneous Media 9 (ETOPIM 9),
Marseille, France
Grants
2012—2013
Office of Naval Research (ONR) Grant N00014-12-10861
“Spectral Theory of Advective Diffusion in the Ocean,” PI: K. M. Golden,
Co-PI’s: N. B. Murphy and J. Zhu, $50,000
Departmental Scholarships and Research Grants
University of Utah, Department of Physics
2001—2002
Departmental Full Tuition Scholarship, Department of Physics
2003—2004
Departmental Full Tuition Scholarship, Department of Physics
University of Utah, Department of Mathematics
2002—2003
National Science Foundation (NSF) Division of Mathematical Sciences (DMS)
Vertical Integration of Research and Education in the Mathematical Sciences
(VIGRE) Research Experiences for Undergraduates (REU) Grant, Department of
Mathematics
2005—2007
NSF Integrative Graduate Education and Research Traineeship (IGERT) Grant,
Department of Mathematics
2008
NSF-VIGRE Undergraduate Research Grant, Department of Mathematics,
Spring
2008
NSF-DMS Undergraduate Research Grant, Department of Mathematics, Fall
2009
NSF-VIGRE Undergraduate Research Grant, Department of Mathematics,
Spring
2010
NSF-VIGRE Undergraduate Research Grant, Department of Mathematics, Fall
2011—2012
NSF-DMS Graduate Research Grant, Department of Mathematics
Computer Languages
Matlab, C, Maple, Mathematica
Conferences Attended
2005
2006
2006
2010
2011
2012
2012
2013
2014
2015
2015
Electrical, Transport, and Optical Properties of Inhomogeneous Media (ETOPIM 6),
Snowbird, Utah
Biophysical Society Annual Meeting, Salt Lake City, Utah
Gordon Research Conference on Theoretical Biology and Biomathematics, Tilton, New
Hampshire
American Mathematical Society (AMS) Sectional Meeting, Session on Random Matrix
Theory and Applications, Albuquerque, New Mexico
AMS Western Sectional Meeting, Session on Electromagnetic Wave Propagation in
Complex and Random Environments, Salt Lake City, Utah
ETOPIM 9, Marseille, France
Ocean Sciences Meeting, Salt Lake City, Utah
Joint Mathematics Meetings, San Diego, CA
Continuum Models and Discrete Systems (CMDS 13), Salt Lake City, UT
American Mathematical Society (AMS) Mathematics Research Communities (MRC),
Session on Differential Equations, Probability, and Sea Ice, Snowbird, Utah,
Session leader for the Spectral Measure Group
Pacific Institute for the Mathematical Sciences (PIMS), Mathematics of Sea Ice,
Vancouver, Canada.
Scientific Lectures and Presentations
University of Utah, Department of Mathematics
2003 REU Presentation Seminar, “Percolation Properties of Binary Composite Media”
2004 Undergraduate Research Symposium, “Phase Transitions in Binary Composites”
2005 Neuroscience Group Research Symposium, “The Fluctuation Dissipation Theorem and
Dynamic Equilibrium”
2006 Mathematical Biology Journal Club Presentation, “The Integrate and Fire Model of
Neurophysics”
2007
2007
2008
2009
2010
2011
IGERT Fellowship Laboratory Rotation Presentation, In collaboration with R. Rabbitt,
University of Utah, Department of Biomedical Engineering, “Fractional Differential
Equations and the Responses of Toadfish Vestibular Semicircular Canals”
Electromagnetics Group Presentation, “The Ising Model and Phase Transitions in Binary
Composite Media”
Electromagnetics Group Presentation, “Statistical Mechanics Characterization of Phase
Transitions in Binary Composites”
Graduate Seminar, “Mathematics of Phase Transitions”
Applied Math Seminar, “Random Matrix Theory and Statistical Mechanics
Characterizations of Phase Transitions in Binary Composite Media”
Applied Math Seminar, “Critical Theory of Two-Phase Random Media”
Hong Kong University of Science and Technology, Department of Physics
2009 Graduate Research Symposium, “Energy Representations of the Analytic Continuation
Method”
ETOPIM 9, Marseille, France
2012 Session Presentation, “Random Matrix Theory for Composites”
2012 Session Presentation, “Statistical Mechanics of Homogenization for Composites”
Invited Lectures
2012
2014
2014
2015
2015
2016
2016
Electrical, Transport, and Optical Properties of Inhomogeneous Media 9 (ETOPIM 9),
Marseille, France, “Random Matrix Theory for Composites”
University of California, Irvine, Interdisciplinary Computational and Applied
Mathematics Program (iCAMP) Presentation, “Disordered Media and Computation of
Effective Properties”
Continuum Models and Discrete Systems (CMDS 13), Salt Lake City, “Random Matrix
Universality, Spectral Measures, and Composite Media”
Duke University, Applied Math/Analysis Seminar, “Random Matrices, Spectral
Measures, and Transport in Composite Media”
Pacific Institute for the Mathematical Sciences (PIMS), Mathematics of Sea Ice,
Vancouver, Canada, “Random Matrix Theory for Transport in Sea Ice”
Joint Mathematics Meetings, AMS Mathematics Research Communities (MRC) Special
Session on Differential Equations, Probability, and Sea Ice, Seattle, Washington,
“Spectral Analysis of Transport in Sea Ice”
Society for Industrial and Applied Mathematics (SIAM) Conference on Mathematical
Aspects of Materials Science, Philadelphia, Pennsylvania, “Spectral Analysis and
Computation of Effective Diffusivities for Steady Random Flows”