About Me

I am a Ph.D. candidate in my 4th year at the University of Utah. I work with my advisor Paul Bressloff as well as Sean Lawley as part of the Biophysics and Stochastics Research Group. My current research interests involves modeling the diffusion of particles that depends on the state of some discrete, possibly non-Markovian random variable. I approach these problems using an combination of analytical and approximation techniques, and well as numerical PDE solvers and Monte Carlo methods to confirm or extend analytical results.


Diffusion with Spatially Dependent Switching Rates

Particles binding and unbinding within a spatially heterogeneous environment change diffusive states based on spatially changing rates. We have done some preliminary investigation into this phenomenon.

  • P C Bressloff, S D Lawley, and P Murphy. Protein concentration gradients and switching diffusions. Phys. Rev. E. Under Review (2019)
  • Age-Structured Gates

    We investigate the effects of a cellular gate changing between open and closed conformational states where some memory of the occupation time of the current state is retained. This leads to diffusing particles experiencing a changing environment where the transition times are not necessarily exponentially distributed.

  • P C Bressloff, S D Lawley, and P Murphy. Effective permeability of gap junctions with age-structured switching. SIAM J. Appl. Math. Submitted (2018)
  • P C Bressloff, S D Lawley, and P Murphy. Diffusion in an age-structured randomly switching environment. J. Phys. A 51 315001 (2018)
  • Teaching

    • MATH 1310 Mathematics in Medicine · Lab Instructor, Spring 2019
    • MATH 1310 Mathematical Biology I · Lab Instructor, Fall 2018
    • MATH 1080 Precalculus · Instructor of Record, Spring 2018
    • MATH 1080 Precalculus · Instructor of Record, Fall 2017
    • MATH 1010 Intermediate Algebra · Instructor of Record, Fall 2016
    • MATH 2250 Differential Equations & Linear Algebra · Lab Instructor, Spring 2016
    • MATH 1310 Engineering Calculus I · Lab Instructor, Fall 2015


    The best way to get in contact with me is through email at
    pmurphy [at] math [dot] utah [dot] edu

    University of Utah
    Department of Mathematics
    155 S. 1400 E. JWB 233
    Salt Lake City, UT 84112

    Office: LCB 302

    Email: pmurphy [at] math [dot] utah [dot] edu