Publications

 
 

I. Partial Differential Equations and Kinetic Theory



  1. 23. "Global Sensitivity Metrics and Active Subspaces for Kinetic Simulations of Plasma Dynamics," (with D. Seal and B. Sattelberg) in revision.

  1. 22. "A Kernel-based Lagrangian Method for Imperfectly-Mixed Chemical Reactions," (with M. Schmidt and D. Benson) submitted.

  1. 21. "On the spatially homogeneous and isotropic Einstein-Vlasov-Fokker-Planck system with cosmological scalar field" (with S. Calogero) submitted.

  3. 20. "Separated Characteristics and Global Solvability for the One and one half dimensional Vlasov Maxwell System'" (with J. Schaeffer and R. Glassey) Kinetic and Related Models 9 (2016) 455-467 (.pdf)

  1. 19. "Global Classical Solutions of the "One and one-half dimensional" Vlasov-Maxwell-Fokker-Planck system” (with J. Schaeffer) Communications in Mathematical Sciences 14 (2016) 209–232 (.pdf)

  3. 18. "A Short Proof of Increased Parabolic Regularity" (with N. Michalowski) Electronic Journal of Differential Equations 205 (2015) 1-9 (.pdf)

  5. 17. “Global Classical Solutions to the One and one-half dimensional relativistic Vlasov-Maxwell-Fokker-Planck system” (with N. Michalowski) Kinetic and Related Models 8 (2015) 169-199 (.pdf)

  1. 16. “Instability of some BGK Waves for the Vlasov-Poisson System” (with R. Allen) European Physical Journal D 68 (2014) 363-370 (.pdf)

  3. 15. “A One-dimensional Kinetic Model of Plasma Dynamics with a Transport Field" (with C. Nguyen) Evolution Equations and Control Theory 3 (2014) 681-698 (.pdf)

  1. 14. “Spatially homogeneous solutions of the Vlasov-Nordstrom-Fokker-Planck System” (with J. Felix and S. Calogero) Journal of Differential Equations 257 (2014) 3700-3729 (.pdf)

  1. 13. “Nonlinear instability of solutions in parabolic and hyperbolic diffusion” (with P. Radu) Evolution Equations and Control Theory 2 (2013) 403-422 (.pdf)

  3. 12. “A Particle Method for a Collisionless Plasma with Infinite Charge” Mathematics and Computers in Simulation 82 (2012) 1278-1286 (.pdf)

  5. 11. “Computational Methods for a One-dimensional Plasma Model with a Transport Field” (advisor/sponsor for D. Brewer) SIAM Undergraduate Research Online 4 (2011) 81-104 (.pdf)

  7. 10. “Large Time Behavior of the Relativistic Vlasov-Maxwell System in Low Space Dimension” (with J. Schaeffer and R. Glassey) Differential & Integral Equations 23 (2010) 61-77 (.pdf)

  9. 9. “Time Decay for Solutions to the One-dimensional Equations of Plasma Dynamics” (with J. Schaeffer and R. Glassey) Quarterly of Applied Mathematics 68 (2010) 135-141 (.pdf)

  11. 8. "Time Decay for Solutions to One-dimensional Equations of Plasma Dynamics" (with J. Schaeffer and R. Glassey), In Proceedings of the Brown University Conference on Nonlinear Wave Equations in Honor of Walter A. Strauss on his 70th Birthday, edited by Walter Freiberger,  American Mathematical Society (2010).

  1. 7. “Long-time Behavior of Monocharged and Neutral Plasmas in ‘One and one-half ’ Dimensions” (with J. Schaeffer and R. Glassey) Kinetic and Related Models 2 (2009) 465-488 (.pdf)

  3. 6. “Decay in Time for a One-Dimensional, Two Component Plasma” (with J. Schaeffer and R. Glassey), Math. Meth. Appl. Sci. 31 (2008) 2115–2132 (.pdf)

  5. 5. “Explicit solutions for the One-Dimensional Vlasov-Poisson System with Infinite Mass.” Math. Meth. Appl. Sci. 31 (2008), 375-389 (.pdf)

  7. 4. “Global Existence and Increased Spatial Decay for the Radial Vlasov-Poisson System with Steady Spatial Asymptotics.” Trans. Theory Stat. Phys. 36 (2007), 531–562 (.pdf)

  9. 3. “Recent Trends in the Kinetic Theory of Plasma Physics”, Proceedings of the International Conference on Trends and Challenges in Applied Mathematics (2007).

  11. 2. “Local Existence for the One-Dimensional Vlasov-Poisson System with Infinite Mass.” Math. Meth. Appl. Sci. 30 (2007) 529-548 (.pdf)

  13. 1. “Global Existence for the Three-Dimensional Vlasov-Poisson System with Steady Spatial Asymptotics.” Communications in PDE 31 (2006) 349-370 (.pdf)


  14. II. Multiscale Analysis, Computational Biophysics, and in-host HIV dynamics

  16. 20. “Population Dynamics of Spatially-heterogeneous Epidemic Models” (with K. Martinez and A. Porter) in revision.

  18. 19. “The Zika crisis in Colombia, Suriname, and El Salvador: Approximate Bayesian Computation for stochastic models” (with D. Shutt, C. Manore, S. Del Valle, and A. Porter) in revision.

  20. 18. "Molecular Fluids and Liquid Crystals: A Coarse-Grained Mean Field Theory" (with P. Ortoleva) in revision.

  1. 17. "A Stochastic SEIR Model for the 2014 Ebola Epidemic within Western Africa" (with A. Porter and D. Shutt) in revision.

  1. 16. "Bistable Dynamics and Hopf Bifurcation in a Model of the Acute Stage of HIV Infection" (with N. Neri and D. Shutt) submitted.

  3. 15. "A Modified SEIR Model for the Spread of Ebola in Western Africa and Metrics for Resource Allocation" (with C. Sandridge, E. Jones, K. Kalmbach,  P. Constantine, and P. Diaz) submitted.

  1. 14. "Mathematical Analysis and Dynamic Active Subspaces for a long term model of HIV" (with T. Loudon) Mathematical Biosciences and Engineering (2017) 14(3): 709-733 (.pdf)

  1. 13. "Mathematical Analysis of an in-host Model of Viral Dynamics with Spatial Heterogeneity" (with C. Parkinson) Discrete and Continuous Dynamical Systems B (2016) 21(4): 1237-1257 (.pdf)

  1. 12. “The effects of latent infection on the dynamics of HIV” Differential Equations and Dynamical Systems (2016) 24(3): 281-303 (.pdf)

  1. 11. "An in-host model of HIV incorporating Latent Infection and Viral Mutation" (with D. Shutt), Dynamical Systems, Differential Equations, and Applications, AIMS Proceedings (2015) 913-922 (.pdf)

  1. 10. "A Review of Two Multiscale Methods for the Simulation of Macromolecular Assemblies: Multiscale Perturbation and Multiscale Factorization" (with P. Ortoleva) Computation 3 (2015) 29-57 (.pdf)

  2. 9. “Analysis and Simulation of the three-component model of HIV dynamics” (with M. Raghupathi; advisors/sponsors for P. Roemer and E. Jones) SIAM Undergraduate Research Online 7 (2014) 89-106 (.pdf)

  4. 8.“Hierarchical Multiscale Modeling of Macromolecules and their Assemblies” (with P. Ortoleva and A. Singharoy) Soft Matter 9 (2013) 4319-4335 (.pdf)

  6. 7. “Nanosystem Self-Assembly Pathways Discovered via All-Atom Multiscale Analysis” (with P. Ortoleva) J. Phys. Chem. B. 116 (2012) 8355-8362 (.pdf)

  8. 6. “Multiscaling for Systems with a Broad Continuum of Characteristic of Lengths and Times: Structural Transitions in Nanocomposites” (with P. Ortoleva) J. Math. Phys. 51 (2010) 063303 (.pdf)

  10. 5. “Liquid-crystal transitions: A first-principles multiscale approach” (with Z. Shreif and P. Ortoleva) Phys. Rev. E. 80 (2009) 031703 (.pdf)

  12. 4. “Self-Assembly of Nanocomponents into Composite Structures: Derivation and Simulation of Langevin Equations” (with Z. Shreif, Y. Miao, and P. Ortoleva) J. Chem. Phys. 130 (2009) 194115 (.pdf)
  13. *Featured in Virtual Journal of Nanoscale Science and Technology, Volume 19, Issue 22 (2009)

  15. 3. “Multiscale Theory of Boson Droplets: Implications for Collective and Single-Particle Excitations” (with Z. Shreif, Y. Chen, and P. Ortoleva) Phys. Rev. A. 79 (2009), 013628 (.pdf) 

  17. 2. “Multiscaling for Classical Nanosystems: Derivation of Smoluchowski and Fokker-Planck Equations” (with Z. Shreif and P. Ortoleva) Physica A  387 (2008), 4053–4069 (.pdf)

  19. 1. “Stochastic Dynamics of Bionanosystems: Multiscale Analysis and Specialized Ensembles” (with Y. Miao, J. Ortoleva, Z. Shreif, and P. Ortoleva) J. Chem. Phys. 128 (2008) 234908 (.pdf)

*Featured in Virtual Journal of Biological Physics, Volume 16, Issue 1 (2008) and
Virtual Journal of Nanoscale Science and Technology, Volume 18, Issue 1 (2008)



III. Other Papers and Articles


2. "Preparing Graduates for Careers in the Mathematical Sciences: NSF

    Programs Offer Unique Real-World Experience" (with S. Minkoff, W. Menasco,

    F. Santosa, and R. Laugesen) SIAM News 49 (9), December 2016 (.pdf).


1. “Principal Components Analysis: Resources for an essential application of

     Linear Algebra" (with R. Swanson) Problems, Resources, and Issues in

     Mathematics Undergraduate Studies (2015), 25 (5) 400-420 (.pdf)



Mathscinet Author’s Page


ArXiv Author’s Page