# Research

### Current research and publications

A fair amount of my recent activities have been related to global sensitivity analysis. My former student Joey Hart has played a key role in this. Here is a recent talk that will give you the flavor of what we are doing and some related pubs

*Robustness of the Sobol’ indices to marginal distribution uncertainty*, J.L. Hart, P.A. Gremaud. Accepted in SIAM/ASA J. U.Q..*Robustness of the Sobol’ indices to distributional uncertainty,*J.L. Hart, P.A. Gremaud. Accepted in Int. J. U.Q..*Global Sensitivity Analysis of High Dimensional Neuroscience Models: An Example of Neurovascular Coupling*, J.L. Hart, P.A. Gremaud, T. David. Bull. Math. Biol., 81 (2019), 1805–1828. draft version.*Variance-based sensitivity analysis for time-dependent processes*, A. Alexanderian, P.A. Gremaud, R.C. Smith. Submitted.*An approximation theoretic perspective of Sobol’ indices with dependent variables,*J.L. Hart, P.A. Gremaud. Int. J. UQ, 8 (2018), 483–493.*Efficient computation of Sobol’ indices for stochastic models*, J.L. Hart, A. Alexanderian, P.A. Gremaud. SIAM J. Sc. Comp., 39 (2017), A1514–A1530.

In collaboration with Daniel Tartakovsky, we have taken a good look at the “PDF method” and made some measurable progress

*Methods of distributions for uncertainty quantification*, D.M. Tartakovsky, P.A. Gremaud. Handbook for Uncertainty Quantification, R. Ghanem, D. Higdon and H. Owadhi (Eds.), Springer (2016).*Nonlocal PDF methods for Langevin equations with colored noise*, T. Maltba, P.A. Gremaud, D.M. Tartakovsky. J. Comput. Phys., 367 (2018), 87–101.

Against my best judgment, I am again involved with the modeling of, and numerical methods for, granular flows

*Constitutive relations for compressible granular flow in the inertial regime*, D.G. Schaeffer, T. Barker, P.A. Gremaud, M. Shearer, D. Tsuji, J.M.N.T. Gray. J. Fluid Mech. 874 (2019), 926–951..