Publications

Joshua Lee Padgett's articles on arXiv.

Below are a list of accepted (or submitted) publications. Note that authors are listed in alphabetical order and graduate students are designated with an *.

arXiv:2110.08297
M. Hutzenthaler, A. Jentzen, B. Kuckuck, and J. L. Padgett, Strong Lp-error analysis of nonlinear Monte Carlo approximations for high-dimensional semilinear partial differential equations, 2021 (submitted).
arXiv:2109.05345
J. L. Padgett and E. Servin*, A positivity- and monotonicity-preserving nonlinear operator splitting approach for approximating solutions to quenching-combustion semilinear partial differential equations , 2021 (submitted).
arXiv:2102.09344
R. Banka*, T. W. Hyde, E. G. Kostadinova, C. D. Liaw, L. S. Matthews, and J. L. Padgett, Active turbulence in a dusty plasma monolayer, Physics of Plasmas, Volume 28, Issue 7, 2021. Official link
arXiv:2101.03629
T. F. Jones, E. G. Kostadinova, J. L. Padgett, and Q. Sheng, A series representation of the discrete fractional Laplace operator of arbitrary order, Journal of Mathematical Analysis and Applications, Volume 504, Issue 1, 2021. Official link
arXiv:2012.11092
T. F. Jones, J. L. Padgett, and Q. Sheng, Intrinsic properties of strongly continuous fractional semigroups in normed vector spaces, 2020 (to appear in Operator Theory: Advances and Applications).
arXiv:2008.02740
S. Gautam*, Y. Geldiyev*, A. Ibraguimov, Y. Mechref, J. L. Padgett, and W. Peng, Object classification in analytical chemistry via data-driven discovery of partial differential equations, Computational and Mathematical Methods, Volume 3, Issue 4, 2021. Official link
arXiv:2006.01068
T. W. Hyde, E. G. Kostadinova, C. D. Liaw, L. S. Matthews, and J. L. Padgett, Anomalous diffusion in semi-crystalline polymer structures, Physical Review Research, Volume 2, Issue 4, 2020. Official link
arXiv:1907.10824
K. Busse*, T. W. Hyde, E. G. Kostadinova, C. D. Liaw, L. S. Matthews, and J. L. Padgett, Anomalous diffusion in one-dimensional disordered systems: A discrete fractional Laplacian method, Journal of Physics A: Mathematical and Theoretical, Volume 53, Issue 13, 135205, 2020. Official link
arXiv:1902.03503
J. L. Padgett, Analysis of an approximation to a fractional extension problem, BIT Numerical Mathematics, Volume 60, pp. 715-739, 2019. Official link
arXiv:1901.06371
J. L. Padgett and Q. Sheng, Convergence of an operator splitting scheme for abstract stochastic evolution equations, Advances in Mathematical Methods and High Performance Computing, Springer, pp. 163-179, 2019. Official link
arXiv:1901.06049
M. A. Beauregard and J. L. Padgett, A variable nonlinear splitting algorithm for reaction-diffusion systems with self- and cross-diffusion, Numerical Methods for Partial Differential Equations, Volume 35, Issue 2, pp. 597-614, 2019. Official link
arXiv:1901.06605
J. L. Padgett, The quenching of solutions to time-space fractional Kawarada problems, Computers and Mathematics with Applications, Volume 76, Issue 7, pp. 1583-1592, 2018. Official link
arXiv:1901.10039
J. L. Padgett and Q. Sheng, Numerical solution of degenerate stochastic Kawarada equations via a semi-discretized approach, Applied Mathematics and Computation, Volume 325, pp. 210-226, 2018. Official link
arXiv:1706.02800
K. Busse, N. Ellis, T. W. Hyde, E. G. Kostadinova, C. D. Liaw, L. S. Matthews, and J. L. Padgett, Delocalization in infinite disordered 2D lattices of different geometry, Physical Review B, Volume 96, Issue 23, 235408, 2017. Official link
arXiv:1901.06365
J. L. Padgett and Q. Sheng, Nonuniform Crank-Nicolson scheme for solving the stochastic Kawarada equation via arbitrary grids, Numerical Methods for Partial Differential Equations, Volume 33, pp. 1305-1328, 2017. Official link
arXiv:1510.07694
M. A. Beauregard, J. L. Padgett, and R. D. Parshad, A nonlinear splitting algorithm for systems of partial differential equations with self-diffusion, Journal of Computational and Applied Mathematics, Volume 321, pp. 8-25, 2017. Official link
(not on arXiv)
J. L. Padgett and Q. Sheng, On the stability of a variable step exponential splitting method for solving multidimensional quenching-combustion equations, Modern Mathematical Methods and High Performance Computing in Science and Technology, Editor-in-Chief: V. K. Singh, Springer Verlag, Singapore, pp. 155-167, 2016. Official link
arXiv:1901.06356
J. L. Padgett and Q. Sheng, On the positivity, monotonicity, and stability of a semi-adaptive LOD method for solving three-dimensional degenerate Kawarada equations, Journal of Mathematical Analysis and Applications, Volume 439, Issue 2, pp. 465-480, 2016. Official link

Below is a link to my dissertation:

Personal PDF file
Solving Degenerate Stochastic Kawarada Partial Differential Equations via Adaptive Splitting Methods. Official link

Drafts

Below are a list of manuscripts and projects currently in preparation (or actively being pursued):

(not on arXiv, yet)
A. Jentzen, B. Kuckuck, and J. L. Padgett, Overcoming the curse of dimensionality in the approximation of high-dimensional nonlinear partial differential equations via deep neural networks in the Lp-sense, (in final stages).
(not on arXiv, yet)
A. Jentzen, B. Kuckuck, and J. L. Padgett, Expressivity of deep neural networks for space-time solutions of high-dimensional nonlinear PDEs, (in preparation).
(not on arXiv, yet)
J. Miller, J. L. Padgett, R. Ramirez*, On the construction of stochastic operator splitting methods of arbitrarily high order via Hopf algebraic techniques, (in preparation).
(not on arXiv, yet)
J. L. Padgett, Weak convergence of the abstract Lie-Trotter stochastic operator splitting, (in preparation).