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I am currently a Postdoctoral Research Associate in the Department of Mathematics and Statistics at Texas Tech University. I received my Ph.D. in Mathematics from Baylor University in August 2017 under the advisement of Qin "Tim" Sheng. Before that I received my B.S. in Mathematics from Gardner-Webb University, where I also was a member of the Track and Field team (I competed in the javelin and hammer throw). My undergraduate studies also included cellular biology, which led to several semesters worth of research into various aspects of cancer metabolism.

Here is a copy of my most recent Curriculum Vitae (updated August 2019).

Joshua Lee Padgett's Google Scholar profile.

Joshua Lee Padgett's ResearchGate profile.

NSF Grant: Onset of Turbulence in Dusty Plasma Liquids

A link with the information regarding the JMM Special Session I am co-organizing, may be found here.


Research Interests


Topics of interest: Applied mathematics, numerical analysis, computational mathematics, geometric and Lie group integration methods, operator splitting methods, quenching-combustion differential equations, predator-prey models nonlinear differential equations, fractional differential equations, stochastic differential equation

Detailed research interests.


Publications


Joshua Lee Padgett's articles on arXiv.

Below are a list of accepted (or submitted) publications.

arXiv:1907.10824
J. L. Padgett, E. G. Kostadinova, C. D. Liaw, K. Busse, L. S. Matthews, and T. W. Hyde, Anomalous diffusion in one-dimensional disordered systems: A discrete fractional Laplacian method (Part I), (submitted).
arXiv:1902.03503
J. L. Padgett, Analysis of an approximation to a fractional extension problem, (accepted).
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, 2019, pp. 163-179. doi:10.1007/978-3-030-02487-1_9
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, Vol. 35, Issue 2, 2019, pp. 597-614. doi:10.1002/num.22315
arXiv:1901.06605
J. L. Padgett, The quenching of solutions to time-space fractional Kawarada problems, Computers and Mathematics with Applications, Vol. 76, Issue 7, 2018, pp. 1583-1592. doi:10.1016/j.camwa.2018.07.009
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, Vol. 325, 2018, pp. 210-226. doi:10.1016/j.amc.2017.12.034
arXiv:1706.02800
E. G. Kostadinova, K. Busse, N. Ellis, J. L. Padgett, C. D. Liaw, L. S. Matthews, T. W. Hyde, Delocalization in infinite disordered 2D lattices of different geometry, Physical Review B, Vol. 96, 235408, 2017. doi:10.1103/PhysRevB.96.235408
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, Vol. 33, 2017, pp. 1305-1328. doi:10.1002/num.22144
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, Vol. 321, 2017, pp. 8-25. doi:10.1016/j.cam.2017.02.019
(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, 2016, pp. 155-167. doi:10.1007/978-981-10-1454-3_13
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 Vol. 439, 2016, pp. 465-480. doi:10.1016/j.jmaa.2016.02.071

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)
J. L. Padgett, Weak convergence of the abstract Lie-Trotter stochastic operator splitting, (draft available upon request).
(not on arXiv, yet)
J. L. Padgett, E. G. Kostadinova, C. D. Liaw, K. Busse, L. S. Matthews, and T. W. Hyde, Anomalous diffusion in one-dimensional disordered systems: A discrete fractional Laplacian method (Part II), (draft available upon request).
(not on arXiv, yet)
J. L. Padgett, Symmetry-based adaptive numerical methods for reaction-diffusion systems with self-diffusion, (in preparation).
(not on arXiv, yet)
J. L. Padgett and J. Miller, The Hopf algebraic structure of splitting methods for Lévy-driven stochastic differential equations, (in preparation).
(not on arXiv, yet)
Y. J. Nam* and J. L. Padgett, Numerical simulations for an improved stochastic Alzheimer's model, (in preparation).
(not on arXiv, yet)
E. Servin* and J. L. Padgett, Approximating Kawarada equations on a disk via nonlinear splitting methods, (in preparation).
(not on arXiv, yet)
Y. Geldiyev*, J. L. Padgett, and A. Ibraguimov, GUI data assimilation methods for absorption-diffusion models, (in progress).
(not on arXiv, yet)
J. L. Padgett, K. Ebrahimi-Fard, and H. Z. Munthe-Kaas, Algebraic structures of singular integro-differential operators, (early stages).

What my preparation "stages" mean:

"draft available upon request"
This typically means that the mathematics for the manuscript is complete and is being proofread. There still may be a need to generate numerical simulations.
"in preparation"
This typically means that the ideas for the article have been well-articulated, but are still in the process of being typeset. Articles in this stage can easily be discussed and personal time-constraints are the main hurdle in finalizing the article.
"in progress"
This typically means that the ideas are actively being developed. The work is actively being pursued, but results are still being finalized. Articles in this stage can be summarized, as the primary goals are clear, but there may be finer details that are still being "ironed out."
"early stages"
This is typically reserved for projects that are in the early stages of being developed. The project has some initial results, but there is still much work to be completed. Such classifications will be used sparingly, and are only used when a project is "significant" in nature and consuming a nontrivial amount of research efforts. Projects in this stage can be discussed, but specific details will typically be withheld until the project reaches a later "stage."

Authors with a "*" designation are my graduate or undergraduate students (more information on these students may be found below).


Presentations


Here is a link to a list of my invited and contributed talks.

Many of my presentations are contributions to the wonderful seminars maintained by the department, here at Texas Tech University. Those interested may find more information about these seminars in the links below:

Analysis Seminar

Applied Math Seminar

Biomathematics Seminar

Topology and Geometry Seminar



Students


Graduate Students:
Yu Jung Nam (co-advised with Madgalena Toda)
Yusup Geldiyev (co-advised with Akif Ibraguimov)

Undergraduate Students:
Eduardo Servin

Interested students may email me to request a meeting to discuss potential research topics (of which I have many).

Teaching


Request an appointment with me (this links directly to my Outlook calendar so that you may see my schedule).

More information regarding my courses may be found below or by logging into Blackboard (if you are a student).

Courses taught at Texas Tech University:

Fall 2019:
MATH 4330 (Mathematical Computing)
Fall 2019:
MATH 5099 (Numerical Methods for Singular and Nonlinear Differential Equations)
Fall 2019:
MATH 5368 (Abstract Algebra Applied I)
Summer 2019:
MATH 2360 (Linear Algebra)
Summer 2019:
MATH 4330 (Mathematical Computing)
Spring 2019:
MATH 5369 (Abstract Algebra Applied II)
Fall 2018:
MATH 5368 (Abstract Algebra Applied I)
Summer 2018:
MATH 4330 (Mathematical Computing)
Summer 2018:
MATH 3360 (Foundations of Algebra)
Spring 2018:
MATH 3430 (Computational Techniques for Science and Mathematics)
Fall 2017:
MATH 2450 (Calculus III), 2 sections

Courses taught at Baylor University:

Spring 2017:
MTH 3326 (Partial Differential Equations)
Spring 2017:
CSI 2350 (Discrete Structures)
Fall 2016:
MTH 2321 (Calculus III)
Spring 2016:
MTH 1322 (Calculus II)
Fall 2015:
MTH 1321 (Calculus I)
Spring 2015:
MTH 1321 (Calculus I)
Fall 2014:
MTH 1309 (Calculus for Business Students)
Spring 2014:
MTH 1320 (Precalculus)
Fall 2013:
MTH 1320 (Precalculus)

You can find some useful material for getting started with LaTeX here (intended for students with zero LaTeX knowledge). If you have any material that you feel would be helpful for students starting out, please share it with me and I will add it to the linked page (and give you your appropriate credit, of course).


Resources


MathSciNet • arXiv • MathOverflow • Kerodon • Library Genesis • Sci-Hub 1 • Sci-Hub 2 • Sci-Hub 3 • Google Scholar