Current and Former students actively involved in research:

27. Uthman Rasaq, M.Sc. in Applied Mathematics (January 2023-date).

26. Sk Md Ibrahim Khalilullah (RCAP grant), M.Sc. in Applied Mathematics (January 2023-date).

25. Md Mulfiqur Haider (RCAP grant), M.Sc. in Applied Mathematics (2022-date).

24. Jacob Walterman (KY NSF EPSCoR, FUSE, and RCAP grants). Jacob will be working on implementing algorithms for an energy harvester model. He will be working on the mathematical and computational legs of the project. (May 2022-July 2023).

23. Rafi Emran, M.Sc. in Applied Mathematics: Rafi is currently working on understanding discretized piezoelectric beam equations  (2021-2023).

Past Students:

22. Ahmet Kaan Aydin (KY NSF EPSCoR grant), M.Sc. in Applied Mathematics: Ahmet worked on understanding the applications of continuous and discrete Ingham's theorems to the Mead-Marcus-type beams (2020-2022).

• Ahmet received the highest research award "John D. Minton award" at WKU. The competition is at the university level.

21. Matthew Poynter (KY NSF EPSCoR grant): Matthew worked on the Wolfram Demonstration Project for certain smart systems  (August 2021-2023).

Matthew has presented his findings at the KAS meeting (virtual) (2021) - Matthew is the Joint winner of the student competition.  Matthew also presented research at the WKU Math Symposium (2022), and KY-MAA meeting (2022). Matthew's poster is the best poster in his session at the Student Research Conference (2022). Matthew has co-presented a poster at the Super Collider Conference for the Kentucky NSF EPSCoR supported research participants in April 2022.

20. Samuel Leveridge (KY NSF EPSCoR grant). Samuel worked on implementing algorithms for an energy harvester model. (September 2022-December 2022).

19. Mason Woolridge (Gatton Academy), Independent Research. Mason helped develop an algorithm for the reduced models of a class of wave equations with different damping mechanisms (Summer 2022).

18. Alex Driehaus (KY NSF EPSCoR grant), Senior Thesis Project, Math 498. Alex worked on estimates for the boundary-feedback stabilized difference-differential equations by the multipliers technique (Spring 2022). 

1. • Alex gave a talk at the Math Symposium in February 2022, and another one  at the Student Research Conference in March 2022.

17. Trey Crouch (KY NSF EPSCoR grant), Independent Research, Math 275. Trey worked on implementing algorithms for the wave and beam systems in the Wolfram's Demonstration Project (Spring 2022).

• Trey gave a talk at the Math Symposium in February 2022, and two  other talks at the Student Research Conference and the KY-MAA symposium in March 2022.

16. Logan Stewart, Independent Research Project on the Wolfram Demonstration Project for certain smart systems  (August 2021-date).

1. • Logan has presented his findings at the KAS meeting (virtual) in November 2021. Logan is the joint winner of the student competition. Logan also presented research at the WKU Math Symposium (2022), Student Research Conference (2022), and KY-MAA meeting (2022). Logan has also presented a poster at the Gatton Fair. Logan has co-presented a poster at the Super Collider Conference for the Kentucky NSF EPSCoR supported research participants in April 2022.

15. Emma Moore, CE/T - Hon 403/404, Math Undergraduate (FUSE Spring 2019 winner, KY NSF EPSCoR and RCAP-funded): Emma is from KY, and she is currently working on obtaining estimates for difference-differential equations, obtained by the Finite Differences and Finite Elements, by the multipliers. She is also working towards implementing certain control designs for single piezoelectric beam structures (Fall'18-date). Emma passed the CE/T-Hon 403/404 with distinction. Emma participated in the SIAM Southeastern Sectional Meeting in Auburn, AL in September 2021.

14. Wilson Horner, M.Sc. in Applied Mathematics: "Analysis of Boundary Observability of Strongly Coupled One-dimensional Wave Equations With Mixed Boundary Conditions", graduated in spring 2021. Currently working in as a Data Scientist in Louisville.

13.  Joey Lyvers, Gatton Academy Student: Developing demonstration projects for vibrations on a string by a dynamic controller (Fall 2020).

12. Katelynn Huddy, Gatton Academy Student: Developing demonstration projects for vibrations on a string by a dynamic controller (Summer, Fall 2020).

11. Donald Price, Math undergraduate (KY NSF EPSCoR-funded): Donald worked on developing efficient algorithms and reliable Mathematica codes for Wolfram Demonstration Project for certain systems of difference-differential equations (Winter'19-May 2020).

10. Ryan St. Clair, Math undergraduate (RCAP-funded), Senior Thesis, Title: Lack of observability/controllability of well-known partial differential equations discretized by Finite Differences. (Spring 2020).

9. Emrick Swan, Math Undergraduate, Senior Thesis, Title: Lack of observability of Finite Element approximations of a Drichlet-Neumann wave equation controlled/observed through its boundary. (Spring 2020).

8. Sydney New, Math Undergraduate, Senior Thesis. Sydney worked on detailing the mathematical analysis of approximations of the differential equation-models for piezoelectric beams (Fall 2019). 

7. William Poteet, Math Undergraduate  (RCAP project): He worked on developing efficient algorithms and reliable Mathematica codes for Wolfram Demonstration Project for certain systems of difference-differential equations (Fall 2019). 

6. Camille Wartman, Math Undergraduate ((KY NSF EPSCoR project) - Camille worked on developing algorithms and reliable Mathematica codes for certain systems of difference-differential equations of beam equations (Fall 2019).

5. Kamala Dadashova, Independent Research, Analysis and control of discretized system of wave equation (Fall 2018).

4. Camille Wartman, Honors Augmentation, The Collapse of the Tacoma Narrows Suspension Bridge, Spring 2018.

3. Alexandria Scoville, The Gatton Academy of Mathematics and Science in Kentucky, Independent Research, Numerics for a damped nonlinear piezoelectric beam, HON 303, Fall 2017.

2. Clayton Phelps, Honors Augmentation, “Earthquake shaking of a Two-story Building,” Spring 2017.

1. Lauren Cooper, Honors Augmentation, "A Forensic study: Murder at the Mayfair Diner", Fall 2017.

Job Opportunity for a recently-funded NSF ESPoR grant in Control Theory - Applied Mathematics

I have several projects available in the following topics (priority will be given to students from Women in Science Club and WKU SIAM Student Chapter):

1. Active Current project: I am currently working on the controllability of nonlinear smart laminates. So far, I have obtained the PDE models through a consistent variational approach.These models are shown to be well-posed in corresponding energy spaces. Related projects are the following

• Using Galerkin-type (Finite Element) and Finite Difference-type approximations to look for stable approximations 

  • for the control-free model.

  • for the damped model due to the middle viscoelastic layer.

  • for the closed-loop model with stabilizing feedback controllers.

  • for the open-loop model with the energy harvesting applications

For the problems above, good knowledge of programming in Mathematica, Linear Algebra, and ODE (or PDE) are necessary. 

• Using continuous/discrete multiplier techniques to show that the continuous/discrete models are locally controllable and globally stabilizable. For this part of the project, you should have taken a fundamental "Functional Analysis" course and Calculus II.

Other projects:

1. Control and Stabilization for smart-layered structures

2. Continuum mechanical modeling of smart structures. e.g. biomorphs, magneto-elastic materials, thermo-piezoelectric materials, different geometries in 2D and 3D.

3. Controllability/Stabilizability/Observer Design for Linear and Nonlinear Systems Theory.

4. Optimal location actuators and sensors for layered structures.

Some of the projects above are at the graduate level and some are at the undergraduate level. Before asking for a research project, make sure that you know at least one programming language at the intermediate level, i.e. Mathematica or Matlab,  and check the following next:

• Undergraduate students:

  • • Have GPA > 3.25/4. 

    • Getting done with Calculus series with at least "B" is essential. For coding projects, taking Calculus I and being proficient in Mathematica is enough.

    • If you have already taken Linear Algebra and Differential Equations, it is a plus. 

• Graduate students: 

  • • Have GPA > 3.0/4. 

    • Getting done with Intermediate Analysis, Numerical Analysis, Ordinary and Partial Differential Equations (at any level) is not necessary but a plus. 

    • Knowledge of basic Functional Analysis and Applied Mathematics is also a big plus.

• Other Requirements:

  • Available for 5-15 hours per week

  • Highly motivated

  • Excellent communication skills

  • Eager to learn and apply new skills

  • Responsible and responsive to project needs