Research experience

Ph.D. (Applied Mathematics) University of Delaware, USA

My research interests lie broadly in:

* Mathematical Modeling and Simulation for Applied Problems.
* Numerical Computing for Calculus and Differential Equations.
* Mathematical and Scientific Computing Software for Aiding Problem Solving.

Website about me: ORCID: https://orcid.org/0000-0001-7531-2891

Research projects

I am interested in using tools that students learn in introductory calculus and differential equation courses to create mathematical models for problems coming from real-world applications. Although problems coming from nature or engineering designs are indeed very complex, a simplified version of the models with many naive assumptions may give us initial insights and steps for improvement. With the help of mathematical software (most of them are free and open-source), one can visualize and simulate the models in seconds to mimic the data obtained from experiments.

Below are mathematical modeling and numerical computing projects that I am currently involved in collaboration with faculty from the mathematics, physics, and engineering departments.

* Simulating tear-film and eye drop on the human eye.
* Modeling control system of unmanned underwater vehicles.
* Automatic inspection and quantification of corrosion on lubricated bearings.
* Computational strategies for fixing design inaccuracies in 3D printing.
* Accurate numerical methods for function approximations.

Potential research projects for students

In addition to the topics above, I am also interested in the following topic:

Modeling electric guitar pedal effect with differential equations

As an amateur guitarist, I am constantly having fun experimenting with creating different sounds with my electric/acoustic guitar. One way to distort/alter the guitar strings’ natural sound (frequencies) is by using pedals or software (e.g., PedalBoard in GarageBand). The price of hardware pedals can range from inexpensive to hundreds of dollars. One of the simplified models to find natural frequencies of a guitar string clamped at both ends is related to solving a differential equation of the form

u” + A(x) u = 0, u(0) = 0, u(L) = 0

By modeling A(x), we can perturb the natural frequencies to create various sounds (gritty, springy, clean, etc.) as digital pedals or even ones’ own unique sound depending on the type of music they want to play. Those unique digital pedals can be added as template libraries in music creation software.