PhD Candidate in Computational & Applied Mathematics
Southern Methodist University, Dallas, Texas
My research combines PDE modeling, numerical simulation, and scientific machine learning to study biological transport in hydrogel and mucus systems, nanofluid heat transfer, electrochemical physics, and biomedical applications including drug delivery and cancer treatment modeling.
Research Assistant — Working with Dr. Vladimir Ajaev on mathematical and computational models of hydrogel swelling, diffusion, and fluid-structure interactions.
Qualifying exams passed — Successfully completed PhD written qualifying examinations and oral defense.
Paper published — "Mathematical Modeling of Arsenic Removal Using Filtration" in Alexandria Engineering Journal (IF 6.8).
Started PhD — Joined the Department of Mathematics at Southern Methodist University as a Teaching Assistant.
Paper published — Hybrid nanofluid flow study in Journal of Petroleum Science and Engineering.
I am a PhD candidate in Computational and Applied Mathematics at Southern Methodist University, working under the supervision of Dr. Vladimir Ajaev. I passed my written qualifying examinations and oral defense in 2025.
My research focuses on PDE-based mathematical modeling for biological transport, hydrogel systems, and biomedical applications. I develop diffusion-driven models of evaporation and absorption in hydrogels, with applications to drug delivery, respiratory mucus transport, and nanoparticle retention. I am currently extending my 1D analytical models to higher-dimensional frameworks to capture realistic geometries and transport mechanisms.
Beyond my core work, I pursue projects in nanofluid heat transfer, electrochemical transport in lithium batteries, mathematical oncology, and scientific machine learning — building neural-network surrogates and physics-informed solvers for PDE systems.
Southern Methodist University, Dallas,
Advisor: Dr. Vladimir Ajaev. Passed qualifying exams (written and oral) in 2025. Research on hydrogel swelling, diffusion, and biological transport models.
University of Dhaka
Thesis: Mathematical Modelling of Filtration — Removal of Arsenic from Drinking Water. Supervisor: Dr. Tania Sharmin Khaleque. UGC-funded research project.
University of Dhaka
Project: Hybrid copper–aluminum oxide nanofluid flow with thermal radiation. Supervisor: Dr. Mohammad Ferdows.
Hydration-controlled virus and drug transport through mucus and hydrogel media. Diffusion–reaction PDEs modeling dehydration, rehydration, binding/unbinding, and epithelial uptake. Moving-boundary models for swelling hydrogel drug release.
Nanoparticle transport and drug release in stenosed arteries. Carrier-based antiviral delivery with spatial optimal control. Hybrid nanofluid magnetic hyperthermia for heat-assisted therapy.
MHD boundary-layer simulations with thermal radiation, Joule heating, and entropy generation. Poisson–Nernst–Planck transport and dendrite suppression in lithium metal batteries.
ANN/DNN/CNN surrogate modeling for PDE systems. Physics-informed neural networks. Uncertainty quantification and ML-based treatment-response prediction in mathematical oncology.
Alexandria Engineering Journal, 132, 264–278, 2025 · Impact Factor 6.8
A two-dimensional axisymmetric model combining porous-media flow, advection–diffusion transport, and Langmuir adsorption kinetics for arsenic removal from drinking water.
Journal of Petroleum Science and Engineering, 215, 110649, 2022
Cu–Al₂O₃/H₂O hybrid nanofluid flow over an exponentially stretching or shrinking sheet with thermal radiation and non-uniform heat source/sink effects.
Developed mathematical and computational models of hydrogel swelling, diffusion, and responsiveness. Modeled fluid-structure interactions in hydrogels with applications to drug delivery, soft robotics, and environmental sensing. Supervisor: Dr. Vladimir Ajaev.
Department of Mathematics. Teaching, grading, and supporting undergraduate courses in calculus and applied mathematics.
Part-time lecturer in the Department of Mathematics, Dhaka, Bangladesh.
Research on mathematical modeling of arsenic removal using filtration, funded by the University Grants Commission. Supervisor: Dr. Tania Sharmin Khaleque.
Two-phase diffusion-driven model of evaporation and absorption in hydrogels. 1D analytical results obtained; extending to higher-dimensional geometries.
GitHub ↗Hydration-controlled virus transport through respiratory mucus. Modeling diffusion, binding, epithelial uptake, and barrier efficiency.
GitHub ↗2D biomedical model of drug-loaded nanoparticle transport through blood flow in stenosed arteries with magnetic field and tissue uptake.
GitHub ↗Poisson–Nernst–Planck ion transport modeling for PVDF/PEI separator design to suppress dendrite growth in lithium metal batteries.
GitHub ↗Mathematical modeling with uncertainty quantification and ANN/ML prediction for monitoring breast cancer treatment response.
GitHub ↗Spatial PDE model with optimal control for antiviral carrier drug release, optimizing dose–efficacy trade-offs and viral load reduction.
GitHub ↗Stanford University
DeepLearning.AI
DeepLearning.AI
DeepLearning.AI
DeepLearning.AI
University of Michigan
I am interested in collaborations related to computational modeling, biological transport, hydrogel systems, drug delivery, electrochemical physics, and scientific machine learning.