"All models are wrong, but some are useful."- George E.P. Box​
Numerical Methods for Partial Differential Equations (PDE) arising in fiber coating
Collaborating with
Dr. Hangjie Ji (NC States, Math)
Dr. Andrea L. Bertozzi (UCLA, Math)
Dr. Abolfazel Sadeghpour (UCLA, Mechanical Engineering)
Dr. Y. Sungtaek Ju (UCLA, Mechanical Engineering)
Kim, B., Ji, H., Bertozzi., A., Sadeghpour A., Ju, S. “A positivity-preserving numerical method for a thin liquid film on a vertical cylindrical fiber (Accepted 2023, To appear).” In Journal of Computational Physics. [Preprint] [Software]
Kim, B. “Theory of Positivity-Preserving Numerical Methods for Thin Viscous
Liquids Flowing Down Vertical Fibers” PhD thesis, University of California, Los
Angeles, 2023. [Link]
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When a thin liquid film flows down on a vertical fiber, one can observe the complex and captivating interfacial dynamics of an unsteady flow. Such dynamics are applicable in various fluid experiments due to their high surface area-to-volume ratio. In this project, we study a mathematical model and present a computationally efficient numerical method that can maintain physical properties of the liquid films.
Barcode Image Analysis
Collaborating with
Dr. Yifei Lou (UT Dallas, Math)
Kim, B., Lou, Y. (2021). Two-Step Blind Deconvolution of UPC-A Barcode Images. In: Demir, I., Lou, Y., Wang, X., Welker, K. (eds) Advances in Data Science. Association for Women in Mathematics Series, vol 26. Springer, Cham. [link]
Barcodes are widely used in supermarkets and tracking systems. One noticeable difficulty in barcode recognition is caused by blurring artifacts. We propose a blind deconvolution method to recover a clean barcode from the blurred data.
Previous projects
Compressed Sensing (CS) method arising in Magnetic Resonance Imaging (MRI)
Advised by
Dr. Deanna Needell (UCLA, Math)
Collaborated with
Sam Birns, Stephanie Ku, Kevin Stangl.
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Birns, S., Kim, B., Ku, S., and Stangl, K. (2016). A Practical Study of Longitudinal Reference-Based Compressed Sensing for MRI. Rose-Hulman Undergraduate Mathematics Journal: Vol. 17: Iss. 2, Article
Mathematical modeling of thermoregulation
REU program hosted by Mathematical Bioscience Institutes (MBI)
Advised by
Dr. Yaroslav Molkov
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Image from
Molkov, Y. I., Zaretskaia, M. V., & Zaretsky, D. V. (2014). Meth math: modeling temperature responses to methamphetamine. American Journal of Physiology-Regulatory, Integrative and Comparative Physiology, 306(8), R552-R566.