Student Research Spotlight

Lidia Mrad Profile Picture

Lidia Mrad

Department:

Mathematics

Advisor:

Dr. Daniel Phillips

Research Title:

Gradient flow of chevron structures in liquid crystal cells


Research Description:

My research project focuses on analyzing the dynamic behavior of a defect in liquid crystals referred to as chevron structure formation. Liquid crystal phases are understood to be intermediate states between a liquid and a crystalline, possessing both flow-like properties of liquids and molecular packing of solids. In a surface-stabilized thin cell, the uniform layers of a smectic liquid crystal tend to tilt symmetrically into a chevron instead of being ideally in a bookshelf structure, perpendicular to the cell substrates. The mathematical model describing this system is an energy functional and studying its dynamics is basically analyzing a gradient flow through an energy minimization process. The techniques used in this analysis are a combination of theoretical techniques of partial differential equations, such as elliptic estimates, and computational techniques, such as time discretization using Rothe method.

About Me:

Mathematics has been an integral part of my academic and professional journey. In my home country Lebanon, I had chances to explore its theoretical depths in my Masters studies and to experience its educational breadth through teaching high school students. Coming to Purdue for my PhD, I wanted to investigate its relation to other sciences and technology. That's when I got introduced to research in liquid crystals which encompasses various areas of science. It was an exciting opportunity to get to learn mathematical and computational techniques that try to solve problems in this interdisciplinary area. The CS&E program was another opportunity that expanded my knowledge of numerical methods in mathematics and increased my exposure to other scientific disciplines. Besides opportunities for academic growth, Purdue has provided me with a rich environment to improve my leadership skills and to make friends from around the globe!


Awards:

  • Certificate of Excellence in Research Award, Spring Reception 2015, Purdue Office of Interdisciplinary Graduate Programs
  • Excellence in Teaching Award, 2012 - 2013, Department of Mathematics, Purdue University
  • CETA Excellence in Teaching Award, 2012 - 2013, Committee for the Education of Teaching Assistants, Purdue University

Leadership:

  • Cofounder and President of Purdue Chapter of the Association for Women in Mathematics (AWM), 2011 - 2013
  • Initiator of a mentoring program (AWMentor) and a mentor for incoming students, 2012 - present
  • Initiator and organizer of a professional development workshop (Basic Skills) for math graduate students, 2012 - present
  • Seminar organizer:Student PDE seminar for graduate students and Junior Analysis Seminar - a joint seminar for students and post-docs, 2013 - present

Personal Page:

Ernest C. Young Hall, Room 170 | 155  S. Grant Street, West Lafayette, IN 47907-2114 | 765-494-2600

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