I nanomechanics or amorphous materials. As a physics

I would like to pursue a doctoral program in mechanical engineering and materials science.
I am particularly interested in conducting research in nanomechanics or amorphous materials. As
a physics and mathematics double major, I have been able to undertake challenging coursework
and research projects in both fields. Through this rigorous academic training, I am ready to attack
any complex problem in mechanical engineering which involves advanced physics and
mathematics.
Design is an integral part of engineering, and I have been able to develop design skills
through extracurricular activities at Rhodes. During my first semester, I had the opportunity to
attend a weekly CAD design workshop from which I was able to learn AutoCAD. In my second
semester, I and two other students founded the Rhodes Engineering Club. After spending two
semesters on learning how to design and manufacture a radio-controlled airplane, we took part in
the 2016/17 and 2017/18 AIAA DBF (American Institute of Aeronautics and Astronautics
Design/Build/Fly) competitions. Through these competitions, I was able to develop many design
related skills, such as MATLAB, Autodesk Inventor and report writing. I was able to use MATLAB
to analyze the lift and drag of airfoils, and run sensitivity analysis for optimizing the mission scores.
I was also responsible for writing the conceptual design, preliminary design, manufacturing and
testing sections of the final report for the 2016/17 competition. Besides working on these
competitions, as the vice president of Rhodes Engineering Club, I am also dedicated to providing
educational resources for those who are interested in engineering. Every Sunday afternoon we
offer a 3-hour workshop to teach students how to use Autodesk Inventor, the 3D-printer, laser
cutter and operating power tools. My experience with the Rhodes Engineering Club has
significantly solidified my design skills and I am prepared to conduct research on more complex
designs during my graduate study.
A good design should have strong theoretical and computational support. By undertaking
challenging coursework in physics and mathematics I have been able to develop strong physical
intuition, and mathematical analysis and computational skills. Additionally, I have had the
opportunity to conduct research in both fields, which has allowed me to apply these skills in
producing new publishable results.  I have been doing research with Dr. Shubho Banerjee in the Physics Department since
Spring 2017. Our research project focuses on the analysis of the electrostatic interaction between
two charged spheres. To prepare for this research project I familiarized myself with Maxwell’s
classical results of the distribution of charges on conducting spheres as well as the method of image
charges. Additionally, since number theory plays an important role in our research I also studied
the properties of the q-digamma function, Lambert series and their asymptotic expansions. We
first started the research project for a system of two equal-sized spheres. I was responsible for
reformulating the classical solutions of the capacitance coefficients in terms of the Lambert series.
Moreover, I derived a new expression of the electrostatic force as a linear combination of two parts;
one that is always attractive and the other that is always repulsive. Much of this work was done
with the aid of Mathematica, which I became proficient with through the course of this research.
The manuscript containing our results is currently under preparation for publication. Our second
project focuses on the system of two unequal-sized spheres. I have been able to obtain new results
by generalizing the methodology from the first project. This research experience has allowed me to utilize my knowledge of both physics and mathematics and employ it in a physical/applied
context.
My research experience in pure mathematics has significantly improved my skills of
analytical thinking. I am currently working with Dr. Christopher Seaton on a project in differential
geometry, which is connected to many branches of mathematics, including abstract algebra and
exterior algebra of multi-covectors. The first part of my research included two semesters of
studying manifolds and symplectic geometry. Afterwards, I focused on adding one more piece to
a theorem developed by Dr. Seaton and his colleagues. The theorem states that if the group action
of a torus on a complex space has certain properties, called “2-principal” and “stable”, then there
is no symplectomorphism between the symplectic quotient and a linear symplectic orbifold. My
goal is to develop a necessary and sufficient condition for inducing a 2-principle and stable action
only in terms of the weight matrix associated to the group action. By using linear algebra and proof
techniques I have made some progress on my objective and obtained several results. I was able to
present them at the 37th Annual West Kentucky University Mathematics Symposium. Through
this research project, I acquired the skill of independent study by learning advanced mathematical
concepts that are beyond the coursework offered at the undergraduate level. Additionally, I gained
the skill of logical thinking through the construction of proofs for deriving theorems.
Yale University is world renowned for its innovative, qualitative and highly regarded
research programs. The exceptional reputation of Yale reflects its abundant academic resources
and the tremendous support for its students. Moreover, the unique research atmosphere which
encourages for close interactions between students with faculty further confirms my belief that
Yale is the place where I can achieve my research goals. There are many research opportunities at
Yale that I find appealing. I am particularly interested in the nanomechanics research, which aligns
well with Dr. Udo Schwarz’s research projects. I am excited by Dr. Schwarz’s research projects
on nanotribology and its effects on surface or interface properties. As friction is a critical
component of our lives, it is necessary to study friction in depth in order to utilize it in the most
efficient way. Motivated by the feet of gecko, I am very interested in the study of adhesion at the
nanoscale and the development of synthetic adhesive materials. I would be excited to learn related
theories and experimental techniques about nanomechanics and conduct future research with Dr.
Schwarz. Additionally, I find the work of Dr. Jan Schroers on amorphous materials equally
fascinating. I am very interested in the physical properties of bulk metallic glass and its promising
applications in replacing certain metals or plastics in the future. However, there are still barriers
preventing the wide application of amorphous materials, such as high cost and difficulty of
processing. I am enthusiastic about studying advanced theories about amorphous materials and
tackling these challenges with Dr. Schroers. I am confident that my academic and practical
background will allow me to fit in well and contribute positively to any research program at Yale
University. The opportunity to do research at Yale University would be a significant stepping stone
towards accomplishing my long-term career goals.