Posts by Collection

academicprojects

Avocado Size Preference in US Cities: Principal Component Analysis (PCA) of Volumetric Sales of Avocados in 2020

The project focused on in-depth exploratory data analysis to uncover trends and preferences in avocado sizes across major US cities. By applying the PCA to volumetric sales data of avocados in three different sizes (small, medium, and large) in 2020 categorized by PLUs 4046, 4225, 4770, respectively, a distinct preference for either small or medium-sized avocados in most cities was revealed, with outliers showing higher sales in all three sizes. The project was implemented using Python, and the dataset was sourced from www.kaggle.com. I opted to analyze this dataset because of my personal fondness for avocados, especially as I include avocado toast in my daily breakfast routine. My preference for using the entire avocado for the toast and my reluctance to store cut avocados for the next day lead me to favor small-sized avocados. However, I occasionally encounter challenges in finding small-sized avocados sold under PLU 4046 at my usual grocery store. This curiosity prompted me to delve into the trends of preferences in avocado sizes in US cities. Read more

Gaussian Mixture Models (GMMs) Based Density Estimation of US Cities Preferring One Size of Avocados

After reducing the dimensionality of the data through PCA, the density distribution of the cities preferring small, medium, or all sizes of avocados, as represented by the score plot, was estimated using GMMs. The expectation maximization (EM) algorithm, an iterative scheme, was used to determine the model parameters. Consequently, the data depicted in the score plot was effectively clustered into three distinct clusters. These clusters represent cities with high sales of small-sized avocados, cities with high-medium sized avocado sales, and cities with outlier sales in large-sized avocados. The project was coded in Python. Read more

Dense Neural Network Based Categorization of Iris Data

The primary goal of this project was to thoroughly understand the core principles of neural networks, involving the implementation of four fundamental steps: initialization of the weights and biases, feedforward and backpropagation algorithms, and optimization using stochastic gradient descent. A small-scale project to classify Iris flowers into three classes based on specific characteristics was undertaken. A dense neural network for this task was developed and implemented in Python, utilizing a dataset from https://archive.ics.uci.edu/ml/datasets/Iris. The secondary objective was to gain hands-on experience with neural network design and optimization using the Keras library. Stochastic gradient descent (SGD) algorithm with a default learning rate of 0.01 was employed for optimizing the weights and biases. Read more

Classification of Iris Flower Based on Sepal Length and Petal Length Using Support Vector Machines (SVMs)

The goal was to comprehend the mathematical formulation of Support Vector Machines (SVM) as an optimization problem and acquire practical experience by implementing SVM using pre-built functions from the scikit-learn library. To achieve this objective, a project was undertaken to classify the Iris flower into one of three classes—Iris setosa, Iris versicolor, and Iris virginica—based on the sepal length and petal length of the flower. For this purpose, three SVMs were established, each employing distinct kernels and inequality constraints, effectively addressing the specified task. The design of the SVM and the optimization of the SVM were executed using the SVC function from scikit-learn, a machine learning library, and the results from the three configurations were compared and evaluated for accuracy. Read more

portfolio

professional

@ Bharat Heavy Electrical Ltd. (BHEL)

Engineering Tech Intern, 2012, Hyderabad, TG, India

Projects:

Technical Comparison of PG6101FA (Fr-6FA), PG9171E (Fr-9E) and PG9351FA (Fr-9FA) Gas Turbines


Timeline: May ‘12 - Jul ‘12
Project Details: This project focused on the examination of axial flow industrial gas turbines, involving a detailed exploration of compressor technology. Read more

@ National Mineral Development Corporation (NMDC)

Engineering Tech Intern, 2013, Hyderabad, TG, India

Projects:

Flow ability study of blended coal & functional design of mass flow silos with mild steel as the liner material


Timeline: May ‘13 - Jul ‘13
Project Details: The goal of this project was to determine the design parameters necessary for ensuring a reliable coal flow from a 500 Ton mass flow coal silo. Read more

@ Indus Refrigeration Private Ltd.

Engineering Tech Intern, 2013 - 2014, Chennai, TN, India

Projects:

Design and fabrication of 3 fluid vapor absorption refrigeration system (VARS) for chilling of milk


Timeline: Sep ‘13 - May ‘14
Project Details: The main objective of this project was to offer a cost-effective solution for the immediate chilling of milk at dairy farms, aiming to enhance the shelf life of the milk. Read more

@ Cyient Ltd.

Mechanical Design Engineer, 2014 - 2017, Hyderabad, TG, India

Projects:

Design and structural analysis of 3D anti-vortex tube (AVT)


Client: Pratt & Whitney
Timeline: Jun ‘16 - Jan ‘17
Project Details: The main objective of this project was to optimize the design of AVT assembly which did not meet the life criteria. Read more

publications

research

Parabolic variational inequality

By utilizing a symmetric dual-wind DG (DWDG) spatial discretization and a backward Euler temporal discretization, we proposed a fully discrete scheme designed to solve a parabolic variational inequality. We also determined the rate of convergence of the error in space and time in suitable norms.

Numerical solution for numerical experiment 1: Zero Obstable Problem
Numerical Solution
Contact sets for numerical experiment 1: Zero Obstable Problem
Contact set $\Omega_0(t)$
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Steady convection-diffusion equation in the convection dominated regime

We proposed and analyzed a numerically stable and convergent scheme for the convection-diffusion (CD) equation in the convection-dominated regime and derived a local order of convergence of $O(ℎ^{1.5})$ whenever the exact solution is of $𝐻^2(\Omega)$ regularity. The following figures illustrate a comparison between the exact and numerical solution from a particular numerical experiment.

exact solution for numerical experiment 2
Exact Solution
numerical solution for numerical experiment 2
Numerical Solution
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Elliptic optimal control problem with control constraints

We proposed a numerical scheme to reduce an elliptic optimal control problem with control constraints to a finite-dimensional optimization problem with equality and inequality-type constraints and established the order of convergence of the error as we refine the triangulation of the polygonal domain $\Omega \subset \mathbb{R}^2$. The figures below present a comparison between the exact solutions and numerical solutions from a specific numerical experiment.

Picture of exact control
Exact control
Picture of numerical control in P0 spanned space
u_h with $\mathbb{P}_0$ functions
Picture of numerical control in P1 spanned space
u_h with $\mathbb{P}_1$ functions

Picture of exact state
Exact state
Picture of numerical state in P1 spanned space
y_h with $\mathbb{P}_1$ functions
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talks

Dual-Wind Discontinuous Galerkin Method for a Parabolic Obstacle Problem and an Optimal Control Problem

Updated:

@SEACDE2022

Presenting at SEARCDE2022
Picture of Dustin Nichols, Keta Henderson, Dr. Elliott Hoffield and I at SEARCDE2022
(left to right) Dustin Nichols, Myself, Dr. Elliott Hollifield, and Keta Henderson at SEARCDE2022

Dinner at SEARCDE2022
Dinner at an Indian restaurant - Anjappar after SEARCDE2022
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Dual-wind discontinuous Galerkin method and its application to an optimal control problem and a parabolic variational inequality

Updated:

@AIMS 2023

Presenting at AIMS 2023
Presenting at AIMS2023

Group picture of all AMS supported students at AIMS 2023
Group picture of all AMS supported students at AIMS2023

Applied math group from UNCG at AIMS 2023
Cultivating knowledge, creating memories at AIMS2023 – where ideas collide and friendships thrive.
(left to right) Dr. Aaron Rapp Dr. Anantha Acharya Dustin Nichols, Dr. Shalmali Bandyopadhyay, Me, and Dr. Elliott Hollifield

Casual chat at lunch
A casual chat at lunch
(left to right) Dr. Anantha Acharya, Keta Henderson, and I

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Novel discontinuous Galerkin methods for optimization problems with inequality constraints

Updated:

@JMM 2024

Presenting at JMM2024
Picture of me presenting at JMM 2024
Picture of me presenting at JMM2024


Having a casual chat after my talk
(right to left) Keta Henderson, Dr. Thomas Weighill and I having a small chit chat after my talk

Interacting with prospective graduate students at graduate school fair
Engaging with prospective graduate students at graduate school fair
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Novel Discontinuous Galerkin Methods for a Parabolic Obstacle Problem and a Convection Dominated Problem

Updated:

@International Conference on Differential Equations 2024

Picture of me presenting at ICDE 2024
Picture of me presenting at ICDE 2024

with colleagues and mentors
Learning from the best while enjoying every moment with amazing company!
Front row (left to right) Dr. Keta Henderson Prof. Maya Chhetri Dr. Shalmali Bandyopadhyay, Prof. Ratnasingham Shivaji Dr. Byungjae Son Xiaohuan Xue (Max)
Back row (left to right) Me, Dr. Dustin Nichols, Dr. Tom Lewis, Prof. Jerome Goddard II.

celebrating Shivaji's 70th birthday
Celebrating Prof. Ratnasingham Shivaji's 70th birthday.
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teaching

@ Florida Poly

Assistant Professor, Department of Applied Mathematics, Lakeland, FL

Instructor of record
CourseSemester
Analytic Geometry and Calculus 1 (MAC 2311)Fall '25
Differential Equations (MAP 2302)Fall '25
Analytic Geometry and Calculus 1 (MAC 2311)Spring '25
Applied Partial Differential Equations (MAP 4341)Spring '25
Precalculus (MAC 1147)Fall '24
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@ UNCG

Graduate Teaching Associate, Department of Mathematics & Statistics, Greensboro, NC

Instructor of record
CourseSemester
Calculus AFall '23
Algebra with Business ApplicationsSpring '23
Foundations of CalculusFall '22
Algebra with Business ApplicationsSpring '22
Algebra with Business ApplicationsFall '21
Contemporary Topics in MathematicsSpring '21
Interacting with students at office hours
Interacting with students at office hours

Interacting with students during office hours

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