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<!doctype html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=5.0, minimum-scale=1.0">
<meta property="og:title" content="Erick White - Student, Researcher, Engineer">
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<title>Erick White - Writing</title>
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content="Erick White - Writing: Some of my best academic and industry work.">
</head>
<body>
<menu id="page-menu"></menu>
<div class="main-background">
<main>
<header>
<div class="intro">
<h1 class="page-title">Writing</h1>
</div>
</header>
<div class="writing-grid">
<div class="container writing-content" id="asc-2025-content">
<img src="assets/images/writing/asc-2025-content.png"
alt="An illustration of the bananoid conjunction visualization.">
</div>
<div class="container dark text right" id="asc-2025">
<h3><em>Showcase and Comparison of Three Methods for Visualizing Near-Earth Satellite Conjunction
Events</em></h3>
<p>
During my second internship with <a class="link" href="https://www.nasa.gov/conjunction-assessment"
target="_blank"
rel="noopener noreferrer">CARA</a>, I focused heavily on
research, and specifically on developing methods for visualizing satellite conjunctions.
A conjunction is a close approach event between two satellites; these are of interest because an
orbital collision could be devastating to the Low-Earth Orbit environment, so knowing where
satellites are and how they are moving is crucial to keeping space safe and usable.
I built on and developed three methods for showcasing these events, each of which is suited to
different conjunction geometries; I analyzed these cases and paralleled the usage of these
visualization algorithms with the algorithms employed by CARA in predicted a probability of
collision.
From this research, I both programmed the visualizations themselves and wrote a paper (on which I
was first author); the paper was accepted to the <a class="link"
href="https://aiaa.org/events/2025-aas-aiaa-astrodynamics-specialist-conference/"
target="_blank" rel="noopener noreferrer">2025
AAS/AIAA Astrodynamics Specialist Conference</a>, which I was unfortunately unable to attend
in-person.
Download my paper <a class="link" href="assets/docs/writing/asc-2025-paper.pdf"
target="_blank" rel="noopener noreferrer">here</a>, and download my poster <a
class="link" href="assets/docs/writing/asc-2025-poster.pdf"
target="_blank" rel="noopener noreferrer">here</a>!
</p>
</div>
<div class="container dark text left" id="dla">
<h3><em>Applications of Computer Vision to Space and Plasma Physics</em></h3>
<p>
As part of the <a class="link"
href="https://www.colorado.edu/engineering/discovery-learning-apprenticeship-dla-program"
target="_blank" rel="noopener noreferrer">Discovery Learning Apprenticeship</a>
program, I was chosen to present my research at an end-of-year symposium in which a panel of
graduate mentors selected top projects from that year's participants.
My research focused on the detection of plasma waves in Van Allen Probe data; I had to first devise
a consistent way of visualizing these waves (a challenge due to their low frequencies, as I was
working with electromagnetic ion cyclotron waves), then annotate the spectrograms I created and
develop a computer vision model to reliably detect these waves autonomously.
I achieved an mAP50 of 0.738 with the latest version of the model and began researching the
distribution of these waves in the Earth's magnetosphere; the goal of this was to better understand
their occurrence locations and frequencies and compare those to theoretical models.
Download my poster <a class="link" href="assets/docs/writing/dla-symposium-poster.pdf"
target="_blank" rel="noopener noreferrer">here</a>!
</p>
</div>
<div class="container writing-content" id="dla-content">
<img src="assets/images/writing/dla-content.png"
alt="A spectrogram of a plasma wave showing hydrogen and helium ion gyrofrequencies.">
</div>
<div class="container writing-content" id="appm-4610-final-project-content">
<img src="assets/images/writing/appm-4610-final-project-content.png"
alt="A sensitivity analysis between the RK4 and Verlet integration methods.">
</div>
<div class="container dark text right" id="appm-4610-final-project">
<h3><em>Analyzing and Solving the N-Body Problem</em></h3>
<p>
Following my numerical analysis class, I decided to also take numerical differential equations -
and, similar to numerical analysis, it, too, had a final project that involved building on a topic
we covered in class.
I teamed up with <a class="link" href="https://edward.wawrzynek.com/" target="_blank"
rel="noopener noreferrer">Edward Wawrzynek</a> again, as well as
<a class="link" href="https://sites.google.com/colorado.edu/brycepfuetze/home" target="_blank"
rel="noopener noreferrer">Bryce Pfuetze</a>, and we decided to tackle the <em>N</em>-body
problem, a common problem across engineering and physics fields.
Specifically, since this problem has no analytical solution, we decided to focus on understanding
and tackling the inherent stiffness in the problem; we also studied symplectic integrators and their
useful energy-conservation properties.
We compared our own implementations of the Euler, RK2, RK4, and Stormer-Verlet methods and studied
energy error over time; we also compared integrated ephemerides to those given by the JPL Horizons
database.
This work led directly into my <a class="link" href="work-and-experience.html#csml-2025"
target="_blank" rel="noopener norefferer">work at the Celestial
and Spaceflight Mechanics Laboratory</a>.
Download our paper <a class="link" href="assets/docs/writing/appm-4610-final-project.pdf"
target="_blank" rel="noopener noreferrer">here</a>, or check out our code
repository
<a class="link" href="https://github.com/brycepfuetze/APPM-4610-stiff-ODEs" target="_blank"
rel="noopener noreferrer">here</a>!
</p>
</div>
<div class="container dark text left" id="mcm-2025">
<h3>COMAP MCM 2025</h3>
<p>
Once again, <a class="link" href="http://www.linkedin.com/in/elizabethscutting" target="_blank"
rel="noopener noreferrer">Elizabeth Cutting</a>,
<a class="link" href="https://www.linkedin.com/in/madison-p-jones" target="_blank"
rel="noopener noreferrer">Madison Jones</a>, and I decided to compete in a mathematical modeling
competition - this time, in the
<a class="link" href="https://www.contest.comap.com/undergraduate/contests/index.html"
target="_blank" rel="noopener noreferrer">Mathematical Contest in Modeling</a>, a more math-heavy
variant of the
<a class="link" href="writing.html#icm-2023" target="_blank" rel="noopener noreferrer">Interdisciplinary
Contest in Modeling</a> we partook in in 2023.
This year, we chose a problem focused on modeling wear on stairs, and using such wear patterns to
inform archaeologists to the age of the stairs, their usage patterns, and other quantities that
could be derived only from non-destructive measurements of the steps.
We chose to approach this by constructing an empirical distribution of footfalls on the stairs; from
this distribution (we used a Gaussian mixtured model), we backed out values such as the means and
covariances of the Gaussians which we then used to back out properties related to the age and usage
of the stairs.
We again won an Honorable Mention for our work.
Download our paper <a class="link" href="assets/docs/writing/comap-2025.pdf" target="_blank"
rel="noopener noreferrer">here</a>, or view a repository with the paper and
code <a class="link" href="https://github.com/ErickWhiteDev/COMAP_2025" target="_blank"
rel="noopener noreferrer">here</a>!
</p>
</div>
<div class="container writing-content" id="mcm-2025-content">
<img src="assets/images/writing/mcm-2025.png"
alt="A Monte Carlo simulation of footfalls on a stair step.">
</div>
<div class="container writing-content" id="appm-4600-final-project-content">
<img src="assets/images/writing/appm-4600-final-project-content.png"
alt="A spectrogram of an EMIC wave in Earth's magnetosphere.">
</div>
<div class="container dark text right" id="appm-4600-final-project">
<h3><em>Derivations and Applications of the Discrete, Fast, and Short-Time Fourier Transforms</em></h3>
<p>
My numerical analysis class included a final project that built on a topic we covered and presented
results we had not previously discussed.
I teamed up with two of my friends from the <a class="link" href="https://cuengineeringhonors.com/"
target="_blank" rel="noopener noreferrer">Engineering
Honors Program</a> and we decided to study further the Fourier transform - an important tool in
signal processing, electronics, and many other fields.
As part of <a class="link" href="work-and-experience.html#lair-2024" target="_blank"
rel="noopener noreferrer">my work with the LAIR lab</a>, I had been exposed to the
short-time Fourier transform, a tool used for generating spectrograms of time-varying signals; we
utilized this knowledge, as well as
<a class="link" href="https://edward.wawrzynek.com/" target="_blank" rel="noopener noreferrer">Edward
Wawrzynek's</a> experience working with frequency domain analysis, to explore the use cases of
the discrete, fast, and short-time Fourier transforms.
We used several real-life datasets in this study as well, studying both patterns in weather around
Boulder, Colorado and attempting to visualize some of the same EMIC waves I was studying in my
research!
Download our paper <a class="link" href="assets/docs/writing/appm-4600-final-project.pdf"
target="_blank" rel="noopener noreferrer">here</a>, or check out our code
repository
<a class="link" href="https://github.com/ErickWhiteDev/APPM-4600-Final-Project" target="_blank"
rel="noopener noreferrer">here</a>!
</p>
</div>
<div class="container dark text left" id="asen-3036-semester-project">
<h3><em>Design Proposal for Crewed Interplanetary Mission</em></h3>
<p>
As part of my Introduction to Human Spaceflight Class under former NASA astronaut Jim Voss, I wrote
a report detailing a living module and Environmental Control and Life Support Systems (ECLSS) for a
hypothetical crewed mission to Mars.
This report involved analyzing existing ECLSS technologies, deciding which were best fit for the
mission, conducting research on them, and explaining how they would be implemented in this mission.
Also included in the report is a concept of operations (CONOPS) and interior and exterior views of
the living module.
Download my paper <a class="link" href="assets/docs/writing/asen-3036-semester-project.pdf"
target="_blank" rel="noopener noreferrer">here</a>!
</p>
</div>
<div class="container writing-content" id="asen-3036-semester-project-content">
<img src="assets/images/writing/asen-3036-semester-project.png"
alt="A concept of operations for a hypothetical crewed mission to Mars">
</div>
<div class="container writing-content" id="appm-3310-final-project-content">
<img src="assets/images/writing/appm-3310-final-project.png"
alt="A plot of a satellite's orbit around the Earth">
</div>
<div class="container dark text right" id="appm-3310-final-project">
<h3><em>Applications of Covariance Matrices and Jacobians in Orbital Mechanics</em></h3>
<p>
My partner <a class="link" href="https://sites.google.com/view/audrarissmeyer/home" target="_blank"
rel="noopener noreferrer">Audra Rissmeyer</a> and I wrote this paper as our final
report for our applied matrix methods class.
The paper explored the concepts of observational covariance matrices, transformations between
celestial
coordinate systems, and transformations of covariance matrices (and why these transformations would
be done).
We used MATLAB functions provided by NASA CARA to run the transformations discussed in Alfano and
Vallado’s
<em>Updated Analytical Partials for Covariance Transformations and Optimization</em> and illustrated
covariance
through our own MATLAB visualizations. We also illustrated the difference between Cartesian and
equinoctial
covariance distributions and briefly explained the significance that these distributions have.
Download our paper <a class="link" href="assets/docs/writing/appm-3310-final-project.pdf"
target="_blank" rel="noopener noreferrer">here</a>, or view a repository with
the paper and code <a class="link"
href="https://github.com/ErickWhiteDev/Matrix-Methods-For-Orbital-Mechanics"
target="_blank" rel="noopener noreferrer">here</a>!
</p>
</div>
<article class="container dark text left" id="icm-2023">
<h3>COMAP ICM 2023</h3>
<p>
As a member of a team of three, I participated in the <a class="link"
href="https://www.contest.comap.com/undergraduate/contests/index.html"
target="_blank" rel="noopener noreferrer">Interdisciplinary
Contest in Modeling</a>, a yearly competition in which thousands of teams around the world pick one
problem out of three (or a separate set of three for the closely-related Mathematical Contest in
Modeling), research the problem, develop a model to represent the situation at hand, and write a
paper with their results, all over the span of only 100 hours.
This year, my team tackled a problem regarding the United Nations' Sustainable Development Goals
(SDGs) and how to best prioritize them to create the most beneficial change over the next decade.
The paper won an Honorable Mention, meaning it was in the top 30% of papers submitted for that
particular problem; we also presented this paper at the
<a class="link"
href="https://www.colorado.edu/amath/organizations/siam-undergraduate-chapter/2023-siam-front-range-student-conference"
target="_blank" rel="noopener noreferrer">2023 SIAM Front Range Student Conference</a>, and it
was accepted into the
<a class="link" href="https://journals.colorado.edu/index.php/honorsjournal/issue/view/205"
target="_blank" rel="noopener noreferrer">2024 issue of the University of Colorado Honors
Journal</a>.
Download our paper <a class="link" href="assets/docs/writing/comap-2023.pdf" target="_blank"
rel="noopener noreferrer">here</a>, or view a repository with the paper and
code <a class="link" href="https://github.com/ErickWhiteDev/COMAP_2023" target="_blank"
rel="noopener noreferrer">here</a>!
</p>
</article>
<div class="container writing-content" id="icm-2023-content">
<img src="assets/images/writing/icm-2023.jpg" alt="My ICM 2023 team">
</div>
</div>
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