Physical Sciences and Mathematics Commons^™

Using The Taylor Center To Teach Odes, Alexander Gofen

CODEE Journal

This article introduces a powerful ODE solver called the Taylor Center for PCs (http://taylorcenter.org/Gofen/) as a tool for teaching and performing numeric experiments with ODEs. The Taylor Center is an All-in-One GUI-style application for integrating ODEs by applying the modern Taylor Method (Automatic Differentiation). The Taylor Center also offers dynamic graphics (including 3D stereo vision). After a brief review of the features of the Taylor Center, we consider instructive examples of ODEs in various applications and also several particular examples illustrating intricacies of numeric integration. The article therefore continues the thesis of Borrelli and Coleman (CODEE Journal, http://www.codee.org/ref/CJ09-0157) that awareness …

Spectral Clustering: An Empirical Study Of Approximation Algorithms And Its Application To The Attrition Problem, B. Cung, T Jin, J. Ramirez, A. Thompson, C. Boutsidis, Deanna Needell

CMC Faculty Publications and Research

Clustering is the problem of separating a set of objects into groups (called clusters) so that objects within the same cluster are more similar to each other than to those in different clusters. Spectral clustering is a now well-known method for clustering which utilizes the spectrum of the data similarity matrix to perform this separation. Since the method relies on solving an eigenvector problem, it is computationally expensive for large datasets. To overcome this constraint, approximation methods have been developed which aim to reduce running time while maintaining accurate classification. In this article, we summarize and experimentally evaluate several approximation …

Examining The Impact Of Pau Jacaré (Piptadenia Gonoacantha) Growth On Soil Fertility In The Brazilian Atlantic Rainforest, Aleksandra Ponomareva

Environmental Analysis Program Mellon Student Summer Research Reports

The Atlantic Rainforest of Brazil is an area of astounding diversity in both flora and fauna, taking its place among the top five “biodiversity hotspots” in the world. However, in the past 40 or 50 years the area has been increasingly threatened by the presence of humans – approximately 93% of the Rainforest has disappeared as a result of exploitation (Turner 2004). Unsustainable farming practices, as well as logging, cattle ranching and mining activities have caused soil infertility, water depletion, erosion and destruction of ecosystems. This project examines the effects of the Pau Jacaré, Piptadenia gonoacantha, tree on soil health …

The Awards Project: Promoting Good Practices In Award Selection, Betty Mayfield, Francis Su

All HMC Faculty Publications and Research

Every year the MAA honors many members of our community with a wide variety of prizes, awards, and certificates for excellence in teaching, writing, scholarship, and service (see maa.org/awards). The winners exemplify our ideals as an association; consequently, they are often viewed as role models and leaders. So it is important to ask: Do these awards, as a whole, reflect the outstanding contributions of the breadth of association membership?

Uniqueness Of Nonnegative Solutions For Semipositone Problems On Exterior Domains, Alfonso Castro, Lakshmi Sankar, Ratnasingham Shivaji

All HMC Faculty Publications and Research

We consider the problem

−Δu = λK(|x|)f(u), x∈Ω

u=0 if |x|=r₀

u→0 as |x|→∞,

where λ is a positive parameter, Δu = div(∇u)is the Laplacian of u, Ω = {x ∈ Rⁿ; n > 2,|x| > r₀}, K ∈ C¹([r₀,∞),(0,∞)) is such that lim r→∞ K(r) = 0 and f ∈ C¹([0,∞),R) is a concave function which is sublinear at ∞ and f(0) < 0. We establish the uniqueness of nonnegative radial solutions when λ is large.

3d Imaging And Mechanical Modeling Of Helical Buckling In Medicago Truncatula Plant Roots, Jesse L. Silverberg, Roslyn D. Noar, Michael S. Packer, Maria J. Harrison, Christopher L. Henley, Itai Cohen, Sharon J. Gerbode

All HMC Faculty Publications and Research

We study the primary root growth of wild-type Medicago truncatula plants in heterogeneous environments using 3D time-lapse imaging. The growth medium is a transparent hydrogel consisting of a stiff lower layer and a compliant upper layer. We find that the roots deform into a helical shape just above the gel layer interface before penetrating into the lower layer. This geometry is interpreted as a combination of growth-induced mechanical buckling modulated by the growth medium and a simultaneous twisting near the root tip. We study the helical morphology as the modulus of the upper gel layer is varied and demonstrate that …

A Tale Of Two Workshops: Two Workshops, Three Papers, New Ideas, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Trace Element Soil Contamination At Urban Community Gardens In Washington, Dc, Adam J. Long

Environmental Analysis Program Mellon Student Summer Research Reports

In recent years, urban gardening has become a popular form of environmental, food, and social justice. Urban community gardens such as those in Washington, DC can reduce the environmental footprint of food production, provide access to healthy produce in “food deserts,” and provide other social, educational, and even financial benefits. However, the rising popularity of urban gardening has put many people in close contact with urban soils, which are likely to contain various contaminants due to concentrated human activity over extended periods of time. This study investigates heavy metal soil contaminants found in community gardens located in Washington, DC. 45 …

Locust Dynamics: Behavioral Phase Change And Swarming, Chad M. Topaz, Maria R. D'Orsogna, Leah Edelstein-Keshet, Andrew J. Bernoff

All HMC Faculty Publications and Research

Locusts exhibit two interconvertible behavioral phases, solitarious and gregarious. While solitarious individuals are repelled from other locusts, gregarious insects are attracted to conspecifics and can form large aggregations such as marching hopper bands. Numerous biological experiments at the individual level have shown how crowding biases conversion towards the gregarious form. To understand the formation of marching locust hopper bands, we study phase change at the collective level, and in a quantitative framework. Specifically, we construct a partial integrodifferential equation model incorporating the interplay between phase change and spatial movement at the individual level in order to predict the dynamics of …

Black Hole Thermalization, D0 Brane Dynamics, And Emergent Spacetime, Paul L. Riggins '12, Vatche Sahakian

All HMC Faculty Publications and Research

When matter falls past the horizon of a large black hole, the expectation from string theory is that the configuration thermalizes and the information in the probe is rather quickly scrambled away. The traditional view of a classical unique spacetime near a black hole horizon conflicts with this picture. The question then arises as to what spacetime does the probe actually see as it crosses a horizon, and how does the background geometry imprint its signature onto the thermal properties of the probe. In this work, we explore these questions through an extensive series of numerical simulations of D0 branes. …

How The Cucumber Tendril Coils And Overwinds, Sharon J. Gerbode, Joshua R. Puzey, Andrew G. Mccormick, L. Mahadevan

All HMC Faculty Publications and Research

The helical coiling of plant tendrils has fascinated scientists for centuries, yet the underlying mechanism remains elusive. Moreover, despite Darwin’s widely accepted interpretation of coiled tendrils as soft springs, their mechanical behavior remains unknown. Our experiments on cucumber tendrils demonstrate that tendril coiling occurs via asymmetric contraction of an internal fiber ribbon of specialized cells. Under tension, both extracted fiber ribbons and old tendrils exhibit twistless overwinding rather than unwinding, with an initially soft response followed by strong strain-stiffening at large extensions. We explain this behavior using physical models of prestrained rubber strips, geometric arguments, and mathematical models of elastic …

On The Occasion Of Your Graduation, Robert Dawson

Journal of Humanistic Mathematics

A letter from an absent supervisor to a doctoral student about to graduate reveals a terrible secret.

Math Moment, Paige S. Orland

Journal of Humanistic Mathematics

A short poem comparing Exponential and Logistic functions.

Confidence Interval, Ursula Whitcher

Journal of Humanistic Mathematics

A poem about estimating probabilities.

Joanne Growney's Poetry-With-Mathematics Blog -- An Appreciation, Gregory E. Coxson

Journal of Humanistic Mathematics

Now is a good time to work on the boundaries of practice and theory, of art and science. We are seeing a rising tide of interest in these boundaries. Witness the growing Bridges movement, which has been exploring the connections between mathematics and the arts. Similarly, JoAnne Growney's blog, Intersections -- Poetry with Mathematics, explores the connections between mathematics and poetry. Through this review, I aim to give readers a taste of what can be found in Intersections as a way of encouraging others, be they mathematicians, poets, or neither, to visit the blog.

Mathematics And The Hunger Games, Michael A. Lewis

Journal of Humanistic Mathematics

The Hunger Games plot features a dystopian future in which twelve outer districts are oppressed by a centralized capital. The story focuses on the heroism of a sixteen-year-old girl named Katniss and how she tries to rise above the oppression that she experiences. It also features a special lottery and other twists that are sources of mathematical interest. This essay focuses on some of the mathematical issues raised by The Hunger Games in an effort to show that this story can be used to teach students (as well as other interested parties) some important concepts from mathematics.

A Definition Of Mathematical Beauty And Its History, Viktor Blåsjö

Journal of Humanistic Mathematics

I define mathematical beauty as cognisability and trace the import of this notion through several episodes from the history of mathematics.

Report Supplement: Poetry Folder -- Selections From The Poetry Reading At Joint Mathematics Meetings 2012

Journal of Humanistic Mathematics

No abstract provided.

For The Love Of Poetry And Mathematics: January 6, 2012, Charlotte Henderson

Journal of Humanistic Mathematics

Together we combine to become twice what 60 could ever be.
The same ghost looked into my eyes.
Also, the center of the circle is inside the circle.
There is no way to draw a line, other than a border line,
A language as precise as poetry to delineate universe and being,
Deceptive as one over n as n goes to infinity, summed.
The world is a complex system
not defined by any voice factored out of my voicelessness,
the hypotenuse of course is the man who came between us
doubting every figured guess,
so, inductively, all of God’s natural …

Raphael's School Of Athens: A Theorem In A Painting?, Robert Haas

Journal of Humanistic Mathematics

Raphael's famous painting The School of Athens includes a geometer, presumably Euclid himself, demonstrating a construction to his fascinated students. But what theorem are they all studying? This article first introduces the painting, and describes Raphael's lifelong friendship with the eminent mathematician Paulus of Middelburg. It then presents several conjectured explanations, notably a theorem about a hexagram (Fichtner), or alternatively that the construction may be architecturally symbolic (Valtieri). The author finally offers his own "null hypothesis": that the scene does not show any actual mathematics, but simply the fascination, excitement, and joy of mathematicians at their work.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Gromov-Witten Theory Of P^1 X P^1 X P^1, Dagan Karp, Dhruv Ranganathan

All HMC Faculty Publications and Research

We prove equivalences between the Gromov-Witten theories of toric blowups of P^1xP^1xP^1 and P^3. In particular, we prove that the all genus, virtual dimension zero Gromov-Witten theory of the blowup of P^3 at points precisely coincides with that of the blowup at points of P^1xP^1xP^1, for non-exceptional classes. It follows that the all-genus stationary Gromov-Witten theory of P^1xP^1xP^1 coincides with that of P^3 in low degree. We also prove there exists a toric symmetry of the Gromov-Witten theory of P^1xP^1xP^1 analogous to and intimately related to Cremona symmetry of P^3. Enumerative applications are given.

Analysis Of Biodiesel Quality Using Reversed Phase High-Performance Liquid Chromatography, Kellyann M. Murphy

Pomona Senior Theses

The alternative fuel biodiesel is produced from the transesterification of vegetable oils or animal fat to fatty acid methyl esters. Pomona has a reactor on campus that can be used to run this reaction and produce biodiesel. The use of biodiesel has been found to lower air pollutant and greenhouse gas emissions, but can be potentially harmful to the engines if it contains impurities. This paper proposes a method using high-performance liquid chromatography to test the quality of biodiesel. This method utilizes instrumentation and materials that are available in Pomona College's Chemistry Department, requires very little sample preparation, and is …

Agricultural Efficiency And The End Of The Oil Age; Building A Future Of Longevity, Keith Mchugh

Pomona Senior Theses

This thesis uses an efficiency analysis of agricultural systems to assert that, in lieu of rising prices of fossil fuel, people need to come into more direct contact with their food systems. With a switch to smaller, more efficient farms that rely less on fossil fuel and are connected with the communities they supply for, we can avoid an energy crisis turning into a famine. These smaller-scale systems can help create self-contained, carbon-neutral communities.

Bikeurious: A Transportation Reorientation, Aerienne Russell

Pomona Senior Theses

Since a young age, I have been interested in bicycling as a form of fun and fanciful recreation, but it wasn’t until the summer of 2011 that a serious shift occurred in my understanding of the bike as more than a mere machine. A spontaneous 700-mile journey redefined my relationship with travel, transcended my notions of transportation, and enabled me to better mediate myself within my environment. In writing about these experiences, I hope to offer some insight into how American culture currently frames transportation and how I hope the construction of a bike positive culture can instill social, environmental, …

The Full Cost Of Renewables: Managing Wind Integration Costs In California, William Savage

Pomona Senior Theses

Wind power will be an important component of California's aggressive strategies to meet its greenhouse gas reduction targets by the year 2020. However, the costs of integrating wind power's variable and uncertain output are often ignored. I argue that California must take prudent action to understand, minimize, and allocate wind integration costs. A review of numerous studies suggests that for wind penetration levels below 20%, integration costs should remain modest. However, costs are heavily dependent on market structure, and I suggest numerous ways that California can optimize its market design to manage wind integration costs.

San Antonio High School Food Justice Program: A Handbook And Evaluation Of Edible Education, Katherine B. Tenneson

Pitzer Senior Theses

This senior environmental studies thesis explains and analyzes edible education through a food and gardening program at a continuation high school in Claremont, California. The first chapter situates the program-specific analysis by providing background information of the edible education movement, a history of the Edible Schoolyard in Berkeley, California, and an explanation of why food is a powerful teaching tool. The second chapter delineates the program by describing all of its components and compiling essential resources and teaching documents. The third chapter is based on interviews with 9 of 12 involved students and 7 teachers, and thoroughly explains the outcomes …

“Dismantling The Big” Critiquing The Western Development Model And Foreign Aid And Analyzing Alternatives For Domestic Development Of Dams In Nepal, Ana Berry

Pitzer Senior Theses

This paper argues for the importance of scale, management and sovereign-led development in considering a more human-centric model for Third World development. It begins by reviewing the history of the mainstream Western development model through the evolution of modernization theory and foreign aid. It explores general critiques of this model offered by scholars, focusing on unequal power relations, the high cost of aid, and problems with ‘cookie cutter’ style development projects that don’t take into account disparate environments. As the paper progresses, focus shifts more specifically to hydropower development and ‘Big Dams’. Nepal is the main case study for exemplifying …

Resonant Solutions And Turning Points In An Elliptic Problem With Oscillatory Boundary Conditions, Alfonso Castro, Rosa Pardo

All HMC Faculty Publications and Research

We consider the elliptic equation -Δu + u = 0 with nonlinear boundary conditions ∂u/∂n = λu + g(λ,x,u), where the nonlinear term g is oscillatory and satisfies g(λ,x,s)/s→0 as |s|→0. We provide sufficient conditions on g for the existence of sequences of resonant solutions and turning points accumulating to zero.

Arsenic Contamination In Groundwater In Vietnam: An Overview And Analysis Of The Historical, Cultural, Economic, And Political Parameters In The Success Of Various Mitigation Options, Thuy M. Ly

Pomona Senior Theses

Although arsenic is naturally present in the environment, 99% of human exposure to arsenic is through ingestion. Throughout history, arsenic is known as “the king of poisons”; it is mutagenic, carcinogenic, and teratogenic. Even in smaller concentrations, it accumulates in the body and takes decades before any physical symptoms of arsenic poisoning shows. According to the World Health Organization (WHO), the safe concentration of arsenic in drinking water is 10 µg/L. However, this limit is often times ignored until it is decades too late and people begin showing symptoms of having been poisoned.

This is the current situation for Vietnam, …