Dynamical Systems Commons^™

Math Meets Climate: The Energy Balance Model, Maria I. Sanchez Muniz

Open Educational Resources

This assignment introduces students to the mathematics of Earth’s climate through the classical energy balance model. Students analyze how incoming solar radiation, outgoing thermal radiation, and temperature-dependent albedo interact to determine Earth’s equilibrium temperature. Using analytical calculations and computational tools, students identify equilibrium states, assess their stability, and interpret the results through the lens of dynamical systems and bifurcation theory. The activity builds conceptual understanding of climate feedbacks, greenhouse effects, and tipping behavior using a transparent, one-variable model. Designed for applied mathematics and interdisciplinary STEM courses, this assignment emphasizes computation, physical interpretation, and real-world relevance. It is released as a …

Understanding Enso Through Mathematical Models, Maria I. Sanchez Muniz

Open Educational Resources

This assignment introduces students to conceptual models of the El Niño–Southern Oscillation (ENSO) and guides them through a structured investigation of their physical and mathematical foundations. Students analyze the recharge–oscillator and delayed–oscillator frameworks, explore how differential equations capture ocean–atmosphere interactions, and evaluate parameter-driven changes in oscillatory behavior. A key component of the work is the guided use of generative AI as a research tool: students employ AI models to locate peer-reviewed literature, interrogate model extensions, and refine their understanding of complex mechanisms, while synthesizing all final explanations in their own words. By blending classical climate modeling with modern AI-supported inquiry, …

The Computational Search For Unidentified Central Configurations Of The Newtonian N-Body Problem, Hannah G. Havel

CURE Proceedings

The N-body problem is a field of study in mathematics and physics that involves predicting the motion of particles moving under their mutual gravitational attraction. It is vital in celestial mechanics, such as planning collision-free satellite orbit trajectories. When beginning to understand the N-body problem, we can start by looking at equal masses of these particles or celestial bodies. As particles move, their position and velocity change, both energy and angular momentum are conserved. Sets of constant energy and angular momentum, known as integral manifolds, are higher-dimensional figures that represent constraints of movement to a system. Integral manifolds are described …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost

All Dissertations

In confocal single-molecule FRET experiments, the joint distribution of FRET efficiency and donor lifetime distribution can reveal underlying molecular conformational dynamics via deviation from their theoretical Forster relationship. This shift is referred to as a dynamic shift. In this study, we investigate the influence of the free energy landscape in protein conformational dynamics on the dynamic shift by simulation of the associated continuum reaction coordinate Langevin dynamics, yielding a deeper understanding of the dynamic and structural information in the joint FRET efficiency and donor lifetime distribution. We develop novel Langevin models for the dye linker dynamics, including rotational dynamics, based …

Rigid Body Constrained Motion Optimization And Control On Lie Groups And Their Tangent Bundles, Brennan S. Mccann

Doctoral Dissertations and Master's Theses

Rigid body motion requires formulations where rotational and translational motion are accounted for appropriately. Two Lie groups, the special orthogonal group SO(3) and the space of quaternions H, are commonly used to represent attitude. When considering rigid body pose, that is spacecraft position and attitude, the special Euclidean group SE(3) and the space of dual quaternions DH are frequently utilized. All these groups are Lie groups and Riemannian manifolds, and these identifications have profound implications for dynamics and controls. The trajectory optimization and optimal control problem on Riemannian manifolds presents significant opportunities for theoretical development. Riemannian optimization is an attractive …

Compilación De Procesos Investigativos En Educación Matemática, Martha Lidia Barreto Moreno, Yeferson Castellanos Novoa, María Alejandra Mayorga Henao, Diana Marcela Contento Sarmiento, Jesús Antonio Villarraga Palomino, Andrés Alberto Gutiérrez Morales, Juan David Firigua Bejarano, Yineth Marleidy Parra Ubaque, Lady Johanna Silva Marín

Educación

En el libro Compilación de procesos de investigación en educación matemática, consta de cuatro capítulos donde se presentan los procesos desarrollados en el marco de proyectos de investigación a nivel de pregrado y postgrado en Educación.

El primer capítulo consiste en la sistematización de la acción docente desarrollada en el marco de los Talleres Itinerantes de Alfabetización Computacional en la provincia de Sumapaz, propuesta de innovación para implementar procesos didácticos que contribuyan al desarrollo del pensamiento matemático computacional en educación básica primaria rural.

El segundo capítulo contiene el proceso investigativo que dio continuidad al trabajo realizado en la Fase1, sobre …

Role Of Inhibition And Spiking Variability In Ortho- And Retronasal Olfactory Processing, Michelle F. Craft

Theses and Dissertations

Odor perception is the impetus for important animal behaviors, most pertinently for feeding, but also for mating and communication. There are two predominate modes of odor processing: odors pass through the front of nose (ortho) while inhaling and sniffing, or through the rear (retro) during exhalation and while eating and drinking. Despite the importance of olfaction for an animal’s well-being and specifically that ortho and retro naturally occur, it is unknown whether the modality (ortho versus retro) is transmitted to cortical brain regions, which could significantly instruct how odors are processed. Prior imaging studies show different …

Efficient Control Methods For Stochastic Boolean Networks, David Murrugarra

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Semi-Tensor Product Representations Of Boolean Networks, Matthew Macauley

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Simulating The Electrical Properties Of Random Carbon Nanotube Networks Using A Simple Model Based On Percolation Theory, Roberto Abril Valenzuela

Physics

Carbon nanotubes (CNTs) have been subject to extensive research towards their possible applications in the world of nanoelectronics. The interest in carbon nanotubes originates from their unique variety of properties useful in nanoelectronic devices. One key feature of carbon nanotubes is that the chiral angle at which they are rolled determines whether the tube is metallic or semiconducting. Of main interest to this project are devices containing a thin film of randomly arranged carbon nanotubes, known as carbon nanotube networks. The presence of semiconducting tubes in a CNT network can lead to a switching effect when the film is electro-statically …

On The Analysis Of The Sir Epidemic Model For Small Networks: An Application In Hospital Settings, Martin Lopez-Garcia

Biology and Medicine Through Mathematics Conference

No abstract provided.

On The Three Dimensional Interaction Between Flexible Fibers And Fluid Flow, Bogdan Nita, Ryan Allaire

Department of Mathematics Faculty Scholarship and Creative Works

In this paper we discuss the deformation of a flexible fiber clamped to a spherical body and immersed in a flow of fluid moving with a speed ranging between 0 and 50 cm/s by means of three dimensional numerical simulation developed in COMSOL . The effects of flow speed and initial configuration angle of the fiber relative to the flow are analyzed. A rigorous analysis of the numerical procedure is performed and our code is benchmarked against well established cases. The flow velocity and pressure are used to compute drag forces upon the fiber. Of particular interest is the behavior …

A Group-Permutation Algorithm To Solve The Generalized Sudoku, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Sudoku can be generalized to squares whose dimensions are n^2 × n^2 , where n ≥ 2, using various symbols (numbers, letters, mathematical symbols, etc.), written just one time on each row and on each column; and the large square is divided into n 2 small squares with the side n × n and each will contain all n 2 symbols written only once. In this paper we present an elementary solution for the generalized sudoku based on a group-permutation algorithm.

Finding The Beat In Music: Using Adaptive Oscillators, Kate M. Burgers

HMC Senior Theses

The task of finding the beat in music is simple for most people, but surprisingly difficult to replicate in a robot. Progress in this problem has been made using various preprocessing techniques (Hitz 2008; Tomic and Janata 2008). However, a real-time method is not yet available. Methods using a class of oscillators called relay relaxation oscillators are promising. In particular, systems of forced Hopf oscillators (Large 2000; Righetti et al. 2006) have been used with relative success. This work describes current methods of beat tracking and develops a new method that incorporates the best ideas from each existing method and …