Stability Analysis Of Thermohaline Convection With A Time-Varying Shear Flow Using The Lyapunov Method,
2025
University of Connecticut - Storrs
Stability Analysis Of Thermohaline Convection With A Time-Varying Shear Flow Using The Lyapunov Method, Kalin Kochnev
Honors Scholar Theses
This work applies the Lyapunov method to identify instabilities and compute the growth rate of a linear time-varying system. The linear system studied describes cold fresh water on top of hot salty water with a periodically time-varying background shear flow. A time-dependent weighting matrix is employed to construct a Lyapunov function candidate. The resulting linear matrix inequalities are discretized in time using the forward Euler method. As the number of temporal discretization points increases, the growth rate predicted by the Lyapunov method or Floquet theory, used for comparison, will converge to the same value obtained from numerical simulations. Furthermore, the …
Math Meets Climate: The Energy Balance Model,
2025
City College of New York
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,
2025
City College of New York
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, …
(R2136) Dimensionless Modeling And Analytical Insights Into Botanical Biofiltration Systems For Voc Reduction,
2025
The Madura College, India
(R2136) Dimensionless Modeling And Analytical Insights Into Botanical Biofiltration Systems For Voc Reduction, N. Jeeva, K. M. Dharmalingam, M. Veeramuni
Applications and Applied Mathematics: An International Journal (AAM)
This paper investigates the mathematical modeling of volatile organic compound (VOC) removal using a botanical biofiltration system, an effective biological treatment method. It examines mass balance concentrations in the gas and biofilm phases, highlighting their significance in VOC degradation and indoor air quality enhancement. The governing equations of the proposed model are converted into a dimensionless form, resulting in second-order nonlinear differential equations. Derived from mass transfer and reaction kinetics principles, these equations incorporate specific boundary conditions to capture gas-biofilm interactions and VOC removal dynamics in biofiltration. The modified Adomian decomposition method (MADM) is utilized to derive analytical solutions for …
(R2134) Continuous Shooting Approach With Improved Shooting Slope For Solving Higher Integer Order Boundary Value Problem,
2025
Ladoke Akintola University of Technology (LAUTECH), Nigeria
(R2134) Continuous Shooting Approach With Improved Shooting Slope For Solving Higher Integer Order Boundary Value Problem, Razaq Adekola Oderinu, Adebowale Niyi Aderibigbe, Saheed Alao, Ahmed Adeyi Yahaya
Applications and Applied Mathematics: An International Journal (AAM)
This study presents a semi-analytical shooting method for solving nonlinear higher-order boundary value problems by integrating the Adomian Decomposition Method into the shooting technique, enabling series-form solutions. To enhance convergence, new higher-order shooting slopes and their corresponding supplementary equation formulas were introduced. Three numerical examples demonstrated the method’s accuracy: for the first two, absolute errors were computed using available exact solutions, while the third was compared with reference literature due to the absence of an exact solution. The method achieved very small absolute errors in the first two cases, and results from the third closely matched the literature. Tolerance values—defined …
(R2107) Analysis Of A Bivalent Vaccine Model With Peer Influence Effect On Testing,
2025
Banasthali Vidyapith Rajasthan, India
(R2107) Analysis Of A Bivalent Vaccine Model With Peer Influence Effect On Testing, Manoj Kumar Singh, Anjali .
Applications and Applied Mathematics: An International Journal (AAM)
The coronavirus caused havoc around the world. There was a terrible situation in villages and cities, and no one knew how to deal with it. Although the governments of each country tried their best to save the common people, vaccination programs and testing centers were built everywhere. However, people were not utilizing it due to fear. Because of this, the infection spread rapidly. The qualitative study of the mathematical model here is in context with the situation when bivalent vaccination and testing are available for an epidemic. The mathematical model combines the exposed period and influenza model with vaccination included …
The Odds Don’T Lie: Mathematical Reasoning And Societal Ignorance In Don’T Look Up,
2025
West Morris Central High School
The Odds Don’T Lie: Mathematical Reasoning And Societal Ignorance In Don’T Look Up, Nysa Vedwan, Shane Carey
LASER Journal
In Adam McKay’s 2021 satirical sci-fi movie Don’t Look Up, two astronomers discover a comet heading directly toward Earth. Despite overwhelming evidence and near-certainty of global extinction, their warnings are ignored and ridiculed. This paper discusses the mathematical and scientific foundations of the movie’s social and political reception, and specifically focuses on orbital prediction and probabilistic modeling as they relate to public understanding of risk. This paper shows how data is often undermined by political and social dynamics, by connecting the fictional events of the movie with real-world crises like the COVID-19 pandemic and the climate emergency. In Don’t Look …
Using Compartmental Systems Of Ordinary Differential Equations And Optimal Control Theory To Compute Ideal Quantities Of Mentors For Student Populations,
2025
George Mason University
Using Compartmental Systems Of Ordinary Differential Equations And Optimal Control Theory To Compute Ideal Quantities Of Mentors For Student Populations, Timofey B. Gafurov
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Data-Driven Modeling Of Dynamics And Adaptation In Mapk Pathway,
2025
George Mason University
Data-Driven Modeling Of Dynamics And Adaptation In Mapk Pathway, Elisha Erzoah, Maria Emelianenko, Mariaelena Pierobon
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Multi-Resolution Graph Neural Networks For Spread Prediction,
2025
Illinois State University
Multi-Resolution Graph Neural Networks For Spread Prediction, Petr Kisselev
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Modeling And Analysis Of The Impacts Of The Rise In Ai Use On Data Center Growth, Resulting Workforce Displacement, And Environmental Impacts Through A Coupled System Of Ordinary Differential Equations Within A Feedback Framework,
2025
Freedom High School
Modeling And Analysis Of The Impacts Of The Rise In Ai Use On Data Center Growth, Resulting Workforce Displacement, And Environmental Impacts Through A Coupled System Of Ordinary Differential Equations Within A Feedback Framework, Divya Laddha, Alonso Gaberial Ogueda, Padmanabhan Seshaiyer
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Investigating The Basic Reproduction Number For An Avian Influenza Model,
2025
Virginia Polytechnic Institute and State University
Investigating The Basic Reproduction Number For An Avian Influenza Model, Omar Saucedo
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
[Kyda] Biologically Grounded Surrogate-Driven Parameter Inference For Sparsely Observed Dynamical Systems,
2025
Johns Hopkins University
[Kyda] Biologically Grounded Surrogate-Driven Parameter Inference For Sparsely Observed Dynamical Systems, Joshua C. Macdonald
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
[Kyda] The Behavioral Spillover Effect: Modeling Behavioral Interdependencies In Multi-Pathogen Dynamics,
2025
Virginia Tech
[Kyda] The Behavioral Spillover Effect: Modeling Behavioral Interdependencies In Multi-Pathogen Dynamics, Leah Lejeune, Omar Saucedo, Lauren M. Childs, Navid Ghaffarzadegan
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Modeling Synaptic Dysfunction As Neural Contagion: A Graph-Based Sedr Framework For Simulating Signal Spread,
2025
Osbourn Park High School
Modeling Synaptic Dysfunction As Neural Contagion: A Graph-Based Sedr Framework For Simulating Signal Spread, Michelle Marfo, Dr. Padmanabhan Seshaiyer, Alonso Ogueda-Oliva
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Metapopulation Model To Evaluate C.Difficile Potential Vaccine Interventions.,
2025
Illinois State University
Metapopulation Model To Evaluate C.Difficile Potential Vaccine Interventions., Archana Neupane Timsina
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Following Carbon: Pathway And Flux Representations Of Ecosystems,
2025
University of Georgia
Following Carbon: Pathway And Flux Representations Of Ecosystems, Caner Kazanci
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Exploring Solutions To Food Addiction Challenges Using Mathematical Modeling, Simulation, And Analysis Applying Optimal Control Theory,
2025
University of Maryland at College Park
Exploring Solutions To Food Addiction Challenges Using Mathematical Modeling, Simulation, And Analysis Applying Optimal Control Theory, Dia Bonsu, Padmanabhan Seshaiyer, Alonso Ogueda-Oliva
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Immune Dysregulation In Covid-19: Mathematical Modeling Of The Within-Host Dynamics,
2025
Elon University
Immune Dysregulation In Covid-19: Mathematical Modeling Of The Within-Host Dynamics, Pagnapech Ngoun, Nicolas Alvarez, Ayesh Awad, Hwayeon Ryu
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Culture Mediates Climate Opinion Change: A System Dynamics Model,
2025
University of Tennessee, Knoxville
Culture Mediates Climate Opinion Change: A System Dynamics Model, Louis (Lou) Gross, Yoon Ah Shin, Sara M. Constantino, Ann Kinzig, Katherine Lacasse, Brian Beckage
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
