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Full-Text Articles in Dynamic Systems
Human-Centered Modeling Of Traffic As A Complex System, Poorendra P. Ramlall
Human-Centered Modeling Of Traffic As A Complex System, Poorendra P. Ramlall
Discovery Day - Daytona Beach
Traffic systems are driven not only by motion, but by interaction: vehicles influence one another, drivers continuously adapt to surrounding behaviour, and cognitive processes shape decisions that can propagate through the flow of traffic. Understanding these layered interactions is essential for improving traffic safety and for designing the next generation of intelligent, connected, and automated transportation systems. This PhD research develops a multiscale, data-driven framework for identifying, modelling, and ultimately interpreting interaction structure in traffic systems. The work first established an information-theoretic basis for this problem, demonstrating how information flow can uncover directional relationships in traffic dynamics and help infer …
Supply Chain Analysis: The Oregonator Autocatalytic Case Study, Abigail Butcher
Supply Chain Analysis: The Oregonator Autocatalytic Case Study, Abigail Butcher
Discovery Day - Daytona Beach
Understanding stability in complex supply chains remains a critical challenge due to nonlinear feedback, delayed responses, and sensitivity to parameter changes. This project presents a novel framework that applies bifurcation analysis to evaluate system stability, using the Oregonator autocatalytic chemical reaction model as an analog for supply chain dynamics. A parameter sweep of key model variables, particularly the stoichiometric factor f and the reaction rate constants k, is used to identify transitions between stable and oscillatory regimes. These transitions provide insight into how variations in feedback strength can drive instability in real-world systems. The framework will then be extended to …
Numerical Modeling Of Thermo-Poroelasticity Using Finite Element Method, Maya Mckean
Numerical Modeling Of Thermo-Poroelasticity Using Finite Element Method, Maya Mckean
Discovery Day - Daytona Beach
We propose a numerical method for solving and modeling thermo-poroelasticity problems using a finite element formulation. Thermo-poroelasticity models describe the coupled interaction between mechanical deformation, fluid flow, and heat transfer in specific materials or environments over time. These models demonstrate the evolution of displacement, pressure, and temperature; we compute these fields in this work using backward Euler time discretization and Enriched Galerkin finite element spatial discretization. For these computations we used FreeFEM, a partial differential equation solver that uses the finite element method, which produced our numerical results. We then compared these values with the expected analytical solution. This was …
Ai-Driven Scheduling Algorithms For Private Aviation, Tayan Benson, Jessica Buskey, Gabriel Camacho, Caitlyn A. Gabrinowitz
Ai-Driven Scheduling Algorithms For Private Aviation, Tayan Benson, Jessica Buskey, Gabriel Camacho, Caitlyn A. Gabrinowitz
Discovery Day - Daytona Beach
Private aviation scheduling is complex and dynamic, requiring frequent aircraft repositioning based on demand and operational constraints, unlike fixed commercial airline schedules. As fleets grow beyond 300 aircraft, traditional deterministic methods become too slow, leading to the use of approaches such as genetic algorithms, but neural network-based methods have not seen in-depth exploration. This project models aircraft scheduling as a network, where airports and flights form a graph. It explores advanced AI methods, including graph neural networks and spatio-temporal graph neural networks (STGNNs), to capture both network structure and time constraints. The goal is to generate efficient daily schedules from …
The Motion Of A Falling Object Under Linear Drag And How Differential Equations Can Be Used To Find It, Lukas Estrella
The Motion Of A Falling Object Under Linear Drag And How Differential Equations Can Be Used To Find It, Lukas Estrella
Discovery Day - Daytona Beach
This project, "The Motion of a Falling Object Under Linear Drag and How Differential Equations Can Be Used To Find It," investigates the motion of a falling object subject to air resistance through a combination of mathematical modeling and fundamental physical principles. The analysis is grounded in Newton’s second law, which yields a differential equation describing the forces acting on the object. Assuming a linear drag model, in which the resistive force is proportional to velocity, the governing equation reduces to a first-order ordinary differential equation for velocity. This equation is solved using the integrating factor method, yielding an explicit …
Modeling Population Growth With Logistic And Modified Logistic Equations, Mihil Dimpal Patel
Modeling Population Growth With Logistic And Modified Logistic Equations, Mihil Dimpal Patel
Discovery Day - Daytona Beach
Population growth models are essential tools for understanding how biological populations change over time under environmental constraints. This study examines population dynamics by comparing the classical exponential growth model with the logistic growth model. While exponential growth assumes unlimited resources and results in unbounded population increase, the logistic model incorporates a carrying capacity that limits growth as resources become scarce. To better represent real-world conditions, the logistic model is extended by introducing modifications such as harvesting terms and time-varying carrying capacities, which account for external removal of individuals and changing environmental limits. The equilibria of these models are determined, and …