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Articles 1 - 8 of 8
Full-Text Articles in Dynamic Systems
A Categorical Framework For Modeling Genetic Drift, Taylor G. Mendes
A Categorical Framework For Modeling Genetic Drift, Taylor G. Mendes
Rose-Hulman Undergraduate Mathematics Journal
Genetic drift describes changes in allele frequencies that arise from chance sampling in finite populations. This paper develops a categorical framework for organizing the structural features of drift. Population states are modeled as objects, evolutionary transitions as morphisms, reversible transitions as groupoid morphisms, and structure-preserving comparisons between models as functors. Group actions are used to describe deterministic evolutionary operators such as mutation and selection, while orbits and fixed points identify reachable allele-frequency states and stable absorbing outcomes. Universal properties are then used to describe drift as a coherence condition connecting stochastic transitions with deterministic evolutionary maps. The resulting framework complements …
Convergence Properties Of Solutions Of A Length-Structured Density-Dependent Model For Fish, Geigh Zollicoffer
Convergence Properties Of Solutions Of A Length-Structured Density-Dependent Model For Fish, Geigh Zollicoffer
Rose-Hulman Undergraduate Mathematics Journal
We numerically study solutions to a length-structured matrix model for fish populations in which the probability that a fish grows into the next length class is a decreasing nonlinear function of the total biomass of the population. We make conjectures about the convergence properties of solutions to this equation, and give numerical simulations which support these conjectures. We also study the distribution of biomass in the different age classes as a function of the total biomass.
Mathematical Modeling Of Quadcopter Dynamics, Qikai Huang (Bruce Wingo)
Mathematical Modeling Of Quadcopter Dynamics, Qikai Huang (Bruce Wingo)
Mathematical Sciences Technical Reports (MSTR)
Recently, Google, Amazon and others are attempting to develop delivery drones for commercial use, in particular Amazon Prime Air promising 30 minute delivery. One type of commonly used drone proposed for such purposes is a quadcopter. Quadcopters have been around for some time with original development in the 1920’s. They are popular now because they are mechanically simple and provide a good vehicle for unmanned flight. By controlling the speed of the four propellers, a quadcopter can roll, change pitch, change yaw, and accelerate. This research will focus on the study of classical mechanics theories on rigid body motion using …
Mathematical Modeling Of Quadcopter Dynamics, Qikai Huang (Bruce Wingo)
Mathematical Modeling Of Quadcopter Dynamics, Qikai Huang (Bruce Wingo)
Rose-Hulman Undergraduate Research Publications
Recently, Google, Amazon and others are attempting to develop delivery drones for commercial use, in particular Amazon Prime Air promising 30 minute delivery. One type of commonly used drone proposed for such purposes is a quadcopter. Quadcopters have been around for some time with original development in the 1920’s. They are popular now because they are mechanically simple and provide a good vehicle for unmanned flight. By controlling the speed of the four propellers, a quadcopter can roll, change pitch, change yaw, and accelerate. This research will focus on the study of classical mechanics theories on rigid body motion using …
Spontaneous Synchrony On Graphs And The Emergence Of Order From Disorder, Dylan Linville, Daniel Trugillo Martins Fontes
Spontaneous Synchrony On Graphs And The Emergence Of Order From Disorder, Dylan Linville, Daniel Trugillo Martins Fontes
Mathematical Sciences Technical Reports (MSTR)
From pulsars to pedestrians and bacteria to brain cells, objects that exhibit cyclical behavior, called oscillators, are found in a variety of different settings. When oscillators adjust their behavior in response to nearby oscillators, they often achieve a state of synchrony, in which they all have the same phase and frequency. Here, we explore the Kuramoto model, a simple and general model which describes oscillators as dynamical systems on a graph and has been used to study synchronization in systems ranging from firefly swarms to the power grid. We discuss analytical and numerical methods used to investigate the governing system …
Spontaneous Synchrony On Graphs And The Emergence Of Order From Disorder, Dylan Linville, Daniel Trugillo Martins Fontes
Spontaneous Synchrony On Graphs And The Emergence Of Order From Disorder, Dylan Linville, Daniel Trugillo Martins Fontes
Rose-Hulman Undergraduate Research Publications
From pulsars to pedestrians and bacteria to brain cells, objects that exhibit cyclical behavior, called oscillators, are found in a variety of different settings. When oscillators adjust their behavior in response to nearby oscillators, they often achieve a state of synchrony, in which they all have the same phase and frequency. Here, we explore the Kuramoto model, a simple and general model which describes oscillators as dynamical systems on a graph and has been used to study synchronization in systems ranging from firefly swarms to the power grid. We discuss analytical and numerical methods used to investigate the governing system …
Intrinsic Contact Geometry Of Protein Dynamics, Yosi Shibberu, Allen Holder, David Cooper
Intrinsic Contact Geometry Of Protein Dynamics, Yosi Shibberu, Allen Holder, David Cooper
Mathematical Sciences Technical Reports (MSTR)
We introduce a new measure for comparing protein structures that is especially applicable to analysis of molecular dynamics simulation results. The new measure generalizes the widely used root-mean-squared-deviation (RMSD) measure from three dimensional to n-dimensional Euclidean space, where n equals the number of atoms in the protein molecule. The new measure shows that despite significant fluctuations in the three dimensional geometry of the estrogen receptor protein, the protein's intrinsic contact geometry is remarkably stable over nanosecond time scales. The new measure also identifies significant structural changes missed by RMSD for a residue that plays a key biological role in …
A Variable Time-Step Midpoint Scheme For Hamiltonian Systems, Yosi Shibberu
A Variable Time-Step Midpoint Scheme For Hamiltonian Systems, Yosi Shibberu
Mathematical Sciences Technical Reports (MSTR)
A smooth time-step selection formula for the midpoint method is derived which minimize deviations in the Hamiltonian function along piecewise-linear phase space trajectories of autonomous Hamiltonian systems. The time-step formula is implemented in a second order predictor/corrector scheme and applied to Kepler's problem. The formula significantly improves energy conservation as well as the accuracy of the configuration space trajectory. Peak errors in position and momentum coordinates are not significantly reduced, but the time behavior of the errors is markedly more regular.