Non-linear Dynamics Commons^™

Self-Correcting Kelly Strategies For Skeptical Traders, Aaron C. Brown

International Conference on Gambling & Risk Taking

The Kelly criterion gives the appropriate bet size in idealized situations with known parameters. In financial trading situations parameters are generally unknown and the mathematical assumptions underlying the Kelly proof are not met precisely. Moreover a risk manager typically must cooperate with a trader who may be skeptical about both the Kelly criterion specifically and the concept of mathematical optimization of bet size in general.

This presentation tackles the problem of designing a Kelly-based system for setting trade risk management parameters that is both self-correcting (the system delivers good results even if initial parameter are misestimated or parameters change) and …

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 …

Nonlinear Harmonic Modes Of Steel Strings On An Electric Guitar, Joel Wenrich

Senior Theses

Steel strings used on electric and acoustic guitars are non-ideal oscillators that can produce imperfect intonation. According to theory, this intonation should be a function of the bending stiffness of the string, which is related to the dimensions of length and thickness of the string. To test this theory, solid steel strings of three different linear densities were analyzed using an oscilloscope and a Fast Fourier Transform function. We found that strings exhibited more drastic nonlinear harmonic behavior as their effective length was shortened and as linear density increased.

Determinants Of The Efficacy Of Hiv Latency Reversing Agents And Implications For Drug And Treatment Design, Ruian Ke

Biology and Medicine Through Mathematics Conference

No abstract provided.

Using Mathematical Modeling To Unmask The Concealed Nature Of Long Qt-3 Syndrome, Steven Poelzing, Amara Greer-Short, Seth H. Weinberg

Biology and Medicine Through Mathematics Conference

No abstract provided.

Anticipating Elimination Of Mosquito-Borne Diseases, Suzanne M. O'Regan, Jonathan Lillie, John M. Drake

Biology and Medicine Through Mathematics Conference

No abstract provided.

Toward Adaptive Control Of Acute Inflammation, Judy D. Day, Seddik M. Djouadi, Ouassim Bara, Gregory L. Zitelli

Biology and Medicine Through Mathematics Conference

No abstract provided.

Dynamics Of Discrete Planar Systems That Model Stage-Structured Populations, Shushan Lazaryan, Hassan Sedaghat

Biology and Medicine Through Mathematics Conference

No abstract provided.

Low Energy Defibrillation By Synchronization; 90 % Less Energy Compared To One Shock., Flavio H. Fenton, Yanyan Ji, Ilija Uzelac, Niels Otani, Elizabeth M. Cherry

Biology and Medicine Through Mathematics Conference

No abstract provided.

General Models For Ecological Drivers Of Poverty, Calistus Ngeh Ngonghala

Biology and Medicine Through Mathematics Conference

No abstract provided.

Wilson-Cowan Coupled Dynamics In A Model Of The Cortico-Striato-Thalamo-Cortical Circuit, Anca R. Radulescu

Biology and Medicine Through Mathematics Conference

No abstract provided.

Robust Traveling Waves In Chains Of Simple Neural Oscillators, Stanislav M. Mintchev

Biology and Medicine Through Mathematics Conference

No abstract provided.

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 …

On The Flow Of Non-Axisymmetric Perturbations Of Cylinders Via Surface Diffusion, Jeremy Lecrone, Gieri Simonett

Department of Math & Statistics Faculty Publications

We study the surface diffusion flow acting on a class of general (non--axisymmetric) perturbations of cylinders Cr in IR3. Using tools from parabolic theory on uniformly regular manifolds, and maximal regularity, we establish existence and uniqueness of solutions to surface diffusion flow starting from (spatially--unbounded) surfaces defined over Cr via scalar height functions which are uniformly bounded away from the central cylindrical axis. Additionally, we show that Cr is normally stable with respect to 2π--axially--periodic perturbations if the radius r>1,and unstable if 0

Models Of Internal Waves In The Presence Of Currents, Alan Compelli, Rossen Ivanov

Conference papers

A fluid system consisting of two domains is examined. The system is considered as being bounded at the bottom and top by a flatbed and wave-free surface respectively. An internal wave propagating in one direction, driven by gravity, acts as a free common interface between the fluids. Various current profiles are considered. The Hamiltonian of the system is determined and expressed in terms of canonical wave-related variables. Limiting behaviour is examined and compared to that of other known models. The linearised equations as well as long-wave approximations are formulated. The presented models provide potential applications to modelling of internal geophysical …

Topological Data Analysis For Systems Of Coupled Oscillators, Alec Dunton

HMC Senior Theses

Coupled oscillators, such as groups of fireflies or clusters of neurons, are found throughout nature and are frequently modeled in the applied mathematics literature. Earlier work by Kuramoto, Strogatz, and others has led to a deep understanding of the emergent behavior of systems of such oscillators using traditional dynamical systems methods. In this project we outline the application of techniques from topological data analysis to understanding the dynamics of systems of coupled oscillators. This includes the examination of partitions, partial synchronization, and attractors. By looking for clustering in a data space consisting of the phase change of oscillators over a …

Hamiltonian Formulation For Wave-Current Interactions In Stratified Rotational Flows, Adrian Constantin, Rossen Ivanov, Calin-Iulian Martin

Articles

We show that the Hamiltonian framework permits an elegant formulation of the nonlinear governing equations for the coupling between internal and surface waves in stratified water flows with piecewise constant vorticity.

The Dynamics Of Flat Surface Internal Geophysical Waves With Currents, Alan Compelli, Rossen Ivanov

Articles

A two-dimensional water wave system is examined consisting of two discrete incompressible fluid domains separated by a free common interface. In a geophysical context this is a model of an internal wave, formed at a pycnocline or thermocline in the ocean. The system is considered as being bounded at the bottom and top by a flatbed and wave-free surface respectively. A current profile with depth-dependent currents in each domain is considered. The Hamiltonian of the system is determined and expressed in terms of canonical wave-related variables. Limiting behavior is examined and compared to that of other known models. The linearised …

A Study Of The Effect Of Harvesting On A Discrete System With Two Competing Species, Rebecca G. Clark

Theses and Dissertations

This is a study of the effect of harvesting on a system with two competing species. The system is a Ricker-type model that extends the work done by Luis, Elaydi, and Oliveira to include the effect of harvesting on the system. We look at the uniform bound of the system as well as the isoclines and perform a stability analysis of the equilibrium points. We also look at the effects of harvesting on the stability of the system by looking at the bifurcation of the system with respect to harvesting.

Simulating And Animating The Spatial Dynamics Of Interacting Species Living On A Torus, Boyan Kostadinov

Publications and Research

The goal of this talk is to present a student research project in computational population biology, which aims at creating a computer simulation and animation of the spatial dynamics of interactions between two kinds of species living on a torus-shaped universe. The habitat for spatial interactions is modeled by a 2D lattice with periodic boundary conditions, which wrap the rectangular grid into a torus. The spatial interactions between the species have two components: 1. Population dynamics modeled by the classical Nicholson-Bailey two-parameter family of models for coupled interactions between species, extended to incorporate space and 2. Two-parameter migration dynamics, modeled …