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Ordinary Differential Equations and Applied Dynamics Commons™
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Articles 1 - 10 of 10
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Deterministic Global 3d Fractal Cloud Model For Synthetic Scene Generation, Aaron M. Schinder, Shannon R. Young, Bryan J. Steward, Michael L. Dexter, Andrew Kondrath, Stephen Hinton, Ricardo Davila
Deterministic Global 3d Fractal Cloud Model For Synthetic Scene Generation, Aaron M. Schinder, Shannon R. Young, Bryan J. Steward, Michael L. Dexter, Andrew Kondrath, Stephen Hinton, Ricardo Davila
Faculty Publications
This paper describes the creation of a fast, deterministic, 3D fractal cloud renderer for the AFIT Sensor and Scene Emulation Tool (ASSET). The renderer generates 3D clouds by ray marching through a volume and sampling the level-set of a fractal function. The fractal function is distorted by a displacement map, which is generated using horizontal wind data from a Global Forecast System (GFS) weather file. The vertical windspeed and relative humidity are used to mask the creation of clouds to match realistic large-scale weather patterns over the Earth. Small-scale detail is provided by the fractal functions which are tuned to …
Masked Instability: Within-Sector Financial Risk In The Presence Of Wealth Inequality, Youngna Choi
Masked Instability: Within-Sector Financial Risk In The Presence Of Wealth Inequality, Youngna Choi
Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works
We investigate masked financial instability caused by wealth inequality. When an economic sector is decomposed into two subsectors that possess a severe wealth inequality, the sector in entirety can look financially stable while the two subsectors possess extreme financially instabilities of opposite nature, one from excessive equity, the other from lack thereof. The unstable subsector can result in further financial distress and even trigger a financial crisis. The market instability indicator, an early warning system derived from dynamical systems applied to agent-based models, is used to analyze the subsectoral financial instabilities. Detailed mathematical analysis is provided to explain what financial …
Simplicity And Sustainability: Pointers From Ethics And Science, Mehrdad Massoudi, Ashwin Vaidya
Simplicity And Sustainability: Pointers From Ethics And Science, Mehrdad Massoudi, Ashwin Vaidya
Department of Mathematics Facuty Scholarship and Creative Works
In this paper, we explore the notion of simplicity. We use definitions of simplicity proposed by philosophers, scientists, and economists. In an age when the rapidly growing human population faces an equally rapidly declining energy/material resources, there is an urgent need to consider various notions of simplicity, collective and individual, which we believe to be a sensible path to restore our planet to a reasonable state of health. Following the logic of mathematicians and physicists, we suggest that simplicity can be related to sustainability. Our efforts must therefore not be spent so much in pursuit of growth but in achieving …
Modeling Mayfly Nymph Length Distribution And Population Dynamics Across A Gradient Of Stream Temperatures And Stream Types, Jeremy Anthony, Jennifer Baccam, Imanuel Bier, Emily Gregg, Leif Halverson, Ryan Mulcahy, Emmanuel Okanla, Samira A. Osman, Adam R. Pancoast, Kevin C. Schultz, Alex Sushko, Jennifer Vorarath, Yia Vue, Austin Wagner, Emily Gaenzle Schilling, John Zobitz
Modeling Mayfly Nymph Length Distribution And Population Dynamics Across A Gradient Of Stream Temperatures And Stream Types, Jeremy Anthony, Jennifer Baccam, Imanuel Bier, Emily Gregg, Leif Halverson, Ryan Mulcahy, Emmanuel Okanla, Samira A. Osman, Adam R. Pancoast, Kevin C. Schultz, Alex Sushko, Jennifer Vorarath, Yia Vue, Austin Wagner, Emily Gaenzle Schilling, John Zobitz
Faculty Authored Articles
We analyze a process-based temperature model for the length distribution and population over time of mayfly nymphs. Model parameters are estimated using a Markov Chain Monte Carlo parameter estimation method utilizing length distribution data at five different stream sites. Two different models (a standard exponential model and a modified Weibull model) of mayfly mortality are evaluated, where in both cases mayfly length growth is a function of stream temperature. Based on model-data comparisons to the modeled length distribution and the Bayesian Information Criterion, we found that approaches that length distribution data can reliably estimate 2–3 model parameters. Future model development …
Flow Anisotropy Due To Thread-Like Nanoparticle Agglomerations In Dilute Ferrofluids, Alexander Cali, Wah-Keat Lee, A. David Trubatch, Philip Yecko
Flow Anisotropy Due To Thread-Like Nanoparticle Agglomerations In Dilute Ferrofluids, Alexander Cali, Wah-Keat Lee, A. David Trubatch, Philip Yecko
Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works
Improved knowledge of the magnetic field dependent flow properties of nanoparticle-based magnetic fluids is critical to the design of biomedical applications, including drug delivery and cell sorting. To probe the rheology of ferrofluid on a sub-millimeter scale, we examine the paths of 550 μm diameter glass spheres falling due to gravity in dilute ferrofluid, imposing a uniform magnetic field at an angle with respect to the vertical. Visualization of the spheres’ trajectories is achieved using high resolution X-ray phase-contrast imaging, allowing measurement of a terminal velocity while simultaneously revealing the formation of an array of long thread-like accumulations of magnetic …
On The Three Dimensional Interaction Between Flexible Fibers And Fluid Flow, Bogdan Nita, Ryan Allaire
On The Three Dimensional Interaction Between Flexible Fibers And Fluid Flow, Bogdan Nita, Ryan Allaire
Department of Mathematics Facuty 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 Hybrid Agent-Based And Differential Equations Model For Simulating Antibiotic Resistance In A Hospital Ward, Lester Caudill, Barry Lawson
A Hybrid Agent-Based And Differential Equations Model For Simulating Antibiotic Resistance In A Hospital Ward, Lester Caudill, Barry Lawson
Department of Math & Statistics Faculty Publications
Serious infections due to antibiotic-resistant bacteria are pervasive, and of particular concern within hospital units due to frequent interaction among health-care workers and patients. Such nosocomial infections are difficult to eliminate because of inconsistent disinfection procedures and frequent interactions among infected persons, and because ill-chosen antibiotic treatment strategies can lead to a growth of resistant bacterial strains. Clinical studies to address these concerns have several issues, but chief among them are the effects on the patients involved. Realistic simulation models offer an attractive alternative. This paper presents a hybrid simulation model of antibiotic resistant infections in a hospital ward, combining …
The Weak Euler Scheme For Stochastic Delay Equations, Evelyn Buckwar, Rachel Kuske, Salah-Eldin A. Mohammed, Tony Shardlow
The Weak Euler Scheme For Stochastic Delay Equations, Evelyn Buckwar, Rachel Kuske, Salah-Eldin A. Mohammed, Tony Shardlow
Articles and Preprints
We study weak convergence of an Euler scheme for non-linear stochastic delay differential equations (SDDEs) driven by multidimensional Brownian motion. The Euler scheme has weak order of convergence 1, as in the case of stochastic ordinary differential equations (SODEs) (i.e., without delay). The result holds for SDDEs with multiple finite fixed delays in the drift and diffusion terms. Although the set-up is non-anticipating, our approach uses the Malliavin calculus and the anticipating stochastic analysis techniques of Nualart and Pardoux.
Discrete-Time Approximations Of Stochastic Delay Equations: The Milstein Scheme, Yaozhong Hu, Salah-Eldin A. Mohammed, Feng Yan
Discrete-Time Approximations Of Stochastic Delay Equations: The Milstein Scheme, Yaozhong Hu, Salah-Eldin A. Mohammed, Feng Yan
Articles and Preprints
In this paper, we develop a strong Milstein approximation scheme for solving stochastic delay differential equations (SDDE's). The scheme has convergence order 1. In order to establish the scheme, we prove an infinite-dimensional Itô formula for "tame" functions acting on the segment process of the solution of an SDDE. It is interesting to note that the presence of the memory in the SDDE requires the use of the Malliavin calculus and the anticipating stochastic analysis of Nualart and Pardoux. Given the non-anticipating nature of the SDDE, the use of anticipating calculus methods appears to be novel.
Lyapunov Exponents Of Linear Stochastic Functional-Differential Equations. Ii. Examples And Case Studies, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow
Lyapunov Exponents Of Linear Stochastic Functional-Differential Equations. Ii. Examples And Case Studies, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow
Articles and Preprints
We give several examples and examine case studies of linear stochastic functional differential equations. The examples fall into two broad classes: regular and singular, according to whether an underlying stochastic semi-flow exists or not. In the singular case, we obtain upper and lower bounds on the maximal exponential growth rate $\overlineλ1$(σ) of the trajectories expressed in terms of the noise variance σ . Roughly speaking we show that for small σ, $\overlineλ1$(σ) behaves like -σ2 /2, while for large σ, it grows like logσ. In the regular case, it is shown that a discrete Oseledec …