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Articles 1 - 4 of 4
Full-Text Articles in Non-linear Dynamics
An Exploration Of The Autorotating Pendulum Model, Vlad Nita
An Exploration Of The Autorotating Pendulum Model, Vlad Nita
Theses, Dissertations and Culminating Projects
Autorotation is the spontaneous rotation of an object, usually caused by an external fluid flow. The study of autorotation has many physical applications, such as in the design of wind/water turbines. In this thesis, we explore a nonlinear pendulum ordinary differential equation (ODE) which is used to model rotating plates in a fluid and has the capacity to reveal autorotation. In the context of an ODE, autorotation emerges as a bifurcation past oscillations, when the initial velocity of the system crosses a particular threshold. In his classic study from 1983, Lugt [14] utilizes this equation to capture experimental autorotation. Copeland’s …
Numerical Computations Of Vortex Formation Length In Flow Past An Elliptical Cylinder, Matthew Karlson, Bogdan Nita, Ashwin Vaidya
Numerical Computations Of Vortex Formation Length In Flow Past An Elliptical Cylinder, Matthew Karlson, Bogdan Nita, Ashwin Vaidya
Department of Mathematics Faculty Scholarship and Creative Works
We examine two dimensional properties of vortex shedding past elliptical cylinders through numerical simulations. Specifically, we investigate the vortex formation length in the Reynolds number regime 10 to 100 for elliptical bodies of aspect ratio in the range 0.4 to 1.4. Our computations reveal that in the steady flow regime, the change in the vortex length follows a linear profile with respect to the Reynolds number, while in the unsteady regime, the time averaged vortex length decreases in an exponential manner with increasing Reynolds number. The transition in profile is used to identify the critical Reynolds number which marks the …
Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya
Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya
Department of Mathematics Faculty Scholarship and Creative Works
Fluid mechanics occupies a privileged position in the sciences; it is taught in various science departments including physics, mathematics, environmental sciences and mechanical, chemical and civil engineering, with each highlighting a different aspect or interpretation of the foundation and applications of fluids. Doll’s fluid analogy [5] for this idea is especially relevant to this issue: “Emergence of creativity from complex flow of knowledge—example of Benard convection pattern as an analogy—dissipation or dispersal of knowledge (complex knowledge) results in emergent structures, i.e., creativity which in the context of education should be thought of as a unique way to arrange information so …
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 …