Browsing by Subject "Mathematics"

Now showing 1 - 7 of 7
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    Chambers in the symplectic cone and stability of symplectomorphism group for ruled surface
    (arXiv, 2022-02-14) Buse, Olguta; Li, Jun; Mathematical Sciences, School of Science
    We continue our previous work to prove that for any non-minimal ruled surface $(M,\omega)$, the stability under symplectic deformations of $\pi_0, \pi_1$ of $Symp(M,\omega)$ is guided by embedded $J$-holomorphic curves. Further, we prove that for any fixed sizes blowups, when the area ratio $\mu$ between the section and fiber goes to infinity, there is a topological colimit of $Symp(M,\omega_{\mu}).$ Moreover, when the blowup sizes are all equal to half the area of the fiber class, we give a topological model of the colimit which induces non-trivial symplectic mapping classes in $Symp(M,\omega) \cap \rm Diff_0(M),$ where $\rm Diff_0(M)$ is the identity component of the diffeomorphism group. These mapping classes are not Dehn twists along Lagrangian spheres.
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    Family as Faculty as an Infrastructure to Engage Pre-Admission Teacher Candidates in Family-Driven STEM Learning
    (National Association for Family, School, and Community Engagement (NAFSCE), 2024-03) Santamaría Graff, Cristina; Price, Jeremy F.
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    Helping Students Explore the Cartesian Coordinate System
    (2017-07-01) Tillema, Erik; Gatza, Andrew
    This paper explores a problem-based approach to developing the Cartesian coordinate system as a set of whole number, integer, and rational number ordered pairs. We share our approach, discuss student work, and outline a sequence of problems and key conversations for classroom discussion that we have used with this approach.
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    Impact of Race on Mathematics Self-Efficacy
    (Office of the Vice Chancellor for Research, 2016-04-08) Membres, Brianna A.
    According to Bandura (1986), self-efficacy is defined as the belief one has in their ability to complete a task or reach a goal. Oftentimes, learner’s success is dependent on how learners view themselves because their beliefs affect their perceived ability. The purpose of this study is to explore the mathematics self-efficacy of Black high school females. Qualitative research methods are used to explore the primary research question, how do Black girls describe the impact of race on their mathematics self-efficacy? Preliminary findings suggest that although every interviewee feels that race does not correlate with ability, most of them work harder because of their race.
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    Mechanical and geometric considerations for the airgapless motor
    (2018-08) Wheeler, Nathan W.; Rovnyak, Steven
    The purpose of this thesis is to perform modeling from different perspectives for an airgapless motor. The airgapless motor is a proposed type of electric machine whose purpose is to replace hydraulic machines in low speed high torque applications. Because of the nature of the movement for this device, modeling of this device is atypical to the modeling done with other electric machines. This thesis will present the operating principle of the airgapless motor and take an analytical approach to modeling the torque and total energy in the device. In addition, this thesis will present the power electronics necessary to drive this device and offer recommendations to maximize the torque and minimize the torque ripple. MATLAB simulations are used to verify that the conclusion of this thesis are consistent with observations made by previous publications and prototypes.
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    Volumetric lattice Boltzmann method for wall stresses of image-based pulsatile flows
    (Springer Nature, 2022) Zhang, Xiaoyu; Gomez‑Paz, Joan; Chen, Xi; McDonough, J.M.; Islam, Md Mahfuzul; Andreopoulos, Yiannis; Zhu, Luoding; Yu, Huidan; Mechanical and Energy Engineering, School of Engineering and Technology
    Image-based computational fluid dynamics (CFD) has become a new capability for determining wall stresses of pulsatile flows. However, a computational platform that directly connects image information to pulsatile wall stresses is lacking. Prevailing methods rely on manual crafting of a hodgepodge of multidisciplinary software packages, which is usually laborious and error-prone. We present a new computational platform, to compute wall stresses in image-based pulsatile flows using the volumetric lattice Boltzmann method (VLBM). The novelty includes: (1) a unique image processing to extract flow domain and local wall normality, (2) a seamless connection between image extraction and VLBM, (3) an en-route calculation of strain-rate tensor, and (4) GPU acceleration (not included here). We first generalize the streaming operation in the VLBM and then conduct application studies to demonstrate its reliability and applicability. A benchmark study is for laminar and turbulent pulsatile flows in an image-based pipe (Reynolds number: 10 to 5000). The computed pulsatile velocity and shear stress are in good agreements with Womersley's analytical solutions for laminar pulsatile flows and concurrent laboratory measurements for turbulent pulsatile flows. An application study is to quantify the pulsatile hemodynamics in image-based human vertebral and carotid arteries including velocity vector, pressure, and wall-shear stress. The computed velocity vector fields are in reasonably well agreement with MRA (magnetic resonance angiography) measured ones. This computational platform is good for image-based CFD with medical applications and pore-scale porous media flows in various natural and engineering systems.