More Like this

1. Absolute continuity, Lyapunov exponents, and rigidity II: systems with compact center leaves

   https://doi.org/10.1017/etds.2021.42  

   AVILA, A.; VIANA, MARCELO; WILKINSON, A. (February 2022, Ergodic Theory and Dynamical Systems)

   Abstract We explore new connections between the dynamics of conservative partially hyperbolic systems and the geometric measure-theoretic properties of their invariant foliations. Our methods are applied to two main classes of volume-preserving diffeomorphisms: fibered partially hyperbolic diffeomorphisms and center-fixing partially hyperbolic systems. When the center is one-dimensional, assuming the diffeomorphism is accessible, we prove that the disintegration of the volume measure along the center foliation is either atomic or Lebesgue. Moreover, the latter case is rigid in dimension three (this does not require accessibility): the center foliation is actually smooth and the diffeomorphism is smoothly conjugate to an explicit rigid model. A partial extension to fibered partially hyperbolic systems with compact fibers of any dimension is also obtained. A common feature of these classes of diffeomorphisms is that the center leaves either are compact or can be made compact by taking an appropriate dynamically defined quotient. For volume-preserving partially hyperbolic diffeomorphisms whose center foliation is absolutely continuous, if the generic center leaf is a circle, then every center leaf is compact. 

   more » « less
2. One Solution to Addressing Assessment Logistical Problems: An Experience Setting Up and Operating an In-person Testing Center

   https://doi.org/10.1145/3626252.3630902  

   Downey, Kelly; Miller, Kris; Silva, Mariana; Zilles, Craig (March 2024, Proceedings of the 55th ACM Technical Symposium on Computer Science Education)

   To address the challenges of running exams in large enrollment CS courses, we set up and operated an in-person testing center at a minority serving institution. We have run the testing center for two quarters, proctoring over 6,000 exams for eight CS courses with approximately 1,800 students. In this experience report, we discuss the motivation for the testing center, its set-up and operation, and the lessons that we have learned from our first two quarters of operation. In addition, we present student and instructor feedback regarding use of the testing center, future steps, and improvements. By sharing, we hope that other schools can learn from our experience and improve upon our methods to help establish best practices for testing center configuration and operation. 

   more » « less
3. Faithful guiding-center orbits in an axisymmetric magnetic field

   https://doi.org/10.1063/5.0145035  

   Brizard, Alain J.; Hodgeman, Brook C. (April 2023, Physics of Plasmas)

   The problem of the charged-particle motion in an axisymmetric magnetic geometry is used to assess the validity of higher-order Hamiltonian guiding-center theory, which includes higher-order corrections associated with gyrogauge invariance as well as guiding-center polarization induced by magnetic-field non-uniformity. Two axisymmetric magnetic geometries are considered: a magnetic mirror geometry and a simple tokamak geometry. When a magnetically confined charged-particle orbit is regular (i.e., its guiding-center magnetic moment is adiabatically invariant), the guiding-center approximation, which conserves both energy and azimuthal canonical angular momentum, is shown to be faithful to the particle orbit when higher-order corrections are taken into account. 

   more » « less
4. Automatic Identification of Center Pivot Irrigation Systems from Landsat Images Using Convolutional Neural Networks

   https://doi.org/10.3390/agriculture8100147  

   Zhang, Chenxiao; Yue, Peng; Di, Liping; Wu, Zhaoyan (October 2018, Agriculture)

   Being hailed as the greatest mechanical innovation in agriculture since the replacement of draft animals by the tractor, center pivot irrigation systems irrigate crops with a significant reduction in both labor and water needs compared to traditional irrigation methods, such as flood irrigation. In the last few decades, the deployment of center pivot irrigation systems has increased dramatically throughout the United States. Monitoring the installment and operation of the center pivot systems can help: (i) Water resource management agencies to objectively assess water consumption and properly allocate water resources, (ii) Agro-businesses to locate potential customers, and (iii) Researchers to investigate land use change. However, few studies have been carried out on the automatic identification and location of center pivot irrigation systems from satellite images. Growing rapidly in recent years, machine learning techniques have been widely applied on image recognition, and they provide a possible solution for identification of center pivot systems. In this study, a Convolutional Neural Networks (CNNs) approach was proposed for identification of center pivot irrigation systems. CNNs with different structures were constructed and compared for the task. A sampling approach was presented for training data augmentation. The CNN with the best performance and less training time was used in the testing area. A variance-based approach was proposed to further locate the center of each center pivot system. The experiment was applied to a 30-m resolution Landsat image, covering an area of 20,000 km2 in North Colorado. A precision of 95.85% and a recall of 93.33% of the identification results indicated that the proposed approach performed well in the center pivot irrigation systems identification task. 

   more » « less
5. Unification of mathematical descriptions of compliant behavior centers with physical realizations of those behaviors

   https://doi.org/10.1017/S0263574725000190  

   Huang, Shuguang; Schimmels, Joseph M (March 2025, Robotica)

   Abstract A more intuitive appreciation of spatial compliant behavior can be obtained through analysis and description of the behavior in terms of itscenters, specifically the center of stiffness, the center of compliance, and the center of elasticity. This paper investigates the properties of each of these centers. Necessary and sufficient conditions for the coincidence of these centers are identified. A physical appreciation of those compliant behaviors that have coincident centers is obtained in terms of restrictions on the geometry of topologically simple mechanisms that realize those behaviors. The results can be used in the design of compliant mechanisms for robotic manipulation, especially when the compliance is characterized by the location of its center. 

   more » « less