The catwalk task: Reflections and synthesis: Part 2

In this article we recount our experiences with a series of encounters with the catwalk task and reflect on the professional growth that these opportunities afforded. First, we individually reflect on our own mathematical work on the catwalk task. Second, we reflect on our experiences working with a group of community college students on the catwalk task and our interpretations of their mathematical thinking. In so doing we also detail a number of innovative and novel student-generated representations of the catwalk photos. Finally, we each individually reflect on the entire experience with the catwalk problem, as mathematics learners, as teachers, and as professionals.     

Updating beliefs about variables given new information on how those variables relate

Bayesian techniques specify how to update beliefs about a variable given information on that variable or related variables. In many cases, statistical analyses also provide information about the relationship between variables, but the Borel Paradox prohibits many natural ways of updating beliefs conditioned on information about a relationship. This paper presents a method by which beliefs can be updated without violating the Borel Paradox under certain circumstances. We apply our approach to relationships specified by a statistical model (i.e., regression), and relationships described by statistical simulation.     

Interactive decision software and computer graphics for architectural and space planning

We describe the development and successful implementation of a decision support system now being used by several leading firms in the architecture and space planning industries. The system, which we call SPDS (spatial programming design system) has the following characteristics: (i) user-friendly convenience features permitting architects and space planners to operate the system without being experienced programmers; (ii) interactive capabilities allowing the user to control and to manipulate relevant parameters, orchestrating conditions to which his or her intuition provides valuable input; (iii) informative and understandable graphics, providing visual displays of interconnections that the computer itself treats in a more abstract methematical form; (iv) convenient ways to change configurations, and to carry out ‘what if’ analyses calling on the system’s decision support capabilities; (v) a collection of new methods, invisible to the user, capable of generating good solutions to the mathematical programming problems that underlie each major design component. These new methods succeed in generating high quality solutions to a collection of complex discrete, highly nonlinear problems. While these problems could only be solved in hours, or not at all, with previously existing software, the new methods obtain answers in seconds to minutes on a minicomputer. Major users, including Dalton, Dalton, Newport, and Marshal Erdwin, report numerous advantages of the system over traditional architectural design methods.     

Comparative study of corona discharge simulation techniques for electrode configurations inducing non-uniform electric fields

Numerical modeling of corona discharges has followed the same set of procedures for many years. Corona discharges on large scales are modeled only for ion drift, neglecting ionization. Studies of the ionization zone are often conducted in uniform axisymmetric configurations. However, in configurations that induce non-uniform electric fields, a combination of the two procedures is necessary to accurately capture the discharge physics and ion distribution. The present study conducts numerical simulations of a wire-cylinder corona using both the models and demonstrates the necessity of including the ionization physics to obtain improved accuracy, particularly in the presence of non-uniform electric fields.     

Modeling and deformation analyzing of InSb focal plane arrays detector under thermal shock

A higher fracture probability appearing in indium antimonide (InSb) infrared focal plane arrays (IRFPAs) subjected to the thermal shock test, restricts its final yield. In light of the proposed equivalent method, where a 32 × 32 array is employed to replace the real 128 × 128 array, a three-dimensional modeling of InSb IRFPAs is developed to explore its deformation rules. To research the damage degree to the mechanical properties of InSb chip from the back surface thinning process, the elastic modulus of InSb chip along the normal direction is lessened. Simulation results show when the out-of-plane elastic modulus of InSb chip is set with 30% of its Young’s modulus, the simulated Z-components of strain distribution agrees well with the top surface deformation features in 128 × 128 InSb IRFPAs fracture photographs, especially with the crack origination sites, the crack distribution and the global square checkerboard buckling pattern. Thus the Z-components of strain are selected to explore the deformation rules in the layered structure of InSb IRFPAs. Analyzing results show the top surface deformation of InSb IRFPAs originates from the thermal mismatch between the silicon readout integrated circuits (ROIC) and the intermediate layer above, made up of the alternating indium bump array and the reticular underfill. After passing through both the intermediate layer and the InSb chip, the deformation amplitude is reduced firstly from 2.23 μm to 0.24 μm, finally to 0.09 μm. Finally, von Mises stress criterion is employed to explain the causes that cracks always appear in the InSb chip.     

Modeling and simulation of vibrational breathing-like modes in individual multiwalled carbon nanotubes

We study the collective vibrational breathing modes in the Raman spectrum of multiwalled carbon nanotubes (MCNTs). First, a bond polarization theory and the spectral moment's method (SMM) are used to calculate the non-resonant Raman frequencies of the breathing-like modes (BLMs) and the tangential-like ones (TLMs). Second, the Raman active modes of MCNTs are computed for different diameters and numbers of layers. The obtained low frequency modes in MCNTs can be identified to each single-walled carbon nanotubes. These modes that originate from the radial breathing ones of the individual walls are strongly coupled through the concentric tube–tube van der Waals interaction. The calculated BLMs in the low-frequency region are compared with the experimental Raman data obtained from other studies. Finally, special attention is given to the comparison with Raman data on MCNTs composed of six layers.     

Fleet algorithm for X-ray pulsar profile construction and TOA solution based on compressed sensing

X-ray pulse profile and time of arrival (TOA) are the two important physical quantities for pulsar navigation. With the standard and integrated X-ray pulse profiles modeled, X-ray pulse profile construction is studied and TOA is solved using compressed sensing (CS) technology. The observation matrix and waveform complete dictionary are mainly examined. A column vector-based matching pursuit algorithm is presented. The feasibility of obtaining X-ray pulse profile construction by compressed sensing technology is verified by numerical simulation. Compared with the X-ray pulse profile construction method based on epoch folding, the proposed method exhibits improved real-time performance, and its detection time for integrated X-ray pulse profile could be reduced by one order of magnitude. This proposed method can also solve for TOA solution and construct the X-ray pulse profile simultaneously, which is essential to improve pulsar navigation efficiency.     

Electromechanical response of (3–0, 3–1) particulate,fibrous, and porous piezoelectric composites with anisotropic constituents: A model based on the homogenization method

An analytical framework based on the homogenization method has been developed to predict the effective electromechanical properties of periodic, particulate and porous, piezoelectric composites with anisotropic constituents. Expressions are provided for the effective moduli tensors of n-phase composites based on the respective strain and electric field concentration tensors. By taking into account the shape and distribution of the inclusion and by invoking a simple numerical procedure, solutions for the electromechanical properties of a general anisotropic inclusion in an anisotropic matrix are obtained. While analytical forms are provided for predicting the electroelastic moduli of composites with spherical and cylindrical inclusions, numerical evaluation of integrals over the composite microstructure is required in order to obtain the corresponding expressions for a general ellipsoidal particle in a piezoelectric matrix. The electroelastic moduli of piezoelectric composites predicted by the analytical model developed in the present study demonstrate excellent agreement with results obtained from three-dimensional finite-element models for several piezoelectric systems that exhibit varying degrees of elastic anisotropy.     

开挖对岩体稳态扰动与滑移机制的模拟试验研究

矿山岩体工程开挖将引起周围岩体的移动和变形 ,如果某区域的岩体受到不同开挖工程的共同作用 ,那么岩体内应力状态将是各个影响因素综合作用的结果。本文将应用底面摩擦模型试验方法 ,主要研究和探讨在先期进行地下开采 ,然后进行露天开采条件下 ,边坡岩体的动态滑移机制及其变形规律 ,以便为此类矿山后续开采设计及边坡岩体动态分析提供科学依据。