An Eigenvalue Analysis of finite-difference approximations for hyperbolic IBVPs

The eigenvalue spectrum associated with a linear finite-difference approximation plays a crucial role in the stability analysis and in the actual computational performance of the discrete approximation. The eigenvalue spectrum associated with the Lax-Wendroff scheme applied to a model hyperbolic equation was investigated. For an initial-boundary-value problem (IBVP) on a finite domain, the eigenvalue or normal mode analysis is analytically intractable. A study of auxiliary problems (Dirichlet and quarter-plane) leads to asymptotic estimates of the eigenvalue spectrum and to an identification of individual modes as either benign or unstable. The asymptotic analysis establishes an intuitive as well as quantitative connection between the algebraic tests in the theory of Gustafsson, Kreiss, and Sundstrom and Lax-Richtmyer L(sub 2) stability on a finite domain

Alternating direction implicit methods for parabolic equations with a mixed derivative

Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A sub 0-stable linear two-step methods in conjunction with the method of approximation factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A sub 0-stable method. The parameter space for which the resulting ADI schemes are second order accurate and unconditionally stable is determined. Some numerical examples are given

Numerical calculations of two dimensional, unsteady transonic flows with circulation

The feasibility of obtaining two-dimensional, unsteady transonic aerodynamic data by numerically integrating the Euler equations is investigated. An explicit, third-order-accurate, noncentered, finite-difference scheme is used to compute unsteady flows about airfoils. Solutions for lifting and nonlifting airfoils are presented and compared with subsonic linear theory. The applicability and efficiency of the numerical indicial function method are outlined. Numerically computed subsonic and transonic oscillatory aerodynamic coefficients are presented and compared with those obtained from subsonic linear theory and transonic wind-tunnel data

The asymptotic spectra of banded Toeplitz and quasi-Toeplitz matrices

Toeplitz matrices occur in many mathematical, as well as, scientific and engineering investigations. This paper considers the spectra of banded Toeplitz and quasi-Toeplitz matrices with emphasis on non-normal matrices of arbitrarily large order and relatively small bandwidth. These are the type of matrices that appear in the investigation of stability and convergence of difference approximations to partial differential equations. Quasi-Toeplitz matrices are the result of non-Dirichlet boundary conditions for the difference approximations. The eigenvalue problem for a banded Toeplitz or quasi-Toeplitz matrix of large order is, in general, analytically intractable and (for non-normal matrices) numerically unreliable. An asymptotic (matrix order approaches infinity) approach partitions the eigenvalue analysis of a quasi-Toeplitz matrix into two parts, namely the analysis for the boundary condition independent spectrum and the analysis for the boundary condition dependent spectrum. The boundary condition independent spectrum is the same as the pure Toeplitz matrix spectrum. Algorithms for computing both parts of the spectrum are presented. Examples are used to demonstrate the utility of the algorithms, to present some interesting spectra, and to point out some of the numerical difficulties encountered when conventional matrix eigenvalue routines are employed for non-normal matrices of large order. The analysis for the Toeplitz spectrum also leads to a diagonal similarity transformation that improves conventional numerical eigenvalue computations. Finally, the algorithm for the asymptotic spectrum is extended to the Toeplitz generalized eigenvalue problem which occurs, for example, in the stability of Pade type difference approximations to differential equations

An extension of A-stability to alternating direction implicit methods

An alternating direction implicit (ADI) scheme was constructed by the method of approximate factorization. An A-stable linear multistep method (LMM) was used to integrate a model two-dimensional hyperbolic-parabolic partial differential equation. Sufficient conditions for the A-stability of the LMM were determined by applying the theory of positive real functions to reduce the stability analysis of the partial differential equations to a simple algebraic test. A linear test equation for partial differential equations is defined and then used to analyze the stability of approximate factorization schemes. An ADI method for the three-dimensional heat equation is also presented

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: Stationary modes

Spatially discrete difference approximations for hyperbolic initial-boundary-value problems (IBVPs) require numerical boundary conditions in addition to the analytical boundary conditions specified for the differential equations. Improper treatment of a numerical boundary condition can cause instability of the discrete IBVP even though the approximation is stable for the pure initial-value or Cauchy problem. In the discrete IBVP stability literature there exists a small class of discrete approximations called borderline cases. For nondissipative approximations, borderline cases are unstable according to the theory of the Gustafsson, Kreiss, and Sundstrom (GKS) but they may be Lax-Richtmyer stable or unstable in the L sub 2 norm on a finite domain. It is shown that borderline approximation can be characterized by the presence of a stationary mode for the finite-domain problem. A stationary mode has the property that it does not decay with time and a nontrivial stationary mode leads to algebraic growth of the solution norm with mesh refinement. An analytical condition is given which makes it easy to detect a stationary mode; several examples of numerical boundary conditions are investigated corresponding to borderline cases

Metal tube used as solar engine

Ends of metal tube are fastened to axles which are supported on bearings so tube can rotate about its long axis while subjected to invariant bending moment that stresses it along longitudinal axis of rotation. Heat absorbed leads to expansion of metal, which unbalances internal forces and generates rotational moment in tube

Solid medium thermal engine

A device is described which uses a single phase metallic working substance to convert thermal energy directly into mechanical energy. The device consists of a cylindrical metal tube which is free to rotate about its axis while being subjected to continuous bending moment stresses along the longitudinal axis of rotation. The stressing causes portions of the tube to be under compression while other parts are under tension which in turn causes the tube to rotate and provide mechanical energy

Do Different Learning Environments Influence Graduate Students’ Professional Communication?

Purpose: The purpose of this study was to investigate the impact of two educational environments (jigsaw learning activity and standardized patient encounters) on speech-language pathology students’ professional communication when assessing and treating a voice disorder case study. Jigsaw activities are cooperative learning experiences that provide students opportunities to learn from one another. Studies have shown that students have improvements in learning new material, self-confidence, and communication skills (Wong & Driscoll, 2008; Asif et al., 2021). A standardized patient encounter provides a real-life clinical experience for students. There has been a mixed response to students improving their communication skills through the use of standardized patients (Hill et al., 2010; Johnson & Kopp, 1996; Zraick, 2020). Both environments provided opportunities for students to practice and refine their professional communication behaviors. Our study examined whether one environment influences students’ professional communication more so than the other. Method: Thirty-five graduate students in Advanced Voice Disorders at West Virginia University participated in a jigsaw activity set up like medical rounds. The cohort was set up into two groups: experts and clinicians. On the first medical rounds day, groups of experts presented a voice disorder case to groups of clinicians. On the second medical rounds day, the students who were presenters on the first day became clinicians. Every student had the chance to diagnose four voice disorder cases. Later in the semester, students completed the same activity with a standardized patient in the WVU STEPS simulation lab. Results: Two related-samples Wilcoxon signed-rank tests were used to evaluate the median difference in student professional behaviors during the beginning and end of medical rounds (MR1 and MR4, respectively) and MR4 and a standardized patient encounter (SPE). Significance value was adjusted for multiple tests (p = .025). Students increased their median percentage of professional communication behaviors from MR1 (median = 75%) to MR4 (median = 88.89%; z = 3.686, p \u3c .0005). A significant increase in professional communication behaviors was also observed from MR4 to SPE (median = 93.67%; z = 3.233, p = .001). Conclusion: The current work contributes to the scholarship of teaching and learning (SoTL) literature regarding professional communication behaviors in graduate student learning in communication sciences and disorders (CSD). In the medical SoTL literature, the type of communication behaviors learned during jigsaw activities was unclear (Asif et al., 2021; Rathore et al., 2017; Sanaie et al., 2019; Wong & Driscoll, 2008) and not examined in CSD SoTL work. The results of this study suggest CSD graduate students learn professional communication behaviors relevant to clinical practice during jigsaw learning activities. Moreover, our study results suggest there is a benefit to placing students in higher fidelity learning activities to further enhance their professional communication skills (cf. Zraik et al., 2003)

Emotional Intelligence and Team Cohesiveness

Emotional Intelligence is generally defined as encompassing the awareness and understanding of emotions. Emotional Intelligence also incorporates the application of this understanding to decision making, regulation, and self-management. Many theorists have shown that Emotional Intelligence has a significant positive impact on various aspects of teamwork. Today, more companies and organizations use teamwork to solve problems and complete tasks, so exploring elements that enhance teamwork would be beneficial. This study was designed to support the notion that Emotional Intelligence is an integral part of teamwork. It was hypothesized that Emotional Intelligence has an impact on teamwork by making the team more cohesive. A Spearman’s rho score was calculated between the individual’s Total Emotional Quotient (EQ) score and his/her team rating. The analysis showed that there was a moderate positive correlation (r=.415) between an individual’s Total EQ score and his/her team cohesion rating. This result indicates that as a person’s Total EQ score increases, so does his/her team’s cohesion rating