Vertical Y-axis Research Articles

The role of the Silberstein/Thomas/Wigner-rotation in the rod and slit paradox

The rod and slit paradox, as first proposed by Shaw, is revisited. In this paradox, a rod of rest length l0 moves parallel to the horizontal x-axis. Simultaneously, a thin sheet parallel to the horizontal xz-plane with a rod-shaped slit of rest length d<l0 moves along the vertical y-axis. The rod passes through the slit due to relativistic effects. Earlier papers do not link the thought experiment to the Silberstein/Thomas/Wigner-rotation (STW-rotation), which is essential to its outcome. In this paper, the role of the STW-rotation is discussed, and additional clarifying figures are provided. Some misleading aspects of earlier treatments are pointed out and corrected.

Particle shape matters: Flow and heat transfer characteristics of nonspherical particles

The primary shape considered for the present numerical study is the spherical segment dissected from the spherical particle at an angle α from its vertical y-axis. The shape effect of the spherical segments on momentum and heat transfer characteristics are presented in terms of shape factor (ψ) spanning over the range of 0.424 (α = 300) ≤ ψ ≤ 0.996 (α = 1500) for Reynolds number, 1 ≤ Re ≤ 150. The results of drag, heat transfer coefficient, and streamlines have been compared with the closest shapes of spherical segment, i.e., cone (0.324 ≤ ψ ≤ 0.658) and short cylinder (0.541 ≤ ψ ≤ 0.872) to identify the role of the particle shape. The range of shapes has been correlated for drag and average Nusselt number as a function of Re, shape factor, ψ and particle longest chord length or base diameter to height ratio (1 ≤ dc/h ≤ 7.463).

An Ultra-Wideband Linear-to-Circular Polarization Converter Based on a Circular, Pie-Shaped Reflective Metasurface

In this paper, we present an ultrawideband reflective metasurface with the properties of an LTC-PC, which is an orthotropic composition with two mutually orthogonal symmetric axes, v and u, and 45° rotation about the vertical y-axis. Based on the metasurface unit cell, it seems like a circular pie embedded with a rectangular patch. The converter can convert LP electromagnetic (EM) waves to CP waves over the bands from 20.18 GHz to 33.93 GHz, with a 3-dB AR bandwidth of up to 50.8% and a circular polarization wave that is RHCP (right hand CP). Moreover, the linear-to-circular PCR exceeds 98% in the frequency bands of 20–34 GHz. A comprehensive theoretical investigation was conducted to determine the fundamental cause of the LTC polarization conversion. The ∆φuv between two reflection coefficients at v- and u-polarized incidences is ±90°, which fully anticipates the axial ratio of the reflected wave. Any reflective metasurface can be used as an efficient LTC-PC if the ∆φuv is close to ±90°.

New evaluation index for the retainability of a swimmer's horizontal posture.

This study aims to investigate the effect of changes in buoyancy when a swimmer respires in a horizontal posture. We attempted to evaluate the levelness of swimmers’ streamline posture by simultaneously measuring the lung capacity and buoyancy under water. The buoyancy was measured based on the changes in the vertical loads of the upper and lower limbs on the subjects’ streamline posture under water. The horizontal x-axis as lung ventilation and the vertical y-axis as buoyancy forms a linear equation y = ax + b. The relation between hand (upper-limb) buoyancy and lung ventilation is defined as y = a1x + b1 and that between foot (lower-limb) buoyancy and lung ventilation as y = a2x + b2. Horizontal levelness was calculated as a ratio by dividing a2 by a1 using the inclination (a) values from these formulas for an underwater streamline posture. We defined this ratio as the breathing–balance (BB) ratio. Although the performance levels in the present study did not show any difference in the absolute quantity of air that humans can inhale in a streamline posture, the BB ratio was higher in a statistically significant manner in junior swimmers competing at international levels compared with the other groups of subjects (P < 0.001). This statistical difference in horizontal levelness, despite the absence of a noticeable difference in the absolute quantity of inhaled air, may be attributable to the way in which each person inhales and exhales air. Top-level junior swimmers that exhibited a high BB ratio might have inhaled in a way that would counteract the sinking of the lower limbs, for example, through abdominal respiration. When exhaling, on the other hand, they might have let out air gradually to mitigate the acceleration force involved in submerging the lower limbs.

The Sakai spinner: A paperclip top

A challenge: Can you create a stable top from a single paper clip? Several interesting solutions to this problem were provided by Takao Sakai1 from Japan, the requirement of each being that the center of gravity be located on the vertical y-axis at the center of the top. In the simplest configuration, we see that there exists a single angle θ between the spokes for which this requirement is met (Figs. 1 and 2). While a rigorous calculation of this angle is a nice task for first-year university students, one simple approximation allows for a more high school-ready analysis.2 Even a qualitative study without any math makes for interesting and fun science.

Supply, Demand, and Equilibrium: The Algebra

This technical note refreshes the algebraic representation of linear demand and supply, how to account for shifting curves, and how to include taxes. This is part of the refresher course in Economics at Darden. Excerpt UVA-G-0592 Supply, Demand, and Equilibrium: The Algebra Understanding supply and demand is invaluable for any structured analysis of the real markets where firms compete. So far, to develop intuition we have drawn these markets. We approximated supply and demand with straight lines. In this note, we calculate the exact price and quantity at which goods are bought and sold. To do so, we use algebra and represent supply and demand with an equation instead of a graph. Equation of a Straight Line Figure 1. Straight line. Figure 1 plots a line. It touches both the vertical Y-axis and the horizontal X-axis. With the help of the X-axis and the Y-axis, we can define any point on the graph. A double (X,Y) contains the coordinates of any point. The variables X and Y tell us how far a point lies from the origin, which is the point (0.0) where the X-axis and Y-axis meet. As we see, our line cuts the X-axis and Y-axis respectively at the horizontal and vertical intercept at the points (4,0) and (0.2). . . .

Major Theories of Personality Disorder, Second Editionedited by Mark F. Lenzenweger and John F. Clarkin. New York, Guilford Press, 2004, 464 pp., $55.00.

Major Theories of Personality Disorder, Second Editionedited by Mark F. Lenzenweger and John F. Clarkin. New York, Guilford Press, 2004, 464 pp., $55.00.