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Constant-Stiffness Structures and Crash Plots
Published in Donald E. Struble, John D. Struble, Automotive Accident Reconstruction, 2020
Donald E. Struble, John D. Struble
If the left-hand side of the equation is plotted on the ordinate (vertical y axis) and (βc¯) is plotted on the abscissa (horizontal x axis), we recognize the above as the equation of a straight line: y = mx + b, where the slope of the line is m, and the intercept is b. A graph of this equation will have the following properties: Ordinate=2β(CE)L=ECF
Methods for the Reduction of Dimensionality
Published in Shayne C. Gad, Carrol S. Weil, Statistics and Experimental Design for Toxicologists, 1988
Construction of a rectangular graph of any form starts with the selection of the appropriate form of graph followed by the laying out of the coordinates (or axes). Even graphs which are going to encompass multivariate data (that is, more than two variables) generally have as their starting point two major coordinates. The vertical axis, or ordinate (also called the Y axis), is used to present a dependent variable. The horizontal axis (or abscissa, also called the X axis) is used to present an independent variable. Each of these axes is scaled in the units of measure which will most clearly present the trends of interest in the data. The range covered by the scale of each axis is selected to cover the entire region for which data are presented. The actual demarking of the measurement scale along an axis should allow for easy and accurate assessment of the coordinates of any data point, yet should not be cluttered.
Upward Flame Spread over Two Parallel Paper Sheets under Reduced Ambient Pressure and Elevated Oxygen Concentration
Published in Combustion Science and Technology, 2022
Wenlong Wang, Luyao Zhao, Jun Fang, Yongming Zhang
Flame spread is determined by the complicated heat and mass feedback between the gas-phase combustion and solid-phase pyrolysis. The heat generated from the gas-phase combustion is transferred into the virgin sample, and in reverse, fuel vapor is released from the pyrolysis region to support a steady flame. Thus, a closed-loop interaction forms and the flame spreads to the unburned region over the sample surface. For the flame far from the extinction regime, the flame spread is primarily dominated by the thermal effect, due to the much lower chemical reaction time compared with the diffusion time, namely the infinite Da number. Therefore, thermal analysis is the key to revealing the underlying mechanisms of the flame spread. As presented in Figure 3, a Cartesian coordinate system was established with the normal orientation of the sample surface as the abscissa x, the opposite orientation of the gravity as the ordinate y and the pyrolysis front as the origin. Itoh and Kurosaki (1985) established an analytical model for the downward flame spread over several parallel sheets, which was validated by experimental results. Similarly, a theoretical formula for the upward flame spread over two parallel samples is proposed as follows,
Numerical Inspection of Heterogeneity in Materials using 2D Heat-Conduction and Hybrid GA-tuned Neural-Network
Published in Applied Artificial Intelligence, 2020
Suman Ghosh, Ankit Kumar Dubey, Arup Kumar Das
Figure 1 shows the test problem consisting of a square steel slab with a copper intrusion of circular shape. Each of the sides of the square slab (represented by a) is considered as 1.0 m. The radius of the circular intrusion is denoted by r. The intrusion can take any position within the square b (each of the sides of the square b is 0.96 m) on the slab. Positions of the intrusion within the slab are measured with respect to a 2D Cartesian coordinate system with its origin at the center of the slab, whereas positive abscissa and ordinate are chosen along horizontal-right and vertical-top directions, respectively. Constant heat flux is maintained at the bottom wall of the slab whereas constant temperature is specified at all the remaining edges.
Establishing the link between the graph of a parametric curve and the derivatives of its component functions
Published in International Journal of Mathematical Education in Science and Technology, 2020
After all groups had filled in the table, they were asked to complete the blank spaces in the conclusion statements given below, drawing on their experiences and observations so far to form their responses. The italicized words below were the correct responses that the students were expected to provide. If the sign of the function x′(t) is positive, then the abscissa of the point is increasing. Hence, point A moves horizontally to the right.If the sign of the function x′(t) is negative, then the abscissa of the point is decreasing. Hence, point A moves horizontally to the left.If the sign of the function y′(t) is positive, then the ordinate of the point is increasing. Hence, point A moves upward vertically.If the sign of the function y′(t) is negative, then the ordinate of the point is decreasing. Hence, point A moves downwards vertically.