Simulating Gradient Contour and Mesh of a Scalar Field

Authors: Usman Ali Khan, Bismah Tariq, Khalida Raza, Saima Malik, Aoun Muhammad

Abstract:

This research paper is based upon the simulation of gradient of mathematical functions and scalar fields using MATLAB. Scalar fields, their gradient, contours and mesh/surfaces are simulated using different related MATLAB tools and commands for convenient presentation and understanding. Different mathematical functions and scalar fields are examined here by taking their gradient, visualizing results in 3D with different color shadings and using other necessary relevant commands. In this way the outputs of required functions help us to analyze and understand in a better way as compared to just theoretical study of gradient.

Keywords: MATLAB, Gradient, Contour, Scalar Field, Mesh

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1077611

References:

[1] Matthew N. O. Sadiku, Elements of Electromagnetics, 3rd ed. Section 3.5, Gradient of a Scalar. Oxford University Press, 2001, pp. 20-56.
[2] Wilfred Kaplan, Advanced Calculus, 4th ed. Section 3.3, The Gradient Field. Addison-Wesley, 1991, pp. 145-165
[3] Schey, H. M. Div, Grad, Curl, and All That: An Informal Text on Vector Calculus, 3rd ed. New York: W. W. Norton, 1997,pp 220-260.
[4] N. von Ellenrieder, C. Muravchik, E. Spinelli, A. Nehoraiy, J. Roitmanz, W. Silvaz and S. Kochenz, Performance of the Electroencephalography Inverse Problem using the Electric Potential Gradient Measurements. IEEE 2003.E. H. Miller, "A note on reflector arrays (Periodical styleÔÇöAccepted for publication)," IEEE Trans. Antennas Propagat., to be published.
[5] Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, 1953,ch-6,7
[6] David A. Rothstein, Craig E. Manning. Geothermal gradients in continental magmatic arcs: Constraints from the eastern Peninsular Ranges batholiths, Baja California, México, Geological society of America, USA 2003.
[7] Fundamental of Electromagnetics with MATLAB, by Karl.E.Lonngren and Sava V.Savov, Randay.J.Jost, 2nd ed. 2007.M. Young, The Techincal Writers Handbook. Mill Valley, CA: University Science, 1989.