Table Of ContentONE HUNDRED PHYSICS
VISUALIZATIONS USING MATLAB
8853_9789814518437_tp.indd 1 12/11/13 2:41 PM
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
ONE HUNDRED PHYSICS
VISUALIZATIONS USING MATLAB
Dan Green
Fermi National Accelerator Laboratory, USA
World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI
8853_9789814518437_tp.indd 2 12/11/13 2:41 PM
Published by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
ONE HUNDRED PHYSICS VISUALIZATIONS USING MATLAB
(With DVD-ROM)
Copyright © 2014 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance
Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy
is not required from the publisher.
ISBN 978-981-4518-43-7
ISBN 978-981-4518-44-4 (pbk)
Printed in Singapore by Mainland Press.
November 13, 2013 14:26 9in x 6in One Hundred Physics Visualizations Using MATLAB b1610-fm
“The soul should always stand ajar, ready to welcome the ecstatic
experience.”
— Emily Dickinson
“The effort to understand the Universe is one of the very few things
that lifts human life above the level of farce, and gives it some of the
grace of tragedy.”
— Steven Weinberg
v
November 13, 2013 14:26 9in x 6in One Hundred Physics Visualizations Using MATLAB b1610-fm
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
November 13, 2013 14:26 9in x 6in One Hundred Physics Visualizations Using MATLAB b1610-fm
vii
Preface
“Computers are useless. They can only give you answers.”
— Pablo Picasso
“The purposeof computingis insight, not numbers.”
— Richard Hamming
There are only a very few solvable problems in physics. They are
extremely useful because the equations for the solutions can be plot-
ted and the parameters defining the solutions can be varied in order
to explore the dependence of the solutions on the variables of the
problem. In that way the student can build up an intuition about
the Kepler problem, for example.
However, this can only be done in a few cases and even then the
effortneededistedious.Fortheothers,numericalmethodsareneeded
and thecomputation becomes somewhat cumbersome.As a result,it
is more difficultto vary the inputsto the problem numerically rather
than symbolically and develop an intuition about the dependence
of the solution on those parameters. In particular time development
is often obscure and “movies” can be a welcome tool in improving
physical intuition.
Nevertheless, the advent of powerful personal computing has
considerably reduced the difficulties. Indeed, the aim of this book
is to use the ensemble of symbolic and numeric tools available in
the MATLAB suite of programs to illustrate representative numer-
ical solutions to more than one hundred problems spanning several
November 13, 2013 14:26 9in x 6in One Hundred Physics Visualizations Using MATLAB b1610-fm
viii OneHundredPhysicsVisualizationsUsingMATLAB
physics topics. The student typically works through the demonstra-
tion and alters the inputs through a menu driven script. In that way
the user driven menu allows for parametric variation.
MATLAB is a good vehicle for the computational tasks. It has
a compiler, editor and debugger which are very useful and user
friendly.TheHELPutility isveryextensive. TheMATLABlanguage
issimilartoamodernC++languageanditisvectorial/matrix which
makes codingsimplerthanolderlanguages suchasFORTRAN.Data
is easily imported and exported in a variety of formats.
MATLAB contains many special functions. Matrices and linear
algebra are covered well. Curve fitting, polynomials and fast Fourier
transforms are supplied. Numerical integration packages are avail-
able.Differential equations,symbolic,ordinaryandpartial,aswellas
numerical solutions are available for both initial value and boundary
value versions.
As an additional package, MATLAB has symbolic mathematics.
Withinthatpackage,calculus,linearalgebra,algebraicequationsand
differential equations are covered. It is easy to combine a symbolic
treatmentofaproblemwithanumericaldisplayofthesolutionwhen
that is desirable. In this way converting from symbols to numbers is
easily achieved.
Finally, and very importantly, MATLAB has an extensive suite
of display packages. One can make bar, pie, histogram and simple
data plots. There are several contour and surface plots which are
possible. The time evolution of solutions can be made into “movies”
that illustrate the speed of a process. These extensive visualization
tools are crucial in that the student can plot, vary and then re-plot.
There are two- and three-dimensional plots of all types available.
Complex as well as real data can be shown.
The aim of using these tools is to create intuition, not to solve a
specificproblem or tocomplete aspecificnumbercrunchingexercise.
Indeed,theaimofthetextisnottoteach physicsbuttogivetheuser
a sense of how the solutions of a given physics problem depend on
theparametersofthatproblemandtoshowtheconnectionsbetween,
say, wave optics and quantum mechanics.
November 13, 2013 14:26 9in x 6in One Hundred Physics Visualizations Using MATLAB b1610-fm
Preface ix
Thescriptforthesedemonstrationsismadeavailable. Usingthat
material the student can write his/her own additions and explo-
rations with the supplied scripts as jumping off points. In this way,
a path is available to extend well beyond the specific demonstrations
enclosed in the book itself, making the search for further possible
insights open ended.
