Introduction to Computation in Physical Sciences. Interactive Computing and Visualization with Python

264 Pages·2023·3.896 MB·English

by  Jay Wang, Adam Wang

Synthesis Lectures on
Computation and Analytics
Jay Wang
Adam Wang
Introduction to
Computation in
Physical Sciences
Interactive Computing and
Visualization with PythonTM
Synthesis Lectures on Computation and
Analytics
This series focuses on advancing education and research at the interface of qualitative
analysisandquantitativesciences.Currentchallengesandnewopportunitiesareexplored
with an emphasis on the integration and application of mathematics and engineering to
createcomputationalmodelsforunderstandingandsolvingreal-worldcomplexproblems.
Appliedmathematical,statistical,andcomputationaltechniquesareutilizedtounderstand
the actions and interactions of computational and analytical sciences. Various perspec-
tives on research problems in data science, engineering, information science, operations
research, and computational science, engineering, and mathematics are presented. The
techniques and perspectives are designed for all those who need to improve or expand
their use of analytics across a variety of disciplines and applications.
Jay Wang · Adam Wang
Introduction
to Computation in Physical
Sciences
Interactive Computing and Visualization
with Python™
JayWang AdamWang
Dartmouth,MA,USA Nashville,TN,USA
ISSN2766-8975 ISSN2766-8967 (electronic)
SynthesisLecturesonComputationandAnalytics
ISBN978-3-031-17645-6 ISBN978-3-031-17646-3 (eBook)
https://doi.org/10.1007/978-3-031-17646-3
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2023
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Preface
This book introduces computation and modeling of problems in physical sciences with
emphasisoninteractivejust-in-timecomputing,dataanalysis,andeffectivevisualization.
Computational modeling has long been an established practice in science and engi-
neering and is regarded as the third pillar alongside experimentation and theory. It is
also becoming increasingly inseparable and integral in a wide range of industry sectors.
In education, computational thinking—broadly construed as the mindset and skillset of
problem-solvingwithcomputationalmethodologiesincludingmodeling,abstraction,sym-
bolic and algorithmic representations, and numeric processing—is being embraced as a
standard component, and even a requirement, at all levels.1
Experience and evidence from physics educators and physics education research have
shown that computation and integration thereof into physics has many positive ben-
efits including increasing student engagement, active learning, and improved learning
outcomes and understanding. However, there are also well-documented challenges to
effective implementation in terms of pedagogical consideration and practical constraints.
We developed this book with the goal of lowering such barriers. In terms of coverage,
wehavecarefullyselectedasetoftopics,drawnfromexperienceandbestpracticeinthe
physics education community, that is pedagogically significant and also reflective of the
current trend in academia and in industry. In terms of access to computing resources, we
have adopted a COD (computing on demand) and JIT-C (just-in-time computing) model
wherenearlyallprogramsarecloud-based,requiringnosoftwareinstallationofanykind
for easily accessing or running them in a web browser on any machine, especially on
mobile devices. Running a simulation, or sharing one, is just a click away. We designed
most programs as minimally working programs (MWP) as part of intentional scaffolding
to help beginners develop computational problem-solving and thinking skills. MWPs are
effective pedagogically to teaching and learning computational modeling. They may be
used as basis templates to be modified, extended, or combined for further exploration in
projects and exercises.
1SeeJ.M.Wing,Computationalthinking, CommunicationsoftheACM,49,33–35(2006).
vii
viii Preface
The book is broadly organized into two parts. Part one consists of Chaps. 1 to 4 and
describes basic programming and tools, including programming environments, Python
tutorial, interactive computing, and elementary algorithms. Part two includes Chaps. 5 to
9andfocusesonapplicationofcomputationalmodelingofselectproblemsinfundamental
areasofphysicalanddatascienceincludingclassicalmechanics,modernphysics,thermal
andcomplexsystems,aswellasfromcontemporarytopicsincludingquantumcomputing,
neural networks and machine learning, and global warming and energy balance.
The materials are arranged as follows. In Chap. 1, we introduce programming and
development environments including Jupyter notebook—the recommended environment,
its cloud-based counterpart Binder, a close variant Colab, the native Python IDLE—inte-
grated development and learning environment, Spyder, and sharing-friendly GlowScript
and Trinket. We also describe the online program repository, how to access and run
programs in the cloud, and optional software installation to run programs locally. An
interactive Python tutorial is given in Chap. 2 on basic programming elements, including
the important aspect of error handling, debugging, and troubleshooting. Next, Chap. 3
focuses on interactive computing and visualization methods with Python widgets and
VPython animation libraries. Key scientific computing libraries are also described with
interactive examples including symbolic and numeric computation with Sympy, Numpy,
Scipy,aswellasNumbaforoptimization.Roundingoutpartone,weintroduceinChap.4
common elementary algorithms such as finite difference, numerical integration including
that of differential equations, finding of roots and minima or maxima, and curve fitting.
We begin part two with Chap. 5 on force and motion where we pedagogically intro-
duce kinematic concepts, and discuss projectile motion with and without air resistance,
harmonic oscillation, planetary motion, and motion in electromagnetic fields. In Chap. 6
we discuss classical coupled oscillations and wave propagation and introduce linear sys-
tems and fundamental modes, leading up to simulations of matter waves in modern
and quantum physics next in Chap. 7 where we consider relativity of space and time,
diffractionanddouble-slitinterference,formationofdiscretequantumstatesanditsvisu-
alization. We also introduce quantum information processing and quantum computing
withaninteractivequantumsimulatorandastep-by-stepwalkthroughofanontrivialreal-
world example: quantum search—the Grover algorithm. We consider random processes
and thermal physics in Chap. 8 such as nuclear decay, Brownian motion, Monte Carlo
simulations of thermal energy distribution and spin systems. We close the chapter with a
discussion of greenhouse effect, energy balance, and global warming. Lastly, we discuss
complex systems in Chap. 9 including cellular automata, traffic modeling, and nonlinear
dynamics and chaos. We conclude with an introduction to neutral network and machine
learning, and describe a worked example with details in the training and prediction of
game of life.
Intermsofbackgroundandpreparation,readerswithoutpriorprogrammingexperience
shouldstartwithpartone,focusingontheinteractivetutorial(Chap.2)andmovingonto
Pythonlibraries(Chap.3)andbasicalgorithms(Chap.4).Togetthemostoutofparttwo,
Preface ix
thereadershouldbecalculus-ready,havingstudiedprecalculusifnotcalculusalready.We
took care to make the book as self-contained as possible in terms of explaining physical
concepts necessary for a particular simulation. Even so, a basic understanding of physics
atintroductorylevelisveryhelpfulsuchasfamiliaritywithbasicconceptsofmotionand
Newton’s second law. We recommend covering Chap. 5, not necessarily in its entirety,
before Chap. 6. The other individual chapters are sufficiently decoupled from each other
that they may be used as separate modules and studied independently.
Integraltothemaincontent,thebookcontainsextensivesetsofcarefullydesignedand
testedexercisesattheendofeachchapter.MostexercisesarecloselyrelatedtotheMWPs
discussedinthemaintext,andcanbeusedforfurtherexplorationofagivenproblem,as
projectassignmentsorself-pacedstudy.Exercisesvaryindepthanddifficultylevels,and
the more challenging ones are marked by asterisks.
We thank Susanne Filler, Executive Editor at Springer Nature, and her team for the
assistance and timely guidance in this project. JW is grateful to his colleagues at UMass
DartmouthandinthePICUPcommunity(PartnershipforIntegrationofComputationinto
Undergraduate Physics, http://gopicup.org) for their support and inspiration; and to the
countless students who participated in research projects or through coursework and pro-
vided feedback in various ways: you have had more impact on this project than you ever
knew. Finally, we are fortunate to have the unwavering encouragement, understanding,
and patience of our loved ones: Huihua, Kathy, and Greg. Thank you.
Dartmouth, USA Jay Wang
Nashville, USA Adam Wang
Contents
1 ProgrammingEnvironments .......................................... 1
1.1 Jupyter Notebook Environments .................................. 1
1.1.1 Jupyter Notebook ........................................ 1
1.1.2 Colaboratory ............................................ 4
1.2 Integrated Development Environments ............................. 4
1.2.1 IDLE .................................................. 5
1.2.2 Spyder ................................................. 5
1.3 GlowScript and Trinket .......................................... 6
1.4 Program Access and Installation .................................. 8
2 PythonTutorial ...................................................... 11
2.1 Python as a Calculator ........................................... 11
2.1.1 Arithmetic Operators ..................................... 11
2.1.2 Types of Numbers ....................................... 12
2.2 Variables ....................................................... 13
2.2.1 Assigning Variables ...................................... 13
2.2.2 Variable Names ......................................... 14
2.3 Comments ..................................................... 14
2.4 Text Strings .................................................... 15
2.4.1 Syntax ................................................. 15
2.4.2 String Operations and Indexing ............................ 16
2.5 Functions ...................................................... 17
2.5.1 Defining Custom Functions ............................... 17
2.5.2 Variable Scope .......................................... 19
2.5.3 Default Argument Values and Keyword Arguments .......... 20
2.6 Conditional Statements .......................................... 20
2.6.1 Comparison and Logical Operators ........................ 21
2.6.2 if Statements ........................................... 21
xi