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January 8
lecturer: Jean Bellissard
1.
Continuous matter
A broad outline of the transition from molecules to
continuous matter, from point particles to fields. The
central theme of the course is the recasting of Newton's laws
for point particles into a systematic theory of continuous
matter.
ContinuousMatter
Chapter 1
Continuous matter
The appendices are meant to be recaps of what you mostly
already know. Quickly glance through them now, return to them
later in the course when needed.
mechanics
Appendix A
Newtonian Mechanics
A recap of mechanics.
space
Appendix B
Cartesian coordinates
A recap of Cartesian formalism: vectors, tensors.
fields
Appendix C
Field calculus
Spatial derivatives etc.
cylindrical
Appendix D
Cylindrical coordinates
Cylindrical coordinates are suited for problems that are
invariant under rotations around a fixed axis
(First part of what used to be "Curvilinear coordinates").
spherical
Appendix E
Spherical coordinates
Cylindrical coordinates are suited for problems that are
invariant under rotations around a fixed axis,
Spherical
coordinates are suited for problems that are invariant under
arbitrary rotations (Second part of what used to be "Curvilinear coordinates").
Info
Editions
This preface explains what is different in the Lautrup edition 2.
All problems are re-numbered, we will use only problems from edition 2.
*
click for fun
Check out these numerical simulations of continuum matter.
January 10
2.
Pressure
Pressure
Chapter 2
Pressure
Read sects. 2.1-2.3, "Effective potential" in sect. 2.4, skip "Polytropic water"
in sect. 2.5, the rest is optional.
#1
with solutions
- due Thu
Jan 17, in class
January 15
3.
Buoyancy
buoyancy
Chapter 3
Buoyancy and stability
shapes
Chapter 4
Hydrostatic shapes
Optional reading. The theory of tides had preoccupied
practically every English and French mathematician / physicist of note,
from Newton up to 20th century. Technically demanding, so
will cover in class only specific sections,
upon a specific and detailed request.
January 17
4.
Stress
stress
Chapter 6
Stress
Skip section 6.5
#2
problems
- due Thu
Jan 24, in class
[solutions to homework #2]
January 21
Martin Luther King Day
January 22
5.
Strain
Extending Newton's 2nd law to continua. 'Stress' generalizes force on a
point particle (via the concept of hydrostatic pressure) to
tensorial force density appropriate to any material. 'Strain'
generalizes the 'mass x acceleration' side of the law.
strain
Chapter 7
Strain
sections 7.1-7.4
elasticity
CalTech chapter 11
Elastostatics
Box 11.2 is a very nice explanation of (irreducible) tensors,
worth a read.
January 24
6.
Hooke's Law
elasticity
Chapter 8
Hooke's Law
sects. 8.1, 8.2 and 8.4
elasticity
CalTech chapter 11
Elastostatics
For more of a theoretical physics flavor, try the
very fine unpublished textbook by Roger Blandford and Kip Thorne.
It combines general relativist's sophistication with the practical
need for designing instruments like Ligo.
#3
problems
- due Thu
Jan 31, in class
[solutions to homework #3]
January 29
7.
Surface tension
This is delightful physics, intuitive, reckless, and almost right;
at the center of much current research.
Rain drops, soap bubbles, much biophysics on cellular level
is shaped by balancing bulk and surface energy.
Covered in class:
capillary length, pressure discontinuity,
Young-Laplace law.
surface
Chapter 5
Surface tension
January 31
8.
Surface tension
Young-Laplace law, Rayleigh-Plateau instability (skipped
Marangoni forces, drops, Tate's Law).
Read sects. 5.1, 5.3 - 5.6.
#4
problems
- due Thu
Feb 7, in class
[solutions to homework #4]
February 5
9.
Elastostatics
solids
Chapter 9
Basic elastostatics
Read sect. 8.4;
sects. 9.1 (skip Saint-Venant), 9.2 up to "Shear-free settling," and 9.3.
caltechPH136
Caltech PH136
Applications of classical physics
To whet your curiosity only. What every physics graduate student at
GaTech of the West Coast is supposed to know as a part of the
required curriculum.
February 7
10.
Bend and buckle
Cantilevers, bridges, yokes.
A prototypical bifurcation: slender rod buckles when
compression requires more force than bending.
rods
Chapter 10
Slender rods
Read sects. 10.1 and 10.2.
#5
problems
- due Thu
Feb 14, in class
[solutions to homework #5]
February 12
11.
Computational elastostatics
ces
Chapter 11
Computational elastostatics
Read this: Bend and twist: sect. 10.4, the Frenet-Serret basis.
Sects. 11.1 and 11.2.
February 14
12.
Computational elastostatics
grading
Homeworks, a take-home mid-term, and a final exam; the grades will be based on these (50%/20%/30%). Exams and homeworks include problems mandatory for graduate students, but optional ("bonus" = extra credit) for undergraduates. Homework assignments will be posted on the web every Thursday, and graded by students by next Tuesday.
#6
midterm, paper part
#6
midterm, computational part
Compute gravitational settling of a two dimensional block, Figure 11.1
(30 points).
You can compare with Lautrup or your friends' code, but write your own,
in the language of your choice. Comment the code
copiously, so that even your mother can read it
- due Thu
Feb 21, paper version (no code) in class, put code in Predrag's DropBox.
[solutions to the midterm exam]
February 19
13.
Fluids in motion
velocity
Chapter 12
Continuum dynamics
Read sects. 12.1-12.4, skip "Eulerian displacement field" in sect. 12.3,
read up to "Field equations of motion"
in sect. 12.4, sect. 14.5 "Big Bang," the rest is optional.
movies
NCFMF movies
Flow visualization
This collection of videos was created to explain fluid mechanics in an accessible way for undergraduate engineering and physics students.
Perhaps no other series of videos explains the basics of fluid mechanics better than this.
February 21
14.
Cosmology for dummies
Read sects. 12.5 "Big Bang," 12.6 "Newtonian cosmology."
You get a pretty sensible cosmology just out of Hubble's
empirical law + Newton 2nd law + Newtonian gravity.
#7
problems
- due Thu
Feb 28, in class
[solutions to homework #7: Chap 12]
February 26
15.
Euler equation, Bernoulli field
ideal
Chapter 13
Nearly ideal flow
Read sects. 13.1, 13.3. Note that this chapter is slightly rewritten
in the 2. edition.
February 28
16.
Vorticity
Read sects. 13.4-13.7, 13.9.
#8
problems
- due Thu
Mar 7, in class
[solutions to homework #8: Chap 13]
March 1
last day to drop the course
March 5
17.
Compressible flow
You need to know when the standard wave equation is valid, and
when the incompressibility assumption is valid (Mach number).
compressible
Chapter 14
Compressible flow
Read
14.1 (skip Jeans instability), 14.2 up to Bernoulli's theorems.
Note that the 2. edition Chapter 14 is a slightly rewritten
and truncated Chapter 17 of the 1. edition, whose sections 17.4
and 17.5 have been moved to the current Chapter 15.
March 7
18.
Viscosity
viscosity
Chapter 15
Viscosity
Read sects. 15.1 and 15.2.
Note that the 2. edition Chapter 15 s the
Chapter 14 in the 1.edition, unchanged, except for new sections 15.5, 15.6, formerly Sections 17.4 and 17.5.
#9
problems
- due Thu
Mar 14, in class
[solutions to homework #9: Chap 15]
March 12
19.
Navier-Stokes equations
Read sects. 15.3 and 15.4: Dynamics of incompressible flows
noisePC
ChaosBook.org Chapter 28
Noise
Optional reading sects. 28.1 to 28.3: From Brownian motion to Fokker-Planck equation
March 14
lecturer: David Hu
20.
Pipes and shooting straight
pipes
Chapter 16
Plates and pipes
Read sects. 16.1 and 16.2 (skip "Entry length").
Note that the 2. edition Chapter 16 is the
Chapter 15 in the 1.edition, unchanged.
#10
problems
- due Thu
Mar 28, in class
[solutions to homework #10: Chap 16]
March 18-22
spring break
March 26
21.
Pipe flows
Read sect. 16.4. Skip "Ostwald", "Entry length", "Laminar drain".
TrefethenKS
:)
PDE Coffee Table Book
Kuramoto-Sivashinsky equation - a PDE with chaotic solutions
#11
problems
(bonus for all = bonus points also for grad students, not required)
- due Thu
Apr 4, in class
[solutions to homework #11: energetics]
March 28
22.
Phenomenology of turbulence
Read sect. 15.5. (Skip "Laminar drain").
April 2
23.
Creeping flow
creep
Chapter 17
Creeping flow
Read sects. 17.1 to 17.2.
For fun:
Check out Linda Turner's movies of E. Coli flagella swimming at 1/Re = 10^5.
April 4
24.
Stokes law
Read sect. 17.2.
rotating
Chapter 18
Rotating fluids
Read sect. 18.1.
#12
problems
- due Thu
Apr 11, in class
[solutions to homework #12]
April 8
A wish list?
Pick and chose: look cursorily through the remining chapters
and let me know if you would like me to cover anything in particular.
I'm most tempted by
"Elastic waves",
"Gravity waves", and/or
"Boundary layers".
Other possible picks:
"Whirls and vortices",
"Mechanical balances",
"Action and reaction",
"Energy",
"Jumps and shocks",
and/or
"Subsonic flight".
April 9
25.
Rotating fluids
Read sect. 18.2
(skip "Water level in an open canal" and the rest of the section);
sect. 18.3
(skip "Structure of the Ekman layer" and the rest of the section);
read sect. 18.4 for fun only (not on the final).
Dylan
:)
Subterranean Homesick Blues
You don't need a weatherman
to know which way the wind blows
April 10
A challenge?
If you are doing research that uses continuum physics,
let me know if you want to do a presentation for the class.
April 11
26.
Surface tension
surfaceTension
MIT 1.63J Fluid Dynamics Chapter 7.b
Surface tension
#13
problems
- due Thu
Apr 18, in class
[solutions to homework #13]
April 16
27.
Stability
Base flow; linearized Navier-Stokes for small deviations;
norms; a sketch of Boussinesq equations.
Trefethen
:)
PDE Coffee Table Book
starting information about the garden variety PDEs
April 18
28.
Benard convection
Please check out in your DropBox:
Physics/Bernard-Marangoni Convection
convection
Chapter 30
Convection
Read sect. 30.1. "The Boussinesq approximation" only;
skim through sect. 30.2; study 30.3-30-4
- 30.4.
April 19
presentation: Michael Dimitriyev
29a.
Planar vortices
Integrability,
geometric phase, and statistics.
Howey S104 12:05-12:55
April 23
29.
Turbulence in the 3rd millenium
CBtutorial
ChaosBook
Geometry of turbulence
We take you on a tour of this newly breached, hitherto inaccessible territory. Mastery of fluid mechanics is no prerequisite, and perhaps a hindrance: the tutorial is aimed at anyone who had ever wondered how we know a cloud when we see one, if no cloud is ever seen twice? And how do we turn that into mathematics?
April 25
30.
The Theory of Every Thing 1.0
vortices
:)
Beautiful Losers: Kelvin's Vortex Atoms
For fun only: The fundational paper of the theory of vortex motion
was Helmholtz's 1858 memoir. He wanted to understand the sound of organ pipes,
but also he founded modern atmospheric science in the process.
Thompson (Lord Kelvin) saw much further: the theory of matter with ether as the
perfect fluid, and molecules as
self-knotted collections of vortex ring atoms, indestructable by the
conservation of vorticity. Thus string theory (the faith that
beauty of mathematics trumps Nature) was born. 20 years later Thompson
gave up.
until May ?
course opinion survey
please do give your input on the course
CETL web link
April 26
GT classes end
Final exam syllabus:
An overview of material covered by the final exam.
May 2
final exam 11:30am - 2:20pm
closed book, closed lecture notes, smart devices off,
you can use a calculator.
solutions to the final exam
May 6
GT grades due at noon
May 7
the future looks bright