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January 11
Predrag Cvitanović
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").
Special offer - 1/2 of the midterm grade -
check formulas of appendices D and E,
cylindrical coordinates and spherical coordinates:
offer taken by Sharan Devaiah.
For fun:
Check out these numerical simulations of continuum matter.
January 13
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.
homework #1:
Problems
(1.1) and (1.3), optional (B.12), (B.14) and (C.12)
- due Wed
Jan 22
[solutions to homework #1: Chap 1]
[solutions to homework #1: Appe B]
Predrag Cvitanović
January 15
3.
Turbulence at GaTech
NOTE changed time, the same room: 3:05-3:55pm Howey S204
tutorial
Tutorial
Geometry of turbulence in wall-bounded shear flows:
a stroll through 61,506 dimensions
January 18
Martin Luther King Day
January 20
Scribe: Sharan Devaiah
4.
"Redesigning Education" at Georgia Tech
A 25 min discussion: share your views on the future of
teaching and learning at Tech. The
class discussion will be based on a
scenario depicting a possible future improvements at Tech.
buoyancy
Chapter 3
Buoyancy and stability
January 22
5.
Stressed out I
stress
Chapter 6
Stress
sections 6.1-6.2
For the remaining chapters, get the login from Predrag
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 25
6.
Stressed out II
!! NOTE change of the room:!!
2:05-2:55pm Howey, CNS conference room W505 (across from the elevator)
stress
Chapter 6
Stress
sections 6.3-6.4
homework #2:
exercises
(3.8), (3.9), (6.3), and (6.5), optional (3.10), (6.6) and (6.10)
- due Fri
January 29
[solutions to homework #2: Chap 3]
[solutions to homework #2: Chap 6]
January 27
7.
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
Supplicant: Ekapop Pairam
January 29
8.
Surface tension I
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.
By Ekapop's request covered in class:
capillary length, pressure discontinuity,
Young-Laplace law.
surface
Chapter 5
Surface tension
Optional reading.
For you delectation only - not included for the midterm.
February 1
9.
Surface tension II
Young-Laplace law, Rayleigh-Plateau instability (skipped
Marangoni forces, Bond number, pendant drops, Tate's Law).
Read sects. 5.1, 5.3 and 5.4.
February 3
10.
Hooke's Law I
elasticity
Chapter 8
Hooke's Law
Read sects. 8.1 and 8.2.
Research presentation: Ekapop Pairam
February 5
11.
Toroidal droplets
Liquid droplets are naturally driven into a spherical shape
by surface tension. We generate droplets of genus one
(toroidal droplets) and study their instability and collapse
into spherical droplets. The transformation of thin toruses
is mediated by Rayleigh-Plateau instabilities. Unlike
cylindrical jets, in the case of a torus only integer values
of the perturbation wavelength can fit, as shown in the
videos on Ekapop's homepage (click on his name above). We
control the instability (capillary) wavelength by varying
the aspect ratio of the torus and the viscosity ratio between
the inside and outside liquid.
February 8
12.
Hooke's Law II
Elastodynamic energy, anisotropic elasticity tensor.
Agonizing about how to get tensors across to the innocent -
5 min course in group theory that will go undocumented unless
you are present and taking notes.
Read sect. 8.4.
February 10
13.
Symmetries, tensors, and their reduction
Got tensors across to the innocent -
25 minutes of group theory that went go undocumented unless
you were present and taking notes.
solids
Chapter 9
Basic elastostatics
Read sects. 9.1 (skip Saint-Venant), 9.2 up to fig 9.2, and 9.3.
homework #3:
exercises
(7.2), (7.4), (7.10), (8.1) and (8.4), optional (7.5) and (8.6)
- due Mon
February 15
[solutions to homework #3, Chap 7]
[solutions to homework #3, Chap 8]
February 12
14.
Bend, twist and buckle
rods
Chapter 10
Slender rods
Read sects. 10.1 and 10.2.
February 15
15.
Slender rods
Sect. 10.1. Cantilevers, bridges, yokes.
February 17
16.
Buckling threshold, instability
Sect. 10.2. Slender rod buckled solutions.
A prototypical bifurcation: slender rod buckles when
compression requires more force than bending.
February 19
17.
Bend and twist
Sect. 10.4, the Frenet-Serret basis.
For you delectation only - not included for the midterm.
February 22
18.
Computational elastostatics
ces
Chapter 11
Computational elastostatics
Sects. 11.1 and 11.2.
For you delectation only - not included for the midterm.
NOTE: solutions to homeworks #1, #2 and #3 posted above
February 24
2:05-2:55pm Howey S204: midterm exam
What does midterm cover:
All the assigned reading up to February 19. The problems will
be much like the assigned exercises.
Scores:
from 8 to 29, out of 30 max.
[solutions to the midterm exam]
February 24
Midterm review
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. Check out the elastostatics part.
Please study the midterm solutions; they are very detailed,
I will answer only questions that are not in the solutions
provided. My advice: (1) Do work through the assigned problems,
there is no other way to learn theoretical physics. (2) Do come
to lectures, they can help you sort out what is important
and what is not.
(3) Seize the opportunities of
the small class, participate and discuss unclear points. (4) Do
stop by my office if you do not understand something off the bat.
February 26
19.
Fluids in motion
velocity
Chapter 12
Velocity fields
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.
homework #4:
Problems
(12.1) and (12.4), optional (12.9)
- due Mon
March 8
[solutions to homework #4: Chap 12]
March 1
20.
Big bang
Optional reading: sect. 12.6 "Newtonian cosmology"
- you get a pretty sensible cosmology just out of Hubble's
empirical law + Newton 2nd law in presence of gravity.
March 3
21.
Euler equation, Bernoulli field
ideal
Chapter 13
Nearly ideal flow
Read sects. 13.1-13.2.
March 5
22.
Vorticity
Read sect. 13.3.
homework #5:
Problems
(13.3) and (13.12), optional (13.4), (13.5)
- due Mon
March 15
[solutions to homework #5: Chap 13]
March 8
23.
Potential flow
Read sect. 13.4.
March 10
24.
Viscosity
Read sect. 14.1: Sheer viscosity
viscosity
Chapter 14
Viscosity
March 12
25.
Viscosity
Read sect. 14.2: Velocity-driven planar flow
homework #6:
Problems
(14.2) and (14.3), optional (14.4), (14.5)
- due Mon
March 29
[solutions to homework #6: Chap 14]
March 15
26.
Navier Stokes equations
Read sects. 14.3 and 14.4: Dynamics of incompressible flows
noisePC
ChaosBook.org Chapter 26
Noise
Read sects. 26.1 to 26.3: From Brownian motion to Fokker-Planck equation
March 17
27.
Pipes and planes
pipes
Chapter 15
Plates and pipes
Read sects. 15.1 and 15.2 (skip "Entry length").
March 19
28.
Pipe flows
Read sect. 15.4. Skip "Ostwald", "Entry length", "Laminar drain").
homework #7:
Problems
(15.6) and (15.8), optional (15.9), (15.10)
- due Mon
April 5
[solutions to homework #7: Chap 15]
March 22-26
spring break
March 29
29.
Phenomenology of turbulence
Read sect. 15.5. (Skip "Laminar drain").
March 31
Daniel Borrero
30.
Couette flows
Read sects. 15.6 and 15.7 (will not be included in the final exam)
NOTE A brief overview (5th floor Howey, as usual), followed by a
lab demonstration. See the cutting edge shmurbulence. Cool.
April 2
Roman Grigoriev
31.
Creeping flow
creep
Chapter 16
Creeping flow
Read sects. 16.1 to 16.3 (skip "16 2").
creepRG
R. Grigoriev
lecture notes
For fun:
Check out Linda Turner's movies of E. Coli flagella swimming at 1/Re = 10^5.
April 5
32.
Compressible flow
compressible
Chapter 17
Compressible flow
Read sects. 17.1 and 17.2 up to Example 17.3; 17.4 up to Eq. (17.30).
You need to know when the standard wave equation is valid, and
when the incompressibility assumption is valid (Mach number).
April 7
33.
Rotating fluids
rotating
Chapter 18
Rotating fluids
Read sects. 18.1 and 18.2
(skip "Water level in an open canal" and the rest of the section).
April 9
34.
Rotating fluids
Read sect. 18.3
(skip "Structure of the Ekman layer" and the rest of the section);
read sect. 18.4 for fun (not on the final).
April 12
35.
Computational fluid dynamics
cfd
Chapter 19
Computational fluid dynamics
Read sects. 19.1, 19.2 and 19.3.
homework #8:
Problems
(16.1), (17.1) and (18.1), optional (17.2), (18.5)
- due Mon
April 19
[solutions to homework #8: Chap 16]
[solutions to homework #8: Chap 17]
[solutions to homework #8: Chap 18]
April 14
36.
Computational fluid dynamics
Read sect. 19.4. Implementing this is too time-consuming for the course,
but understanding the basic principles: discrete derivatives,
why staggered lattice? why Poisson equation? is important.
April 14-27
spring registration
April 16
no lecture
Pick and chose: look cursorily through the remining chapters
and let me if you would like me to cover anything in particular.
Otherwise we will probably follow Lautrup's picks and go through
"Mechanical balances",
"Action and reaction",
"Energy",
"Gravity waves",
"Jumps and shocks",
"Whirls and vortices", and
"Subsonic flight".
NOTE: no lecture today
global
Chapter 20
Mechanical balances
reaction
Chapter 21
Action and reaction
energy
Chapter 22
Energy
entropy
Chapter 23
Entropy
Skipped.
April 19
37.
Gravity waves
waves
Chapter 24
Gravity waves
Read sects. 24.1, 24.2 to 24.3.
Main points: group vs. phase
velocity, dispersion laws.
April 21
38.
Gravity waves
Read sects. 24.4 and 24.5.
Main points: gravity vs. capillary group
velocities. Instabilities.
April 23
39.
Elastic waves
vibrations
Chapter 25
Elastic waves
Read sect. 25.1.
Main points: fast pressure/primary P-wave,
slower shear/secondary S-wave.
vibrationsPC
Lecture notes
Elastodynamics
Main points: use projection operators (rather than curls) to
separate out the longitudinal/transverse waves.
April 26
40.
Elastic waves
Read sect. 25.3.
Main points: under reflection/refraction a P- or S-wave
generates a mixture of both.
Scan through sect. 25.4 (not on final): Rayleigh surface
are important.
shocks
Chapter 26
Jumps and shocks
Skipped.
April 28
41.
The Theory of Everything 1.0
vortices
Chapter 27
Whirls and vortices
Read sect. 27.2.
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.
boundary
Chapter 28
Boundary layers
Skipped.
flight
Chapter 29
Subsonic flight
Skipped.
April 30
42.
Convection
convection
Chapter 30
Convection
Read sect. 30.1.
up to "Entrance length for heath"; skim through sects. 30.2
- 30.4.
Good to know something about: Boussinesq approximation,
convective instabilities, critical fluctuations,
Rayleigh-Benard convection.
turbulence
Chapter 31
Turbulence
Skipped.
April 30
GT classes end
Final exam syllabus:
An overview of material covered by the final exam.
May 7
final exam 8:00am - 10:50am
closed book, closed lecture notes, you can use a calculator.
solutions to the final exam, version of May 8
until May 8
course opinion survey
CETL web link
May 10
GT grades due at noon
grade distribution
May 12
the future looks bright
the rest has yet to be worked out