]> 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