]> 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