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  1. J

    Numerical Plot of Particle Orbits in Kerr Equatorial Plane

    I don't know. But it occurs to me that conservation of energy might be a problem. The only cases of spiral orbits I can think of immediately involve some change of orbital energy--drag from viscous forces, emission of gravitational waves or absorption of electromagnetic energy as in a cyclotron.
  2. J

    Numerical Plot of Particle Orbits in Kerr Equatorial Plane

    Not that's obvious to me. But it might be worth trying to narrow the range of possibilities first. Are you sure that spiral orbits are possible? Are there stable closed orbits in the Kerr metric? If so, it might be worth starting from one of those and trying to perturb it. ( Perhaps replace r...
  3. J

    Most efficient temperature to evaporate water?

    It might help if you told us a bit more about your set-up. What sort of quantities of water, in what sort of vessels? (Other things being equal, water evaporates faster from a shallow open pool than from a deep tank.) What are your heat sources?
  4. J

    Numerical Plot of Particle Orbits in Kerr Equatorial Plane

    Did you consider what relations between r and φ would give you a spiral and going from there?
  5. J

    Transmission for double delta-potential vs single delta

    I suspect this is a strong hint. Is there a relation between the separation of the two deltas and the wavelength of the wave-function?
  6. J

    Rod falling faster than gravity

    The weight of the rod has a component directed through the pivot and a tangential component causing acceleration.
  7. J

    Most efficient temperature to evaporate water?

    The vapour-pressure of water increases much more than linearly with in creasing temperature. But vapour pressure isn't the only factor that determines the evaporation rate. In general air flowing over a water surface (or bubbled through water) will cause faster evaporation than still air (the...
  8. J

    Finding an indefinite integral

    Try putting x=sinθ again and simplifying. Note that you seem to have made a sign error in your last integration.
  9. J

    Geometric average versus arithmatic average

    Unweighted, the arithmetic mean is always >= geometric mean, so I suspect your weights may have to have a sum > 1. Think what happens if one of the numbers you're averaging is zero.
  10. J

    Occupancies in sub bands of a quantum well

    I think it may be. Depends what "it" is, of course.
  11. J

    Why does (-1)^n(sin(pi/n)) converge when (sin(p/n)) diverges

    How about this: For large n, sin(π/n) is approximately π/n, so the series is approximately πΣ(1/π) which is known to diverge. With alternating signs, the series approximates πΣ( (1/n) - 1/(n+1) ) which approaches π.ln(2). Actually I think I find it more persuasive to group pairs of successive...
  12. J

    Inertia tensor of a body rotating about 3 axes

    It can't do that simultaneously, if that's what you're thinking. The body's angular momentum is represented by a vector--and that direction of that vector is the axis about which it rotates. The axis may not coincide with any of the coordinate axes, but it is a single axis.
  13. J

    I What does the magnetic moment of a particle depend on?

    For elementary particles, the magnetic momentum depends on the angular momentum and the mass, though not necessarily in a simple way. For similar particles the magnetic moment increases with the angular momentum*. For particles of the same spin, the magnetic moment is roughly inversely...
  14. J

    I How to remove Ethanol from Gasoline?

    Doing two separations with half a gallon of water in each should be more effective than a single separation with one gallon (and three separations would be more effective still). That principle would help you use less water.
  15. J

    I Light and the nature of space

    I thought this was strictly for local measurements.
  16. J

    A Penetration Depth of General Complex Conductivity

    I just looked at Tinkham's page 40 on the web; he says he's "solving the skin depth problem", as though it's an understood procedure, presumably with standard assumptions and approximations. And he's talking about good conductors the whole time; so I think "general" here simply means both real...
  17. J

    A Penetration Depth of General Complex Conductivity

    I still suspect it's semantic. As far as I can tell a real, frequency-dependent skin-depth implies a good conductor. How does Tinkham set up the problem?
  18. J

    A Penetration Depth of General Complex Conductivity

    Given the title of the book, does "general" solution simply mean it's true all superconductors (or even all reasonably good conductors)?
  19. J

    Occupancies in sub bands of a quantum well

    Perhaps the way to think about this question is to imagine the hypothetical well with one sub-band as a kind of "bucket" that would have been filled with electrons to a "depth" of 50 meV. (This seems to explain why the occupancy is expressed in meV.) How would you picture the real well in those...
  20. J

    Occupancies in sub bands of a quantum well

    As I understand it, the total energy is the fermi energy you have the equation for, plus the potential energy referred to some chosen zero level. I think it might be useful to draw an energy-level diagram comparing the assumed quantum well with one sub-band and the real well with two sub-bands.
  21. J

    Occupancies in sub bands of a quantum well

    That sounds promising. Do you understand why the occupancies are apparently measured in meV? I admit that's not clear to me.
  22. J

    Occupancies in sub bands of a quantum well

    Do you know of a relation between the energy of the system and the number of levels that are occupied?
  23. J

    Question about Legendre elliptic integrals

    No shipwrecks or monstrous squid, I take it?
  24. J

    A Frequency in K

    Actually you can. As DrClaude says the frequency corresponds to ℏ ω / k. Maybe think of it this way. We have an energy E that could be the energy of a photon with frequency ν, where hν = E. So we could just agree to talk about the frequency, knowing that if necessary we could always convert...
  25. J

    Half life question

    It's not exactly clear but this probably means that the decay rate was still appreciable after 40 days, so you can rule out a half-life that is much less than that.
  26. J

    Half life question

    I think I'd approach it this way. Assume the source is reasonably pure and macroscopic--say a few grams. Pick a credible mass number, and estimate the number of alpha emitters in the source. Compare that number to the number of decays, at the specified rate, in one second, an hour, a day, 40...
  27. J

    Half life question

    Good questions. To which I would add: What is the mass of the source and its atomic weight, or equivalently the number of gram-moles it contains? A flux of 3.5x10^6 particles per second is one thing if it's coming from a 5 kg source, and something else if it's produced by 1 mg. Reference...
  28. J

    Half life - Calculate the length of time

    What are the units? Are you told anything about the half-life of the source?
  29. J

    Negative Values of the Frictional Force?

    I don't know if you'd find it helpful, but I like to start from Newton's law for this type of problem. Net Force = Mass x Acceleration. You've found the acceleration. The mass is 100/g kg. The net force is the applied force less the frictional force = 40 - 100.μ N (where μ is the frictional...