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bio website sjbyrnes.com
location Massachusetts
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visits member for 4 years, 2 months
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Aug
14
revised Four questions on color
correct reference to brain per @Ben Crowell's comment
Aug
14
answered Four questions on color
Aug
13
comment Can the Lorentz force expression be derived from Maxwell's equations?
@LarryHarson - "work done on charge" is the most common textbook definition of EMF; the line-integral of E is a less common definition (although I concede that you'll find it in some textbooks). Under your line-integral definition, "motional EMF" is not really EMF. Under your line-integral definition, a generator with a stationary wire and spinning magnet creates an EMF, but a generator with a spinning wire and stationary magnet does not create an EMF. Line-integral of E is a bad definition of EMF because it doesn't correspond to what a voltmeter measures or how experts actually use the term.
Aug
12
awarded  Nice Answer
Aug
11
comment Does tritium hydride exhibit measurable spontaneous fusion via proton tunneling?
1nm is a 10X overestimate of how far apart the nuclei are. 1 angstrom is closer. Googling suggests 0.74 angstroms (0.074nm) as the H-H separation in H$_2$.
Aug
9
answered Does $E$ cause $B$ or does $B$ cause $E$ in Maxwell's equations?
Aug
6
revised Simulation of an one dimensional driven diffusive system
added 430 characters in body
Aug
6
answered Simulation of an one dimensional driven diffusive system
Aug
5
comment Simulation of an one dimensional driven diffusive system
I looked superficially at the code. It looks fine (albeit not optimized for speed), the only obvious problem is that you don't have any assertions / unit-tests / "sanity-checks". The python assert command is great, you should use it as often as possible. You are in good company -- most scientists don't put in assertions or tests -- but it is nevertheless a problem. Also, don't use lower-case L because it looks too much like 1. :-P
Jul
27
comment Why is glass much more transparent than water?
For example, pure water strongly absorbs light at ~100 trillion hertz due to a vibrational resonance. You can say "The electrical conductivity of pure water is very high when the field is oscillating at 100 trillion hertz...Much higher than if the field was oscillating at 10 trillion hertz, or at DC". This is correct, but the statement doesn't really help you understand anything better. So people don't normally say that. They don't discuss "AC conductivity" directly, they just say it "absorbs light at 100 trillion Hz".
Jul
27
comment Why is glass much more transparent than water?
The skin depth relationship is fine for any material at any frequency ... if you use the AC permittivity and AC conductivity. And it's very nice for metals at low frequencies. People discussing visible light in glass could talk about glass's AC conductivity, and use the skin depth formula, if they wanted to. But they usually don't - they use other notations & parametrizations instead. See en.wikipedia.org/wiki/Mathematical_descriptions_of_opacity
Jul
26
comment Why is glass much more transparent than water?
(A) Electric and magnetic fields push around atoms and electrons; (B) The atoms and electrons in turn alter the electric and magnetic fields. You use Maxwell's equations for part (B) but not (A). (A) depends on how easily the electrons can move at each frequency, etc., and includes things like the frequency-dependence of permittivity and resistivity. I'm glad you've seen the skin depth derivation, but it assumes frequency-independent resistivity. That's a bad assumption at optical frequencies. (It's OK for metals at lower frequencies like radio frequencies).
Jul
26
revised Why is glass much more transparent than water?
added 130 characters in body
Jul
26
answered Any physical example of an “explosive” differential equation $ y' = ky^2$?
Jul
26
answered Why is glass much more transparent than water?
Jul
26
comment It appears that stationary states aren't so stationary
@Wildcat - Yes (for a stationary state). Your proof of that (in the question) is spot-on.
Jul
23
comment It appears that stationary states aren't so stationary
@Wildcat - I think your term "external" is about right. Most of the time that somebody writes down an operator with explicit time dependence, it's because something "externally" (to the quantum system) is changing. (Not because it's mathematically necessary, but because that's the situation where such operators are useful, unlike my $O(t)$ example which is useless.) I wouldn't use the term "two different parameters", but yes you shouldn't confuse explicit time dependence with implicit time dependence. BTW the latter is different in the "Schrödinger picture" vs "Heisenberg picture".
Jul
23
comment It appears that stationary states aren't so stationary
@Wildcat - There is no operator like that, not even H. Explicit time dependence always means representing different things at different times. For example, maybe I have an electron in a variable applied electric field, and I treat the electron quantum-mechanically and E-field classically. Then there's a time-dependent Hamiltonian H. At $t=0$ H would represent, say, "the energy of an electron in an environment where there's a uniform 1.3V/m electric field". At $t=1$ H would represent, say, "the energy of an electron in an environment where there's a uniform 2.8V/m electric field".
Jul
23
answered It appears that stationary states aren't so stationary
Jul
22
answered Lasers and Collimation