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Dec
12
comment Proving susceptibility in Lorentz Model satisy Kramers-Kronig relations
@Vesnog: The relation I refer to in my answer is of course the KK relation, because that is the objective of this exercise, is it not? Also $\gamma$ should take on the negative (not positive, please read carefully) sign if KK is to hold, as I have clearly stated in my answer. The first thing you ought to do then is to study the Cauchy Integral Theorem if you have not done so en.wikipedia.org/wiki/Cauchy%27s_integral_formula. It will also be more efficient if you can make your questions more to the point since it is hard to discern what you are trying to get at.
Dec
12
answered How does the Ocean polarize light?
Dec
11
comment Proving susceptibility in Lorentz Model satisy Kramers-Kronig relations
@Vesnog: It is not clear what your comment is contending. Are you trying to say you do not agree with or not understand my proof?
Dec
11
comment Proving susceptibility in Lorentz Model satisy Kramers-Kronig relations
I do not see why this is off topic. By the criteria listed in the help center on topics that can be asked, this question obviously falls in the category of "Mathematics in the context of physics" as the question asks about the specific relationship resulting from Lorentz model of electric susceptibility.
Dec
10
revised Proving susceptibility in Lorentz Model satisy Kramers-Kronig relations
added 1 character in body
Dec
10
comment Proving susceptibility in Lorentz Model satisy Kramers-Kronig relations
@Vesnog: I have added the explicit verification. You may need to fill in the details according to my description when writing your report.
Dec
10
revised Proving susceptibility in Lorentz Model satisy Kramers-Kronig relations
Added explicit derivation for this particular expression.
Dec
10
revised Proving susceptibility in Lorentz Model satisy Kramers-Kronig relations
Detailed the contour.
Dec
10
answered Proving susceptibility in Lorentz Model satisy Kramers-Kronig relations
Dec
9
comment Total Momentum From a Standing Electromagnetic Wave
I am revisiting this post because of others, such as @lionelbrits, are. The assertion "no energy is being transferred to the matter of the cavity from inside so kinetic energy of the material cavity is constant in time. Therefore momentum of the material cavity is constant in time as well" is patently wrong. Consider a particle running with constant speed in a circle. Besides, I am asking for the spatial integral of the field momentum. This so called answer does not answer the question.
Dec
5
comment Total Momentum From a Standing Electromagnetic Wave
How is this kind of standing wave generated in an arbitrarily shaped cavity? I think one can only define standing wave as each component of a time Fourier transform of the field.
Nov
9
comment Why are our planets in the solar system all on the same disc/plane/layer?
@Dronz: Thank you. I will check them out.
Nov
5
comment Why are our planets in the solar system all on the same disc/plane/layer?
@Dronz: I know what you are saying. Even for spherical initial distribution, as assumed in your last sentence, with perhaps some perturbation, why should most the resulting semi-stable orbits lie on a single plane?
Nov
5
comment Why are our planets in the solar system all on the same disc/plane/layer?
@Dronz: "local concentrations"? If the elliptical regions that different orbits reside in are all disjoint and sufficiently far, there would be no collisions and no cancellations, and concentrations. You, just like the others, seem to put cart in front of the horse and cherry pick the reasons just to be able to draw the prescribed conclusion. That seems to fit more the characteristic of logical fallacy than scientific method.
Nov
5
comment Why are our planets in the solar system all on the same disc/plane/layer?
@Dronz: Yes, I have heard these before, and again this line of argument appears to form in hindsight: because in most of the examples we have observed --- I would not think the number is high as most planets and dust clouds in other solar systems are dark and thus unobservable --- the orbits are almost planar, so we fill whatever SEEMINGlY plausible reasons to convince ourselves this is almost always the case, whatever the mathematical rigor. It is a bit akin to the joke about psychologist's theory. Now to be more specific, why does "the large-scale distribution tend to have no major ...
Nov
4
comment Why are our planets in the solar system all on the same disc/plane/layer?
@Dronz: The concentration should be local. My question is why there can not be, with high probability, disjoint concentric elliptical annuli, at the distance of the solar planets in scale or larger for dust cloud, that are stable at the current solar system time scale, that planets or dust can rotate around the central star about very distinct axises.
Nov
3
comment Why are our planets in the solar system all on the same disc/plane/layer?
@Dronz: "Stable" here is not required to be for time infinite and is defined relative to a given time interval. However, how does your comment relate to my question at all?
Oct
24
comment Why are our planets in the solar system all on the same disc/plane/layer?
@zibadawatimmy: I know many body gravitation problem is chaotic. Yet the solar system in the time scale of the earth life time until now is "relatively" stable. My question is what mathematical prohibition is there against a spherically distributed planet or dust orbital axis system with the same size orbit just like the solar system? Our solar planet system happens to be mostly planar. Is there a mathematical rationale stipulating the axis of rotation have all to be almost parallel and stable within the earth-life-time-until-now time scale?
Oct
24
comment Why are our planets in the solar system all on the same disc/plane/layer?
@zibadawatimmy: Thank you for introducing me to the Oort cloud and supplying evidence of spherical distribution of orbits. Even with the dust and with collisions, why can dust not form, say, different annuli of different orientation at close distance to the sun? The rationale of chaos does not seem to be too convincing, since the planets in the solar system have been pretty stable with the current mutual distance. Does the orientation of the orbit so crucial even when we, say, make the mutual distance of those annuli to ten times that of the current planets?
Oct
24
comment Why are our planets in the solar system all on the same disc/plane/layer?
@zibadawatimmy: Why do the planets belonging to two orthogonal axis of rotation have to be "discs" as you say and interact? The simplest counterexample is two concentric circles of different radii perpendicular to each other.