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seen Jun 7 at 14:13

Nov
8
asked Most sophisticated experiment you could perform in your garage?
Oct
31
comment Cause of buoyant force?
@leonardo - if you'd like a more rigorous proof, you can easily show that this is a consequence of the divergence theorem (Gauss's law).
Oct
20
comment How does one calculate the volume of a nucleus and the volume of an atom (in this case hydrogen)?
Do you mean, how do you find the volume from the given radii, or how these radii are obtained? The former is straightforward (see answer below), the latter is a bit more complicated.
Oct
9
answered Simple 2D Vehicle collision physics
Oct
6
answered Linear Algebra for Quantum Physics
Oct
5
answered How can such a high exponent arise in this physics equation?
Oct
5
comment Acausality in solving time-domain inhomogeneous differential equations with Fourier transforms?
So, if I get this right, for $t - t'>0$, I can only integrate the contour on the upper half of the plane, where the pole contributes a non-trivial residue, but for $t - t' < 0$ the exponent only vanishes in the lower half, so I must take the contour there - but no poles means no residue, so the expression is guaranteed to vanish, regardless of the choice of input? Neat. Very Neat.
Oct
5
accepted Acausality in solving time-domain inhomogeneous differential equations with Fourier transforms?
Oct
5
comment Acausality in solving time-domain inhomogeneous differential equations with Fourier transforms?
Do you mean, show that the entire integral vanishes? Wouldn't it be equal to the residue at $i/RC$?
Oct
5
comment How can such a high exponent arise in this physics equation?
What I meant is that the quantity in question is my be an exponential function of the form $y(x) = e^x$. Both quantum tunneling and Boltzmann factors are exponential, and they both come into play in stellar fusion. Try looking up the Gamow Peak. Now, if you have some power law %f(r) = r^n%, notice that its logarithmic derivative %\frac{d(log(f(r))}{d(log(r))}$ is equal to %n%, so this yields the exponent of the law. In principle, it may be applied to any general function, and its value would give the appropriate exponent should you wish to locally approximate that function as a power law.
Oct
5
comment Acausality in solving time-domain inhomogeneous differential equations with Fourier transforms?
So, in principle, could I construct a differential equation which would produce such an $H(\omega )$ that violates causality?
Oct
5
comment Acausality in solving time-domain inhomogeneous differential equations with Fourier transforms?
I'll see if I can get that result this evening.
Oct
4
comment Acausality in solving time-domain inhomogeneous differential equations with Fourier transforms?
I agree, but does that solution not solve the original equation? Since the equation is causal, I expect the solution to maintain that property. I remember from school that when solving wave equations in classical EM, a delta function pops out during integration and enforces this causality (this raises an interesting question of what would happen when it is solved on a finite interval where the wavenumbers are discrete, but that's for another time) - but I can't see a way that such a causality-ex-machina would show up in any general problem.
Oct
4
awarded  Commentator
Oct
4
comment Acausality in solving time-domain inhomogeneous differential equations with Fourier transforms?
Yes, but I can always expand this expression as $v_{o}(t)=\frac{1}{2\pi}\int\int d\omega dt'v_{i}(t')e^{j\omega (t-t')}$ Integrating first over $\omega$, this clearly yields a delta function $\delta (t-t') $ and causality is restored analytically for every input $v_i$. With the RC circuit, the extra $\omega$ dependent terms in the integrand don't allow this triviality. And again, I'm concerned about this is a general issue, not necessarily in circuit analysis.
Oct
4
comment Acausality in solving time-domain inhomogeneous differential equations with Fourier transforms?
I agree that the problem may be solved like you have wrote, but what step goes wrong in the FT approach that seems to break causality? If the solution I outlined above it valid, what would happen if I try to evaluate it for some input function? I suspect that if I switch the order of integration, the first (homogeneous) solution term you wrote may pop out from the transform solution, but I've yet to check it out. Also, as I said in, I'm interested in this difficulty in a more general situation, and only used the RC circuit to illustrate the problem.
Oct
4
comment How can such a high exponent arise in this physics equation?
I would assume it's roughly the value of the power derivative $\frac{d ln(f(r))}{d ln(r)}$, which gives the exponent of a the local approximate power law. It's probably an exponential law like @LuboŇ°Motl said. I remember once I did a calculation about stellar power production that yielded a power derivative of about 22, so why not 40?
Oct
4
asked Acausality in solving time-domain inhomogeneous differential equations with Fourier transforms?
Oct
4
answered The necessity of the B field
Oct
2
comment Are all central forces conservative? Wikipedia must be wrong
In principle, every central force/field with complete azimuthal symmetry, as long as it is also time-independent, can be integrated to find the potential associated with it. That potential may not be analytic, but it exists, and its existence is equivalent to stating that the force is conservative.