the lienard-wiechert potentials

AÎ¼(x)=4Ï€cd4xG(x,t,x,t)jÎ¼(x)
where
jÎ¼(x)=cedÏ„vÎ¼(Ï„)Î´(4)(xrÎ¼(Ï„))
and
G(x,t,x,t)=12Ï€Î¸(ctct)Î´(4)[(xx)2]

AÎ¼(x)=4Ï€cd4x12Ï€Î¸(ctct)Î´(4)[(xx)2]cedÏ„vÎ¼(Ï„)Î´(4)(xrÎ¼(Ï„))

AÎ¼(x)=2ed4xÎ¸(ctct)Î´(4)[(xx)2]dÏ„vÎ¼(Ï„)Î´(4)(xrÎ¼(Ï„))

AÎ¼(x)=2edÏ„vÎ¼(Ï„)d4xÎ¸(ctct)Î´(4)[(xx)2]Î´(4)(xrÎ¼(Ï„))

AÎ¼(x)=2edÏ„vÎ¼(Ï„)Î¸(ctr0(Ï„))Î´(4)[(xrÎ¼(Ï„))2]

where ct=r0(Ï„)$ct' = r_0(\tau)$
using the identity
Î´(n)(f(x))=Î´(n)(x)dfdx

in our case, x=Ï„$x=\tau$ and f(Ï„)=(xrÎ¼(Ï„))2$f(\tau) = (x-r^{\mu}(\tau))^2$
dfdÏ„=2(xrÎ¼(Ï„))(vÎ¼(Ï„))

=2(xr(Ï„))Î¼vÎ¼(Ï„)

substituting this in the above equation gives
AÎ¼(x)=2edÏ„vÎ¼(Ï„)Î¸(ctr0(Ï„))Î´(4)(Ï„Ï„0)2(xr(Ï„))Î¼vÎ¼(Ï„)

AÎ¼(x)=edÏ„vÎ¼(Ï„)Î¸(ctr0(Ï„))Î´(4)(Ï„Ï„0)[(xr(Ï„))v(Ï„)]

AÎ¼(x)=e[vÎ¼(Ï„)[(xr(Ï„))v(Ï„)]]Ï„0

AÎ¼(x)=2edÏ„vÎ¼(Ï„)Î¸(ctr0(Ï„))Î´(4)[(xrÎ¼(Ï„))2]

dÎ±AÎ²(x)=2edÏ„dÎ±[vÎ²(Ï„)Î¸(ctr0(Ï„))Î´(4)[(xrÎ¼(Ï„))2]]

=2edÏ„vÎ²(Ï„)Î¸(ctr0(Ï„))dÎ±Î´(4)[(xrÎ¼(Ï„))2]]

=2edÏ„vÎ²(Ï„)Î¸(ctr0(Ï„))ddxÎ±Î´(4)[(xrÎ¼(Ï„))2]]

=2edÏ„vÎ²(Ï„)Î¸(ctr0(Ï„))ddxÎ±dfdfÎ´(4)[(xrÎ¼(Ï„))2]]

=2edÏ„vÎ²(Ï„)Î¸(ctr0(Ï„))dfdxÎ±ddfÎ´(4)[(xrÎ¼(Ï„))2]]

=2edÏ„vÎ²(Ï„)Î¸(ctr0(Ï„))dfdxÎ±ddfdÏ„dÏ„Î´(4)[(xrÎ¼(Ï„))2]]

=2edÏ„vÎ²(Ï„)Î¸(ctr0(Ï„))dfdxÎ±dÏ„dfddÏ„Î´(4)[(xrÎ¼(Ï„))2]]

where dfdÏ„=2(xr(Ï„))Î¼vÎ¼(Ï„)=2(xr(Ï„))v(Ï„)$\frac{df}{d\tau} = -2(x-r(\tau))_{\mu}v^{\mu}(\tau) = -2(x-r(\tau))\cdot v(\tau)$ and dfdxÎ±=2(xr(Ï„))Î±$\frac{df}{dx^{\alpha}} = 2(x-r(\tau))^{\alpha}$
dÎ±AÎ²(x)=2edÏ„[2(xr(Ï„))Î±vÎ²(Ï„)2(xr(Ï„))v(Ï„)]Î¸(ctr0(Ï„))ddÏ„Î´(4)[(xrÎ¼(Ï„))2]]

=2edÏ„ddÏ„[(xr(Ï„))Î±vÎ²(Ï„)(xr(Ï„))v(Ï„)]Î¸(ctr0(Ï„))Î´(4)[(xrÎ¼(Ï„))2]]

FÎ±Î²=2edÏ„ddÏ„[(xr(Ï„))Î±vÎ²(Ï„)(xr(Ï„))Î²vÎ±(Ï„)(xr(Ï„))v(Ï„)]Î¸(ctr0(Ï„))Î´(4)[(xrÎ¼(Ï„))2]]

is similar to
AÎ¼(x)=2edÏ„vÎ¼(Ï„)Î¸(ctr0(Ï„))Î´(4)[(xrÎ¼(Ï„))2]

therefore, we can say that
FÎ±Î²=2e[(xr)v]ddÏ„[(xr)Î±vÎ²(xr)Î²vÎ±(xr)v]

Animation using GNUPlot

Animation using GNUPlotI've been trying to create an animation depicting a quasar spectrum moving across the 5 SDSS pass bands with respect to redshift. It is important to visualise what emission lines are moving in and out of bands to be able to understand the color-redshift plots and the changes in it.
I've tried doing this using the animate function in matplotlib, python but i wasn't able to make it work - meaning i worked on it for a couple of days and then i gave up, not having found solutions for my problems on the internet.
And then i came across this site, where the gunn-peterson trough and the lyman alpha forest have been depicted - in a beautiful manner. And this got me interested in using js and d3 to do the animations and make it dynamic - using sliders etc.
In the meanwhile, i thought i'd look up and see if there was a way to create animations in gnuplot and whoopdedoo, what do i find but nirvana!

In the image, you see 5 static curves and one dynam…

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I'm talking about MOOCs because one of my new year resolutions is to take online courses, atleast 2 per semester (6 months). And I've chosen the following two courses on edX - Analyzing Big Data with Microsoft R Server and Data Science Essentials for now. I looked at courses on Coursera but I couldn't find any which was worthy and free. There are a lot more MOOC providers out there but let's start here. And I feel like the two courses are relevant to where I …

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I am not going to give you a tl;dr version of the talk because it is a talk that I believe everyone should watch, that everyone should learn from. Instead, I am going to give my own parallel-ish views on programmers and programming.
As pointed out in the talk, there are mythical creatures in the software development industry who are revered as gods. Guido Van Rossum, the creator of Python, was given the title Benevolent Dictator For Life (BDFL). People flock around the creators of popular languages or libraries. They are god-like to most programmers and are treated like gods. By which, I mean to say, we assume they don't have flaws. That they are infallible. That they are perfect.
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