A Gravitational Journey

October 12, 2019 Leave a Comment

One of curses or blessings of being a nerd is that just out of the blue a crazy question pop into your head and you cannot rest until you settle it. A few weeks ago suddenly, and I swear to the principles of science, with no trigger whatsoever, this question came to my mind, how stars are formed, i.e., if we have a huge cloud of gas in the vacuum of space, how it get dense enough to form a star? And another question that immediately followed was how the gravitational pull of the material inside a star causes a star to collapse into a blackhole? Is it possible to answer these questions with the physics I know?

To simplify this problem assume that we have a homogeneous sphere and we want to calculate the exact pull of gravity in every particle of gas inside this sphere from the material in the rest of the sphere.

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Testing equations

October 11, 2019 Leave a Comment


At first, we sample f(x) in the N (N is odd) equidistant points around x^*:

    \[ f_k = f(x_k),\: x_k = x^*+kh,\: k=-\frac{N-1}{2},\dots,\frac{N-1}{2}\]


where h is some step.
Then we interpolate points \{(x_k,f_k)\} by polynomial 

(1)   \begin{equation*} P_{N-1}(x)=\sum_{j=0}^{N-1}{a_jx^j}\end{equation*}


Its coefficients \{a_j\} are found as a solution of system of linear equations:

(2)   \begin{equation*} \left\{ P_{N-1}(x_k) = f_k\right\},\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2}\end{equation*}


Here are references to existing equations: (1), (2).
Here is reference to non-existing equation (??).

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Finally I have started!

March 29, 2013 Leave a Comment

It is a long time since I decided to start this blog, but always it delayed due to busy schedule of the last months of my doctoral studies. Anyway, I am going to use this space and my digital retreat for stress release. I will also write about my research.

Writing about whatever comes to one’s mind is one way to overcome the author’s block and as time passes the writings start to get a direction.

I think that is all for now, I have to get back my branch and cut algorithm!

 

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