John Niclasen

Email: niclasen@fys.ku.dk

"Everything should be made as simple as possible, but not simpler."
- A. Einstein

"It's more important to get it right than to get it fast."

"Most people don't have access to education. Most people, who have access to education, are not interested in education. Most people, who are interested in education, don't get it right."

Contents:

jsMath I'm using jsMath to produce formulas. To be able to see the formulas, you have to activate JavaScript in your browser. (It's probably on already.)

1. Notes

These are notes, I've written for the different courses, I've taken.

Astronomy 1 - Cosmology

Physics 1 - Mechanics 1 and Relativity Theory
Physics 2 - Classical Mechanics 2
Physics 3 - Thermodynamics
Physics 4 - Electromagnetism
Physics 6 - Electrodynamics
Physics 7 - Statistical Physics
Physics 8 - Quantum Mechanics II

MathIntro
Linear Algebra
Math F
Math F2

2. Papers

2.1 Being worked on

2.1.1 The Principle of Equivalence and Newtonian Mechanics

• Ækvivalensprincippet 100 år (PDF, danish)
• Ækvivalensprincippets Konsekvenser i Den Newtonske Mekanik (PDF, danish)
• Geometric Explanation for Newtonian Gravity (PDF, english)
• The Gravitational Constant (PDF, english)

2.1.2 Linear Physics

• Lineær Fysik (PDF, danish)

3. REBOL

REBOL is a programming language made by Carl Sassenrath. You need REBOL/View to run my examples found on these pages.

Get the Mac version!
Get the Linux and other versions!
Get the Windows version!

I have more than 20 years of programming experience and have seen a lot of programming languages, but no other language comes close to REBOL, as I see it. If you would like to program in REBOL, this is a good place to start:

REBOL Quick Start by Carl Sassenrath.

4. Astronomy

4.1 NGC 7635 - The Bubble

NGC 7635 was showed on Astronomy Picture of the Day. I made a program in REBOL to give it some colours.

Big version!

You might want to try this program:

To run this program, start REBOL and in the console type:

do http://www.fys.ku.dk/~niclasen/rebol/space/ngc7635.r

4.2 M1 - Crab Nebula

This REBOL program combines two images of M1 the Crab Nebula, one is composed of 24 exposures from Hubble Space Telescope (Crab Nebula Mosaic from HST), the other combines optical data (red) from the Hubble Space Telescope and x-ray images (blue) from the Chandra Observatory (Composite Crab). Use the slider to change the transparency.

To run this program, start REBOL and in the console type:

do http://www.fys.ku.dk/~niclasen/rebol/space/m1.r

Press <ctrl>-q to quit the program.

Another composite of the Crab Nebula: Composite Crab

4.3 McMurdo Panorama on Mars

How would it look, if you could stand on the surface of Mars and look around 360 degrees? This is what the Spirit robot see:

Try for yourself to look around with this REBOL program. Start REBOL and in the console type:

do http://www.fys.ku.dk/~niclasen/rebol/space/McMurdo.r

Use mouse to look around. <ctrl>-q to quit.
(You might wanna change the offset 0x44 at the bottom of the script to something better for your OS resolution.)

4.4 V838 Monocerotis

New images was released of V838 Monocerotis. Try these two REBOL animations of this amazing "Light Echo".

Start REBOL and in the console type:

do http://www.fys.ku.dk/~niclasen/rebol/space/v838.r

Start REBOL and in the console type:

do http://www.fys.ku.dk/~niclasen/rebol/space/v838_06.r

Use the slider to see the different images, or press the "Anim" button to see an animation. Press <ctrl>-q to quit the scripts.

4.5 Sun4

Four images of the upper solar atmosphere was released from the Stereo Ahead spacecraft. I made a REBOL program to combine them into one.

Start REBOL and in the console type:

do http://www.fys.ku.dk/~niclasen/rebol/space/sun4.r

The images are initially stacked as yellow, green, blue and red. Control the program with these keys:

	1	Make yellow image more transparent.
	2	Make yellow image less transparent.
	3	Make green image more transparent.
	4	Make green image less transparent.
	5	Make blue image more transparent.
	6	Make blue image less transparent.
	7	Make red image more transparent.
	8	Make red image less transparent.
	0	Set all transparency to half.
	f	Flip the order of the four images.
	<ctrl>-q	Quit program.

5. Astronomy 2 - Galaxies

5.1 Supernova SN2007gr

15-Aug-2007 a supernova in galaxy NGC 1058 was discovered. As a computer exercise, we should reduce some image data. The supernova is the bright star at the edge of the galaxy between two other stars, which are in our galaxy, the Milky Way. Results from the reduction:

SN1.jpeg
SN2.jpeg
SN3.jpeg

5.2 Spiral arms

A little program to simulate formation of spiral arms seen in many galaxies.

Start REBOL and in the console type:

do http://www.fys.ku.dk/~niclasen/rebol/space/spiral.r

6. Astronomy - Observation Tenerife

Observationskursus Tenerife (PDF, danish)

7. Geophysics 4 - Terrestrial Planets

7.1 Three Body

A simulation of the three body problem.

Start REBOL and in the console type:

do http://www.fys.ku.dk/~niclasen/rebol/space/threebody.r

8. Physics - First Year Project

TideJord (PDF, danish)

9. Physics 7 - Statistical Physics

9.1 Binomial Distribution and Bézier Curves

I discovered similarities between the equation for Binomial distribution and the equation used to calculate Bézier curves in computer graphics. They are both based on Bernstein polynomial.

The equation for Binomial distribution looks like this:

\displaylines{f(k;n,p)={n\atopwithdelims () k}p^k(1-p)^{n-k}\cr {n\atopwithdelims () k}={n!\over k!(n-k)!}\quad ,\quad n\ge k\ge 0\cr }

The equation to calculate a Bézier curve looks like this:

\displaylines{X(t)=\sum _{i=0}^n{n\atopwithdelims () i}t^i(1-t)^{n-i}P_i=\sum _{i=0}^nB_i(t)P_i\quad ,\quad t\in \lbrack 0;1\rbrack \cr {n\atopwithdelims () i}={n!\over i!(n-i)!}\quad ,\quad n\ge i\ge 0\cr }

I've made a REBOL script to explore a Bézier curve with five points. It looks like this:

To run this program, start REBOL and in the console type:

do http://www.fys.ku.dk/~niclasen/rebol/fysik/bezier.r

It's possible to move the points around with the mouse.

10. Science Theory and Ethics for Physicists

Eksisterer Kuhnske Paradigmer i det 21. Århundredes Videnskabelige Verden?
Er Sorte Huller en Myte? (PDF, danish)

11. Links

Testing Einstein's General Relativity: First results from Gravity Probe B

We should do more to deal with future meteor strikes. Here's a link to
Plot of the Inner Solar System

Astronomy Picture of the Day
Celestia 3D Space Simulation
Google Earth now with Sky view
Hubble Europe
Hubble Heritage
HubbleSite
Mars Express
Spitzer Space Telescope

Researchers may have solved information loss paradox to find black holes do not form
Black Holes -- An Astronomical Myth by Tarun Biswas