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### Messages - Alberto Dominguez

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31
##### Physics / Physics Simulations
« on: February 02, 2012, 07:06:54 PM »

32
##### Electromagnetism / Electromagnetic Spectrum
« on: January 30, 2012, 07:08:38 PM »

33
##### Astronomy and Astrophysics / Black Holes, White Dwarfs and Neutron Stars
« on: January 28, 2012, 05:53:00 PM »
In the stars like our Sun when the H and He fusion reaction finish, they become to White Dwarfs (degenerate electron stars).  These are cooling to their death, become to Black Dwarfs.

The stars with 1,4 to 3 mass of the Sun at the end of their life die exploding as Supernovas.  They left as residue a Neutron Star that we can observe like a Pulsar or cosmic beacon.  Their radiation comes to us like radio waves or also in the visible spectrum.

The most massive stars that at the end of their life have even more than 3 times the mass of the Sun collapse into Black Holes.

Example of Supernova: Hubble space telescope image showing the supernova 1994D on the bottom left and the NGC 4526 galaxy:

And some Stars size:

34
##### Astronomy and Astrophysics / This is a galaxy
« on: January 28, 2012, 02:02:18 PM »

35
##### Physics / Re: Physics Publications
« on: January 28, 2012, 09:37:14 AM »
Some Magazines:

Physics Today:
www.physicstoday.org

Nature:
www.nature.com

Science:
www.sciencemag.org

Revista española de Física y Revista Iberoamericana de Física:
www.rsef2.com (Spanish)

36
##### Functional Analysis / Topological Space
« on: December 18, 2011, 07:42:40 PM »
A topological space is a set X together with $\tau$ (a collection of subsets of X) satisfying the following axioms:
The empty set and X are in $\tau$.
$\tau$ is closed under arbitrary union.
$\tau$ is closed under finite intersection.
The collection $\tau$ is called a topology on X. The elements of X are usually called points, though they can be any mathematical objects. A topological space in which the points are functions is called a function space. The sets in $\tau$ are called the open sets, and their complements in X are called closed sets.

Four examples and two non-examples of topologies on the three-point set {1,2,3}. The bottom-left example is not a topology because the union of {2} and {3} [i.e. {2,3}] is missing; the bottom-right example is not a topology because the intersection of {1,2} and {2,3} [i.e. {2}], is missing.

Source: http://en.wikipedia.org/wiki/Topological_space

37
##### Functional Analysis / Countable sets
« on: December 18, 2011, 07:40:57 PM »

38
##### Mathematics / Useful Trigonometric Identities
« on: December 17, 2011, 09:47:19 AM »
$cosxcosy=\frac{cos(x+y)+cos(x-y)}{2}$

$senxseny=\frac{cos(x-y)-cos(x+y)}{2}$

$senxcosy=\frac{sen(x+y)+sen(x-y)}{2}$

More Identities: http://web.mit.edu/wwmath/trig/identities02.html

39
##### Classical Mechanics / The Law of Conservation of Energy
« on: November 27, 2011, 01:43:31 PM »
Total work (increment of Kinetic Energy):

$W_{total}=\overset{b}{\underset{a}{\int}}(F_{c}+F_{nc})dr=E_{k_{b}}-E_{k_{a}}$ (Theorem of Live Forces)

Convervative forces work (increment of Potential Energy):

$W_{c}=\overset{b}{\underset{a}{\int}}F_{c}dr=-(E_{p_{b}}-E_{p_{a}})$

Non conservative forces work (increment of Mechanical Energy):

$W_{nc}=\overset{b}{\underset{a}{\int}}F_{nc}dr=(E_{k}+E_{p})_{b}-(E_{k}+E_{p})_{a}=E_{T_{b}}-E_{T_{a}}$

For example, when we take an stone from the floor and get it up to a height of 1 meter, there are two forces: gravity force and our hand force to raise the stone.  Gravity force do the negative conservative work, and our hand is doing the non conservative work.  Total work would be zero, but the Potential Energy has increased and its increment is equal to conservative work with sign changed (conservative work would be negative, but increment of Potential Energy would be positive).

40
##### Astronomy and Astrophysics / Cosmic Microwave Background (CMB)
« on: November 06, 2011, 02:16:29 PM »
Looking at the sky with our instruments we can see background noise of the Universe beginning:

COBE Satellite image:

WMAP Satellite image:

If we suppose an Universe without expansion after inflation, these satellites pictures would be showing us the emitted radiation 13,000 millions years ago by the part of the universe that was far from what we would be approximately the same light-years.

If we suppose an Universe in expansion after inflation and when this radiation was emitted, 13.000 millions years ago, the Universe size was 1000 times smaller than now, these satellites pictures would be showing us the emitted radiation 13,000 millions years ago by the part of the universe that was far from what we would be a d distance.

To calculate distance d:

Where:

$T=13\cdot10^{9}\: years$

We have:

$d+2x=1000d$

$d+x=d_{foton}=13\cdot10^{9}\: light-years$

$d\simeq26\cdot10^{6}\: light-years$

Diagram to see where would be 13,000 millions of years ago the radiation of the CMB that we can capture now:

Spanish:
Si supusiéramos un universo sin expansión después de la inflación, estas imágenes de satélites nos estarían enseñando la radiación emitida hace 13.000 millones de años por la parte del universo que estaba alejada de lo que luego seriamos nosotros aproximadamente esos mismos años-luz.

Si supusiéramos un universo en expansión después de la inflación y que cuando esta radiación fue emitida, hace unos 13.000 millones de años, el tamaño del Universo era 1000 veces menor que el de ahora, estas imágenes de satélites nos estarían enseñando la radiación emitida hace 13.000 millones de años por la parte del universo que estaba alejada de lo que luego seriamos nosotros una distancia d.

NASA Diagram of Timeline:

Graphical Explanation:

41
##### Robotics / LEGO MindStorms NXT
« on: August 16, 2011, 09:21:21 AM »
LEGO MindStorms robot solves the RUBIK's cube:

http://mindstorms.lego.com/en-us/products/default.aspx
http://rbtnxt.blogspot.com/

42
##### Robotics / Re: Robot walking...
« on: August 16, 2011, 09:16:11 AM »
Amazing!

43
##### Robotics / Robot walking...
« on: August 15, 2011, 08:20:02 PM »
Walking:

Crashing:

44
##### Physics / Particles Zoo
« on: August 14, 2011, 11:23:35 PM »

45
##### Astronomy and Astrophysics / Interesting Links
« on: July 26, 2011, 02:52:10 PM »

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