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Messages - Alberto Dominguez

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1
Astronomy and Astrophysics / Re: Cosmic Microwave Background (CMB)
« on: April 20, 2014, 10:30:09 PM »

2
Astronomy and Astrophysics / Astronomy Picture Of the Day (APOD)
« on: November 30, 2012, 11:44:49 PM »

3
Astronomy and Astrophysics / The Celestial Sphere
« on: November 30, 2012, 11:40:17 PM »

4
Astronomy and Astrophysics / Constellations
« on: November 30, 2012, 11:38:00 PM »

5
General Discussion / University Ranking to obtain job
« on: October 27, 2012, 06:13:27 AM »

6
Astronomy and Astrophysics / Re: Journey to the Starts
« on: October 07, 2012, 07:54:30 AM »
Same video with subtitles:

7
Electromagnetism / Maxwell's Equations
« on: October 07, 2012, 06:13:35 AM »

8
Tools / Re: Using LaTeX in forums...
« on: October 07, 2012, 05:52:08 AM »
To modify Row Height on LyX:

Insert Code:

Code: [Select]
\renewcommand{\arraystretch}{2.5}

9
Neurobiology / Some numbers...
« on: September 30, 2012, 07:16:51 AM »
From human brain and always approximate:

Number of Neurons: 100.000 millions
Number of Glial Cells: 1.000.000 millions
Neurons size (Soma size): 0,01-0,05 mm
Axon length: 1mm-1m
Axon diameter: 1mm-25mm
Dendrite length: max 2mm

10
General Discussion / Online Courses Caltech, MIT, etc...
« on: September 29, 2012, 01:34:15 PM »

11
Classical Mechanics / Resonance phenomena
« on: August 31, 2012, 08:29:21 PM »
Driven Harmonic Oscillators Equation

Periodic force with frecuency of vibration $\omega$:

$F=F_{o}cos(\omega t+\alpha_{o})$

Movement equation:

$\frac{d^{2}x}{dt^{2}}+2\gamma\frac{dx}{dt}+\omega_{o}^{2}x=\frac{F_{o}cos(\omega t+\alpha_{o})}{m}$

$\omega_{o}^{2}=\frac{k}{m};\gamma=\frac{b}{2m}$

$x(t)=x_{h}(t)+x_{p}(t)$

Transient solution (depends on initial conditions):

$x_{h}(t)=Ce^{-\gamma t}sen(\sqrt{\omega_{o}^{2}-\gamma_{o}^{2}}t+\delta)$

Steady State (independent of initial condition):

$x_{p}(t)=\frac{F_{o}}{m\sqrt{(\omega_{o}^{2}-\omega^{2})^{2}+4\gamma^{2}\omega^{2}}}sen(\omega t+\alpha_{o}+\beta)$

Solution:

$x(t)=Ce^{-\gamma t}sen(\sqrt{\omega_{o}^{2}-\gamma_{o}^{2}}t+\delta)+\frac{F_{o}}{m\sqrt{(\omega_{o}^{2}-\omega^{2})^{2}+4\gamma^{2}\omega^{2}}}sen(\omega t+\alpha_{o}+\beta)$

When $\omega=\omega_{o}$ the Amplitude is maximum and if b=0 then it is infinite, so a not too great force can collapse an strong structure if this force is applied at this frecuency of vibration.  This is the resonance phenomena.  All materials or structures have several natural frecuencies ($\omega_{o}$) and they can enter into resonance.  Perhaps the most famous sample is the Tacoma bridge:

12
Mathematics / Re: Useful Trigonometric Identities
« on: August 31, 2012, 08:09:13 PM »
$Asen\alpha+Bcos\alpha=\sqrt{A^{2}+B^{2}}sen(\alpha+\varphi)$
$\varphi=arctg\frac{B}{A}$

13
Mathematics / Re: Useful Trigonometric Identities
« on: August 27, 2012, 08:01:18 PM »
$
sen(x+y)=senxcoxy+cosxseny

sen(x-y)=senxcoxy-cosxseny

cos(x+y)=cosxcoxy-senxseny

cos(x-y)=cosxcoxy+senxseny
$

14
General Discussion / Wheather on Mars
« on: August 25, 2012, 10:26:44 AM »
On this link we can see the atmospheric conditions on MARS:

http://cab.inta-csic.es/rems/marsweather.html

Atmosphere on Mars is very light and its average pressure is between 7 and 9 hPa versus on Earth we have 1013 hPa at sea level.  Also we can see that on the day of the pic, there was winds about 90 Km/h (25m/s).

Also the gravity on Mars is lower than the Earth, the Martian gravity is 38% of Earth's, thus its atmosphere is higher than Earth's.  Its composition consists of 95% carbon dioxide, 3% nitrogen, 1.6% argon and contains traces of oxygen and water.

Martian sunset by Spirit at Gusev crater:

Source of pic: Wikipedia

15
General Discussion / Schools and Workshops
« on: August 15, 2012, 10:10:36 PM »