Lighter than Air

I'll be the last person to cite a yawhoo (sic) news article, but that's where I read about this: World's Lightest Solid

In the summer of 2009 before entering Caltech I went to D.C for some congressional seminar. During a tour of the city two friends and I ditched the group and headed to the Smithsonian Air n Space Museum. I'd heard about aerogel, and I knew the museum had it on display so I was itching to see it. It looks so ethereal:


 silica-based frozen smoke

It's particularly useful in space missions when you want to bring back airtight samples in a zero gravity environment. You can trap space dust which would otherwise vaporise in a solid medium and pass through a gaseous one. Aerogel seemed like the Goldilocks zone between solid and gas.

a star dust collector with aerogel blocks


 

The Smithsonian sample was developed in JPL earlier on and had 3 times the density of air; current samples are less dense than air, some as low as 43% of the density of air. (But these technically aren't 'aerogels' because they are composed of nanotubes and not a dendritic lattice with evenly spaced pores) Aerogel can be structurally very diverse, consisting of 99.9% air.
It is constructed by surrounding the material mass with an impermeable film and flooding it with light gases like hydrogen and helium, or pump out the air in the material to create vacuums within the structures.

Structurally aerogels are very porous and either are crosslinked polymers all looped together or dendritic polymers branching outwards.

Aerogels can easily shatter (friable) but are incredibly strong structurally and can support up to 1000 times their weight. Since they are so light, this is still less than an atmosphere which is why squeezing it will shatter the cube.

The yawho? article really a distinction between monolithic aerogels and carbon nanotube aerogels (what the article means by an Eiffel tower structure). The stronger, less dense aerogels are made of carbon nanotubes so the lattice structure is more organized than dendritic aerogel, which is weaker by virtue of its random structure.

P.S read the image tag in the article! Caltech worked to develop this new model

P.P.S as best as I could understand it by monolithic structure purists mean aerogel has a singular dendritic structure, while the nanotube structures consist of multiple carbon cylinders woven together. In this case, aerogel is 'cut' off a single stone of chemical building material

Ghosts in the Mirror

Professor Johnson explained atmospheric effects as decreasing the image resolution by increasing the full-width half maximum of the intensity plot. When we had first covered n-slit diffraction I would have thought that simply making the telescope lens bigger would counter this effect since resolution is proportional to lens diameter (resolution = \[Lambda]/diameter so a larger diameter means better resolution). 

Here's a simple explanation of how deformable mirrors work: In response to John's post Happy Halloween where he identified molecular cloud ghosts, here's a toast to making ghosts out of deformable mirrors.

Back to the problem of resolution - Naturally it is very expensive to make larger telescopes. The white board explanation showed each incoming wavefront as a line (assuming a very distance source,/k /circular wavefronts become lines), and atmospheric perturbation introduce phase differences so you had a bump readout instead of the flat line.

Another question I had but forgot to ask - how large are the disturbances in the wavefront and how much does deforming mirrors adjust this?

Another cool video about deformable mirrors and the private industry:

I liked this one more (barring the lack of ghosts) because the music was more motivating. I felt like scientists were superheroes.

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1. It take an impressive amount of background knowledge of all the facets of physics and astronomy even to specialize in a particular area.
2. Interestingly enough, at the same time there are so many areas of astronomy to specialize in. It's as if each star has its own field! This makes my initial aspirations of studying general areas like 'black holes' or 'dark energy' sound naive and uninformed.
3. I am amazed by the breadth of each of our class speakers' knowledge - where between our time as undergraduates and graduates will we acquire that amount of expertise? It's as if there's some huge knowledge discontinuity forming over just a matter of years.

A quick aside -

At the same time I dispelled some prior prejudices about astronomy. I felt that the distinction between a practical an theoretical astronomer is not always as clear cut as I imagined.

I used to think of practical astronomers as having to wake early in the morning and work late at night at the lab or telescope to catch a fleeting star or make a late report, while theoretical scientists would (in theory at least) stay at home and watch reruns for most of the time, then dedicate an intense amount of time and concetration on researching and publishing the next paper. If we think of our work as an astronomer as an evolutionary progression, I saw practical scientists as examples of gradualism while theorists exemplified punctuated equilibrium. A practicer of the dark arts would have to follow an engraved work schedule plus anomalies, while a theorist could blow bubbles all day as long as he periodically published something.

But of course, to be any good as a practicing astronomer, you need a luscious theory backbone, and to be able to say anything as a theorist you need observations to verify your ideas and sometimes even come up with them.

Back to the list:

4. Being a professional astronomer requires a quirky sense of humor of at all times.

5. Computer programming- This winter I plan on going through and teaching myself C+ (sic) since so far I've tried to do everything with Mathematica.

My ultimate goal is to ultimately have a goal. I used to be certain that I wanted to study the hidden and unobservable universe, but now I'm not sure what I want to specialize in. I'd like to develop the vast breadth of background knowledge and fine-tuned intuition astronomers uniformly possess. At the same time I don't want to put off deciding a particular field too long so I can focus my SURFs and try to bridge that knowledge discontinuity between grads and undergrads.

I want to say that the ultimate goal of astronomy is to find a theory of unification, but I know that's insufficient. Even if we find out everything we can about the beginning of the universe and map out its evolution we will still not know much more about observable stellar and galactic properties.

A drunk photon randomly walks into a bar

a. The dot product of all the random path lengths in the random walk determines the distance D squared.


If the angle between two consecutive vectors is greater than 90 degrees, the dot product is negative, and if less it is positive (at 90 degrees it equals 0). Therefore, although our sum involves dot products between vectors pointing at different directions as well as identical vectors, we can say that the sum of all dots of different vectors is 0. We are assuming we have many vectors (the pathlength of a photon is small compared to D, and scattering is frequent), so we have a Gaussian distribution of dots of different vectors centered around 0 (dot of two vectors at 90 degrees to each other) so we have as many positive dot products as negative and they average to 0. The dot of a vector with itself is just its magnitude squared, so our sum reduces to:
 

so the average number of steps n of a drunk photon is:


b. The photon travels a total distance of n * l. It travels each pathlength l at the speed of light c, so it takes time t = l/c to traverse one pathlength. There are n pathlength ys, so it takes total time n*l/c to go from core to surface. This covers a displacement D, so the photons average velocity is:

v (diffusion) =

c. The mean free path l has units of cm; mass density rho has units g/cm^3, absorption coefficient \kappa has units of cm^2/g. From inspection we see that rho*/kappa ~ 1/l to be dimensionally correct. Daniel asked why we had cross sectional area of observers rather than volume (since by introducing a constant with desired units the equation could still be dimensionally correct). 

We can answer this, and show the pathlength is equal not merely proportional to the rhs as follows:
Consider a cube with face area A and edge length l. Assume it has N particle density each with cross sectional area c, so the total cross sectional area is NAlc (assuming particles don't overlap).
The probability of  a photon going through and hitting a particle is P=NAlc/A = Nlc (equivalently the number of particles in that volume). The particle has moved a distance l, so the average distance between collisions (pathlength) is l/Nlc = 1/Nc. We can convert number density to mass density and cross sectional area to cross-sectional area per gram and maintain consistent units.

d. There is a flux of photons moving through concentric shells of the sun. We have a difference in energy density since there is a flux into a radius of disk r to a disk of radius r + \delta r, and flux varies inversely with radius so it decreases for outer shells. Thus the inner shells have a high energy density \delta u since flux F equals luminosity L over surface area, and energy density equals F over the speed of light c.



e. Since u= aT^4,



and the change in flux F is proportional to the opacity (total cross-section per volume, or the inverse pathlength) times the flux and the distance traveled, so




There is a negative sign since the flux decreases with radius due to absorption.
Taking the differential limits of both equations and equating we have



The worksheet equation has a coefficient of 3, which might arise from some quantum effects we don't have the background to consider.