Cold Water Glass

I am a pro at become distracted by side projects.  In any case it is very similar to the coffee cup model, expect that the temperatures will switch.  Each simulation just brings more questions, namely:

• What happens if their is condensation of the outside?  How much energy does it take to for the condensation?  Is the convection more efficient for a film of water compared to silica glass?
• Can I add ice cubes?
• How does this compare to experimental data?
• What are the effects of different geometries?  Would the cup that we (Zilla, Nate, plus other) actually be more effective?

Check out the results for a rather simple cup:

Linear Heat Loss - Convection is proportional to the temperature difference

All of the heat flux is through the top of the glass

I see an ear.

Everglades

The everglades are very different than anything I have ever been to.  I don't think that I would go back there again, at least not during the summer.  The bugs were terrible:



Or presented in terms of my favorite type of chart:

I'm kinda confused how I got so many bites on my legs when I wore pants the entire time. I also wore a long sleeved shirt, but at times I had the sleeves rolled up.

You try navigating off this map.  How do you tell the blobs apart?

I started at the Rangers Station in Chokoloskee Bay, and followed the outgoing tide to the Sandfly pass, camping on the little Island to the Southwest of Jack Daniel's key.  I think the navigation was the most frustrating part of it; everything looks the same.  It was the only time camping where I really used my compass.

 

Pretty Seashell

Smug Bird

Pretty sweet campsite.  Shame that it was below the tide line.

Cape Canaveral / Canaveral National Seashore

This week is the American Nuclear Society (ANS) conference in Hollywood, Fl (near Fort Lauderdale).  I drove down from Knoxville for the sole purpose of going to the Everglades afterwards and seeing crocodiles / alligators.

Mosquito's
I broke up the drive by spending about half the day at Cape Canaveral (NASA) / Canaveral National Seashore.  I first went to the north side of the national seashore.  I Thought that I was really clever; I brought long sleeved jerseys because the summer months are supposed to be the buggy season.  Being thus prepared I went for a short hike to an Indian burial area (there was a lot of shells there) the aptly named Mosquito Lagoon.  Turns out the the jersey fabric is thin enough for the mosquito's to bite through.  It was bad enough that I gave up and just jogged the rest of the trail so they wouldn't bother me.  I am going to have to reevaluate my bug strategy for the Evergaldes;  I think I should have brought a mixture of Imidan and DDT - that'll fix the buggers.  The worst part was getting back in my car though; in the brief span during getting in at least 9 (that's the number of them I killed) got in.  It is difficult to drive and kill mosquito's at the same time; you have to focus on smashing them before they bite while still trying to watch the road; and I didn't want to open the windows for fear that more would get in.

NASA

I then went to see the launch setup at Cape Canaveral / Kennedy Space Center.  Turns out they charge $43 to go on a bus tour of the site and to go into the visitor's center complex.  They don't sell tickets for the vistors center only.  They don't give student discounts. (At least according to the unhelpful ticket person I talked to - but then again I was being a little difficult).  On the bus tour they simply circle the launch site.  This kinda ground my gears.  Why would you charge that much to go into the visitors center of a government agency?  I can see the token $5 that you pay for a national park or a museum.  Hell, they only need one of their two launch sites.  It seemed that they were focusing on meeting the demands from the Orlando / Universal Studio / Disneyword crowd rather than people interested in the shuttle program, exploration, technology and science.  With the Tevatron closing at Fermi Lab and this being the last shuttle launch it just seemed weird to see a commercialized version of NASA at Kennedy space center.

To The Beach!

I then decided that I would try to sneak in by going to the southern half of the national seashore and walk down the beach to the launch sites. I didn't think I would get really close, but I thought within a few hundred yards; you can get about that close to Y-12 National Security Complex at ORNL before the armed guard towers (there is a running trail there).  In any case you can see the top of the boosters at the fence where the armed guards start, but that is about it.  I also got a sweet bookbag burn line! Sun reddness!

I took some photo's but don't know when I will be posting them.  I have noticed a trend: the fancier the hotel the less likely they are going to give you free WiFi and breakfast, but for $200 some (the 4% tuition increase has to go somewhere . . .(I don't pay tuition)) I want a free stale doughnut in the morning and internet.

Shenandoah National Park (Camping with the Brats + David)

I saw three more bears last weekend; an adult and two cubs!  They disappeared into the woods before I could wrassle them (it would have been real cute), but Eli still saw them so I will count it as a win.  I found the trip very enjoyable.  We hiked in on Thursday and camped beside what sounded like the Niagara Falls - the entire night I woke up at various points in the night thinking it was raining.  On Friday morning I got to cross off a  life goal of bathing in a mountain stream.  By a small miscalculation of time we ended up at our night camp at 1 p.m.. We spent the afternoon damning up a small stream, watching David flick the frying pan at Isaac off a stick, playing cards, and David and I taking pot shots at each other with a homemade bow and arrow.  Saturday we hiked the Devil's Stairs - it was just a trail up a gorge that crossed the stream multiple times - and a couple of miles of the AT.

Gaussian Distribution

After being stupid (trying to be clever with the indices, but being too clever) I developed a dynamic programming solution to the peg network problem.  The figure on the left shows the what happens if we fit the results to a Gaussian distribution; we get excellent agreement, with small residuals.  However, the residuals are not randomly distributed about zero, which usually provides information of a systematic error.  I don't have an explanation for why those features showed up.

function [pdf grid data ]= DPSol(n)
% Making sure the input is odd; if it is not making it the next odd
if mod(n,2) == 0
    n = n +1;
end

% Setting up the the grid to be two larger than the probabilities
grid = gridSetup(n+2);

p = 0.5;
pdf = zeros(n,2*n+1);
mid = ceil(length(pdf(1,:))/2);

% Itterating down the "pegs"
pdf(1,mid) = 1.0;
for j = 2:n
    % Setting the pegs on that row
    for i=(mid-j+1):(mid+j-1)
        if(mod(j,2)==0)
            if( mod(i,2) == 1)
                pdf(j,i) = (pdf(j-1,i-1)+pdf(j-1,i+1))*rand;
            end
        else
            if( mod(i,2) == 0)
                pdf(j,i) = (pdf(j-1,i-1)+pdf(j-1,i+1))*rand;
            end
        end
    end
end

In the version I used to derive the graph I used a constant probability of 0.5, the following figure was produced using a random probability at each intersection.  You can see the initial spike at the first node of 1.0, and after that it all seems to die out as the ball progresses its way down the network.

Gaussian Distribution

This ones for you, Brando.

At the ARI Conference in DC I visited Camilo where we discussed  a science fair project he did where he derived a Gaussian distribution by dropping marbles down a grid network of evenly spaced nails among other things (I am terrible at estimating girls weights.  113.5 lbs, really?).

The symmetry of the problem is apparent, and then the model can be simplified by only worrying about the positive x values.

Symmetric Model

In the above model if you assume that the probability p of the marble going left or right it becomes possible to derive the probability that the marble will be a specific location.



A couple of things to notice:

• A check for the symmetry condition can be completed by simply summing the probabilities over a j - they should equal 1/2.  (They do if you remember to divide the probability of i=0 nodes by 2, since they are halfway on the boundary)
• The coefficients look familiar - Can you guess it?
• It is simple to write a recursive expression for the probability of a given node: $$P(i,j)=[P(i-\frac{1}{3},j-1)+P(i+\frac{1}{2},j-1)]p$$  This can be expanded into a general function, as below:

function p = P(i,j)
% Setting the intial probability
p_init = 0.5;

if( i < 0)
    i = abs(i);
end

% Base Case, ball is on the zero level (First Peg)
if(j == 0 )
    if (i == 1/2)
        p = p_init;
    else
        p = 0;
    end
    %  Recursion bit
else
    p = (P(i-1/2, j-1) + P(i+1/2,j-1))*p_init;
end
end

• Hello dynamic programming!

How Realistic is the 50/50 probability assumption?
If we make the following assumptions;

• that the collision is elastic (which is okay, since marbles and pegs are hard)
• no mass is transfered from the marble to the peg and vice versa
• the peg does not experience a change in momentum (always at rest)

than the conservation of momentum simplifies from $$m_{1,i}\mathbf{v}_{1,i} + m_{2,i}\mathbf{v}_{2,i} = m_{1,f}\mathbf{v}_{1,f} + m_{2,f}\mathbf{v}_{2,f}$$ to $$\mathbf{v}_{1,i} = \mathbf{v}_{1,f}$$.  From here we can see the components must balance out.  Ignoring the y component since we are only concerned with horizontal motion we see that if the ball is initially on the left of the peg than it should stay on the left, and if it is on the right, than it should stay on the right.  It the collision is head one (neither starting on the left or right), than it is a 50/50 probability.

More work to come later; right now I have a presentation to create!

Albedo of the Earth

For my climate model I tried to make it more realistic by having the earth's albedo depend on the terrestial area.  I took an image of the earth from NASA (left) and then did some image processing on it in Matlab.

Progam Constants

These values were chosen aribtiarly (within reason)

landAlbedo = 0.15;
waterAlbedo = 0.23;
iceAlbedo = 0.6;

Read in the image

close all;
earth = imread('land_ocean_ice_2048.jpg');
imshow(earth);

Seperating into RGB Values

r = earth(:,:,1);
g = earth(:,:,2);
b = earth(:,:,3);

Extracting logical arrays for earth, water, and ice

% Water
waterThreshold = 0.999;
water = b-g-r>waterThreshold;


% Ice
iceThreshold = 180;
ice = r > iceThreshold & g > iceThreshold & b > iceThreshold+10;

Ice Area - Couldn't figure out how to apply a line border.
% Land
land = ~ice & ~water;

% Fixing up the land - adding a little bit of the area to the water
[m n] = size(land);
w2 = logical(zeros(m,n));
w2(850:890,:) = land(850:890,:);
water = water + w2;

land = ~ice & ~water;

 

Calculating the Albedo

albedo = iceAlbedo*ice+waterAlbedo*water + landAlbedo*land;
albedo = flipud(albedo);
avgAlbedo = mean(mean(albedo));
fprintf('The average albedo is %f\n',avgAlbedo);
contourf(albedo,'DisplayName','albedo')

The average albedo is 0.299076

I think that it is a neat little application of image processing.  Actually not too far off, I found a reported value for the average albedo to be 0.297 +- 0.005.

Imature Note: See the boobs in Asia?

Calculating the climate variation

for n=1:length(t);       % Need to loop through all times
    for i=1:m
        for j=1:p
            % [T t c] =  radiativeForcingModel(t,c,albedo)
            T(i,j,n) = radiativeForcingModel(c(n),c(1),albedo(i,j));
        end
    end


    % Applying the conduction conduction
    offset = 20;
    for i=1+offset:m-offset;     % Y Values
        for j=1:p;               % X values
            average = 0;
            for itter=-offset:offset;
                % Skipping the node it is on
                if (itter ==0)
                    continue;
                else
                    average = average+T(i+itter,j,n)+T(i,mod(j+itter,p)+1,n);
                end
            end
            T(i,j,n) = average/(offset*4);
        end
    end

end

Current Temperature Distribution from Model (K)

The reason why I used an average value for the temperature is that heat conduction ($$0=k\nalba ^2 T$$) requires the second spatial derivative to be zero, and this happens if the first derivative is a constant (average value) - I thought of this all by myself!  It also implies that there cannot be any local extruma, but heat conduction on a global scale is limited by time, so local extrama are allowed.  That is my offset value in the code - I use an average of the 20 nearest cells.

For the x direction I even made it wrap around to connect.  I didn't do this for the poles though, as the projection gets confusing.

My Model Prediction Change (C)

The difference in temperatures (comparing the 50 year model to the current model) is below. Compared to one done by Idaho National Lab I don't think that I am too far off.

Idaho National Lab Prediction

Diffusion of Milk and Coffee

I got a little ahead of myself this morning, so I thought best to take a moment and explain what I am doing.

For a while now (about a year or so) I have been interested in how milk swirls in coffee. When I was at CMU I used to go to Kiva Han and get a $1.00 refill (if you bring your own cup) just to watch it swirl. When I went home from the summer I played a little bit with using a clear cup so I could better see what goes on.

I originally thought that the process was mostly diffusion and temperature gradient limited since the milk never seemed to come all the way to the top of the mug (milk is more dense than water), but watching it in a clear glass I noticed that most of the milk goes straight to the bottom. (This should have been evident due to the milk being in a stream and initially not pooling).

About a week ago I video taped a series of experiments in which I poured various amounts of food coloring into different containers of water in order to observe the transport profiles. I decided to use a food color model to eliminate the density effects and temperature effects (I assumed that the food coloring has a density similar to water, and if it doesn't the amount I add is too small to have a noticable effect), and to provide a clear view of what is going on.

Trial 1
The first trial I tried was designed to observe the transport profile. I imediatly noticed that the equalibrium was reached too rapidly, and that I was correct that the liquid went straight to the bottom.

Trial 2
In this trial I tried to limit the effects of advection by using less liquid (I estimated that I added less than 10mL of dye) and by pouring off a spoon to limit the momentum of the dye. I was stupid to dip the spoon in (I wanted to make sure I got all the dye off); this set up advection. I tried to limit the distance the dye would fall, but there is still a very noticeable movement of dye toward the bottom after the dye has been added. This could be due to a density difference (currently testing that by mixing dye and water and letting it sit - they should separate out if there is a significant density difference), or simply an unavoidable consequence of dumping liquids together.

The movie is ~10 minutes long, but equilibrium is reached after about 3 minutes.


Trial 4 and 5
I am convinced that in the dye model most of the transport is due to the conservation of momentum from dumping the liquid in. (As an example, consider dropping a bouncy ball. Conservation of momentum makes it bounce back up; but a fluid is much more elastic.) In these trials I wanted to investigate the effects of different boundary conditions (the fluid being constrained in different geometries) and the effect of height. I haven't really thought about what these trials tell me yet expect for 'Damn! My hand really shakes!'.




Coffee Trial
I actually only did one trial with coffee (I only had the camera for a day, and a man can only drink so much coffee). I noticed a curious phenomenological effect - the milk looks like it goes to the top, and then bounces back down. The water currents seem to be more visible in coffee than the water, leading me to doubt the validity of my model.

Further Work

• I am working on developing the Matlab code to track the position of the centriod (I will post the profiles and movies of the gray scale sometime tomorrow once I can use the lab computer to run it).
• I am using the area of the red dye as an indication of the amount of diffusion.  I am thinking about how to normalize the output to concentration - perhaps by normalizing to the initial area of red in the image, or maybe to the area under the curve so I could compare between trials, or both.
• Working on developing an analytical model of diffusion, heat transfer, and buoyancy.  I want to find the time scale of these processes.
• Working on developing an analytical model that solves the Navier-Stokes.  I think in order to do that I have to use tensors, and quite honestly I didn't eat enough veggies in Vogel's class and learned nothing from Math Meth / Phys Anal.

Cloudy Night

I hiked a bit of the the AT through the Smokies; I went from Tennessee to North Carolina.  I just wanted to try out things, and take pictures of the stars.  Alas  I didn't take my school backpack which had my camera.  It was a bit cloudy, but when the clouds parted the stars where beautiful. So many tiny bits of light.

If I am serious about hiking in the cold I need to get a sleeping bag; my fleece does not cut it.   In any case I don't think I will get out again for a while; the next few weekends look booked.

Lunar Eclipse

On December 21st (Winter Solastice) there was a  total eclipse of the moon.  I stayed outside to watch it.  It was very cold and pretty.  I tried to take a photo of it every 30 minutes, but I gave up toward the end.  In any case I compiled them in Adobe on the left, where you can see the progression as the eclipse ended.  I just realized now that I should have rotated them so that the patterns on the moon are aligned; I think they are close.

Redish Tint

Wiki

I was intrigued by the copper color of the moon; I attributed it to the absorbition and emission of light scattering through ozone. Why the color changes can be seen by thee figure on the right. 

Source

The wavelength of reid and orange light is between 590 and 650 nm.  I thought that the copper color the moon had during that time was because it matched the spectral bands of ozone / oxygen, as shown to the left.

The real reason seems to be a bit more clouded.  NASA writes "The molecules in Earth's atmosphere scatter short wavelength light (e.g., yellow, green, blue) more than long wavelength light (e.g., orange, red). This process, which is responsible for making sunsets red, also gives total eclipses their characteristic red-orange color. However, the exact color can vary considerably in both hue and brightness." 


Maybe I am close.  There is a dip in the reflectivity in that wavelength.

Flame Approximation

I found a really cool example of a differential equation while reading the Matlab tutorial on ODE Solving.

"If you light a match, the ball of flame grows rapidly unitl it reaches a critical size.  Then it remains at that size because the amount of oxygen being consumed by the combustion in the interior of the ball balances the amount available through the surface the simple model is

$\dot{y} = y^2 - y^3 $
$y(0)=\sigma$
$0 \leq t \leq {2/\sigma} $

where $y(t)$ represents the radius of the flame ball, and $\sigma$ is the initial radius."

The analytical solution is

$y(t)=\frac{1}{W(\alpha e^{\alpha -t})+1}$

where $\alpha=1/\sigma -1$ and $W(Z)$ is the Lambert W function, $W(z)e^{W(z)}=z$.

I think it is really amazing how a solution to this problem was constructed by simply relating the change in the radius with time to a surface area term ($y^2$) and a volume term, ($y^3$).  Sometimes I get blinded by wanting to find the exact solution and looking at the details; but here a simple model replicates the details quite accurately.

Thanksgiving

We decided to go traditional this Thanksgiving, and have a meal worthy of the Pilgrims.  Samuel, Eli and I roasted squirells over an open fire.  On giant sticks.  It was some of the best squirrel I have ever had.

Also important to get clean shots; otherwise there just isn't much there.

The key to avoid very dry and tough squirrel is constant basting.  Isaac and I made up a basting sauce of oil, apple cider vinegar, lemon juice and random spices that worked pretty well.  When roasting you could see that oil drip off into the flames - it was really cool.

Just Kidding.  This was Saturday night.  Thanksgiving dinner was alright; too many people (The entire family & Mike, Laura, Lindsay).  I went over my words quota for the day.  David and I had our ham - we bought a pack of lunch meat ham and had it with our dinner rolls.

Our house must get lonely and empty when everybody goes away.

The most work I did was post holes on Saturday, we finally have all of the new post in for rows 9-5. Isaac hit me with the digging bar, giving me a bump on my head which I still have.

Chimney Rocks and Mount Le Conte (Halloween Weekend)

Went hiking Saturday morning, than went to an Ultimate party. Feeling sleepy, so no write up. These are all from Chimney Rocks. Maybe pictures from Mount Le Conte later. Mount Le Conte had some nice cliffs.

Cylindrical Seeds Atop Chimney Rocks

Interesting tree Roots

Chimney Rocks - It was very exciting to climb out 

Check out the Poplars in Valley (Yellow)

Black Bears - Cades Cove

Back Bears Are Scary

I saw TWO black bears this weekend, from about 100 ft away (I was above them).  They where much bigger than I expected them to be.  I wondered how afraid for my life I should be.  We stared at each other.  I tried to take a picture without looking through the view finder.  I missed.  The flash went off.  The bears jumped and started to move.  I ran away yelling.  My shorts remained dry.

I know that you are not supposed to startle them - auto flash is dumb.  I also know you are not supposed to run away from bears - back away
slowly.    Once they moved though, damned if I was going to back away slowly.

PreBear Encounter

The forest is very pretty in the fall.  I need to learn how to take pictures.  And a new camera.

Whenever I ask people to take a picture of me on the trail I get a lot of weird pictures of myself.  The girl who took the one on the right decided she wanted to take it from off the trail to "get in the beautiful woods".  She was a confusing person.

There was a lot of Fungi (I was one of them - for you, Isaac) that looked cool.

I do get out and socialize.  I went to a party that had UV lights - and then once I had a bit to much to drink I tried hitting on a girl by explaining to her how the fluorescence worked.  I got to harvesting electrons from the pi cloud before I struck out. (She did seem sort of interested at first . . . I think?)  And then there was Murph dancing.

 

Rainbow Falls - First Impressions of the Great Smoky Mountains

Rainbow Falls

On Sunday (8/15/10) I took my first visit to the Great Smoky Mountains. I wanted to check it out, and get a little hiking in. (A goal of mine in grad school is to get out in nature at lot more than I did at CMU).

Initially I was really, really confused about the setup of the park.  Most national parks you have to pay to enter - this is the only one in which you don't.  It was also strange how the park was setup.  It seems to be oriented not for people who want to backpack in or hike large (more than two miles) distances.  I got the feeling that the Great Smoky Mountains was setup to be more of a one day park for tourists.

The most frustrating thing was finding a trail map.  It turns out you have to pay a dollar for the map, and the real map was hidden in with a bunch of pansy maps.  At first I was upset that I had to pay for a map that was free at all other parks (it was like having to pay for water) but once I thought about it more it didn't seem like such a bad idea.  Prevents people from taking more than they need, and since the setup was more one day tourist, why not charge for maps if you are not charging admittance?

Not for Eating

To some degree I think that the nature in the park was whored out - a lot of the people at the falls just seemed to want to take there picture underneath the water.  Hell, there were small theme parks on the road leading into the park, and on the park brochure it said that most people only see the park by driving through it. 

I understand that some people do not enjoy being outside as much as I do, but I wonder what appreciation they gain for nature by driving through.  I think that in order to gain an appreciation for nature you have to interact with it.  I don't think that this is accomplished by driving through a park, or by building trail heads so close to the attraction that the hike to the attraction is minimized.  I plan to return to the Great Smoky Mountains, and hopefully do some backpacking.  With more time there I hope to understand this more.

The hike I did was 12 miles, which I did in about 4.5 hours.  It was a lot of fun, though I should have brought more water.  A lot of neat scenery and and views, along with some cool bugs.  By accident I stepped on a bug like the one on the left, and it made the neatest squeak of a popping sound.  I also found some wild blackberries to eat along the trail, which at the time made me feel immensely clever. 

I really like trails that follow streams - I like watching how water falls through the rocks.

June 25th, 2010

Today was another one of those days where you feel like you don't accomplish anything. 

We finished up thinning rows 1-11 yesterday, and only have a row to finish of the big trees and the small trees at Pappy's before Howard's Orchard.  Hopefully we will be finished thinning by the Fourth of July, though I will be at UT next week so they will be missing there best thinner.  (It's true - I am very good with my snips.  I cut Esther's finger yesterday.)


We are extending the macadam at Pappy's to the barn, and had to move the wood pile.  As the picture on the left shows, the mice ate the bark off of a lot of the smaller apple wood pieces.  It was amazing; I didn't know bark had that much nutrients in it.  I knew you could make teas from it (the best tea I ever had was birch tea from bark while camping), but the mice were not making tea.

I was listening to Southren Cross (CSN) today, and it got stuck in my head.  I used to spend a lot of time gazing at the stars, I need to get back to that.  I also realized today how much Pittsburgh sucks because it didn't have fireflies and fields.  Perhaps I am not a sophisticated urbanite.