Entropy and Chaos: Order and Disorder in the Universe
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Tuesday Sep 16, 2008
How random is dice tossing?
Jan Nagler and Peter Richter. "How random is dice tossing?" Physical Review E. 78: 036207 (2008) Link to ArticleThis is the article I showed in class, which reports current research on the extent to which dice-tossing is (or isn't!) a random process.
Posted at 08:15PM Sep 16, 2008 by DANIELS, KAREN in MediaHunt1 | Comments[2]
Non-mechanical Chaotic Pendulum
Video LinkAfter playing with the chaotic pendulum in Riddick, I came across several different chaotic pendulum designs on Youtube. Some were more complex and some were simpler. But I stumbled upon a non-mechanical version which interested me as well. Unfortunately, I an pretty sure whoever was posting this, was doing it as a joke, as the horseshoe shaped magnet is covered with a napkin or sheet - nonetheless, the pendulum still acts chaotic and is extremely sensitive to the slightest variation of initial conditions, as our study of chaos suggests.
Posted at 07:33PM Sep 16, 2008 by Adam Keith in MediaHunt1 | Comments[0]
Dry Ice Chips In Water - Interesting Patterns
Video LinkHere is a video demonstrating what happens when dry ice chips are placed in a pan of water. The set up for this experiment is just a cookie sheet painted black to show the patterns better, some water, and dry ice. When the dry ice chips are put in the water, they do not just produce a regular fizz like what might be expected; the chips actually produce their own little patterns. The author suggests that these patterns resemble the early stages of a universe forming. He also tries to use the demonstration to show the gas clouds rotating around a comet nuclei. I think it is interesting how a seemingly random reaction can form such neat patterns like this.
Posted at 07:32PM Sep 16, 2008 by Kristopher Dixon in MediaHunt1 | Comments[0]
Snowflake
There is a widely held belief that no two snowflakes are the same. Probability wise, it is extremely unlikely for any two small objects in the universe to contain identical molecular structure, but there is, nonetheless, no known scientific laws that prevents it. In perfect situations, however, two snowflakes are virutally identical if their environment were similar enough, eithe because they grew very near one another, or simply by chance.
http://upload.wikimedia.org/wikipedia/commons/c/c2/SnowflakesWilsonBentley.jpg
http://www.youtube.com/watch?v=HuwXJlPvkhc&feature=related
Posted at 01:41PM Sep 16, 2008 by Karin Hurwitz in MediaHunt1 | Comments[1]
Non-mechanical Chaotic Pendulum
Video LinkAfter playing with the chaotic pendulum in Riddick, I came across several different chaotic pendulum designs on Youtube. Some were more complex and some were simpler. But I stumbled upon a non-mechanical version which interested me as well. Unfortunately, I an pretty sure whoever was posting this, was doing it as a joke, as the horseshoe shaped magnet is covered with a napkin or sheet - nonetheless, the pendulum still acts chaotic and is extremely sensitive to the slightest variation of initial conditions, as our study of chaos suggests.
Posted at 01:40PM Sep 16, 2008 by Adam Keith in MediaHunt1 | Comments[0]
Air patterns in flowing frozen water
http://www.youtube.com/watch?v=WJMOEkDEt1g
http://www.youtube.com/watch?v=4DYOFvr8S6I&feature=related
These videos depict air bubbles moving through water under frozen brook. The inputs of the system are relatively simple. Under the effects of gravity and surface tension, the air clumps together into large bubbles that move through the brook as a group. Furthermore, these bubbles congregate in areas where the is increased elevation, perhaps due to thinner or broken ice, or mere inconsistencies, such as bumps. However, as more air reaches these areas, it tries to push the existing air out. Likewise, the existing air shows no intention of leaving its spot. Thus the air patterns depend on the volume of the area, and the air pressure (more air tries to get into the same volume, leading to increasing pressure, which in turn pushes more air out). This accounts for the turbulent patterns evident in the second video around the areas where air has congregated. The patterns depend on the flow rate, shape of the river, inconsistencies in the ice, the amount of air, and the air pressure. As all of the behavior in the system is ultimately determined by the laws of physics (whether known or unknown, understood or not understood), this system is definitely not random. One could theoretically produce a computer capable of modeling the behavior of the air and water, if they somehow had the ability to make infinitely accurate measurements. Unfortunately, if one single air bubble is left out, the air pressure changes, the flow rate changes, even the melting rate of the ice and the shape of the river change. This extreme sensitivity to initial conditions is characteristic of a chaotic system. However, as there are essentially no practical applications of this phenomenon, it would probably be better to simply enjoy the patterns and sounds of the frozen brook from a layman's perspective.
Posted at 01:40PM Sep 16, 2008 by Victor Brozovsky in MediaHunt1 | Comments[0]
Cellular Automata: Conway's Game of Life
Video Link: Youtube (Cellular Automata: Conway's Game of Life)This video shows a single run of the simple cellular automation algorithm devised by John Conway. The initial conditions are set by marking "cells" on a grid. The algorithms that run the program determine for each possible cellular location whether a cell will generate there or an occupying cell will die. One of the simplest forms of the game involves the following rules:
- For a space that is 'populated':
- Each cell with one or no neighbors dies, as if by loneliness.
- Each cell with four or more neighbors dies, as if by overpopulation.
- Each cell with two or three neighbors survives.
- For a space that is 'empty' or 'unpopulated'
- Each cell with three neighbors becomes populated.
- (Cite: http://www.bitstorm.org/gameoflife/)
After watching the video, you can see how a few "cells" placed in a formation can "grow" to produce a massive pattern. This video is a bit limited, though, because it does not show other conditions.
Youtube (Another Game Of Life Video)
This video shows another initial condition and the outcome is altogether different.
Finally, we can say that this cellular model is chaotic because it is nearly impossible to predict whether the dramatic patterns that we see will stabilize and reach equilibrium or spawn further patterns.
Posted at 01:10PM Sep 16, 2008 by William Stoy in MediaHunt1 | Comments[0]
Chaotic Double Pendulum
Link: http://www.youtube.com/watch?v=Whvl6CikDxA
This video depicts the chaotic behavior of a double pendulum made from two metal slabs. The beginning of the video shows how the pendulum acts when it is allowed to rotate on only one axis, demonstrating calculable, non-chaotic behavior in the form of a simple back-and forth motion. Next, each slab is allowed to rotate on its own axis. While one slab continues to oscillate back and forth, the other rotates around in a chaotic fashion. Although its movements are based on physical laws, its behavior is almost entirely unpredictable, which constitutes chaotic behavior. The only guarantee is that the pendulum reaches equilibrium and stops moving, as the end of the video suggests.
Posted at 12:12PM Sep 16, 2008 by Nathan Combs in MediaHunt1 | Comments[0]
Nonliear Dynamics and Chaos: Airplane Wing
The link to the video is http://www.youtube.com/watch?v=_Ys8qGxr--M&feature=related
The video depicts the chaotic behavior that an airplane wing can have. Most of the video shows demonstrations done with a model of an airplane wing in a wind tunnel. A simple wing that can only pivot is used first, and then a more realistic wing, which can pivot and move up and down. The wind speed is increased at different parts, and this leads the motion of the wing towards chaos, much like the increasing of driving factors in other models such as the population or the convection roll. There is a point in the wind speed where the wing switches from controlled motion to chaotic motion, much like the 3.4 number for R in the population. The end of the video (I know it's long) is very interesting because it shows the real life ramifications of this behavior, and it is a little scary, if I'm in the plane, I don't want to think of any part of the plane's motion as chaotic. On YouTube, there are the additional movies from that user, which show other chaotic systems, some of which we have discussed in class and some that we haven't.
Posted at 07:29AM Sep 16, 2008 by Timothy Michael Dannenhoffer in MediaHunt1 | Comments[0]
Simple Magnetic Pendulum
video link:
http://www.youtube.com/watch?v=Qe5Enm96MFQ
This is a video that shows the results of a magnetic pendulum swinging between four different colored magnets that are an equal distance from the resting place of the pendulum. As the results of the color of the magnet that the pendulum stops at are recorded, no distinct pattern can be observed; however, as the number of trials increases, it is apparent that at certain starting points (or under certain initial conditions), it is fairly predictable which color the end magnet will be. While the same results are never obtained, it proves that they are not totally random either. This perfectly describes the idea of chaos, which is when a system is not reproducable but still deterministic. It is very similar to the observations made whenever we observed the pendulum in Riddick, as well as when we studied Lorenz and the Butterfly Effect and compared it to the population growth simulation; all showed trends at certain points but not at others, and they all proved how significant initial conditions can be on the outcome of the system.
Posted at 07:29AM Sep 16, 2008 by Molly Wright in MediaHunt1 | Comments[1]
Pendulum
This pendulum exemplifies how even the slightest change in initial conditions will completely alter the path of the pendulum. It is very similar to the one we looked at in Riddick. Instead of using only gravity to propel the pendulum though, this uses magnets as well. Both the ball of the pendulum and the center of the base have the same magnetic force. This causes the ball to veer erratically around the center of the base when it swings back down. Even a small change in the place that the ball swings over the magnet will make a difference in where the ball goes next and throughout the rest of it's path. Here is a link to a video of the pendulum: Video LinkPosted at 07:28AM Sep 16, 2008 by Samantha Baughman in MediaHunt1 | Comments[0]
Chua's Circuit
This picture illustrates Chau's circuit, a simple electronic circuit that behaves chaotically. Leon O. Chua first introduced this circuit in 1983 as a visitor at Waseda University in Japan. In order for an autonomous circuit to display chaotic behavior, it must contain one or more nonlinear elements, one or more locally active resistors, and three or more energy storage elements. As can be seen in the diagram, Chua's circuit is the simplest circuit design containing all of these elements. The energy storage elements are the two capacitors, labeled C1 and C2, and an inductance (labeled L). The active resistor present is labeled R, and the ensamble of linear resistors (labeled R1-5) constitute a nonlinear resistance. When active, the graphed current pattern shows classic chaotic examples of period doubling (shown here)This picture is a direct application of chaos theory. I chose this because I am fascinated by electrical circuit design, and this example masterly integrates my interests with our topic of random and chaotic behavior.
Posted at 07:28AM Sep 16, 2008 by Daniel Evan Piephoff in MediaHunt1 | Comments[0]
Chaotic Magnetic Loops
This video, found at http://www.youtube.com/watch?v=IT2AQC3X5bk is an illustration of magnetic loops. Though the magnetic loops are invisible some are thought to be made somewhat visible by nature- as the narrator says of the corona, scientists "consider ...are in fact pictures of the magnetic field." The movie attempts to illustrate the unpredictable nature of magnetic waves. As the narrator describes, the magnetic loops can sometimes be "in-grown," when they loop back to the source of emission, whereas other waves become part of the solar wind. The waves are constantly changing, highly chaotic, and are largely affected by where we are in the solar cycle (what a wave does one year could be completely different the next). As the solar cycle progresses, the magnetic waves follow the theory of entropy -they get "hairier and messier."Posted at 07:27AM Sep 16, 2008 by Jacob Brennan in MediaHunt1 | Comments[0]
Gray-Scott Model
This video (http://groups.csail.mit.edu/mac/projects/amorphous/GrayScott/greydots-rnd-1.mpg) is a simulations of the Gray-Scott diffusion mechanism as shown on an Intel Paragon supercomputer. The Gray-Scott model of reaction diffusion is a set of partial differential equations that models the patterns seen through reaction and diffusion of chemical species. This video shows evolution on an amorphous layout by 16-step intervals.
The different colors represent varying concentrations of a reactant chemical U(using the equations U+2V-->P and V-->P, where U, V, and P are all chemical species). As seen in the video, the concentrations of this chemical display unique and dividing patterns of dispersion. Although the individual behavior of the equation varies each time, the general form remains fairly constant. The video relates to our class discussion of chaotic liquid diffusion patterns in the lab as well as the autocatalystic behavior of the BZ reaction.
Posted at 07:13AM Sep 16, 2008 by Mary Burroughs in MediaHunt1 | Comments[0]
Monday Sep 15, 2008
Convection Currents
http://www.youtube.com/watch?v=7xWWowXtuvA This video accurately portrays how convection currents work. The tank in the video is placed over a container of hot water and a container of ice water. The colored liquids placed in the tank represent hot and cold fluids and when they are placed in the water, they begin to flow in a circle. The fluid begins to move in a rolling motion and the hot (red) fluid rises. The cool (blue) fluid causes the hot liquid to lose heat in order to set the system in a stable state. This process of convection helped play a key role in the creation of Edward Lorenz's three equations.Posted at 10:51PM Sep 15, 2008 by Brooke bernard in MediaHunt1 | Comments[0]