I’ve been fascinated by aperiodic tilings of the plane since Martin Gardner first wrote about them in Scientific American. In the 1960s, Robert Berger discovered a set of 20 426 prototiles or tile-types that can tile the plane but only with no translational periodicity — a wonderful mix of the expected and the surprising, a kind of visual music.
Over the years, the number of required prototiles has been greatly reduced. In the 1970s, Roger Penrose discovered a set of just two concave aperiodic prototiles. Robert Ammann then dissected these to discover a set of three convex aperiodic prototiles. Can a single prototile, one tile or stone, literally ein stein in German, force a nonperiodic tiling? Despite several near misses and potential applications to quasicrystals, the existence of an ein Stein remains a fascinating unsolved problem.
Three convex Ammann tiles force a nonperiodic tiling of the plane.Two concave Penrose tiles force a nonperiodic tiling of the plane.
As a kid, I devoured the pages of Popular Science magazine and was fascinated by the quest for human-powered flight: Was a flying bicycle possible?
In the mid 1970s, I read that aerospace engineer Paul MacCready had assembled a team to build a large, lightweight, human-powered aircraft that could be rapidly repaired and redesigned. In 1977, after multiple iterations, cyclist Bryan Allen flew MacCready’s Gossamer Condor around a one-mile figure-eight course to win the first Kremer prize. Two years later, Allen flew MacCready’s improved Gossamer Albatross 22 miles across the English Channel to win the second Kremer prize.
Made with a carbon fiber frame and polystyrene ribs covered with transparent plastic film, each Gossamer aircraft had a long tapering wing behind a large horizontal stabilizer. Weighing less than the pilot-engine, the required power was only about 0.3 kW (or 0.4 hp). Currently, an outstanding Kremer prize is to fly a 26 mile marathon course in under an hour.
Bryan Allen powers and pilots Paul MacCready’s Gossamer Albatross across the English Channel in 1979.Allen flies MacCready’s Gossamer Albatross II in NASA tests in 1980.
In the sky is a castle, built in free fall, brick-by-brick, where the sun rises and sets every ninety minutes. The castle derives its energy from sunlight and recycles its water. Sealed against a vacuum, its inhabitants float and glide through its passageways and gaze down at Earth through its expansive cupola.
In an earlier age, the castle would be the magic of legend, but in ours, it’s the International Space Station. Assembled in low Earth orbit, its unique microgravity laboratories are powered by giant solar electric panels that rotate like windmills to track the sun. Arguably the most complex engineering project ever accomplished, the ISS is a model for international cooperation, where former cold-war enemies live and work together.
Astronaut Tracy Caldwell Dyson gazes down at Earth from the International Space Station’s cupola
1930s businessman Edgar Kaufmann Sr. and his family lived in Pittsburgh Pennsylvania. Kaufmann owned a rural retreat outside the city and wanted a weekend home there. He assumed his 67-year-old architect would design the home with a good view of the Bear Run waterfall.
Instead, the architect designed the home on the waterfall.
Frank Lloyd Wright’s Fallingwater masterpiece is a 3.5 hour drive from Wooster and makes a wonderful day trip. In 2013 I thoroughly enjoyed an in-depth guided tour of this iconic residence. I look forward to returning some day.
Frank Lloyd Wright’s Fallingwater in rural Pennsylvania is not far from Wooster. CC0 1.0 Public Domain.
The night sky is full of wonder and splendor. Stars, many more than one can count by themselves, and what a great expanse it truly is, reaching beyond our visible universe. In the vast nothingness, there are things that we can still learn through observation. The first step to learning though is by making sure we have the equipment to do so. My junior independent study consisted of using the Wooster Observatory, to look at the apparent brightness of one of these stars. Despite my [wrong] preconceptions, the stars do in fact change their brightness. Even more surprising, at least to me, was the concept that the stars who are part of constellations also had this happen to them.
I studied, by using a scientific camera and the observatory, the very specific star, Mekbuda which is part of the constellation Gemini. It has a period of about 10 days, which is pretty short compared to others, and changes its apparent brightness by about 0.5 magnitudes, which is a pretty significant change in apparent brightness. I measured and then plotted this data. I must admit, that when I first started this project I had deep concerns that I would not be able to go out to the observatory to collect data as Ohio’s weather does not have the tendency of being friendly towards astronomical research. However, in five weeks, the heavens did clear, permitting for ten days of data collection; five of which were actually used to take data on Mekbuda, three on learning how to do things properly, and two missed by accident.
With such a small amount of data, it seemed unlikely to me that I would be able to get results that had agreement with the currently known data on Mekbuda. However, with stout labor and good science came results which agreed well with the current data (this may be a consequence of having seen three shooting stars in one night though). All it took was a scientific camera, a school’s telescope, a laptop, and the willingness to do science.
When we say that two particles are quantumly entangled, we mean that the particles cannot be looked at independently even when separated by great distances. This means that if we measure one particle, we will automatically get the measurements of the other.
This concept is spooky, and can be useful in studying the nature of the universe. We can also use this as a form of instant communication. If we take a quantum-entangled photon pair and separate them, altering one would alter the other automatically. Hence we would be able to send information automatically.
To be able to use quantum entangled particles to help us communicate over large distances instantaneously, we would need to first transfer these particles over large distances. The problem with doing so currently is that on the way, sometimes entanglement is lost!
FIG1: Quantum Entanglement of Two Particles: A cartoon depicting the spooky entangled relationship between two particles.FIG2: Entanglement getting lost: The entanglement of photons can be lost over large distances.
To fix this issue, scientists have proposed the use of quantum repeaters. These are devices which accept an entangled photon, save its entanglement in a cluster of atoms, and then emit another photon which is now the new quantum-entangled photon. In a way, these are kind of like pit-stops for the quantum-entangled photons as they travel.
The way the entanglement of a photon can be saved onto a cluster of atoms is tricky: it can involve the photon mapping its phase (the current point in the wave of a light wave) onto atoms. The phase that is mapped onto the atom is called the geometric phase. This phase is very interesting as it stores information about the previous polarisation states — the different orientations of how the electric field in light vibrates — that the light has been through.
This is very peculiar and amazing! By saying that the light carries geometric phase which saves information about the previous polarisation states the light has been through, we are saying that light knows about its history. For example, when you travel from Wooster to NYC and back, and when you travel from Wooster to Florida and back, you can distinguish both journeys. This is because they were both different paths, although your final start and end points were the same (Wooster). The geometric phase in light shows that even light stores the information needed to distinguish the different previous polarization paths. Additionally, with the geometric phase, we can determine if light has been through a path of polarisation states or not. For example we can distinguish between a person who has travelled from Wooster to NYC and back, and another person who has stayed in Wooster. All this information about the photon’s polarisation path history is given by the geometric phase!
FIG3: Different journeys give different geometrical phases: The red dot represents the starting and ending point of the path (Wooster), and its polarisation state can be seen on the right. The path in figure (a) has a geometrical phase of 8.19 and the path in figure (b) has a geometrical phase of 6.26. These separate paths are analogous to the journies to NYC and Florida from Wooster. The video below shows how different points along the path have different polarisation states (similar to different gas stations along the way to NYC / Florida).
For my Junior Independent Study, I studied how light can retain memory using geometrical phase. A previous Wooster Student, Drew King-Smith, began this study using a model with simple constraints. Working with Dr. Cody Leary, I expanded upon this model by considering factors which would make the model more applicable to our equipment in the laboratory. Through the model we were able to produce predictions for numerous interferograms (interference patterns of light), which tell us about the geometrical phase. These predictions can guide future experimental work in the verification of these interferograms. By doing so we would learn more about the physics of quantum memory!
FIG4: Predicted interferograms: These are three interferograms that we predict are created with various parameters.
A picture and diagram of the experimental method used. The mirrors reflect the light back and forth through the sample multiple times.
Absorption spectroscopy is popular form of chemical identification and characterization. Typically, light is passed through a sample once and the intensity of the light after passing through the sample is measured. If light is absorbed by a sample, we expect the amount absorb to increase if the concentration of the solution or the thickness of the solution is increased. Absorbance is defined so that we expect the amount of light absorbed to have a linear dependence of thickness and concentration.
Sometimes samples do not absorb a lot of light, so measuring their weak absorbance is difficult. To solve this problem, cavity-enhanced absorption spectroscopy can be used. This method uses a set of mirrors placed around the sample to reflect light through the sample multiple times. This effectively increases the thickness of the sample, making the observed absorbance stronger and more easily measurable. However, this method has been seen to break the linear relation between absorbance and concentration. Instead of seeing a straight line when plotting absorbance versus concentration, they see a curve.
My junior independent study work was to investigate the absorbance dependence on thickness. I used a cavity-enhanced method and a typical single pass method to take absorbance measurements for varied sample thickness. I varied the thickness by using different sizes of sample container. From my experiments, I saw the predicted linear behavior for the single pass data. However, for my cavity-enhanced data I saw a curved trend like had been observed previously for varied concentration. This tells me that the amount that the cavity enhances the measurement depends on how much absorber or sample the light must pass through.
My name is Collin Hendershot. For my Junior Independent Study project I observed the effect of concavity on the aerodynamics of high speed automobiles. The two important aerodynamic characteristics of automobiles are downforce and drag. Downforce is the force of air pushing a car toward the road and drag is the force on the car from air opposing the forward motion of the car. Downforce increases a car’s stability and turning speed, and drag decreases a car’s top speed and fuel economy. An aerodynamically efficient car will have a high downforce to drag ratio. To increase a vehicles downforce designers often include a rear wing on the car. I designed 5 different rear wings with a leading edge defined by the function
which creates wings with increasing concavity as the value for a increases (Figure 1). The downforce and drag for each wing was recorded and then the downforce to drag ratio of each wing was calculated. The results are pictured in Figure 2 and the a = 2 wing design has the largest downforce to drag ratio, 3.8, therefore it is the most efficient wing design.
This Gif shows the operation of the simulation where the red outlined blocks are the Scramjet structure the grey outlined blocks are the energy input to the system, and the colors indicate the direction the water is flowing. The direction is given by a color wheel–for reference, light blue is directly to the right.
I have always thought that one of the most outdated technologies we currently employ in the large scale is propellers for ships. While this isn’t a critical fault in our world it does lead to a lot of inefficiencies. Modern trade ships and super-tankers use millions of tons of fuel annually. This does a great deal of damage to the environment. Air travel was also largely propeller based at its inception, but since then several new types of engine have been developed. Most notably the Scramjet engine ingests air and mixes it with fuel at supersonic speed, exhausting the combustion results to produce thrust. This is a highly effective method of producing thrust, one which has been able to produce speeds of Mach 12. For reference, at Mach 12 one could travel the entire distance of the equator in less than three hours. I believe that it is possible to take some of the principles of the Scramjet engine and develop a version for generating thrust underwater.
My project was to simulate this new kind of underwater propulsion system to determine whether or not it could feasibly operate. I did this by working with legacy code provided by another student that simulated air flowing through a channel. I modified the code to simulate water flowing through the channel, and also added a simple structure to represent a simple Scramjet style water propulsion device, shown above as the red boxes. The simulated Scramjet water propulsion system used heat as a fuel source, this is done by simulating the result of water boiling so quickly it evaporates with explosive force. This is shown with the gray boxes in the center, within each of these the simulated water gets “kicked” in a random direction and gains a high speed. The results of my simulation were inconclusive but I did show that the Scramjet Structure had an effect on the operation of the system. I believe with enough tweaking this simulation would show that such a system would operate in the real world.
Solar sails utilize the change in momentum of photons as a means of propulsion. This allows spacecraft with solar sails to significantly reduce their mass, since they do not have to carry onboard fuel (in comparison to traditional rocket-based spacecraft). This project aims at designing a program to display the dynamics of a solar-sail-based spacecraft in the presence the Sun and Earth.
Depending on the orientation of the sail, it is possible to sail towards or away from the Sun and achieve a variety of orbits. The video shown above displays the program, with the Sun in red, the Earth in blue, the sail in white, the sail’s previous position in purple, and the sail’s position with respect to the Sun in yellow.
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Thanks, Mark! I enjoy reading your posts as well.
Nice post, John! Thanks for writing these. I always enjoy them.
Thanks, Mark! I enjoy reading your posts as well.