Nuclear fusion: Energy of the next generatrion

The use of the fossil fuels dates back to the 1700s, the beginning of the Industrial Revolution. After exploiting fossil fuels for three centuries, human society has made great progress in development.   Fossil fuels power the power tools, fuel the vehicles, and produce electricity. The use of the fossil fuel facilitated the advance in technology and change human's lifestyle dramatically. Although our society has been benefited from the fossil fuel, we suffered from our dependence on it. As our demand for energy grows, the amount of fossil fuel burned per year grows each year. The carbon dioxide released by the combustion of the fossil fuel has broken the balance of the carbon cycle on Earth.
Consequently, the global temperature keeps rising and impacts the eco-system. If the use of fossil fuel is not cut down significantly within the next decade, the global temperature will be raised to a dangerous level. In order to restore the balance and achieve sustainable development, human society needs to seek for the low or non-carbon emission source of energy. At this moment, there are several types of zero carbon emission energy have been applied to electricity production, such as solar energy, hydropower, wind power, etc. Zero carbon emission energy, or green energy, has almost no impact on the environment. However, the energy production efficiency of green energy is usually low. Moreover, green energy is unstable and is limited to the natural resource. For example, solar power is not effective in the area that does not have a lot of exposure to sunlight. Even solar panels are built in the area that has a great sunlight exposure, the intensity of the sunlight is not consistent since it can be influenced by weathers and seasons. Therefore, green energy is not very promising in sustaining our demand for energy. Maybe there will be a significant improvement in green energy, but it does not look optimistic at this moment.
If the green energy cannot solve the problem, does it mean that we should give up? The answer is no. There is a type of energy that has a great potential for replacing fossil fuel entirely. This type of energy does not only exist in the dream or science fiction. In fact, we are feeling it and benefited from it every day. This type of energy is called nuclear fusion. Nuclear fusion is the source of the power of the sun. The nuclear fusion reaction is continuously occurring at the core of the sun and produces energy that is released in the form of light and heat. In the nuclear fusion reaction, two light atoms such as hydrogen are fused together and form a heavier atom such as helium. In this process, some masses are lost, which means that the mass of products is less than the mass of the reactance. The lost mass does not simply disappear, it is converted to the energy. The amount of energy converted can be calculated with the Einstein's formula: E=mc^2. Where m is the lost mass and c is the speed of light. From this formula, we can see that a large amount of energy is produced with a tiny loss of mass. The nuclear fusion reaction can happen between many different atoms. Among various possibilities, deuterium and tritium fusion is the most viable because it occurs most frequently. Nuclear fusion energy has many desirable properties such as producing an abundant amount of energy, zero greenhouse gas emission, and no long-lived radioactive waste production. If one ton of deutirium were to be consumed throught the fusion reaction with tritium, the energy produced would be 8.4*10^20 joules. This can be compared to the energy content of one ton of coal, 2.9*10^10 joules. The fuel for the nuclear fusion, deutirium, is abundant in the Earth ocean. Tritium, however, has to be bred from lithium or gotten from the deuterium cycle. 

To apply nuclear fusion on producing electricity, there are several engineering challenge have yet to be overcome. One of the challenges in controlling fusion reaction is controlling plasma with the temperature up to several millions degree celcius. The research on nuclear fusion energy is challenging, time-consuming, and requires lots of funding. Despite all the effort required, nuclear fusion is definitely worth pursuing due to its great potential. If the nuclear fusion energy were fully developed, it would be able to replace all the fire power plant and restore the balance of the carban cycle. 

Fibonacci numbers and golden ratio

Math is a subject that has been studied for centuries. It has a great influence on our daily life. From basic counting to complex calculation, there are so many circumstances that we need math and our lives would not be able to function normally without math. There is no doubt that math brings us a lot of benefits. What math brings us can be divided into three parts: Ability to calculate, applications, and inspirations. I believe that most of us are familiar with the first two parts already since we encounter these two parts very frequently. Even you are not a student taking math classes, you still do basic calculation almost every day. There is hardly a day that anyone can get away from numbers completely. As for the application of math, the most obvious one is the computer. In the time when personal computers and smartphones are common, billions of people have the access to the application of math every day. At this point, I think I have convinced you that math brings us the ability to calculate and great applications. However, you may still be frowning when I say that math gives us inspirations. You may wonder what kind of inspiration can we find in those goofy notations, crazy looking formulas, and abstract theories. Well, if you think that is what math all about, you are terribly wrong. Math can be simple, elegant, and interesting. You may have a lot of doubts in this statement at this moment. That's ok. Let me give an example to prove my point.

In mathematics, there is a sequence of numbers called "Fibonacci numbers". The Fibonacci sequence follows a simple patter. It goes as the following: 0,1,1,2,3,5,8,13,21,34,55........  With some observation, we can find out that any number in the sequence is the sum of the two numbers that precede it. An interesting thing about this sequence is that if you divide any number (b) by a number (a) that precedes it. The ratio is always closed to 1.6180339887....   For example : 8/5=1.6, 21/13=1.615384615, 55/34=1.617647059.  The ratio gets closer and closer to 1.6180339887 as the number b increases. The ratio of two adjacent Fibonacci number is also known as the Golden ratio. At this point, you may find the fact that Fibonacci sequence yields Golden ratio interesting. If I tell you that Fibonacci numbers and Golden ratio appear in nature very frequently, your mind will be totally blown away. First of all, let's take a look at the numbers of petals on flowers. It turns out that the numbers of petals on different kinds of flowers are Fibonacci numbers. Examples include Lily, which has three petals, buttercups, which have five, the chicory's 21, daisy's 34, and so on. The Golden ratio, just like Fibonacci numbers, appears frequently in nature. In fact, if you look at your fingers, you will find that the length of each section increases as you look from the tip to the wrist. Interestingly, the ratio of the length of the adjacent section is close to the Golden ratio. The same pattern can be found on insects and other animals. The shade of the Golden ratio can also be found on the spiral of shells. If we draw a rectangle that encloses a shell, the ratio of the length and width of the rectangle is surprisingly close to the Golden ratio. To further elaborate that, if we do the same thing to the spiral of the Galaxy and hurricane, we can find the same pattern

.     At this moment, I don't even have to explain why Fibonacci numbers are so amazing. The fact that Golden ratio and Fibonacci numbers can be found everywhere in nature makes us wonder that if there is a rule that governs that universe. Who would ever think that mathematic pattern can be found in nature and is all around us?

The 4th special dimension

Scientists have been pondering whether there exists a dimension beyond the third dimension-The fourth dimension. Some scientists think that the fourth dimension does exist and it is possible to find it while others think that the fourth dimension is merely a mathematical wonder. Recently, an international team of researchers from Penn State, ETH, and Holon Institute of technology has found the "four-dimension version" of quantum Hall effect. A behavior of particles which is theorized that it can only exist in four dimensions. In their experiment, they built an array of light tubes and observed how the light pass through those tubes. In the two dimensional system they set up, scientists observed that light behaved as there are two extra dimensions. After observing the phenomena that are theorized to only exist in four dimensions, researchers assume that there is a fourth dimension involved. The next step for the researchers is figuring how the higher-dimensional physics is relevant to three-dimensional physics.

At this point you may wonder, what is that fourth dimension anyway? How can we visualize it? Thinking about the higher dimension is very tricky but interesting in a way. Before scientists demonstrated the physics in four dimensions, the fourth dimension can only be proved mathematically.  To prove that the fourth dimension can exist mathematically, we can use the concept of projection. Assume that there is a two dimensional plane in front of you and you want to make a projection of this plane on one-dimensional space. You will simply shine a light directly on the edge of this plane and what you will see is a straight line, a one-dimensional object (Note that there's no left and right in one dimension, only forward and backward). Now, there is a box (a three-dimensional object) in front of you and you want to project it on the two-dimensional space. This time, you can shine the light at any angle. What you will see is the shadow of this box on a two-dimensional plane. At this point, we can see some patterns already. In fact, there is a description in math states that an n-dimensional space R^n is the projection of the higher dimension R^(n+1). Based on this description, we can say that the three-dimensional space that we live in is the projection of the four-dimensional space. Therefore, the existence of the fourth dimension is proven mathematically. An implication of this description is that there is no limit for the numbers of dimensions. In other words, you can have an infinite amount of dimensions based on the description. Since an n-dimensional space is the projection of (n+1) dimensional space, we can always move on to a higher dimension and n will go to infinity.

You may argue that thinking higher dimension mathematically does not help anything because it doesn't help you "see" it. Let me tell you something, it is perfectly normal and logical that you can not "see", "fell", or "experience" it. I dare say that there's no one who lives in three-dimensional space can show me where the fourth dimension is. Don't believe me? Let's try! If I ask you to demonstrate one dimension, you will point to either your front or back. If I ask you to add another dimension, you will point to your left or right. When I ask you to add the third dimension, you will point up or down. However, the big problem is what would you do if I ask you to show me the fourth dimension? You may point 45 degrees upward. Ha Ha. Nice try! But you are still demonstrating three dimensions by doing that. None of us three-dimensional creatures can experience the fourth dimension because we are "trapped" in three-dimensional space. Although we can't experience it, we can "deduce" it. To show that deducing a higher dimension from a lower dimension is possible, I will use an example of two-dimensional space. Assume that there is a two-dimensional creature standing on a sphere, how can that creature know that it is standing on a sphere when everything it experiences is two dimensional. That's easy. It can mark the place where it is now standing and start to walk straight forward. After walking for a while, this creature will find out that it returns to the spot where it started walking. Through this observation, that creature can deduce that the space it lives in is curved and have an extra dimension that he can't physically "see". Applying the same logic, we three-dimensional creatures can also deduce the existence of higher dimension by observing the phenomena that can only be explained when we add an extra dimension.

The recent discovery of scientists about the fourth dimension is exciting because it suggests that there may be a higher dimension out there. Although we can not "see" it, the theory suggests that we may be able to "observe" it. If the existence of the fourth dimension is confirmed, I can't wait to see how we relate it to the three dimensions that we have already known.

Wave particle duality

In the 17th century, scientists had a disagreement on whether light is particle or wave. Isaac Newton stated that light is the particle. He argued that since the reflection of the light is a perfectly straight line, it must have particle nature. The other group of scientists like Christiaan Huygens, however, argued that light has wave nature. Their argument based on the fact that light travels at a different speed in different media. This property of light demonstrates its wave nature. The view that light is wave was later supported by the discovery made by Thomas Young. In the double-slit experiment, Young discovered that light creates interference patterns when it passes through two narrow slits. This discovery confirmed the wave nature of the light. Interestingly, Einstein confirmed the particle nature of the light by introducing the "photoelectric effect" in 1905. In the photoelectric effect, it was observed that shining light on a piece of metal creates an electric current in the circuit. To explain the photoelectric effect, scientists assume that there are "light particles" knocking electrons out of the metal. An interesting thing about the photoelectric effect is that the energy of the electrons does not depend on the intensity of light. In addition to that, scientists found out that only the light above the threshold frequency could knock electron free. If we combine these two facts, we can think that one photon (light particle) of the light above threshold frequency could release only one photon. As we can see, photoelectric effect demonstrates the particle nature of light. At this point you may wonder: Who is right? Is light a wave or a bunch of particles? The answer is a little bit ambiguous. Both sides are not quite right but not entirely wrong either. Based on the fact that light has both wave-like and particle-like property, scientists invented a term, "wave-particle duality", to describe the property of light. In modern time, the explanation of wave-particle duality is widest accepted.

After learning that light has wave-particle duality. De Broglie took a bold step and claimed that all mater have both wave and particle-like property. He related the momentum and the wavelength, writing down a formula as follow: λ=h/p   h(Planck's constant), p(momentum), λ(wave length)

De Broglie's claim was proven three years later after the electron diffraction was observed. The fact that a beam of electrons passing through a thin film creates interference patterns proves that even electrons, something that is perceived as particles, has wave-like properties. Later experiments demonstrated that particles that are much heavier than electrons also create interference patterns after passing through a thin film. From the formula above, we can see that the larger the momentum of the object, the shorter the wavelength. Small particles like electrons have small momentum and long wavelength, so their wave property is more obvious. Large objects like baseball and human bodies have large momentum and short wavelength, so the wave property is not so obvious. 

Wave-particle duality is a bizarre phenomenon in the real world. It is also the gate to quantum mechanics. Through years of study, scientists have been revealing the mysterious nature of quantum physics little by little. The study of quantum physics helps us understand how the real world works and how particles behave at the microscopic level. The research on quantum mechanics can not only increase our understanding of this world but also advance the technology. Technology like quantum computer and teleportation may be achieved by applying quantum mechanics. Let's all stay tuned. Because a ground breaking discovery may appear at any time.

The origin of water's range properties

Water, an element that is common and necessary for life on earth, has properties that are different from other substances. How water's density, specific heat, viscosity, and compressibility respond to changes in temperature and pressure is completely opposite to liquids that we know. For instance, the water that has the temperature higher than 4 degrees Celsius increases density when it is cooled down. This is not different from the properties of other liquids. However, when the temperature of the water is below 4 degrees Celsius, its density decreases when it is cooled. This unique property of the water explains why ice floats on the surface of the water instead of sinking to the bottom. Normally, the solid state of a substance should have a higher density than its liquid state. Since the density of the water decrease when it is cooled under 4 degrees Celsius, its solid form has a lower density than its liquid form. When you put an object that has a lower density than that of the water, it floats on the surface. That is why we see ice cubes float on the top of the water in a glass of ice water.

After knowing that water behaves strongly below 4 degrees Celsius, you may wonder if this strangeness had the limit. How cold the water should be when it stops behaving strangely you might ask. Researchers at Stockholm University use x-ray laser to observe the water and figured out how water fluctuates between two different states when it is cooled. They found out that water can exists in two different liquid states that have different ways to bond molecules. Water fluctuates between these states and the fluctuation reaches the maximum at - 44-degree Celsius. The ability of the water to shift between two different states gives it its unusual properties. As the water cools down, the strangeness increase because of the fluctuation increases.

To observes the liquid water at a temperature below the freezing point of the water, researchers had to  "supercool" the water. Supercooling means cooling down a liquid below its freezing point without making it become solid. To understand how supercooling works, we have to understand how a liquid becomes solid. As the temperature of a liquid drop, its molecules movement become slower. When the velocity of the molecules becomes very low, they have more chance to bond with each other and form a solid. However, the low velocity of the molecules does not guarantee the formation of the solid. To form a solid, the presence of a nucleus around which a crystal structure can be formed is essential. Without the nucleus, a liquid can't be crystallized and become solid. Therefore, supercooling of the water can be achieved by preventing the presence of such nucleus. To supercool the water, we must purify the water since the minerals in the water provide the nucleus and allow the water to crystallize. Moreover, a sudden rupture of the water should be avoided since the rupture may allow molecules to cluster and form a nucleus. In fact, there is no professional technique required to make supercool water. We can make supercool water at home by putting the purified water in the freezer and take it out after about two hours. If you make the supercool water successfully, you will see that bottle of water turns to ice suddenly when you shake the bottle.

Building a trebuchet

In this Autumn, I had been working on a project of building a trebuchet. This project is required by a class I was taking at the University of Washington. This class is about studying science in ancient Greece and ancient Rome. The instructor of this class wanted the students to form groups and try to recreate an ancient technology. The ancient technology chosen by our group is the trebuchet. During the whole autumn quarter, our group worked on this project and tried to make a trebuchet that works properly. The whole process was challenging but fun. Although we encountered several challenges, the project was successful in the end. Trebuchet is an amazing invention. From the process of building the trebuchet, I realized that making a trebuchet work properly is not easy. There are many challenges to overcome during the construction and there are many factors that affect the launching. The mechanism of the trebuchet involves a lot of physics. Therefore, I am going to talk about the physics of the trebuchet in this article.

Trebuchet is war machine that launches projectiles. The mechanism of the trebuchet is quite simple. It basically uses the falling energy of the counterweight to throw the projectile. A trebuchet is consist of a beam attached to an axle that is suspended above the ground by a stable frame and base. The beam is attached in a way that makes one end longer and one end shorter. The counterweight is attached to the shorter end while a sling and the projectile is attached to the longer end. Before launching the trebuchet the projectile has to be loaded to a holder attached to the sling and the counterweight has to be lifted to a certain height. When the trigger is pulled, the counterweight will drop and rotate the beam. When the beam rotates to a certain angle, the projectile will be released. The reason for attaching the projectile to the longer arm is to give it a greater linear velocity. In order to launch the projectile at a high speed, the counterweight must be much heavier than the projectile. Various sources on the internet suggest that the optimal weight ratio is 1:133. (If the projectile is 1kg, the ideal weight of counterweight is 133kg ). However, I couldn't find a single source that explains why the optimal weight ratio is 1:133. Therefore, I tried to work it out myself. I end up coming up with my own explanation as follows.

 First, when the counterweight is falling without attaching to anything, it has an acceleration of 9.8m/s^2. When it is attached to the beam, however, it falls with an acceleration smaller than 9.8m/s^2 because the beam and the projectile as a whole have rotational inertia. From Newton's second law we know that: F=ma. Since the motion of the beam is rotational instead of translational, we need to adjust the formula to τ=Iα. (τ is the torque, I is the rotational inertia, and α is the angular acceleration). When the weight of the counterweight increases, the angular acceleration increases as well. However, the angular acceleration has a limit. (Because the greatest acceleration of the counterweight is 9.8m/s^2). When the counterweight is much heavier than the projectile, the acceleration of the counterweight will be very close to 9.8m/s^2, but the acceleration never exceeds that value. Therefore, increasing the weight of the counterweight will have little effect at certain point. That's why the optimal weight ratio is 1:133.

The design of the trebuchet includes a sling attached to the longer end of the beam. When I was constructing the trebuchet, I wondered what is the point of attaching the sling. I tried to find the answer on the internet but failed. Then I worked it out myself again and figured out that the point of attaching the sling is to increase the release height of the projectile. When the release height is increased, the projectile will stay in the air longer. The longer the projectile stays in the air, the further it will fly. Although there are other ways to increase the release height such as lengthening the beam and making the frame taller, simply attaching a sling is a much easier way to get the result more efficiently. 

The construction of the trebuchet is difficult and its launching mechanism is actually very complicated. Our team bade a trebuchet with a 3 feet* 2 feet base, 2 feet tall frame, 4 feet long beam, and 3 feet long sling. Because the launching of the trebuchet was affected by many factors, we adjusted the sling length and the position of the projectile a few time before we can launch it with nearly 45-degree angle (the optimal launching angle). In the end, we can shoot a softball about 50 feet far. We were satisfied with the result and enjoyed the process of making the trebuchet.  

The Lycurgus cup

When we talk about the ancient world like ancient Greece and Roman Empire, people always think that those civilizations are technologically unsophisticated. However, the truth may just be the opposite. Archeologists and historians who research in the science and technology in the ancient time discover some astonishing fact that ancient civilization actually possesses highly advanced technology.

Although there are many construction and invention can prove that highly advanced technology existed in the ancient time, I am going to focus on the Lycurgus cup in this article. The Lycurgus cup is believed to be created in around 4th century AD, and it is a piece of glass work shows that technically sophisticated glass work existed in Roman Empire. The most amazing feature of this cup is that it creates different optic effect depending on whether there's a light pass through or not. When the light shines from outside of the cup, the cup looks green. When the light passes through the cup from the inside, the cup looks red. When scientists use the microscope to examine the cup, they found that there are nanoparticles of gold and silver alloy. Scientists believe that those gold and silver alloy particles are the key to the unusual optic effect. The fact that those particles are in nanoscale indicates that Roman Empire might possess some sort of nanotechnology. The optic effect created by the cup also shows that people at that time have certain level of knowledge in optic. Interestingly, the coloring effect of this cup is a form of the thing film interference in physics. (Thin film interference is basically describing that material with the different index of refraction allows different color of light to pass through and reflect the different color of light.) We may assume that people in that period of time had already known the thin film interference and was able to manipulate the color of the light that passes through the glass.

Not only the optic effect of the cup shows that Roman Empire possesses advanced technology, the fabrication of the Lycurgus cup also shows that some advanced tool or machine existed in that period of time. From the fabrication of the cup, scientists believe that the cup was cut and grind by a high speed spinning tool. The surface of the cup seems to be polished by some sort of spinning tool too. This discovery shows that people in Roman Empire had knowledge of creating spinning power tool and controlling the speed of spinning.

When we talk about ancient civilizations, we always think that people at that time did not have advanced scientific knowledge and technology. However, if we study the history and dive into the ancient science and technology, our mind will be blown away. The Lycurgus cup is just one of the creations in ancient time that shows how advanced the ancient technology was. This amazing glass work which creates unusual optic effect also shows us that we never know the truth before we study and dive deeper.