Author Archives: Ryan Tran

Dark Matter and Dark Energy – the key to the fate of the Universe

Since the Big Bang explosion, the universe keeps expanding and the expansion is accelerating right now, while you are reading this post. However, we still don’t know if the universe will keep expanding forever or it will stop expanding and stay like that or it will collapse at some point in the future.

In the universe, there are approximately 1011 to 1012 galaxies and they are made of stars, gas, dust and dark matter.

Oh wait!! Dark matter? What is it?

The galaxies are rotating due to their gravity just like the way planets orbiting around the Sun. According to Newton’s Law of universal gravitation, gravity is proportional to the mass of the objects and inverse proportional to squared of the distance between them. Therefore, it is expected that the further a star is from the centre of the galaxy, the small its velocity is. In reality, however, when measure the rotational speed of stars in the outer region of galaxies, it turns out to be much much higher than the calculated values, so there must be a very large unseen mass other than ordinary matter that accounts for this . In 1933, Fritz Zwicky, a Swiss astrophysicist, came up with a hypothesis that there must be the existence of a type of matter that couldn’t be seen and he called it Dark Matter.

The graph shows how the rotational speed of a galaxy varies with the distance from its centre

By using rotational speeds of galaxies, the mass of dark matter can be estimated. Surprisingly, dark matter accounts for more than 85% mass of matters in the universe. According to the standard model of cosmology, the universe is made of 5% ordinary matter (electrons, protons, neutrons…), 25% dark matter and the rest is dark energy (a hypothetical type of energy).

Yes, Dark Energy, you didn’t misread the term!

Without dark energy, the universe would collapse as with the large amount of dark matter and ordinary matter, gravity is very large and it could cause the universe to collapse. Dark energy provide the force that overcomes gravity and pushes the matters outwards. It is the reason why the universe is expanding.

This figure shows how dark matter and dark energy account for the expansion of the universe

However, we know very little about dark matter and dark energy. We don’t know the exact amount, or how they distribute in the universe. And they have become one of the most hottest topics in physics of this century.

As physicists believe that dark matter is composed of weakly interacting massive particles (WIMPs), so it can be detected by either direct or indirect methods. But with dark energy, physicists have no clues what it is so the only way to search for it right now is by indirect methods such as exploding stars, sound waves, distortions.

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If we successfully confirm the existence of dark matter and dark energy, we will open the door that leads to the answer of the fate of the universe. However, it is still a long way to go until we can fully understand our universe. Therefore, the fate of the universe is still uncertain.

Ryan Tran.

Exoplanets, how do we detect them?

In the last few decades, our science and technology have been developed with a very high speed and the speed is increasing exponentially; it has become easier for us to search for life beyond our solar system. Since 1988, more than 2000 exoplanets have detected. So, What are exoplanets? And how do we detected them?

Exoplanets (or Extrasolar planets) are planets that locate outside the Solar system, they orbit around a star other than the Sun.

Because planets don’t emit visible lights or other electromagnetic radiations like stars, it’s more difficult for astrophysicists to detect them. To detect and confirm the existence of an exoplanet, different special methods must be used; sometimes, more than one methods need to be used at the same time.

The first method I’m going to talk about is Transit Method. This is an indirect method to detect an exoplanet by measuring the decrease in intensity of the lights coming from a star in a short period of time. The star is usually monitored, and the intensity of light emitted by star is measure constantly. As the planet orbits around the star, when it’s between the star and the Earth, it blocks some of the lights from the star and cause the brightness of the lights measured sure on the Earth decreases. After a short period when the planet moves away, the brightness of the star get back to normal. Using the change in the intensity of the lights from the star, radius of the planet can also be determined. However, using this method alone isn’t enough to confirm the presence of the planet because there are some other factors that can cause the dip in brightness of the star. One of these factors is that the star in a binary star system, and the brightness of the other star in the system makes intensity of the lights from the star dip periodically. The bellow video simulate how intensity of the star changes when there is a planet in transition between the star and the Earth.

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Therefore, Radial velocity method, which is also the most popular method, is used along with Transit method. According to Newton’s law of gravitation, all bodies in a planetary system orbit around a common centre of mass, so not only the planet orbits but the star also orbit the centre of mass. Thus the lights emitted by the star have different wavelengths when they are detected on the Earth, the change in wavelength depends on the fact that the star is moving away or forward the Earth, this phenomena is called doppler effect.

Doppler effect

By measuring the wavelength of the lights emitted by the star at different times and taken the doppler effect into account, astrophysicists can determined the speed of the star when it’s moving away or toward the Earth and also the period and radius of the orbit of the star. Then the presence of other object in the system of that star can be confirm.

There is another method and also the most interesting method, it’s Gravitational Microlensing method. To explain about this method, I’m going to start with Einstein’s general relativity. Einstein’s general relativity states that spacetime curves in the region around a large, massive object. So when lights from a distant star pass through a another star (this is our interested star), they are bent which cause the image of the star that detected by telescope to be distorted. The star acts as an gravitational lens; and if the star has a planet orbiting around it, when the planet is in some particular region near the star, it gravitational field causes the spacetime curves more, and it acts as an additional lens, therefore, the light from the distant star will be distorted more. This happens until the planet moves away from its star.

Lensing effect

In conclusion, there isn’t any particular method that can be used to confirm the presence of an exoplanet. Combinations of different methods must be use to give a reliable result.

Ryan Tran.

 

Mathematics – The magic behind animated movies

Nowadays, most animated movies are made by using computer animation techniques instead of hand-drawn animation. When we watch these computer animation movies, we usually think the producers are artists with a creative mind and great drawing skills. However, not many of us have noticed that some of them are also great mathematicians. So the question is how maths is used in computer animation?

Creating an animated movie is like creating a new virtual world, where new planes need to be defined in a coordinate system. A plane is described by a set of three points or a point and 2 vectors. But imagine a world where everything is on a flat infinite plane, well, this must be a boring world. Therefore, hills, mountains, rivers, valleys are added. It sounds like an easy task, but in fact it isn’t easy at all. First, the objects are sketched by using wire skeletons which are composed by simple polygons. A mathematical methods called Non-uniform rational basis spline (NURBS) is then used to smoothen surfaces of the objects. In a TED-ed talk, Tony DeRose, a Senior Scientist and Research Group Lead at Pixar, gave a presentation about how Non-uniform rational basis spline (NURBS) was used in Pixar’s animated movies. In a paper called Subdivision Surfaces in Character Animation, which was published in 1998 by Tony DeRose, Michael Kass and Tien Truong, the application of NURBS in creating subdivision surfaces was described in detail.

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Now it’s when coordinate systems get involved. As the objects are put together, coordinates are required to make sure the objects locate at where they’re supposed to be. Vectors are used to define the location of every point with respect to the origin of the chosen coordinate system. To describe the motion of an object in space, transformation matrices are used. Depending on the elements of the matrices, the transformation can be rotation, translation, enlargement, reflection or a combination of these.

 

Some examples of simple transformation matrices

The following video shows how maths is use to create more realistic animations

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The above mathematical methods are only a few main methods that are used in computer animation. There are many other mathematical methods that are useful for computer animation, such as Fourier Transformation, Complex Analysis, and so on. Mathematics plays an important role in computer animation. It makes a significant contribution to the success of computer animated movies.

Ryan Tran.
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