The Millennium Problems; The Navier-Stokes Equation

In May 2000, the Clay Mathematics Institute stated 7 of the perhaps most significant problems in Mathematics at the time. One of the most notable problems of them all is the Navier-Stokes Equations.

The Navier-Stokes Equations came about from applying Newton’s Second Law to fluid dynamics; they describe the relations between pressure, temperature, velocity and density of any moving fluid. Think of any fluid and these equations will explain their behaviour. They subsequently become quite useful, describing the physics of many phenomena, not necessarily in physics, but in other fields as well; they are often used to model weather, ocean currents, water flow in a river, or the flow of air around the wing of a plane; aiding in the design of aircraft and automobiles, the study of blood flow, and the analysis of pollution. Surprisingly, they have also been quite important in the world of gaming as well, and have also been used to study magneto hydrodynamics (assuming you model the equations with Maxwell’s equations, which can help understand how stars and galaxies form – this means we could also potentially model the growth of the sun as well as other significant stars in our galaxy.

While we do have the equations and while solutions may exist with the equation, they are only behaved in 2 dimensions, yet we live in 3 dimensions (assuming you ignore the 4^th dimension of space-time), which affects the equations quite a lot, and we mathematicians have been unable to figure out why these equations do not work in further dimensions. This may be because there is either no way of understanding these equations in such dimensions, or of the possibility that we have not made enough progress in order to potentially find out the solution for further dimensions – meaning we may not be able to solve this problem until we have reached the stage in advancements where we’d understand the problem further.

This Millennium Problem, like all the others, has a prize of 1 million dollars. Only one of the seven problems has been solved, which was the Poincare Conjecture by Grigori Perelman in 2003. Shockingly, he refused to accept the million dollar prize, which shows how many mathematicians out there are not doing such questions for the sake of money, but to further our understanding of such mathematical matters, which often change the course of history as well. Now, the CMI is not asking you to exactly ‘solve’ the problem, but to “further our understanding of the Navier-Stokes Equations” which suggests that we do not need to solve it – we could just prove that it cannot be solved. And so the question remains; who will further our understanding? 

 

Is Mars A Waste or the Future of Our Civilisation? Should we travel to Mars, Venus, or Titan?

Two years ago, Elon Musk revealed SpaceX’s plans to colonise Mars; first, SpaceX plans to send two cargo ships to Mars in 2022, and then if successful, SpaceX will land two more cargo ships and two crewed ships in 2024. Now, there are less than 3 years left before this plan occurs and I, like many other physicists, doubt Musk’s plans.

Since 2017, new research has shown that Mars is indeed not the planet we should be focusing on – for example, the issue of radiation. The planet does not offer any natural protection against the galactic cosmic rays – high energy protons which originate from the sun, outside the solar system and even other distant galaxies. Mars has a very thin atmosphere and no magnetosphere which is a huge issue for our species.
Amanda Hendrix, a physicist and a senior scientist with the Planetary Science Institute, stated that “humans with the intention of spending any long period of time on Mars will probably have to live underground, or in some sort of device that will shield them from the rays.”  Now, if Mars is, indeed, a waste of money, where else can we invest our research, time and funding into? From my own research, the following are possible alternatives.

Venus

Our sister planet is often disregarded for its potential to be habitable for our species due to being the hottest planet in our solar system. However, Venus is an easier and cheaper alternative to Mars as the trip from Earth to Venus can be 30% to 50% shorter than a round trip to Mars. Unlike Mars’ very thin atmosphere, Venus’ atmosphere is quite thick, meaning much more protection against meteors and the cosmic rays. And most important of all, Venus has gravity, saving us from losing bone mass, while Mars does not – and we have not reached the advancements in science where we could even suggest ways of creating gravity artificially.
Now even after reading this you may ask, what about the incredibly hot temperature on Venus’ surface – how can we live on a planet where the temperature is over 450 degrees Celsius?
The answer to this question is indeed – cloud cities. NASA has hypothesised the concept of the High Altitude Venus Operational Concept (HAVOC) which would give us a lower temperature which is habitable for our species, whilst still having all the benefits.

Titan

The last alternative is Saturn’s largest moon – Titan. Unlike Mars, Titan has its own natural shielding due to the thick atmosphere, and the properties that make the planet much better for humans due to being an icy moon where water is present and oxygen can be obtained quite easily. Amanda Hendrix believes Elon Musk should be looking into Titan instead of Mars, stating “somebody like Elon Musk who has got the resources with the ability to work on Titan should focus on Titan instead of Mars” and she is quite right – Titan is a much easier and safer alternative than Mars – we would not have to devise a way to protect ourselves from the cosmic rays and the meteors, or worry about trying to find water. Now one might ask; isn’t Titan farthest away in comparison to Mars and Venus?
Despite being farthest away, it is still one of the more promising alternatives than Mars. NASA has recently started working on a ‘dragonfly spacecraft’ which could prepare us for starting a colony there and becoming a multi-planetary species and this would be done much more easily than Mars or Venus – the temperature of Titan would allow the spacecraft to last much longer than the other spacecrafts which travelled to Venus and only lasted up to a couple hours.  

Regardless of which planet we go to, we will certainly see a colony in our lifetimes as all the plans have been made to occur within the next decade – the prospect of our species becoming multi-planetary is imminent.

Quantum Theory and the Nuclear Atom

Quantum Theory and the Nuclear Atom.

There are two ways of finding what atoms or other small particles are like. One is to fire something even smaller at them and see how they break up or how the projectile bounces off of them. The other is to shake them about (giving energy) and seeing what comes out. 

PROBING THE ATOM WITH ALPHA PARTICLES

The initial method was used for a productive experiment in 1909. Alpha particles of a radioactive source were fired at a thin film of metal atoms. This was called the Geiger-Marsden experiment; some particles bounced back at angles, which meant that they had hit something smaller and with mass. From this Rutherford ( a physicist) worked out in 1911 that an atom has a positive nucleus surrounded by negative electrons. He suggested that electrons could be orbiting about the nucleus like planets around the sun. However, such an atom would not be stable; an orbiting electron, like an orbiting planet, has an acceleration directed towards the attracting object. An accelerating electron continuously radiates electromagnetic waves, so should lose energy and spiral into the nucleus.

Rutherford's model was saved in 1913 by Danish physicist Niels Bohr. He used the unique quantum ideas of energy, saying that the electron could have only certain 'allowed' energy states; with definite energy gaps between them corresponding to definite orbits. So electrons could not lose energy continuously and spiral into the nucleus. Electrons could only move between the orbits by gaining or losing definite, set quanta of energy. 

This did indeed seem a very far-fetched idea at the time, but Bohr backed it up with calculations of how much energy an atom could gain/lose and matched this with the energy of the light quanta it had emitted. 

Bohr did not explain why the electron couldn't fall into the nucleus. This had to wait until a later version of quantum theory.

"A physicist is just an atom's way of looking at itself."  

- Niels Bohr.

What is Mitosis?

What is Mitosis?

Mitosis is one type of cell division that takes place in body cells.

A body cell is any cell except those that produce gametes (sex cells).  

The cell that is dividing is called the parent cell, and two new cells are formed because of it; called daughter cells. The daughter cells are identical to the parent cell, so if the parent cell is diploid then the daughter cells will be diploid too. 

There are several stages of mitosis, which repeat and repeat.

1. The first stage of Mitosis is called Interphase; at the end of interphase, chromosomes start to become much more visible. The DNA has already been copied. 
2. The second stage of Mitosis is called Prophase; the nucleolus disappears.
3. The third stage of Mitosis is called Metaphase; which is when the nuclear membrane begins to break down. Chromosomes line up along the middle of the cell.
4. The fourth stage of Mitosis is called Anaphase; the chromatids here separate and one chromatid from each pair is pulled to each pole of the cell. The chromatids can now be called chromosomes. 
5. The fifth stage of Mitosis is called Telophase; The spindle fibres disappear and a new nuclear membrane forms around each group of chromosomes/
6. The cell splits into two, which is called Cytokinesis.

Please note that Mitosis is much more advanced than this; this is a basic description of what Mitosis does.

WELCOME TO THE SCIENCE BLOG!

Dear Reader, Welcome to My Blog!

This is a blog for the scientist, the science and mathematics student, or anyone who just likes science and enjoys reading about it.

My name is Avesta Afshari-Mehr. I am currently a Mathematics student based in the United Kingdom. I hope to study Natural Sciences at Cambridge University in 2 years. 

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