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Selfish species: game theory and the ecosystem

Introduction

I am studying for a PhD in Statistical Physics and Complex Systems at The University of Manchester. My research studies a system of many interacting species where the population of one species can facilitate or hinder the growth of another species. This relationship is determined by a specific interaction coefficient between the species. The interaction coefficients for the relationship between every pair of species are drawn randomly from a two-dimensional Gaussian distribution, and we use the parameters of this distribution to predict how the ecosystem behaves. We can then simulate these interacting species using a computer programme to check our predictions.


In Depth…

I studied Mathematics and Physics for my undergraduate degree at The University of Manchester. I chose this degree because I enjoy understanding how the world works, and appreciate how bizarre and counter-intuitive our reality is. I had a fascination for quantum mechanics and relativity, higher dimensions, and sub-atomic particles. I really enjoyed learning about these concepts as well as being introduced to many other fascinating ideas. I enjoyed the lecture style of teaching but I also developed my ability for independent learning, I became really good at managing my own time, and absorbing information at my own pace from reading textbooks and lecture notes. The most useful skill I learned during my degree was how to computer programme, I learned how use Matlab, C++, and Python, and I learned how to write codes for simulations, data analysis, solving complicated equations, and optimization algorithms. I decided to do a PhD after my undergraduate degree because I really enjoy self-study and programming, and I am further developing these skills with new challenges every day.

I became interested in population dynamics after reading "The Selfish Gene" by Richard Dawkins, where he described behavioural evolution using ideas from Game Theory. He described how an animal’s behaviour, and the behaviours of the other animals it interacts with, would determine how successful the animal would be at surviving and passing on it genes. These successful behavioural strategies would dictate how the behaviour of the population as a whole would change over time, and evolve to an Evolutionary Stable Strategy which could be understood as stable Nash equilibria. During my degree I took the opportunity to study Game Theory further by writing my second year vacation essay on the topic. I researched many areas of Game Theory and went through a short online course. I discovered how it can be applied to statistical physics, in the Ising model for ferromagnets, and really enjoyed learning about how ideas from quantum mechanics could produce Quantum Game Theory, where a player could play multiple strategies at the same time. In my fourth year I undertook a project with my current PhD supervisor on a population of individuals who had the choice of two behavioural strategies to interact with. The population evolved by the number of individuals playing the more successful strategy increasing, but this model also considered the effect of time delay, such as a gestation period in nature. I really enjoyed my project with my supervisor and through this I continued onto a PhD with him.

Going Further…

Here is a link to my supervisor’s webpage, if you are interested in my research you could look at his publications:

https://www.theory.physics.manchester.ac.uk/~galla/

Here are links to the undergraduate Mathematics and Physics courses webpages:

http://www.maths.manchester.ac.uk/

https://www.physics.manchester.ac.uk/

If you are interested in game theory, here is a brief course:

https://www.youtube.com/watch?v=iZKErrvVMaY&list=PL76B0EB6DDFC42D02

If you are interested in “The Selfish Gene” here is a brief summary of the book, chapter 12 discusses game theory:

http://old.unipr.it/arpa/defi/econlaw/SELFISH%20GENE.pdf

and the full text can be downloaded here:

https://www.zuj.edu.jo/download/the-selfish-gene-r-dawkins-1976-ww-pdf/

 

Science and Engineering have the power to change the world we live in!

Introduction

My name is Marcello and I earned my PhD in particle physics at the University of Manchester, in 2013. Since then, I have been working as a researcher for the Science and Technology Facilities Council (STFC). 

STFC is a UK government body that carries out civil research in science and engineering, and funds UK research in areas including particle physics, nuclear physics, space science and astronomy.

I work in the technology department and I am involved in projects dealing with the building of instrumentation for experiments in nuclear physics. This type of instrumentation is not available commercially because it has very particular requirements. Hence, STFC employs dedicated teams of physicists and engineers to build this type of equipment. And I am one of them!

My experience.

I decided to continue my education after the age of 18 and so enrolled in a bachelor’s degree of physics at the University of Manchester. This decision opened up many opportunities in my life.

I gained an objective view of natural phenomena and increased my employability.

Science and engineering have the power to change the world we live in. These subjects produce the most amazing technology and fuel the economy of many countries. For this reason, the analytical thinking of a physicist is highly valued in the job market.

As a student, I did not always find physics easy to understand and did not like all of its different branches equally. My favorite topic is the interaction of radiation with matter, so I decided to specialize in this area for my masters and PhD.

An education in physics gave me the opportunity to study and work in an environment which is professional, multicultural and at the forefront of human knowledge.

From the neighborhood I grew up in, I found myself involved in international projects investigating important questions about our existence. I spent time in laboratories in other countries to exchange information about my work. During this time, I also made strong friendships and discovered new places.

The knowledge I gained in high-school in mathematics, physics and computer science, has been beneficial to my career.

To summarise, I wanted to include some figures about salaries of researches in the initial and middle stages of their careers:

-  PhD student (22-25 years old): about £12,000 per year. 

-  Post-doc researcher (25-35 years old): from £28,000 to £35,000 per year.

-  Academic staff or senior researcher (35-45 years old): from £35,000 to £45,000.

Salaries will increase even further for managerial positions within Universities or Research Institutes and are generally higher in the private sector.

Further details

Apprenticeships are really good opportunities to boost your experience in science and engineering and I’ve found that it is easier to find apprenticeships in engineering than in science. Engineering or IT apprenticeships are valuable opportunities for aspiring scientists.

https://www.stfc.ac.uk/1485.aspx

Some organizations that help people to enter top Universities.

http://www.socialmobility.org.uk/

Get involved and become a STEM Ambassador.

http://www.stemnet.org.uk/


 

Recreating the conditions inside the sun

Introduction

Hello! My name is Asad and I’m a PhD student at the School of Mechanical, Aerospace and Civil Engineering at the University of Manchester. Within my PhD, I work in the relatively recent field of nuclear fusion. More specifically, I look at the effects of plasma damage and neutron irradiation (both known phenomenon that occur within nuclear fusion) on materials that could be used to build a potential fusion reactor.

A little bit about my background first. Before I embarked on my PhD, I completed a Master of Engineering (MEng) in Mechanical Engineering with a minor focus on Nuclear Engineering. I also did some part time study in mathematics and research projects within fluid mechanics. Of the latter, a noteworthy one is that I constructed a mathematical model of the acoustics of a banjo!


In Depth

Science has always intrigued mankind. Some of the foremost questions we have been obsessed with are the simple ones:

·  “Where did we come from?”

·  “Why are we here?”

·  “What do we do?”

No matter who you ask, you will realise that we still don’t really know the answers to these; whether we look for philosophical reasoning or scientific. We search high and low for answers. Our universe is at the centre of such research. And at the centre of our universe: the sun.

The sun can be considered a giant ball of energy. The manner in which this energy is generated is referred to as nuclear fusion. As the human species observed this, we felt the urge to exploit the process to aid our need for energy, in order to survive on a world where resources are rapidly depleting.

What exactly is nuclear fusion? The answer is a result of work done by pioneering scientists such as Ernest Rutherford, Pierre Curie and Marie Curie. We find that certain atoms of elements undergo interesting transitions. We have been able to exploit these, such as nuclear fission which is currently a dominant process to generate electricity. Within fission, we find that under the right conditions, some of the atoms will split and become smaller releasing energy in the process. Fusion is the opposite; some atoms combine and through the process release energy. It has been found that the energy released through fusion could potentially be more sustainable, cleaner, and less fraught with the risks associated with the energy generated through fission. 

Thus we are now engaged in a global technological race to be able to achieve the right conditions for fusion on earth. Thus far we have managed to recreate the conditions. However, we still haven’t managed to be able to maintain these for long enough, nor have we been able to extract power from it. We have some ideas on how to achieve both. One of the questions however is, do we have the materials to be able to do so?


This is where people like me come in. Thus far I have spoken about how this is a relatively new process mingled with a plethora of difficulties. Therefore, it will not be surprising when I say that we don’t exactly have the appropriate facilities to be able to entirely comprehend the extreme effects taking place. So how do we go about solving the problem? Some people try and use proxies, alternative approaches that in some way mimic certain effects we expect. Others try to use computational techniques and our understanding of physics to paint a picture. I’m involved in the latter. I use modelling and simulation to try and deduce what we expect. It isn’t as simple as pushing a button however. One needs to be aware of a lot of inter-related pieces of physics. Sometimes, we also find that we don’t have the computational power to actually be able to process all of these (surprising isn’t it given the progress in the field of IT).  Sometimes my job is therefore to see which processes are negligible. At other times, it is to check and draw conclusions from the results of my simulations. To name a few of the techniques I use; I use solvers for the neutron transport equation, binary collision approximation and molecular dynamics. The last considers how atoms are likely to behave. This generates some interesting perceptions of important chemical and atomic processes.

I’ll stop here. I’ll end on a note that the human race is currently engaged in very exciting things. But to see this realised; we need young, ambitious and creative minds that are keen to learn as well as try new things. 


Going Further

If you want any more information, please feel free to contact me at: asad.hussain@postgrad.manchester.ac.uk . 

To find out more about the chemical and atomic processes generated in molecular dynamics: http://lammps.sandia.gov/movies.html

A more comprehensive yet elementary guide on nuclear physics can be found at (http://hyperphysics.phy-astr.gsu.edu/hbase/nuccon.html)

Here are also some web links pertinent to what I have written: 

Culham Center for Fusion Energy: http://www.ccfe.ac.uk/introduction.aspx

Nuclear Energy Agency: http://www.oecd-nea.org/workareas/

Fusion Center for Doctoral Training: http://www.york.ac.uk/fusion-cdt/


 

Applying mathematics to real-world problems

by YPU Admin on November 13, 2014, Comments. Tags: aerodynamics, appliedmaths, manufacturing, mathematics, maths, and Research

Introduction

I'm Phil, a student at the University of Manchester in the final year of a PhD in Applied Mathematics, which means I apply mathematical ideas to solve physical problems. I started out doing a Mathematics MMath (a four year undergraduate course) here in Manchester and my A-levels included Maths and Further Maths. You might think that all this studying would make me feel like I know a lot of mathematics, but in fact the more you learn, the more you realise there is left to learn.

In Depth

So, what do I actually mean when I say I “apply mathematical ideas to physical problems”? Well, imagine you’re a car manufacturer who wants to test how aerodynamic a certain part of a new car is going to be. You could build a prototype of this part, using your current knowledge of how to build something that’s really aerodynamic, and test this prototype in a wind tunnel. During this experiment you could measure all sorts of useful data such as the drag caused by the wind as it flows past the part.

Now, what if you want to slightly change the shape of the part and test it again? You could, of course, build a slightly different prototype and test this again in the wind tunnel. But this would cost both the time and money necessary to build the prototype all over again. If you want to test a lot of different prototypes, the investment of time and money (on just this single part) could really start to mount up.

This is where an applied mathematician could come in. With mathematics, you can build a model of the prototype in a wind tunnel using all of the physical laws that we know it would obey. You can then write down the equations that the object would satisfy and either use clever mathematical tricks to solve them on paper or put them all into a computer to solve them (essentially using a computer to perform a virtual experiment). This can gain you a crucial advantage; once you’ve built the model, you can (hopefully) solve it for many different versions of a part much faster than the time it would take to build a whole set of prototypes and test them in a real wind tunnel. And, best of all, solving the model doesn’t cost you anything at all!

This kind of thinking can, of course, be applied to an almost limitless array of physical problems. In my specific research, I investigate how flames propagate through gaseous mixtures of fuel and oxidiser. Since my work is all in the form of solving equations on paper or simulating the physical system on a computer, I never have to get burnt or accidentally set myself on fire (you might see this as a positive or a negative, depending on your viewpoint). I’m hoping that this will lead to a post-doctoral position at a university, where I can continue to both research mathematics and teach the mathematicians of tomorrow.

Going Further

The website for the School of Mathematics at the University of Manchester can be found at www.maths.manchester.ac.uk.

Information on the applied mathematics research at the University of Manchester can be found at http://www.maths.manchester.ac.uk/our-research/research-groups/continuum-mechanics/.

It’s not specifically about applied mathematics, but if you’re interested in maths I’d strongly recommend reading a book called “Euclid in the Rainforest” by Joseph Mazur – it’s both interesting and very readable.

Finally, I recently wrote a blog on cryptography for the Young Persons University, which can be found at http://www.ypu.manchester.ac.uk/blog/cryptography-and-the-alan-turing-cryptography-competition.

Find me on twitter @pearce_maths