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Fractals: What are they?

by YPU Admin on May 4, 2017, Comments. Tags: Fractals, Geometry, maths, PhD, Pure Mathematics, Research, STEM, and UoM

Introduction


Hi my name is Catherine Bruce and I’m a first year PhD student in Pure Mathematics at the University of Manchester. I study the geometry of fractals, which are objects deemed too irregular for traditional geometry such as straight lines, area, etc. (They have an infinite perimeter!) During the final year of a 4 year undergraduate degree I realised that I really enjoyed research and was lucky enough to be offered the opportunity to do it full time.

How I got here

After leaving secondary school I did A-levels in Maths, Further Maths and French. I was also interested in Politics and took it as an extra AS-level in my second year at college. I then applied to do a four year undergraduate degree in Mathematics at the University of Manchester. This meant I graduated with an MMATH degree which is called an integrated Masters. I enjoyed my whole degree but realised only while undertaking my final year project that research was for me and applied for a PhD. I took a year out to go travelling after graduating and returned to Manchester in September 2016 to start my research.

In Depth

Fractals are too irregular for their size and structure to be measured using classical geometry. The main tool of fractal geometry is dimension, which has many forms. A lot of research is done into finding the dimension of different fractals and the image of these fractals under different functions. Fractals are often very beautiful – they have detail at all scales which means no matter how much you zoom in to one part of the fractal it will always have an interesting structure, which is not true for classical geometrical objects like 2D and 3D shapes.


An important property of fractals is self-similarity. This vaguely means that an object looks like it’s made up of lots of smaller versions of itself. Notice that each branch of this fern looks like a smaller fern, and each smaller branch looks like an even smaller fern. This is a simple example of self-similarity.

Many things in nature have a fractal-like structure: clouds, mountain skylines and forked lightening. Fractal geometry can be applied to many different things in the real world. Examples that I know of are lasers, cancer treatments and fracking. However, I do not deal with any of these applications as I (along with all other pure mathematicians) study the theoretical side of mathematics.

In the first few months of my PhD I have been reading a lot to learn what everyone else in my field of research already knows. When I have done this I will be able to start answering questions that no one has answered before, and coming up with brand new research. This is the whole point of a PhD and is an exciting if not scary prospect!

Going Further

Learn more about what fractals are:

http://fractalfoundation.org/resources/what-are-fractals/

Have a go at constructing your own fractal:

https://sciencevsmagic.net/fractal/#0060,0090,1,1,0,0,1

Have a look at the exciting research that’s going on in dynamical systems at the University of Manchester:

(http://www.maths.manchester.ac.uk/our-research/research-groups/analysis-and-dynamical-systems/)

 

The Search for Alternative Energy Sources

by YPU Admin on March 16, 2017, Comments. Tags: chemical engineering, energy, Fuel Cells, PhD, Research, STEM, and UoM

Introduction

My name is Romeo Gonzalez and I am a 1st year PhD student at the School of Chemical Engineering and Analytical Sciences. After graduating from my Bachelor degree, also in Chemical Engineering, from my home county, Mexico, I successfully applied for a scholarship from my Government to come and study here in Manchester. I started on a Masters degree called an MPhil. This is sometimes a PhD preliminary year where you research a specific field before starting a full PhD in the same research area and is the path I took to becoming a PhD student.


My PhD focuses on applying new materials, such as graphene and reduced graphene oxide, into fuel cells. Fuel cells are devices capable of generating electricity through a chemical reaction, making my speciality electrochemistry.

In Depth

Currently most of the devices we use in our daily lives require a power supply, from the kettle we use for our morning coffee to the bus we use to get to work or school. This demand of energy is increasing every single day and is one of the most worrying problems humanity is facing.

So far, the solution to this problem hasn’t been found, but, most people believe that the solution lies in the use of multiple types of alternative energy sources. One of those alternative sources are fuel cells, more specifically, PEM fuel cells (proton exchange membrane fuel cells). These are small devices that can generate electricity through a reaction that takes place in the heart of the fuel cell, the Membrane Electrode Assembly. This is comprised of two electrodes stuck together with only a thin membrane separating them. The chemical reactions split a fuel - such as hydrogen, methanol or formic acid - into protons and electrons, which releases the chemical energy trapped inside that goes on to form electricity and water, thus generating power at a high efficiency with a low impact to the environment.

They are similar to batteries in the sense that both are electrochemical devices. However, in the case of batteries, they contain a set amount of power storage within them, whilst fuel cells produce a constant flow of energy as "fuel" flows through it.


So, why are we not already using them? Well unfortunately, fuel cells face different kinds of problems that need to be solved before they become as commonly used as batteries. In the case of hydrogen or formic acid, storage and handling of the fuel is a major safety issue, whilst low power production is an issue facing methanol fuel cells. Another problem this technology is facing is the use of expensive materials as a catalyst (a material used to kick start the chemical reaction), without which the fuel cells would not function. This problem is being tackled by finding alternative materials to try to improve the performance of the device. I’m looking specifically at using graphene in a number of different varieties.

So, what’s Graphene? Graphene is a relatively newly discovered two-dimension material that is known to possess multiple qualities, such as being highly conductive, highly resistant, ultra-light, transparent and is the thinnest material possible that could improve our daily life devices, including fuel cells. The objective of my PhD is to explore the use of this material in formic acid fuel cells to improve its power generation and efficiency, making it an excellent alternative source of energy.

Going Further

If you'd like to know more about fuel cells, visit this page:

http://americanhistory.si.edu/fuelcells/basics.htm  

If you want to know what kind of research is being carried out into fuel cells, visit:

https://energy.gov/eere/hydrogen-fuel-cells-blog  

If you're keen to know more about Graphene, visit the University of Manchester, the home of Graphene: http://www.graphene.manchester.ac.uk/  

Or if you want to know what you can do as a chemical engineer and how to become one, visit:

http://www.whynotchemeng.com/  

 

What is Graphene and what can it do?

by YPU Admin on January 31, 2017, Comments. Tags: graphene, PhD, Research, STEM, and UoM

Introduction

Hi, my name is Rory Brown and I’m in the second year of a PhD in theoretical physics. Specifically, I’m a part of the Graphene NOWNANO CDT at the University of Manchester, a programme that takes in students from all STEM backgrounds and trains them to do research in different areas of nanotechnology, mostly related to graphene and other similar materials – I use computer modelling to study how graphene behaves when we combine it with other materials to make electronic devices, and try predict if anything unusual will happen. I’ll tell you a little bit about what graphene is and hopefully explain why it’s so exciting, then what a PhD is like and how you can get there.


In Depth

Graphene was discovered here in Manchester in 2004, through an experiment so simple you can do it in 5 minutes at home. We start with graphite, the same material that we use in pencils. If you’ve ever held a piece of graphite, you might notice that it feels slippery and waxy – this is because graphite is made of layers of carbon atoms, organised in hexagons and stacked together like a deck of cards. Each layer is strongly held together but can freely slide over one another, and when you write with a pencil you break these layers apart, leaving some behind on the page. Graphene is a single one of these layers, and for a long time people argued that a single layer couldn’t actually be separated from the others, thinking it would be too unstable. It’s actually surprisingly easy to make – reaching in with a piece of scotch tape, the Manchester team was able to pull these layers apart over and over, until they finally had flakes of single layers of graphene, a material 10,000 times thinner than a human hair. Given that it’s only one atom thick we say it’s a ‘2D’ material, and since its discovery we’ve found a whole family of materials that can be made 2D.


Picture a: a sheet of graphene. Picture b: how graphene stacks are weakly bonded to make graphite.

So now that we’ve made it, what can graphene do? As well as being incredibly thin it has some remarkable properties, being incredibly flexible as well as the world’s strongest material: if you had a sheet big enough it would take the weight of an elephant balanced on a pencil to break through it! Industries are already looking into using graphene to make stronger, lighter materials for e.g. cars and aerospace travel. I’m interested in its electronic properties: electricity in graphene travels without any resistance, only 300 times slower than the speed of light, which gives it a lot of potential for energy-efficient electric devices.

One of the ways to make these devices is to combine graphene and other 2D materials, making thin sandwiches of different materials. What we’re left with is a stack only a few atoms thick, and the atoms in each layer can have different properties – one can be an LED, or a sensor. This is where I come in, making computer programmes to try and describe what happens in these layered materials. Working as part of this big group effort to improve our understanding of this new technology is very exciting and rewarding.

How I got here


My path to doing my PhD was fairly straightforward – I studied an MPhys in Physics here in Manchester, and my interest in graphene led to me staying. This isn’t always the case, and the NOWNANO CDT is a great example of how this can work: the people I work with come from a variety of backgrounds across all of STEM, some having spent time in industry beforehand. I’d love to continue with research, but there’s a lot of potential in PhD studies beyond that: you can go into scientific research or work in industry, or if that’s not your thing the skills that you learn (independent research, problem-solving, numeracy, presenting…) can lead to just about any job you can name. It’s a fascinating position to be in that’s full of opportunities all around the world.

Going Further

If you’re interested in some of the cutting-edge graphene research facilities that we have in Manchester, I recommend looking at the National Graphene Institute and NOWNANO websites:

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

http://www.graphene-nownano.manchester.ac.uk/

The Museum of Science and Industry in Manchester also has an exhibit on graphene and other ‘Wonder Materials’ running until June 2017 that’s worth a visit:

http://msimanchester.org.uk/whats-on/exhibition/wonder-materials

Graphene also tends to pop into the news every now and then because of the promising factors just mentioned, so keep an eye on the science sections!


The National Graphene Institute.

 

Applying Maths to Movement

by YPU Admin on January 5, 2017, Comments. Tags: Anomalous Transport, Applied Maths, Equations, PhD, Research, STEM, and UoM

Introduction

Hi! My name is Helena and I am a PhD student in applied maths at The University of Manchester. What that means is that after finishing my undergraduate degree in Physics, where I was taught a multitude of things about the world surrounding us, I decided I wanted to spend some time actually making discoveries for myself.

In Depth

There are hundreds (or even thousands) of equations out there describing ways movement happens; the movements which people observe all the time in experiments or real life are described by the so-called classical equations. Some of these you're probably already learning about at school.

What I do now is study what we call “anomalous transport”, which basically just means movement that somehow looks odd or unusual.  The equations for anomalous transport differ from the classical ones in that they in some way or another require `memory effects' in order to fit experiments. The scientific principles teach us that experiments must always be the starting point of any work we do: we build theories to fit the data, not change the data to fit the theory we already have. And so that's what I do. I try to find mathematical descriptions of the kinds of movements scientists working in e.g. biology see in the lab. Once I manage to find a good fit between my theory and the data they gave me, the experimental scientists can then go away and do more experiments to test the predictions of my models.

Of course it's not just my model, but that of my entire research group. Depending on how difficult a problem is, it can often take several of us to solve it. An example of such a problem is intracellular movement, so movement that happens inside of the cell. For example, researchers in biophysics and biology are interested in how essential nutrients are transported from the nucleus to the cell membrane. This transport happens partly through the work of “motor proteins”, and the movement of these inside the cell are known to be anomalous. An image of how the transport happens is shown below.


Drawing 1: The picture shows a motor protein (brown) moving a cargo (blue) along a microtubule. Microtubules are pathways to transport nutrients across a cell. 

When you think about all the different parts of a cell, and the processes that happen in it, it is not very surprising that the equations one would need to describe this kind of transport would have to be rather complex. In particular, what we find is that the movement you see any point in time will likely also depend on what happened a while ago. For example, if there are several motor proteins all moving on a microtubule they might cause some kind of `traffic jam', which will affect the motors for a while until the path becomes clear again. This, and many other things, can be the cause of `memory effects' in our equations so that we may have to account for all movements up until the point we're looking at in order to predict how the movement will continue.

While this makes the work harder, it is very important in understanding what might cause transport in cell to stop happening, leading to cell degeneration. This is linked to various neurodegenerative diseases and could potentially be instrumental in designing better medications.

Other examples of where you might see this kind of anomalous movement include the flights of bumblebees in a field, sharks hunting for prey in the ocean, and even the optimal part a robotic vacuum might take across your living room floor!

Going Further

If you're interested in learning more about anomalous transport, our research group has a website with more examples.

http://www.maths.manchester.ac.uk/~sf/anomalousdiffusion/index.html

Otherwise, if you want to learn more about intracellular transport there is a very useful introduction here:

http://www.studiodaily.com/2006/07/cellular-visions-the-inner-life-of-a-cell/

Finally, if you want to get an idea of all the other amazing areas maths can be applied to you can visit

http://www.maths.manchester.ac.uk/our-research/research-groups/industrial-and-applied-mathematics/

 

Food for Thought

by YPU Admin on November 29, 2016, Comments. Tags: e-Agri Sensors Centre, PhD, Research, STEM, and UoM

Introduction

My name is Charles, and I have been interested in electronics since high school. Being able to build a solution to a problem, with my hands has always appealed to me. Because of this I went down a scientific path through GCSE’s to A-levels and eventually university. There I learnt the wider impact that my interests could have, and the importance of sharing such knowledge and expertise beyond our realms. Today I am an engineer, and this is my research…

In Depth


With the huge availability of food today in the United Kingdom, it is very easy to forget that this is not the case across the globe. Farmers in developing countries, such as India, lack the fast-evolving knowledge required to manage their crops efficiently, and also the technology required to implement it. This means that small issues such as pests and disease, have a significant impact on their livelihood. This is an age old problem that requires new age technology to help. At the e-Agri Sensors Centre, we are developing a solution that will bring the power back into the hands of local farmers, and reduce the current destruction to their crops. This solution comes in the form of a low-cost attachment to their phone, which will be able to scan for disease signatures. In the field it can be put in the hands of field workers and charities.


Going Further

e-Agri Sensors Centre Website:

http://www.eee.manchester.ac.uk/our-research/research-groups/sisp/syngenta-sensors-uic/

My research project:

http://www.eee.manchester.ac.uk/our-research/research-groups/sisp/syngenta-sensors-uic/projects/e-agri-india/

Related research:

http://www.eee.manchester.ac.uk/our-research/research-groups/sisp/syngenta-sensors-uic/projects/nutrient-sensors/

Radio 4 interview with myself and the centre’s Director:

http://www.bbc.co.uk/programmes/p0306gmn