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Football free-kicks… taken by Newton

This Saturday might be a normal day for many people, but football fans around the world are looking forward to it, as two of the best teams in the the world are playing in the final of the best club football competition, the Champions League, at the National Stadium of Wales in Cardiff.

Here at Chalkdust, we’re quite excited too, and so we decided to analyse the mathematics and physics behind one of the best goals ever scored… and go on to reproduce it mathematically!  You might find it provides an excellent topic of conversation in your preferred pub before the match or during half-time.

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Is it possible to reach absolute zero?

German chemist Walter H Nerst [public domain]

The third law of thermodynamics (sometimes referred to as the heat theorem or unattainability principle) was postulated in 1912 by the German chemist Walther H Nernst and states that it is impossible to reach, by any procedure, the coldest temperature possible: absolute zero (0K, or −273.15C or −459.67F, depending on your preferred choice of units). However, this statement was a matter of some controversy, as there was no real proof of it. Although Nernst spent many years defending his version, many scientists refused to accept it, including such heavyweights as Max Planck and Albert Einstein. Both then started introducing their own versions. Einstein, for example, believed that the third law of thermodynamics must rely on the principles of quantum mechanics.

More than one hundred years went by and physicists and chemists from around the world were still debating the theorem, with some remaining unconvinced of its validity, given the lack of a proof.

However, a recently published paper in Nature Communications aims to clarify this debate. Researchers from the Department of Physics and Astronomy at University College London (UCL) have proven mathematically that it is impossible to reach absolute zero: we went to chat with one of them, Lluis Masanes.

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Snowflake, the symbol of winter: different sizes, infinite shapes

This post was part of the Chalkdust 2016 Advent Calendar.

Winter is coming. Or, to be more precise, the winter season begins on 21 December. Some people hate it, while others (like me) love it. Every time we hear the word winter, we think about that cold time of the year when we wear our scarves, jackets and coats, and we gather with our loved ones and eat (lots) of delicious food. But if you were asked to describe the word ‘winter’ with a simple symbol, what would that symbol be?  Most of us would probably think of a white, beautiful snowflake. And we are not the only ones thinking of that: if you Google the word ‘winter’ and go to the image section, you will find lots of pictures of them.

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Paper snowflakes made by me

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First pictures of snoflakes taken in 1931 by Wilson Bentley

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Recent pictures of snoflakes (made in a laboratory) taken by Prof. Kenneth G. Libbrecht

The snowflake is the most iconic symbol representing cold weather, and is also a traditional image used during the Christmas period. It is well known that most snowflakes have six-sides (hexagonal pattern) and many branches around them; but apart from that snowflakes come in a large variety of shapes and sizes, leading to the common phrase “no two snowflakes are alike”. But how is a snowflake formed? In this blog, we will describe the process of snowflake formation, and explain why they exist in a variety of shapes and sizes. To do that, we just need to understand some basic concepts: humidity and supersaturation.

 

Construct your own snowflakes using just paper and scissors. Follow 
the instructions here.

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Catching criminals with maths

As a result of decades of empirical research, crime science has emerged as the leading multidisciplinary approach to develop new ways to tackle crime and terrorism. As opposed to traditional criminologists, crime scientists commonly use a broad spectrum of different disciplines and sciences to achieve their aim of cutting crime. Using knowledge from chemistry, geography and physics, to architecture, public health, psychology and information technology, crime science has been able to offer new solutions to the most pressing issues that impact on the health and security of millions of people. Among all the fields and disciplines used, applied mathematics, statistics and econometrics are perhaps the most common tools used by crime scientists.  Continue reading