The European Space Agency (ESA) has commissioned ThinkTank Maths to investigate novel mathematics for atmospheric entry problems: how to protect a spacecraft from the intense heat it experiences when entering the atmosphere of a planet and ensuring it lands on the surface intact.

ThinkTank Maths’ fundamental mathematical work will challenge the traditional simplifying assumptions involved in the heat flux calculations with the prospect of improving their accuracy significantly.

A crucial part of the project involves exploring new ways to solve the Schrödinger equation — one of the most famous and fundamental equations in quantum mechanics — without resorting to the Born-Oppenheimer approximation. While this approximation has been used for decades, there is growing evidence that it is not valid in the extreme conditions experienced by spacecraft during re-entry, and it may in fact contribute to the large error margins of the current mathematical models.

Improvements in atmospheric entry modelling would lead to decisive reductions in the amount of heat shielding required. This could make currently unrealistic missions feasible, opening new horizons for planetary exploration of our Solar System.

Every year, the ThinkTank Maths team creates a unique mathematical season’s greeting. Previous cards include algorithmic wrapping paper, personalised constellations and more. You can explore all of them here.

Scottish Enterprise is the Economic Development Agency for Scotland. Read the full article here.

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There are many different images that traditionally appear in holiday greeting cards — snow, winter landscapes, candles, Santa Claus — but they always have one thing in common: they are two-dimensional. This is not surprising: the limitations of paper and computer screens aside, we human beings are most comfortable with two or three dimensions.

Nevertheless, we increasingly have to deal with things that cannot be visualised in such a way: complex data from sensors, control systems and financial transactions, or the additional dimensions that may be needed to explain some of the deepest mysteries of quantum physics. Fortunately, mathematics provides a powerful lens that allows us to catch a glimpse of these strange spaces.

To give you a new perspective of the season and to experience for yourself how counterintuitive it is to try to find structure in complex data, ThinkTank Maths has created an eight-dimensional hypercard.

What you see is an eight-dimensional set of points, with various two-dimensional messages embedded in it. The snowstorm effect corresponds to flying through the dataset and looking at the different projections it creates on a plane as it moves — like multiple shadows cast by the same object as you shine a light on it from several directions. The dataset has been created to ensure that some of these slices correspond to messages like the ones you see.

Using the sliders below the picture allows you to navigate through the data blizzard. We have hidden a secret message — can you find it? Once you succeed, you will be invited to play in the next phase of the game.

Explore other ThinkTank Maths seasonal greetings.

TTM outlined issues with the current generation of automated systems and described how the TRA could act as an intelligent decision aid in oil and gas operations ranging from automated drilling and well planning to process monitoring, allowing human operators to focus on making critical decisions and helping them to avoid information overload.

Other presenters included GDF, Oracle, Petrolink and Rajant Corporation.

TTM’s presentation is viewable below or at the Digital Energy Journal website.

Future space exploration and commercial applications of satellite constellations will require higher levels of spacecraft autonomy than is possible to achieve using traditional control systems. TTM’s Trusted Reasoning Architecture has the potential to overcome many of the shortcomings of current systems.

Autonomous systems and Command and Control decision aids based on TTM’s novel autonomy architecture learn, explain their reasoning and highlight subtle anomalies in sensor data. TTM’s presentation outlined how this capability can impact future spacecraft control systems.

The seminar was organised by the Society of Petroleum Engineering (SPE).

Other presenters included Shell, BP, Total E&P UK Limited, Schlumberger, IHSCera, Apache North Sea, DECC and ITF.

A feature article covering the key messages in TTM’s presentation was published in the Digital Energy Journal.

The behaviour of quantum objects – tiny particles like electrons or photons – contradicts our everyday intuition. Sometimes they behave like solid particles, colliding and bouncing off each other. Sometimes they display wavelike properties such as diffraction – the same phenomenon that creates rainbows.

The laws of this amazing branch of physics called “Quantum Mechanics” resolve this apparent mismatch by including all the information about the tiny objects in a mathematical description called the wave function. It turns out that from a mathematical point of view, waves and particles are two sides of the same coin.

A wave function is said to describe all the possible states that the object can be in – for example, all possible locations where we could observe it. The evolutions of the wave function over time are governed by a famous equation called the Schrödinger equation.

What you see above is not just a random animation but a quantum system created to provide you with a glimpse of the quantum world. The movements of the shape are derived from solutions to the Schrödinger equation, using the letters of your name to determine the possible states.

Different combinations of letters lead to different shapes and behaviours. Feel free to search for interesting quantum systems by trying out the names of friends and relatives.

Season’s Greetings and Happy New Year from everyone at ThinkTank Maths!

Explore other ThinkTank seasonal greetings.

Modern physics and astronomy have revealed that our relationship with the stars is even closer than the ancients could have imagined. Every atom in our bodies and the Earth itself was formed in the nuclear furnace of a nova explosion — the death of a star fusing hydrogen and helium into the heavier elements of the periodic table. We now understand that stars themselves have a lifecycle, and instruments like the Hubble Space Telescope allow us to look at them right in the eye.

We use a mixture of geometry and optimisation to discover a star pattern that matches the letters of your name as closely as possible. To allow you to have a personal relationship with at least one star, we have constrained the algorithm to ensure that at least one star imaged by Hubble is contained in the constellation. It is highlighted in the image above — click the image to read more about your star.

The Astronomy Nexus HYG Database is used to plot star locations, brightness and colours.

Image credit: NASA, ESA and The Hubble European Space Agency Information Centre.

Explore other ThinkTank seasonal greetings.