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April is Math Awareness Month: “Math and Sustainability”

 

April is Math Awareness Month: “Math and Sustainability”

Join the “Sustainability Counts!” challenge.

European Launch and MPE Day at UNESCO on March 5

Press releaseFrenchSpanishSpanish dossierMessage from François Hollande

Details of the programme

Exhibition

Exhibition winners

Notes on the exhibition by Andreas Matt

Impressions on the MPE Day by Ehrhard Behrends


More than 100 scientific societies, universities, research institutes, and organizations all over the world have banded together to dedicate 2013 as a special year for the Mathematics of Planet Earth.

Our planet is the setting for dynamic processes of all sorts, including the geophysical processes in the mantle, the continents, and the oceans, the atmospheric processes that determine our weather and climates, the biological processes involving living species and their interactions, and the human processes of finance, agriculture, water, transportation, and energy. The challenges facing our planet and our civilization are multidisciplinary and multifaceted, and the mathematical sciences play a central role in the scientific effort to understand and to deal with these challenges.     Read more…

National Science Foundation supports MPE2013+: Extending MPE2013 into the future. Read more…|

Chaos in the Solar System

Chaos in the Solar System

The inner planets (Mercury, Venus, the Earth and Mars) have chaotic motions. This means that the motions of the planets could become unstable, and the orbit of one planet could cross that of another. Fortunately, this will not occur for billions of years.

Read More

MPE 2013 National Launches

Canadian launch, December 7, Montreal
UK Launch, December 17, Cambridge
US launch, January 9, San Diego
Australian launch, January 29, Melbourne
Portuguese launch, March 5, Lisbon
European launch, March 5, UNESCO in Paris

Exhibition        Graphic

The MPE Exhibition is now on line. It was launched at UNESCO on MPE Day, March 5, 2013. Part of it comes from the modules of the MPE competition.

Winners
Notes on the exhibition


Lecture Series

The MPE2013-Simons Public Lecture Series will take place at nine locations around the world. Each lecturer is a leading expert who will explain how the mathematical sciences play a significant role in understanding and solving some of Planet Earth’s important problems. Our community’s best expositors and champions will cover a diverse range of topics in lectures aimed for a public audience.

CMS MPE Lecture Series

The Canadian Mathematical Society, in collaboration with the Canadian institutes AARMS, CRM, the Fields Institute and PIMS, is sponsoring a cross-Canada series of lectures for MPE 2013. Eleven of the lectures will be for the general public and the rest for a scientific audience.

MPE2013 thanks the National Science Foundation and the Simons Foundation for their support of MPE2013 activities.

http://mpe2013.org/

MPE2013 Banner

Mathematics of Planet Earth 2013 (MPE2013) is an initiative of mathematical sciences organizations around the world designed to showcase the ways in which the mathematical sciences can be useful in tackling our world’s problems. The exhibition “Mathematics of Planet Earth” was created by the community through a competition: The winning modules are now part of this open source exhibition, staged in 2013 and onwards!

Exhibition

Mathematics of Planet Earth

Credits

Dozens of scientific societies, universities, research institutes, and foundations all over the world have banded together to dedicate 2013 as a special year for the Mathematics of Planet Earth.

Call for entries

To parcticipate in the MPE exhibition, create an account and upload

The MPE Open Source Exhibition is an international virtual exhibition of museum quality exhibits (called modules) on the theme of Mathematics of Planet Earth. The exhibition will continue to grow past its launch on March 5 2013 at the UNESCO Headquarters in Paris.

The modules can be reproduced and utilized by many users around the world from science museums to schools. The exhibition has a virtual part, as well as several material parts. Copies of the material parts can be recreated or travel around the world, and the virtual modules are available on the basis of creative commons licenses.

All exhibits are demonstrating in one way or another the crucial role mathematics plays in planetary issues. The modules cover a wide variety of topics such as astronomy, fluid dynamics, the mathematics of vulcanos or glaciers and problems in cartography.

The virtual modules displayed in the exhibition come from an international competition organized by the initiative MPE 2013. They are of four types: interactive modules, films, posters, and instructions to realize a physical module. The three winners of the competition have received their prize at UNESCOduring the MPE Day in March 2013.

The physical modules were realized by Centre•Sciences CCSTI of region Centre (Orleans-France) and Adecum, Association for mathematic culture development, under the leadership and supervision of Michel Darche. They will form the base of a traveling exhibition that could be rented.

The exhibition is still under development, new ideas and modules are welcome: See the MPE projectfor more information.

Events

MPE2013 Exhibition in Paris

Mar. 5, 2013 toMar. 8, 2013

The first MPE2013 exhibition featuring the winner modules of the…

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IMAGINARY — open mathematics is a project by the Mathematisches Forschungsinstitut Oberwolfach and supported by the Klaus Tschira Stiftung

Mathematicians listen as the Earth rumbles…

General, Geophysics, Image Processing, Mathematics

“Mathematicians listen as the Earth rumbles… ” This was the title of the fourth MPE Simons Lecture given by Ingrid Daubechies in Montreal, Canada, on April 10. Her splendid lecture was delivered in French, but both English and French videos of the lecture will be on display soon on the Simons website.

Too often, we limit Mathematics of Planet Earth to climate change and sustainability problems. On the contrary, this lecture was totally fitting under the first theme of MPE, namely a “planet to discover”. The lecture of Ingrid Daubechies was related to her personal work with geophysicists and very recent results on the problem of understanding the formation of the volcanic islands.

The rocks in the bottom floor of the oceans are much younger than those of the continents. On the bottom of the oceans, the most recent rocks are along the ridges where tectonic plates diverge. And indeed, there is volcanic activity along these ridges, with new rocks being formed by magma coming up from the mantle to the surface. But there are also isolated volcanic islands, like Hawaii, Tahiti, the Azores, Cap Verde, etc. If we look to the archipelago of Hawaii, all islands are aligned, and their age increases from the largest island at one end to the smaller islands further down. This has suggested to the geophysicists that the islands were formed because of a plume, i.e., a kind of volcanic chimney through the mantle. Recall that the mantle goes as deep as half the radius of the Earth. Since the surface plate is moving, this could explain the successive formation of the aligned islands, the difference of age of which would be calculated from the distance between the islands and the speed of the tectonic plates.

But additional evidence is needed for the conjecture to be accepted by the scientific community. For instance, one would like to “see” the plume. One tool for exploring the interior structure of the Earth is remote sensing: one sends waves (signals) and analyzes the signals reflected by the boundary of some layer or refracted inside different layers. But plumes are located so deep under the Earth’s crust that the usual signals are not powerful enough to be of any help. The only waves that carry sufficient energy to analyze details at such a depth are the seismic waves generated by large earthquakes.

Large databases exist which contain the recordings of these seismic waves by seismic stations around the world. So the data exist. We then need an appropriate tool to analyze them. The problem is not trivial. The plumes are very thin regions and, moreover, the difference of the speed of a seismic wave through a plume is only of the order of 1%.

In 2005, seismologists Tony Dahlen and Guust Noleta approached Ingrid Daubechies to see if wavelets could help in their venture. Indeed, the promising results of the student Raffaela Montelli (pictured) had shown that seismic methods could be used to capture regions of perturbations of the pressure waves (P-waves) of earthquakes, see figure.

Pwave Velocity Perturbations

Such regions overlapped exactly the regions with isolated volcanic islands: the temperature of the ocean floor was higher in these regions. But, as mentioned above, the plumes are very thin and the difference of speed of seismic P-waves very small in these regions. Hence, there is a large risk of errors in the numerical reconstruction of the inner structure of the Earth, unless we use an appropriate tool. This is where wavelets proved useful. They are the perfect tool to analyze small localized details. Moreover, one can concentrate all the energy in small regions and neglect the other regions.

In her lecture, Ingrid Daubechies gave a short course on wavelets adapted to digital images made of pixels. A gray-tone image is just an array of numbers giving the gray tone of each pixel. From this matrix, one constructs four smaller matrices consisting of either horizontal or vertical averages of neighboring pixels taken 2 by 2, or horizontal or vertical differences of neighboring pixels taken 2 by 2. One can iterate the process on the matrix of horizontal and vertical averages. She explained how wavelets allow compressing information and how we can extract very fine details in a local region while keeping the size of the data manageable. The use of wavelets to construct the images allows removing all errors in numerical reconstructions and making sure that the special zones identified in the image are indeed special. She showed clean images produced with wavelets in which artificial special regions had been removed, and she could announce “hot off the press” that she and her collaborators had obtained the first results with the whole Earth, and real data!

Christiane Rousseau

This entry was posted in General, Geophysics, Image Processing, Mathematics by Christiane Rousseau. Bookmark the permalink.

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