Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

Math Unites The Celestial And The Atomic

29.09.2005


There is an almost perfect parallel between math describing the motion of celestial objects, like the sun (shown here in an ultraviolet image), and atomic objects. Image courtesy of NASA.


In recent years, researchers have developed astonishing new insights into a hidden unity between the motion of objects in space and that of the smallest particles. It turns out there is an almost perfect parallel between the mathematics describing celestial mechanics and the mathematics governing some aspects of atomic physics. These insights have led to new ways to design space missions, as described in the article, “Ground Control to Niels Bohr: Exploring Outer Space with Atomic Physics” by Mason Porter and Predrag Cvitanovic, which appears in the October 2005 issue of the Notices of the American Mathematical Society.

The article describes work by, among other scientists, physicist Turgay Uzer of the Georgia Institute of Technology, mathematician Jerrold Marsden of the California Institute of Technology and engineer Shane Ross of the University of Southern California.

Imagine a group of celestial bodies—say, the Sun, the Earth, and a Spacecraft—moving along paths determined by their mutual gravitational attraction. The mathematical theory of dynamical systems describes how the bodies move in relation to one another. In such a celestial system, the tangle of gravitational forces creates tubular “highways” in the space between the bodies. If the spacecraft enters one of the highways, it is whisked along without the need to use very much energy. With help from mathematicians, engineers and physicists, the designers of the Genesis spacecraft mission used such highways to propel the craft to its destinations with minimal use of fuel.



In a surprising twist, it turns out that some of the same phenomena occur on the smaller, atomic scale. This can be quantified in the study of what are known as “transition states", which were first employed in the field of chemical dynamics. One can imagine transition states as barriers that need to be crossed in order for chemical reactions to occur (for “reactants” to be turned into “products"). Understanding the geometry of these barriers provides insights not only into the nature of chemical reactions but also into the shape of the “highways” in celestial systems.

The connection between atomic and celestial dynamics arises because the same equations govern the movement of bodies in celestial systems and the energy levels of electrons in simple systems—and these equations are believed to apply to more complex molecular systems as well. This similarity carries over to the problems’ transition states; the difference is that which constitutes a “reactant” and a “product” is interpreted differently in the two applications. The presence of the same underlying mathematical description is what unifies these concepts. Because of this unifying description, the article states, “The orbits used to design space missions thus also determine the ionization rates of atoms and chemical-reaction rates of molecules!” The mathematics that unites these two very different kinds of problems is not only of great theoretical interest for mathematicians, physicists, and chemists, but also has practical engineering value in space mission design and chemistry.

Founded in 1888 to further mathematical research and scholarship, the 30,000-member American Mathematical Society fulfills its mission through programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life.

The Georgia Institute of Technology is one of the nation’s premiere research universities. Ranked among U.S. News & World Report’s top 10 public universities, Georgia Tech educates more than 16,000 students every year through its Colleges of Architecture, Computing, Engineering, Liberal Arts, Management and Sciences. Tech maintains a diverse campus and is among the nation’s top producers of women and African-American engineers. The Institute offers research opportunities to both undergraduate and graduate students and is home to more than 100 interdisciplinary units plus the Georgia Tech Research Institute. During the 2003-2004 academic year, Georgia Tech reached $341.9 million in new research award funding.

David Terraso | EurekAlert!
Further information:
http://www.icpa.gatech.edu

More articles from Physics and Astronomy:

nachricht Measured for the first time: Direction of light waves changed by quantum effect
24.05.2017 | Vienna University of Technology

nachricht Physicists discover mechanism behind granular capillary effect
24.05.2017 | University of Cologne

All articles from Physics and Astronomy >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: A quantum walk of photons

Physicists from the University of Würzburg are capable of generating identical looking single light particles at the push of a button. Two new studies now demonstrate the potential this method holds.

The quantum computer has fuelled the imagination of scientists for decades: It is based on fundamentally different phenomena than a conventional computer....

Im Focus: Turmoil in sluggish electrons’ existence

An international team of physicists has monitored the scattering behaviour of electrons in a non-conducting material in real-time. Their insights could be beneficial for radiotherapy.

We can refer to electrons in non-conducting materials as ‘sluggish’. Typically, they remain fixed in a location, deep inside an atomic composite. It is hence...

Im Focus: Wafer-thin Magnetic Materials Developed for Future Quantum Technologies

Two-dimensional magnetic structures are regarded as a promising material for new types of data storage, since the magnetic properties of individual molecular building blocks can be investigated and modified. For the first time, researchers have now produced a wafer-thin ferrimagnet, in which molecules with different magnetic centers arrange themselves on a gold surface to form a checkerboard pattern. Scientists at the Swiss Nanoscience Institute at the University of Basel and the Paul Scherrer Institute published their findings in the journal Nature Communications.

Ferrimagnets are composed of two centers which are magnetized at different strengths and point in opposing directions. Two-dimensional, quasi-flat ferrimagnets...

Im Focus: World's thinnest hologram paves path to new 3-D world

Nano-hologram paves way for integration of 3-D holography into everyday electronics

An Australian-Chinese research team has created the world's thinnest hologram, paving the way towards the integration of 3D holography into everyday...

Im Focus: Using graphene to create quantum bits

In the race to produce a quantum computer, a number of projects are seeking a way to create quantum bits -- or qubits -- that are stable, meaning they are not much affected by changes in their environment. This normally needs highly nonlinear non-dissipative elements capable of functioning at very low temperatures.

In pursuit of this goal, researchers at EPFL's Laboratory of Photonics and Quantum Measurements LPQM (STI/SB), have investigated a nonlinear graphene-based...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

Marine Conservation: IASS Contributes to UN Ocean Conference in New York on 5-9 June

24.05.2017 | Event News

AWK Aachen Machine Tool Colloquium 2017: Internet of Production for Agile Enterprises

23.05.2017 | Event News

Dortmund MST Conference presents Individualized Healthcare Solutions with micro and nanotechnology

22.05.2017 | Event News

 
Latest News

Physicists discover mechanism behind granular capillary effect

24.05.2017 | Physics and Astronomy

Measured for the first time: Direction of light waves changed by quantum effect

24.05.2017 | Physics and Astronomy

Marine Conservation: IASS Contributes to UN Ocean Conference in New York on 5-9 June

24.05.2017 | Event News

VideoLinks
B2B-VideoLinks
More VideoLinks >>>