It often turns out there is more to commonplace everyday events than meets the eye. The folding of paper, or fall of water droplets from a tap, are two such events, both of which involve the creation of singularities requiring sophisticated mathematical techniques to describe, analyse and predict.
On the positive side, there is much in common between many such singular events across the whole range of scales, from microscopic interactions to the very formation of the universe itself during the Big Bang. In the past these seemingly unconnected events involving singularities have tended to be studied in isolation by different scientists with relatively little interaction or exchange of ideas between them.
Singularities occur at a point of cut off, or sudden change, within a physical system, as in formation of cracks, lightning strikes, creation of ink drops in printers, and the breaking of a cup when it drops. Improved understanding of the underlying mathematics would have many benefits, for example in making materials of all kinds that are more resistant to cracking or breaking. A recent workshop organised by the European Science Foundation (ESF) represented one of the first attempts to unify the field of singularities by bringing together experts in the different fields of application from astronomy to nanoscience, to develop common mathematical approaches.
"Singularities represent a subject that cuts across disciplines and specializations, such as experimental physics, theoretical physics, and rigorous mathematical proofs," noted the workshop's convenor Jens Eggers. "This workshop very much reflected this fact, as we had speakers from very different backgrounds."
The workshop confirmed that most if not all singular events in the universe, ranging from microscopic cracks to the Big Bang, share one important property known as self-similarity. This means that under magnification the event looks almost the same. For example a crack in a piece of plastic exhibits the same jagged structure when magnified say 100 times. This enables common mathematical approaches to be applied.
However it is also true that the "devil lies in the detail" when it comes to comparing different types of singularity. In other words different systems might have some common features such as self-similarity, but also unique aspects that require specialised study. One aim of the workshop therefore was to identify the common methods that could be applied as a foundation for more detailed specific study of a particular type of singularity.
This was reflected in the wide range of systems discussed. One such system, dealing with cracks in structures or rock formations, was presented by Jay Fineberg from the Hebrew University in Jerusalem. He talked about new experiments involving gels, allowing the structure of the crack to be determined in great detail down to very small microscopic dimensions, yielding some unexpected findings. "In particular, the structure of a crack is often more complicated than anticipated. Instead of one single crack path, the crack splits and has many small side branches, which appear to have complicated, if not fractal, structure," said Eggers. Fractal structure here means much the same as self-similarity, involving a geometrical pattern that looks unchanged under magnification or reduction.
Another example of everyday relevance concerned the singularities of crumpling in paper, presented by Tom Witten from the James Franck Institute in Chicago. A crumpled piece of paper comprises many ridges and tips, which defy easy analysis. As Eggers noted, there are many unanswered questions even in describing each individual cone-shaped tip. Yet understanding the underlying mathematics would not just help understand what happens when we crumple up a piece of paper to throw away, but also other physical systems involving ridges and tips, such as the folding of proteins during their manufacture in biological cells.
One question might be what the connection is between singularity theory, and catastrophe theory, which came to prominence in the 1970s, initially developed by French mathematician René Thom and then expanded by UK mathematician Erik Zeeman. In fact catastrophe theory is a sub-branch of singularity theory, dealing with events within physical space-time, such as collisions between wave fronts, as Eggers pointed out. "In that case, a problem that takes place in all of space can be reduced to a problem that takes place along certain lines (caustics), which can be classified according to catastrophe theory," said Eggers. However this simplification cannot be applied to all singularity problems.
The workshop was though highly successful in investigating the common features that do pertain across different fields of singularity, and prepared the ground for further research programmes with greater cross-pollination of ideas than has occurred previously.
Thomas Lau | alfa
Virtual Worlds: Research Trends in Mobile 3D Data Collection
30.11.2016 | Fraunhofer IPM
4th UKP-Workshop 2017 – Save the Date!
15.09.2016 | Fraunhofer-Institut für Lasertechnik ILT
In recent years, lasers with ultrashort pulses (USP) down to the femtosecond range have become established on an industrial scale. They could advance some applications with the much-lauded “cold ablation” – if that meant they would then achieve more throughput. A new generation of process engineering that will address this issue in particular will be discussed at the “4th UKP Workshop – Ultrafast Laser Technology” in April 2017.
Even back in the 1990s, scientists were comparing materials processing with nanosecond, picosecond and femtosesecond pulses. The result was surprising:...
Have you ever wondered how you see the world? Vision is about photons of light, which are packets of energy, interacting with the atoms or molecules in what...
A multi-institutional research collaboration has created a novel approach for fabricating three-dimensional micro-optics through the shape-defined formation of porous silicon (PSi), with broad impacts in integrated optoelectronics, imaging, and photovoltaics.
Working with colleagues at Stanford and The Dow Chemical Company, researchers at the University of Illinois at Urbana-Champaign fabricated 3-D birefringent...
In experiments with magnetic atoms conducted at extremely low temperatures, scientists have demonstrated a unique phase of matter: The atoms form a new type of quantum liquid or quantum droplet state. These so called quantum droplets may preserve their form in absence of external confinement because of quantum effects. The joint team of experimental physicists from Innsbruck and theoretical physicists from Hannover report on their findings in the journal Physical Review X.
“Our Quantum droplets are in the gas phase but they still drop like a rock,” explains experimental physicist Francesca Ferlaino when talking about the...
The Max Planck Institute for Physics (MPP) is opening up a new research field. A workshop from November 21 - 22, 2016 will mark the start of activities for an innovative axion experiment. Axions are still only purely hypothetical particles. Their detection could solve two fundamental problems in particle physics: What dark matter consists of and why it has not yet been possible to directly observe a CP violation for the strong interaction.
The “MADMAX” project is the MPP’s commitment to axion research. Axions are so far only a theoretical prediction and are difficult to detect: on the one hand,...
16.11.2016 | Event News
01.11.2016 | Event News
14.10.2016 | Event News
07.12.2016 | Health and Medicine
07.12.2016 | Life Sciences
07.12.2016 | Health and Medicine