SomaSimple Discussion Lists  

Go Back   SomaSimple Discussion Lists > Physiotherapy / Physical Therapy / Manual Therapy / Bodywork > General Discussion > Eye-deas
Albums Quiz PubMed Gray's Anatomy Tags Online Journals Statistics

Notices

Eye-deas Ideas for our eyes. Food for open minded brains. This forum is dedicated to Diane.

Reply
 
Thread Tools Display Modes
Old 21-12-2005, 06:13 PM   #1
Diane
Human Primate Social Groomer and Neuroelastician
 
Diane's Avatar
 
Join Date: Mar 2004
Location: Weyburn Sask.
Posts: 22,708
Thanks: 3,036
Thanked 6,177 Times in 2,799 Posts
Default Minimal Surfaces

Although this article doesn't specify living structures, I wonder if our bodies build things like this. Surely nature would rather not waste any energy constructing items (i.e. living ones) whose job it is to create entropy. If the cell is the basic unit of life, the cell's basic design is spherical. But that doesn't mean that in order to hang together, to develop locomotion, whatever, cells couldn't devise minimalist structures of their own that are less spherical, built from molecules. In fact the more I think about it the more likely it seems. (What it might have to do with PT, I don't have any idea at this point. Maybe nothing.)

There are some very cool visuals within the list of links inside the article:
http://newsinfo.iu.edu/news/page/normal/2606.html
Quote:
Getting a handle on minimal surfaces
IU mathematician helps solve old problem that may have new applications
FOR IMMEDIATE RELEASE
Dec. 20, 2005

BLOOMINGTON, Ind. -- A twisted soap bubble with a handle?

If you find that hard to visualize, it's understandable. Experts had thought for more than 200 years that such a structure was not even mathematically possible. But no longer.

In a paper published in the Nov. 15 issue of Proceedings of the National Academy of Sciences, mathematicians Matthias Weber of Indiana University, David Hoffman of Stanford University, and Michael Wolf of Rice University presented a proof of the existence of a new minimal surface they call a genus one helicoid.

"This proof tells us that our intuition was not quite right about what is possible and what is not possible," Weber said. "Probably one reason it was not discovered sooner is that no one imagined that something like this could exist."


The top image is a traditional helicoid. The bottom one has a hole in it that would become a handle if the shape were completely untwisted into a flat surface.
Print-Quality Photo
A helicoid is what results when one of the simplest shapes -- a flat plane -- is twisted an infinite number of times. If the helicoid is vertical, its shape resembles a spiral parking ramp.

The new surface looks much like this traditional helicoid with an extra feature: a handle such as one finds on a coffee mug. It turns out that on one "floor" of the parking ramp there is an additional column -- the handle.

All minimal surfaces have something important in common: a minimal surface area.

"A minimal surface is formed when the pressure on both sides of a surface is the same," Weber explained. "'For example, when you dip a bent coat hanger into soapy water, the soap bubble that forms on the hanger is a minimal surface." These soap bubbles can have various shapes, depending on the shape of the coat hanger, but in every case the bubble is trying to minimize surface tension, he said. This happens when the bubble has the smallest possible surface area.

At every point, a minimal surface is either flat or shaped like a saddle or a potato chip.

Minimal surfaces are proving to be important at the molecular level. "Minimal surfaces actually occur in nature at the nanoscale as interfaces between certain substances," Weber said. An example is some copolymers that are plastics used to make new kinds of fabrics. When these copolymers are mixed, there are interfaces between them that are minimal surfaces. Knowing what these interfaces look like can help in determining what the chemical properties of the mixture will be.

Minimal surfaces are extremely stable as physical objects, Weber pointed out, and this can be an advantage in many kinds of structures. He has heard from architects who have seen computerized illustrations of some of his minimal surfaces and are intrigued by the possibility of adapting them to structures, both interior and exterior. He has exchanged information about minimal surfaces with some architects and is exploring ways to collaborate with them.

Calendars are another use for this work, highlighting the aesthetic qualities of minimal surfaces. These aesthetic qualities are on vivid display in Weber's computer gallery of minimal surfaces at http://www.indiana.edu/~minimal/gall...dex/index.html, which shows minimal-surface objects set in imaginary landscapes.

"The images in the gallery are not intended as illustrations of mathematical facts," Weber said. "They more than fulfill their purpose if people see them and can feel some of the intriguing enchantment that a mathematician feels when exploring the mathematical objects."

In a second gallery at http://www.indiana.edu/~minimal/archive/index.html the pictures do illustrate mathematical facts. "This is the most comprehensive collection of minimal surfaces available," Weber said. "Users can download programs that recreate the surfaces, allowing them to conduct numerical and visual experiments."

A detailed article about the helicoid discovered by Weber and his co-workers can be found in the Dec. 17 issue of Science News at http://www.sciencenews.org/articles/20051217/bob9.asp.

The mathematicians' complete proof is more than 100 pages long. The abstract of their report in Proceedings of the National Academy of Sciences is available at http://www.pnas.org/cgi/content/abstract/102/46/16566.

Weber can be reached at 812-855-8724 or matweber@indiana.edu.
__________________
Diane
www.dermoneuromodulation.com
SensibleSolutionsPhysiotherapy
HumanAntiGravitySuit blog
Neurotonics PT Teamblog
Canadian Physiotherapy Pain Science Division (Archived newsletters, paincasts)
Canadian Physiotherapy Association Pain Science Division Facebook page
@PainPhysiosCan
WCPT PhysiotherapyPainNetwork on Facebook
@WCPTPTPN
Neuroscience and Pain Science for Manual PTs Facebook page

@dfjpt
SomaSimple on Facebook
@somasimple

"Rene Descartes was very very smart, but as it turned out, he was wrong." ~Lorimer Moseley

“Comment is free, but the facts are sacred.” ~Charles Prestwich Scott, nephew of founder and editor (1872-1929) of The Guardian , in a 1921 Centenary editorial

“If you make people think they're thinking, they'll love you, but if you really make them think, they'll hate you." ~Don Marquis

"In times of change, learners inherit the earth, while the learned find themselves beautifully equipped to deal with a world that no longer exists" ~Roland Barth

"Doubt is not a pleasant mental state, but certainty is a ridiculous one."~Voltaire
Diane is online now   Reply With Quote
Old 22-12-2005, 09:09 AM   #2
bernard
Admin, Moderator...
 
bernard's Avatar
 
Join Date: Mar 2004
Location: France
Age: 57
Posts: 12,314
Thanks: 669
Thanked 408 Times in 209 Posts
Default

Diane,
Minimal surface is mandatory at every level.
Here is a trial to show how "Nature" creates automatically curves and hopfully these curves create the best shape and minimal surface of the pyramid.
I'm a fan of simple and minimal surfaces.

__________________
Simplicity is the ultimate sophistication. L VINCI
We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. I NEWTON

Everything should be made as simple as possible, but not a bit simpler.
If you can't explain it simply, you don't understand it well enough. Albert Einstein
bernard

bernard is offline   Reply With Quote
Reply

Bookmarks

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

Forum Jump

Similar Threads
Thread Thread Starter Forum Replies Last Post
Hydrophobic membrane surfaces attract Diane Cells and Stars 0 03-08-2006 04:01 PM


All times are GMT +2. The time now is 06:33 PM.


Powered by vBulletin® Version 3.8.8
Copyright ©2000 - 2014, vBulletin Solutions, Inc.
SomaSimple © 2004 - 2014