Lagrangian coherent structures

[sean]

Lagrangian coherent structures: The skeleton of water

Via the Economist

 

What is emerging is a picture of fluid dynamics more subtle and more complex than anything dreamed of even a decade ago. The atmosphere and the ocean are, it seems, dominated by invisible barriers that have come to be known as Lagrangian coherent structures. They govern the movement of everything from the trajectories of aircraft to the distribution of pollution, the migration of jellyfish and the tracks taken by hurricanes. They are, as it were, the skeletons of the sea and the air.

 

To understand what a Lagrangian coherent structure is, it helps to imagine a crowd at a railway terminus, says Thomas Peacock of the Massachusetts Institute of Technology, who studies the structures. Some people will be arriving. Some will be leaving. And, whichever they are doing, they will be going to and from numerous different platforms. The result is chaos, but structured chaos. What emerges is a shifting pattern of borders between groups of people with different goals. These borders are Lagrangian coherent structures. They are intangible, immaterial and would be undetectable if the passengers stopped moving. But they are also real enough to be treated mathematically.

 

Read more ...

[sheng zhen]

oh my... veeery interesting

[TzuJanLi]

Greetings..

 

Aye, Sean.. you're touching on some serious stuff, stuff most people don't want to know about.. but, as we begin to understand the relationships of these 'hidden structures' (there are many), Life will have new meaning.. Good stuff!!

 

Be well..

[EagleShen]

Thanks Sean,

Gives rise to some random musings, makes me think that to a certain extent our Lagrangian structures are our 'consensus reality'. Been a while since i've read a science article as i've had my head stuck in Taoism and Hermetics, but you can see the writers fundamental assumption of separation as plain as day. It makes me wonder what role consciousness plays in these structures, and perhaps it is actually consciousness that is the critical part of these structures.

[voidisyinyang]

Here's graphics -- the red is attraction and the blue is repulsion -- for flow of energy

 

http://www.lekien.com/~francois/papers/lcs3d/

[Creation]

Fascinating. Thanks for posting Sean and Drew.

[Taomeow]

Cool stuff.

 

On the level of the human being, that's the answer to the "no real self" idea -- you've heard it, right? -- the argument goes something like, all cells in your body get replaced over the 7-year period by new ones, so not one of the cells that comprise "you" today was in existence 7 years ago and not one of the current ones will be in existence 7 years from now. Yeah but... but the coherent structure they adhere to when coming in and going out of existence -- THAT was there 7 years ago, and most of it was there 7 million years ago too. (About 99.7% of it all was there then, can you imagine?..) That's "your real self." Your real self is a pattern, and that's pretty stable in time though pretty unstable in space. Just the way those Lagrangian structures are.

 

Which is why, on a personal note, I chose taoism to begin with -- it is concerned with stability in time to a much greater extent than with instability in space. The taoist term for stability in time is heng. It is classically defined as "the main virtue of tao."

[Guest artform]

Hi people! Yes thanks to you both sean and drew!!

 

And thank you Taomeow for your elegant reflection!

 

Cool stuff.

 

On the level of the human being, that's the answer to the "no real self" idea -- you've heard it, right? -- the argument goes something like, all cells in your body get replaced over the 7-year period by new ones, so not one of the cells that comprise "you" today was in existence 7 years ago and not one of the current ones will be in existence 7 years from now. Yeah but... but the coherent structure they adhere to when coming in and going out of existence -- THAT was there 7 years ago, and most of it was there 7 million years ago too. (About 99.7% of it all was there then, can you imagine?..) That's "your real self." Your real self is a pattern, and that's pretty stable in time though pretty unstable in space. Just the way those Lagrangian structures are.

 

Which is why, on a personal note, I chose taoism to begin with -- it is concerned with stability in time to a much greater extent than with instability in space. The taoist term for stability in time is heng. It is classically defined as "the main virtue of tao."

 

Bucky Fuller loved to make this point with his multi-material spliced rope trick! Being a sailor, and all true sailors are inherently Taoist to some degree IMHO, Bucky spliced various rope types and colours into a portable length and used it in his famous marathon lectures by putting a slip knot in it and sliding it along through the different types of rope uninterrupted.

 

The knot he said is you, your "pattern integrity", and the rope running through the knot is the always passing through materiality of your body/processes.

 

all the best slip-sliding along the rope of enfleshed passing through being all

 

artform

[nac]

Cool stuff.

 

On the level of the human being, that's the answer to the "no real self" idea -- you've heard it, right? -- the argument goes something like, all cells in your body get replaced over the 7-year period by new ones, so not one of the cells that comprise "you" today was in existence 7 years ago and not one of the current ones will be in existence 7 years from now. Yeah but... but the coherent structure they adhere to when coming in and going out of existence -- THAT was there 7 years ago, and most of it was there 7 million years ago too. (About 99.7% of it all was there then, can you imagine?..) That's "your real self." Your real self is a pattern, and that's pretty stable in time though pretty unstable in space. Just the way those Lagrangian structures are.

 

Which is why, on a personal note, I chose taoism to begin with -- it is concerned with stability in time to a much greater extent than with instability in space. The taoist term for stability in time is heng. It is classically defined as "the main virtue of tao."

No, even these change as one ages. How can there be an ideal "you" independent of the diverse conditions that shaped your present self? It's true that certain patterns become enmeshed as you get older and less flexible, but that's when your body as a whole (along with all such patterns) begins to deteriorate. Even the subtle structures in the sea and atmosphere are changing as the face of the planet, and thus the inlets and outlets of fluids keep changing. They were born one day and they will die one day like everything else.

Edited November 17, 2009 by nac

[joeblast]

that's not quite contradictory, nac. coherent structure that is stable over time doesnt imply unchanging, in fact it implies that it must change in order to stay stable and coherent

[voidisyinyang]

Well here's another example of this Lagrangian Coherent Structure used as a model for PROPULSION WITHOUT MOTION --

 

I've used this same "sailing" model while sitting in full-lotus because that's how it feels -- the "sloping boundary" creates a "diffusion-driven flow" -- Peacock claims it's previously unknown! haha.

 

Sailing on diffusion

M.R. Allshouse & T. Peacock

Nature, submitted

 

When a density stratified fluid encounters a sloping boundary, diffusion alters the fluid density adjacent to the boundary, producing spontaneous along-slope flow. Here we show that diffusion-driven flow can be harnessed for a remarkable, yet previously unknown, means of propulsion, acting as a diffusion-engine that extracts energy from micro-scale processes to propel macro-scale objects. Like a sailboat tacking into the wind, the forward thrust on an object is due to the surrounding diffusion-driven flow creating a low pressure region at the front relative to the rear. The propulsion speed is found to be a fraction of the underlying diffusion-driven flow speed, this being determined solely by the object's shape; long-range interactions are also found to occur between multiple objects. A potentially significant application is to environmental and biological transport processes at locations of strong stratification, such as pycnoclines in oceans and lakes.

 

Preprint available on request

[TzuJanLi]

Greetings..

 

"pattern integrity"

We are like snowflakes, unique patterns of exactly the same stuff.. ("God", Spirit, or my personal belief, Energy..) Another 'pattern' that survives the individual manifestation is the evolving Human Experience, the sum of Human Knowledge..

 

Be well..

[voidisyinyang]

These Lagrangian Coherent Structures are based on the strange attractors of chaotic systems. I googled chaos and lagrangian coherent structures and this recent NY Times science article popped up -- a much better description: http://www.nytimes.com/2009/09/29/science/...amp;ref=science

 

It's important to keep in mind that while the form changes there is a stable structure in time. I'm reading the below new book which is an excellent overview of chaotic study of mind-body consciousness. Here's a relevant section:

 

"Of course, the very notion of phase and amplitude of chaotic systems

is rather non-trivial. Roughly speaking, the phase of an autonomous selfsustained

oscillatory system is related to the symmetry with respect to

time shifts. Therefore, the phase disturbances do not grow or decay, what

corresponds to the zero Lyapunov exponents. The Lyapunov exponent of

a dynamical system is a quantity that characterizes the rate of separation

of infinitesimally close trajectories. It is common to just refer to the

largest one, i.e. to the Maximal Lyapunov exponent (MLE), because it

determines the predictability of a dynamical system. If the oscillations

are periodic, the phase rotates nearly uniformly, while in the chaotic case

the dynamics of the phase is affected by chaotic changes of the

amplitude, so one can expect a Brownian (random-walk-like) behavior of

the phase."

 

Mind Force, Human Attractions (Studies of Nonlinear Phenoumena in Life Science)

Publisher: World Scientific | ISBN: 9812771212 | edition 2009 | PDF | 164 pages | 4,4 mb

 

Connections between genes and molecules, neurons and hormones, thinking and language, people and organizations create a continuous flow of synchronized interactions. These intermingled interactions form dynamical networks across many scales, from molecular, to biological, to cognitive and social. In a sequence of cycles, the reader is guided in this heterogeneous hypernetwork to discover the fields and landscapes of Mind Force. Mind, brain, body and society emerge from the same stream through the complexity of nature: the energy of Mind Force and human attractions.

 

http://avaxhome.ws/ebooks/science_books/ps...9812771212.html

Edited November 17, 2009 by drewhempel

[Taomeow]

These Lagrangian Coherent Structures are based on the strange attractors of chaotic systems.

Yup, with vast philosophical implications. E.g., the human heart is a textbook strange attractor -- its regularity arises from irregular, slightly "off" rhythms all gravitating toward a certain "average" central rate, strength, amplitude, systolic-diastolic interplay and so on. In a healthy heart these rhythms are not "very" off unlike in arrhythmia, but never machine-regular. In fact, experienced doctors know that when this chaotic strange-attractor behavior disappears and the heart of a patient starts beating in a very regular, exact, mechanical fashion, this is one condition which, regardless of the underlying cause, means death within 24 hours in 100% of cases regardless of any medical interventions or lack thereof. I believe there's vast sociophilosophical implications inherent in this little-known medical fact...

 

I've read about it in a book on fractals. There was a picture of a graph built by fluctuations of rhythms of a healthy heart -- the graph looked like a star, some rays longer, some shorter, there and back, a bit off and back, more and back, less and back... that's a self-regulating live system for you. And then there was a graph of a perfectly rhythmical heart of someone who died later that day. It looked like a cog. A gear. A part of some machine. That's uniformity and lack of self-regulation, lack of self-adjustment of a doomed overcontrolled undersensitive system. It's actually terrifying, sociophilosophically speaking, to live in a society whose ideal is exactly this -- overcontrolled deprived of self-regulation predicament for one and all. I wish I lived in a strange attractor instead...

[voidisyinyang]