Great work. Thank you so much for your efforts. I am a Graduate student at IIT Bombay working on pitching & heaving foils both numerically and experimentally. I regularly watch your videos, it helps me in doing novel analyses for my data.
Thank you professor. You are such a generous person to share us such educational videos. I am always waiting to see new videos from you. I wish one day I could spread my knowledge to other people.
Talks like this really are some of the coolest things of all time -- visualization and quantification come together so splendidly. The only thing more coherent than the fluid flow structures is the presentation!
Also, from a purely practical perspective, I'd be interested to know how you actually produce the video, the production quality integrating you and the models is excellent.
It's fascinating how amazingly simple this can be. After trying to read through various papers on understanding LCSs, I still had no idea what they are, or how the imagine them. Took just a few minutes for you prof, big up!
A fantastic video on Lagrangian coherent structures! I have to admit that since I took the class from Prof. Haller last year, these rich dynamics results by simple PDEs never bored me once. Absolutely looking forward to more videos on this!
I have nothing to do with fluid dynamics, but I check out every new video that is uploaded just to see how the visualization is done. It's just that cool...
Great video professor, I would like to know is there a video of the python and matlab version of computing FTLE ,or is there a chance of making the video in the future.
This is very interesting stuff. Looking forward to the lecture series you mentioned on how to actually compute all this and render it. May I request you cover the math part slow and easy. I am a research student at QMW(London), your lectures I watch as its riveting stuff(not my field of research). I've studied your book and your colleagues as well as most of your lectures so I'm hopeful I should be able to follow the lecture series you're planning.
Hello everyone. Does anyone know how such presentations are made? I mean, what equipment are used for handwriting and slides presentation? It seems as some kind of layer behind the camera but at the same time it's not software thing as I understand. I hope someone understand what am I trying to ask
Couldn't really find a following video to this. In video it is mentioned that you will have video on how to code it up, but I couldn't find anything as such on the channel.
On the large scale, tropical instability waves formed into a wavetrain along the equator. Multiple double-gyres. Analytically driven by tidal forces, all ENSO behavior can be modelled effectively.
The Jelly fish animation was amazing! Didn't get a chance to read the paper yet, but did they happen to calculate the overall "capture" efficiency of the Jellyfish wake? i.e: num_particles captured / num_particles in the flow field? or green / blue+green? or I guess they would do some area under the curve measurement
wow! more beauty!! thanks! and congratulations! one could say. in the first few steps, compressible volumes . act similar , as incompressible volumes . there's also got to be a law of proportion in here somewhere?I know there's one in photography and art ! I see .! It's the law of manifold symmetry's! Haha hplc, liquid chromatography .! Jupiter! Wow total awesome brainstorm! this almost reminds me of statistics!👍🌟
Hi Prof. Brunton. I really appreciate your lecture series and it actually inspired me to go back to graduate school. I will be dealing with data assimilation using ROMs for ocean mixing. I was wondering if you were able to provide a link for the video to your PhD student with regard to navigation in ocean flows mentioned around the 33:30 timestamp? I feel like this would be very helpful for understanding the more applied applications of this methodology.
It is possible to figure out if there exists solutions of finite duration by using the Finite Time Lyapunov Exponents?? With a solution of finite duration I am meaning it becomes by itself exactly zero after a finite time, like x'=-sgn(x)*sqrt(|x|), x(0)=1 could have the solution x(t)=1/4(1-t/2+|1-t/2|)^2 which becomes zero after t=2. I would like to find if the classic nonlinear pendulum could stand solutions of finite duration, if instead if using the traditional Stokes' Law or the quadratic drag force equation, I introduce a sublinear damping term as the friction force F(x') = a*sgn(x')*sqrt(|x'|)*[sqrt(2)/4+|x'|^(3/2)] in the equation x'' + F(x') + b*sin(x) = 0 for some positive constants {a,b} Does this could be studied through FTLE?
Beautiful Professor Steve !! Being all my life fully in Electrical Engineering [Advanced Control Systems Engineering] I want to move to Mathematics + Physics with strong Computational mindset. Would You suggest to me a research topic in the direction of Applied Computational Math with focus on Control System Engineering + Mathematics + Physics ?
Nice lecture, thank u Steve! Can u tell about Lyapunov time with respect to DNS simulation in the next video ? It is defined as the inverse of a Lyapunov exponent and I think it's very important, because Lyapunov time will be different for different initial conditions. Thus for some initial conditions we can't do long simulations, because system will become chaotic too fast... How to handle this problem? How to choose 'good' initial conditions which allow us to do long cfd simulations? And what will happen if the Jacobian matrix is not defined?
Hello Professor, first, wish you a happy Thanksgiving. At the 29:55, you said you will do more videos on how to compute the FTLE in Matlab and Python for some examples. Hopefully, this is still on your list.
Another question: how can this contribute to e.g. your PhD thesis of low Reynolds flapping wing study? (Maybe you’ve discussed about it in your thesis?)
If the time step is large for a simulation then computing FTLE will be difficult? I'm losing the particle information when I go from one time step to another.
Steve, at about 25 minutes into this video you explain the flow map Jacobian. How do you deal with matrix elements that go to infinity, such as when the delta-y of two adjacent points of j is zero in the denominator (the bottom right element let’s say)?
In ideal case, should be prevented by area being preserved. i.e. two opposing neighbors can't touch because area would be zero. And conversely, any arbitrarily tiny squish would be offset by samely arbitrarily large divergence. So in some reasonable physical sense, even if you relax idealized incompressible fluid a bit, you still have the idea that on a finite time and grid, you don't expect a massive divergent blowup nor infinitesimal compression.
Square root is there just to show that lambda is actually the eigenvalue of a matrix that is akin to the square of the Jacobian ( conjugate transpose of the Jacobian times the Jacobian.) It really does not matter much whether we have the square root there or not because there already is a 1/|T| factor.
Great work. Thank you so much for your efforts. I am a Graduate student at IIT Bombay working on pitching & heaving foils both numerically and experimentally. I regularly watch your videos, it helps me in doing novel analyses for my data.
Steve Brunton is the kinda guy who can make videos about stuff you've never heard of and you watch it just because he explains stuff so well
Great work. Thank you so much for your efforts. I am a Graduate student at IIT Bombay working on pitching & heaving foils both numerically and experimentally. I regularly watch your videos, it helps me in doing novel analyses for my data.
Thank you professor. You are such a generous person to share us such educational videos. I am always waiting to see new videos from you. I wish one day I could spread my knowledge to other people.
Greetings from Paraguay! Thank you for such high quality content. We really appreciate it.
Talks like this really are some of the coolest things of all time -- visualization and quantification come together so splendidly. The only thing more coherent than the fluid flow structures is the presentation!
Also, from a purely practical perspective, I'd be interested to know how you actually produce the video, the production quality integrating you and the models is excellent.
This is so great. I am looking forward next video about computing and more theory. 🤯🤯
It's fascinating how amazingly simple this can be. After trying to read through various papers on understanding LCSs, I still had no idea what they are, or how the imagine them. Took just a few minutes for you prof, big up!
A fantastic video on Lagrangian coherent structures! I have to admit that since I took the class from Prof. Haller last year, these rich dynamics results by simple PDEs never bored me once. Absolutely looking forward to more videos on this!
amazing stuff prof! I especially love the focus on the numerical implementation and the cited examples.
This is really gold! Thank you very much.
Great Prof. I am waiting for the next part of this lecture series. Thanks a lot for making this topic so simple to grasp.
This is awesome! You did a great job making this easy to understand!
I have nothing to do with fluid dynamics, but I check out every new video that is uploaded just to see how the visualization is done. It's just that cool...
Very good video. Looking forward to seeing the lecture series.
Amazing density of good content in this one, amongst always good content in your videos! Wow, thank you!
Great lecture. Thank you Dr. Brunton.
Excellent video!
Great video! I hope there are more in this topic, there is so much in this area.
Can you clone yourself, Steve? Can't wait to see such informative and outstanding presentations.
Amazing content!
Great video professor, I would like to know is there a video of the python and matlab version of computing FTLE ,or is there a chance of making the video in the future.
It is very interesting and fascinated
Superb lecture, very interesting and well done.
This is very interesting stuff. Looking forward to the lecture series you mentioned on how to actually compute all this and render it. May I request you cover the math part slow and easy. I am a research student at QMW(London), your lectures I watch as its riveting stuff(not my field of research). I've studied your book and your colleagues as well as most of your lectures so I'm hopeful I should be able to follow the lecture series you're planning.
Hello everyone. Does anyone know how such presentations are made? I mean, what equipment are used for handwriting and slides presentation? It seems as some kind of layer behind the camera but at the same time it's not software thing as I understand. I hope someone understand what am I trying to ask
Couldn't really find a following video to this. In video it is mentioned that you will have video on how to code it up, but I couldn't find anything as such on the channel.
On the large scale, tropical instability waves formed into a wavetrain along the equator. Multiple double-gyres. Analytically driven by tidal forces, all ENSO behavior can be modelled effectively.
Question: have you considered POD/DMD the LCS hence possible to kinda realtime predict it with control?
f'n spectacular! Any other related book suggestions?
It was great ❤
The Jelly fish animation was amazing! Didn't get a chance to read the paper yet, but did they happen to calculate the overall "capture" efficiency of the Jellyfish wake? i.e: num_particles captured / num_particles in the flow field? or green / blue+green? or I guess they would do some area under the curve measurement
wow! more beauty!! thanks! and congratulations! one could say. in the first few steps, compressible volumes . act similar , as incompressible volumes . there's also got to be a law of proportion in here somewhere?I know there's one in photography and art ! I see .! It's the law of manifold symmetry's! Haha hplc, liquid chromatography .! Jupiter! Wow total awesome brainstorm! this almost reminds me of statistics!👍🌟
Amazing
Hi Prof. Brunton. I really appreciate your lecture series and it actually inspired me to go back to graduate school. I will be dealing with data assimilation using ROMs for ocean mixing. I was wondering if you were able to provide a link for the video to your PhD student with regard to navigation in ocean flows mentioned around the 33:30 timestamp? I feel like this would be very helpful for understanding the more applied applications of this methodology.
It is possible to figure out if there exists solutions of finite duration by using the Finite Time Lyapunov Exponents??
With a solution of finite duration I am meaning it becomes by itself exactly zero after a finite time, like
x'=-sgn(x)*sqrt(|x|), x(0)=1
could have the solution
x(t)=1/4(1-t/2+|1-t/2|)^2
which becomes zero after t=2.
I would like to find if the classic nonlinear pendulum could stand solutions of finite duration, if instead if using the traditional Stokes' Law or the quadratic drag force equation, I introduce a sublinear damping term as the friction force
F(x') = a*sgn(x')*sqrt(|x'|)*[sqrt(2)/4+|x'|^(3/2)]
in the equation
x'' + F(x') + b*sin(x) = 0
for some positive constants {a,b}
Does this could be studied through FTLE?
Beautiful Professor Steve !! Being all my life fully in Electrical Engineering [Advanced Control Systems Engineering] I want to move to Mathematics + Physics with strong Computational mindset. Would You suggest to me a research topic in the direction of Applied Computational Math with focus on Control System Engineering + Mathematics + Physics ?
Quite interesting! Maybe the dynamic system course I have now has some good applications after all.
Nice lecture, thank u Steve!
Can u tell about Lyapunov time with respect to DNS simulation in the next video ? It is defined as the inverse of a Lyapunov exponent and I think it's very important, because Lyapunov time will be different for different initial conditions. Thus for some initial conditions we can't do long simulations, because system will become chaotic too fast...
How to handle this problem? How to choose 'good' initial conditions which allow us to do long cfd simulations?
And what will happen if the Jacobian matrix is not defined?
Great presentation 👌
that heart tissue jellyfish simulation was a bit creepy 😨 Great vid nonetheless!
Who was the single person who disliked this video? Why would even a single person do that
Hello. Thanks for the great video. Do you have any advice on how one should choose the integration time?
Hello Professor, first, wish you a happy Thanksgiving.
At the 29:55, you said you will do more videos on how to compute the FTLE in Matlab and Python for some examples. Hopefully, this is still on your list.
really looking forward python examples!
Incredible!
outstanding!
Another question: how can this contribute to e.g. your PhD thesis of low Reynolds flapping wing study? (Maybe you’ve discussed about it in your thesis?)
Görög motívum!
If the time step is large for a simulation then computing FTLE will be difficult? I'm losing the particle information when I go from one time step to another.
Would it be feasable from a snapshot of the fluid field at instant t to determine the position and size of the wing at T0 ?
hype, hype!
Can LCS be used in compressible flows where the velocity divergence is not zero?
Steve, at about 25 minutes into this video you explain the flow map Jacobian. How do you deal with matrix elements that go to infinity, such as when the delta-y of two adjacent points of j is zero in the denominator (the bottom right element let’s say)?
In ideal case, should be prevented by area being preserved. i.e. two opposing neighbors can't touch because area would be zero. And conversely, any arbitrarily tiny squish would be offset by samely arbitrarily large divergence. So in some reasonable physical sense, even if you relax idealized incompressible fluid a bit, you still have the idea that on a finite time and grid, you don't expect a massive divergent blowup nor infinitesimal compression.
Is it on MATLAB or JULIA or some other one, please
Do we have examples on how to apply math to the laminar flow case?
Any one please tell me here, which software is used for Langragian coherent modelling ( ftle) Please.
Why is it `log(sqrt(x))` instead of `.5*log(x)`? Clarity for people who don't speak log identities? Or am I missing something?
You can pull out the exponent and replace it with a coefficient before the log
Square root is there just to show that lambda is actually the eigenvalue of a matrix that is akin to the square of the Jacobian ( conjugate transpose of the Jacobian times the Jacobian.) It really does not matter much whether we have the square root there or not because there already is a 1/|T| factor.
Do you have some matlab code to get de LCS yet?
Same my question
7:02 what?!
Finite-time Lyapunov exponents
Great work. Thank you so much for your efforts. I am a Graduate student at IIT Bombay working on pitching & heaving foils both numerically and experimentally. I regularly watch your videos, it helps me in doing novel analyses for my data.