Fluid dynamics feels natural once you start with quantum mechanics
ฝัง
- เผยแพร่เมื่อ 15 พ.ค. 2024
- This is the first part in a series about Computational Fluid Dynamics where we build a Fluid Simulator from scratch.
We highlight the Microscopic Perspective on Quantum Mechanics, Molecular Dynamics, and the Kinetic Theory of Gases that underlies and justifies Fluid Simulation Formulations in the first place.
The Microscopic Perspective provides the ground for the next part where we focus on the Macroscopic Perspective with concepts such as Pressure, Viscosity, Temperature, and Flow Velocity as well as its evolution with time.
Timetable:
-----------------
00:00 - What We Build
02:06 - Guiding Principle - Information Reduction
04:03 - Measurement of Small Things
07:09 - Quantum Mechanics and Wave Functions
13:45 - Model Order Reduction
16:48 - Molecular Dynamics and Classical Mechanics
26:50 - Kinetic Theory of Gases
30:23 - Recap
Selected Papers and Learning Resources:
-------------------------------------------------------------------
05:03 Experiment:
Paper: "Stodolna, Aneta S., et al. Hydrogen atoms under magnification: direct observation of the nodal structure of stark states. Physical review letters 110.21 (2013): 213001."
06:49 Atomic- and Molecular Orbitals Tomography:
Paper: "Vozzi, Caterina, et al. Generalized molecular orbital tomography. Nature Physics 7.10 (2011): 822-826."
Paper: "Itatani, Jiro, et al. Tomographic imaging of molecular orbitals. Nature 432.7019 (2004): 867-871."
07:24 Matter Waves, Double Slit Experiment:
Paper: "Jönsson, Claus. Elektroneninterferenzen an mehreren künstlich hergestellten Feinspalten. Zeitschrift für Physik 161.4 (1961): 454-474."
Paper: "Jönsson, Claus. Electron diffraction at multiple slits. American Journal of Physics 42.1 (1974): 4-11."
07:57 Quantum Mechanics Overview, Wave packets, Standing Waves, Eigenstates:
E-Book: "Mathur, Samir D. www.asc.ohio-state.edu/mathur..."
E-Book: "van Dommelen, Leon. Quantum mechanics for engineers. web1.eng.famu.fsu.edu/~dommel... (2004)"
16:01 Model Order Reduction, Modes:
Lecture Notes: from "Farhat, Charbel. Model Reduction. web.stanford.edu/group/frg/co..." to "CA-CME345-Ch9"
17:17 Classical Mechanics, Phase Space:
Lecture Notes: "Cerfon, Antoine. Mechanics (Classical and Quantum). www.math.nyu.edu/~cerfon/mech..."
18:15 Molecular Dynamics, Born-Oppenheimer Approximation, Potential Energy Surface, and Non-Quantized Approximation of Energy Levels:
Lecture Notes: "Allen, Michael P. Introduction to molecular dynamics simulation. Computational soft matter: from synthetic polymers to proteins 23.1 (2004): 1-28."
Paper: "Parker, J. G. Rotational and vibrational relaxation in diatomic gases. The Physics of Fluids 2.4 (1959): 449-462."
Paper: "Valentini, Paolo, et al. Direct molecular simulation of nitrogen dissociation based on an ab initio potential energy surface. Physics of Fluids 27.8 (2015): 086102."
E-Book Chapter: "van Dommelen, Leon. Quantum mechanics for engineers. 9.2 The Born-Oppenheimer Approximation. web1.eng.famu.fsu.edu/~dommel... (2004)"
20:11 One-Dimensional Hydrogen Atom Approximation for the Coulomb Potential as opposed to the "true" One-Dimensional Coulomb Potential:
"Loudon, Rodney. One-dimensional hydrogen atom. American journal of physics 27.9 (1959): 649-655."
"Loudon, Rodney. One-dimensional hydrogen atom. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472.2185 (2016): 20150534."
27:06 Kinetic Theory of Gases, (Variable) Hard Sphere Approximation of Molecules:
Lecture Notes: from "volkov.eng.ua.edu/ME591_491_NE..." to "NEGD-06"
Disclaimer:
------------------
This series focuses specifically on the aspect of information reduction in dynamical systems. For the sake of clarity, I had to omit many interesting aspects of the topics addressed in the video. So, the video itself is a reduction. :-)
I hope you enjoyed this little braintruffle!
If you like this series, let the TH-cam algorithm know by subscribing to the channel and ringing the bell icon.
Thank you for watching and see you next time!
![พรากรัก - เต้ย อภิวัฒน์ [ Official MV ]](http://i.ytimg.com/vi/ShT2ltn8GBE/mqdefault.jpg)
I saw the views and my jaw dropped, this is actually insane, the quality is Soo good, continue on brother!! I will be following with my own simulation
Thank you! :-)
@@braintruffle yeah this is insane
Agreed
Well you will obviously grow
I bet
@@braintruffle Hello bro. Does this simulation work on Jupyter Notebook (Anaconda 3 -> Python notebook software)? This simulation looks pretty neat by the way
"How did the monkey fall off the bed?" Well, once upon a time, an electron flipped from a down to an up spin.....
I love the general approach you took, starting at the very bottom of our known reality -- quantum mechanics -- and explaining it's inherent complexity, then acknowledging possible simplifying assumptions and how they sacrifice accuracy in exchange for computational feasibility. And then moving up from there. This "motivated stack of assumptions" explainer style is beautiful. Thank you!
I'm so happy to reach people who feel the same way about this approach. It helps me a lot to step back, realize what is true and build up from there. Thank you!
@@braintruffle you are not alone, when I seen this title I put it immediately on my "watch later list" and was excited the whole day about coming home and watching this. Especially as I am currently trying to teach myself computational fluid mechanics for professional reasons, while reading about quantum physics in free time as a hobby. Knowing high level things but going down to fundaments and trying to reach back to the top is the best approach. Especially to question some dogmas you are not even aware you adopted with years .
Did you stop working on it??? How did I find it so late? 🥺 One of the best video I've found so far. The depth of the topic with visual animations is truly remarkable. Please never stop doing what you are doing, and I would like to contribute if possible.
I don't know if you've seen it already but he made a new video so I guess he didn't stop :)
This is truly masterful. I can't even imagine how long this took to make. Between the beautiful animations, the clear and cohesive script, and the massive amount of research required (as evidenced by the bibliography in the description).
If I were a professor grading this for a project, I would quit my job knowing I could never achieve such clarity.
This video is like finding a treasure in the jungle.
Its not only well made but it ties together all branches of knowledge that is Mathematics, Physics, Quantum Mechanics and Computer Science so seamlessly that you're left with wanting more.
Truly marvelous stuff!
If the author of this video would write a recipe for a cake, he would start with "firstly you'll need a big bang" - I love it!
I am a researcher in mathematics and I have very little knowledge in physics, but the video is so well explained that I could even understand the ideas behind your explanation, excellent work.
3Blue1Brown vibes with the detailed explanation of TwoMinutePapers. I love this
Looks like your video has started to hit the YT algorithm...
Godspeed, I hope this content reaches as many as possible.
Same here. I am a huge science guy. I love science and physics, and hope that this video wins over and crushes all those cruddy Tik Tok videos. :)
By the way, these fluid sims could be used in the future as a way to make more efficient technologies such as aircraft (already happening), and potentially be used in molecular assemblers (far future).
It sure did
This is the best video I have seen on TH-cam, bar none! I am currently starting my second year of studying physics at university, and this video is so _so_ *_so_* helpful for getting an intuitive sense of how different scales connect and interact. The visual demonstrations and interactive style cannot be matched by any textbook. Thank you so much for the wonderful video!
I really appreciate your comment and I'm happy that this video can help a little bit. Best of luck with you studies and thank you very much!
TH-cam just recommended me this video and it's simply wonderful. The way it's animating, the voice, the background music, it's so soothing. Keep on this! It's stunning
I'm speechless, this is so incredibly well made, and the idea for step by step disclosure of the topic is brilliant!
One of a kind educational content, keep it up!
My mind has been thinking about fluid flows for the last 9 months it is so nice to find such well put together information.
Hey Mate, this is soo good quality, here an aerospace engineering that really appreciates your work, I´ll recommend this channel to my followers and as me, they´ll love it
Excellent visualizations! The good microphone sound quality is also appreciable!
Thank you so much! Hearing myself was super weird in the beginning, though; I really had to get used to it. :-)
One of the best recommendations I've ever received from TH-cam. Cheers for the excellent work and phenomenal presentation, content like this deserves to reach the widest audience it can.
This is really great. I am finishing up my PhD specializing in MD simulations, and your QM discussion is the best I have seen to date
This video is incredibly well crafted! You started with the most intuitive explanation of quantum mechanics I’ve seen, and ended with a great framework for how abstraction is used in the sciences!
Hey, this is so wonderfully done. Love your explanation, clean visualization, and the general direction of it. Really looking forward to this series :) Thank you for doing this and wish you luck!
Thank you very much for your kind words! I'm happy you like it.
Absolutely beautiful, well written, thorough, and relevant to my interests. Really can't wait for the next part.
Being a student of Biomedical Engineering, having studied Biofluid Dynamics, I'm in absolute awe to this series. We didn't study the subject as far as going to these depths, but I'm really enjoying it!
I highly recommend a book “life in moving fluids” the fluid dynamics of biological flows.
The clarity of your visualizations and explanations is outstanding. Very well done, you earned my subscription!
Awesome explanations - Love the holistic way you just tied together like 10 of my college classes ranging across campus from chemistry and physics to engineering and math to computing and numerical methods. Fantastic content!
Starting a quantum mechanics and a fluiddynamics lecture next semester, revisiting this series to warm up, thanks again!
This is an absolute masterpiece! Beautiful visuals and clean storytelling!
This is one of the best recommendations youtube has ever given me. Thank you for tickling my brain, what a wonderful presentation you have here! I wish you a very long career in science communication!!
Ive been watching this channel for 5 minutes and I already love it. Clear and consice explanation with fun animation. Awesome job
That is amazing work! The detail, the love, the editing.
This video will be of immense benefit for everyone learning about CFD. Thanks for also contributing to open education
What a great presentation! Not just the knowledge, but also the way how you present it. Amazing!
Your effort and work has not gone unnoticed. Great video!
I'm in awe of this video. Incredible animation and explanations. So many more people need to see this
this is the best channel on youtube for science. you actually understand what you are talking about and it's complex and not just feel good stuff like veritaserum etc. keep it up !!
Incredible amount of work you have put into each of these videos. I binged all of them in a single day and did not skip a second. Sublime
The way you give information out makes you one of the best teachers I've ever listened to...
With such gift you could sell the Eifle Tower to enybody!
This is genuinely amazing. Thank you so much for this beautiful series. I'm beyond impressed!
this is amazing! I tried to model the behavior of particles in a ripple pool once and your video is lightyears more advanced than what I did. You're amazing thank you for producing this video
Absolutely extraordinary video! The graphics are great, the naration is great (though it's also great that you wrote subtitles, for certain specific words), and the explanations are incredible. I saw this video a few days ago, at night, on my recommend section but thought "This looks interesting, but I really don't have the brainpower for this at night" and boy am I happy I got recommended it again, this time at a better time of day. I will for sure go on to watch the next of the series, and you've earned yourself a sub.
Just found this video by accident. Great work, incredible quality. Can't wait for more of the series.
I've not even finished the video yet, but your animations on QM are awesome. The best I've seen
When you said: “looking actually means, interacting”
I knew we were in for an enjoyable ride. What a truly amazing video 🙌
This is hands down 3b1b level quality!
Amazing stuff, keep up the great work!
Dude thats an amazing video. You are so precise in your language and give a fully interconnected picture between different physical scales. I really was able to fill some gaps in my underdranding even as an physics post graduate. Please keep it up!
Please keep going. The quality and information in this video are fascinating!
These are some of the best visualizations I've ever seen! Would love if you explore more aspects of quantum mechanics!
Wow this is so high quality! And the references in the description too! 👏
Absolutely stunning visuals, and told in such an intutive way! A great explanation of building up fluids from the ground'up by investigating which simplying assumptions allow us to retain the overall behavior.
Incredible level of detail and quality !!! Thank you for creating this :)
So hyped for this series
Srsly in my opinion the most underrated and insane Video i've seen so far on YT
10 seconds into the video, I immediatly subscribed. I can't wait to see what comes next! Hell yeah!!!!!!!!!!
Insane graph simulations there! Very well done and explained.
Fantastic content with a great presentation. It is incredible seeing how much effort is put in to making such high quality videos by people like you. Keep up the excellent work and I'm sure the algorithm will reward you. I'm looking forward to the next videos.
This is way too good. Like, you went so far beyond expectations I’m shocked
Not often would I watch 3 minutes into the video and subscribe. This is brilliant! I'm a high school student and I just started using CFD to mess around, but to me, they are always this kind of wizardry that somehow works. I really appreciate how much research have gone into the making of this video, and how much I have learned. It's shameful to think some nonsensical videos could get millions of views, while this one only get less than 100k (as of the making of this comment)
How has the algorithm not picked up on this. This is incredible!
Your visualizations are absolutely amazing!
Well that's an easy A+ for the structure, animations, clarity and overall wisdom present in this video.
As a physics engineer, fluid mechanics is the only big field of physics we never really covered at university. Thank you!
Instantly subscribed after watching! This is so beautifully done and easy to follow. Thank you!
He actually put more work into the video description alone than I did into my bachelor's thesis.
This is outstanding. Can’t wait to see what else you release!
This is one-of-a-kind type of work man, this is amazing content!
This Is The Most Honest, Concise, And Descriptive Explanation Of Computational Fluid Mechanics And Dynamics That I Have Ever Seen. Well Done.
Pinball/Pingpong/Pool/Chess At Play.
Incredible work
The quality! the explanations! the best recap of QM I've ever seen! the awesomeness!! Wow this video is great
this video is astonishing, so informative and well animated
This was the best explanation of how “a quantum particle is in all possible locations until it is observed”. I don’t think I really understood what “observe” it ment.
Amazing video!!!
Yeap,just like"faith". The observer, / the "witness" INFLUENCES the out come of the "endeavour"./ Experiment.". No big deal.
I'm amazed at the quality of this video! Outstanding job man!
I just stumbled on this video. It's super clear and help's in tying together the topics learned in school for physics and math. I wish I had found this sooner while I was doing those courses.
This is a good overview and explanation of fluids and modelling them. Awaiting the next part of this incredible quality video.
That’s very kind of you. Thank you.
I am sold in just first 40 seconds of this video. Good work!
This video should be the example of the word "explanation" in future interactive dictionaries! Masterpiece!
Never seen such a marvellous video ,
Thanks for this amazing content .
Looking for more such videos.
Dude, you're gonna blow up! I trully believe so. Talent like this won't go unnoticed for long. Keep up the great work!!!
Thank you a lot! I am often very self-critical and hearing motivating words helps a lot! :)
The quality of the content is incredible.
I'd love to see how you explain ray tracing and the different ways to simulate light streams.
Please make a video about this.
Thank you for this amazing video! Cant wait to see the next one, this is gold.
I am happy to hear that. Thank you very much!
this might be the best first video of a channel on youtube
Amazing video with insane quality. Really really cool. Thank you!
Outstanding production quality pared with beautiful narration and explanations. What could go wrong? :). Well done! Thank you for this beautiful video. Please do make more :D wish you all the best
I have waited for a video like this for years... unfortunatly so long that I had to figure out most of what goes into coding fluid sims on my own... This is still probably my favourite youtube video. Thank you very much!
Learning this on your own certainly helped you a lot, so this is actually a good thing :) During my studies I spend a lot of time just playing with equations and simulations and that had the biggest impact I would say. Thank you so much!
This just showed up on my front page, love it! Didn't expect quantum mechanics to show up this much for fluid simulation (even though it makes sense).
It also seems like the video is gaining some traction with the influx of new comments, at least I hope it does. This wave of great new educational videos is amazing.
I was very happy that the first part reached many people in the last few month and I was very happy with the feedback (a lot of positivity) and then youtube decided to show it to more all of a sudden. Many thanks :)
WHAT! The quality of this video is far beyond anything I have ever seen before on this topic. You have an amazing way of breaking down an animating complex ideas. What software do you use? What's your story? How did you get started?
Thank you!! This video's quality is amazing, loving the clarity explaining such a complex subject. Keep up
This video is just amazing. I have seen many good educational videos on youtube but none comes even close to this one. If all schools and universities would teach on this level, studying would be much easier and more interesting.
Keep up the great work!
Man the quality of this video is next level, great work!
I dont normally comment, but this was incredible. The ease with which complex topics are explained is unmatched. Will be looking to learn way more
holy moly this is stellar. animations, narration, accent--everythinh
Absolutely stunning video. Great demonstration and explanation!
please keep making these video's The quality and educational value of this video is amazing
Beautiful video with amazing content! Keep up the good work brother
This is absolutely well-made!
In a pervious life, I was a theoretical physicist and did computaional quantum mechanics (ab initio molecular dynamics). This was a nice reminder. Your pedigogical approach is superb and-of course-you viasuals are just stunning.
For example, your choice to use a 1D slice of the 2D single slit problem (at 9:55) was brilliant.
Thanks. I really hope to see more.
Thank you so much for your feedback! You can't imagine how worried I was when I built all this. Since you clearly have the theoretical background, you can see how many more interesting topics I left out, and I was so worried that it would be perceived as too oversimplified. There are so many non-content constraints involved; to hear that this small, stripped down contribution is still perceived as valuable is really motivating. Thank you! :)
Your video is absolutely blowing my mind.
Subscribed.
Love it! Bravo. Respect.
Fantastic video! I love the depth, and at the same time the approachability... not to mention the visuals!
Wow, well done! I haven't really done research on/with fluid dynamics at microscopic levels so this was very insightful for me as an introduction.
i never really understood the principles behind fluid mechanics. Now i have a framework. This is a great video.XD
This is so insanely good, among the best content I've seen on the internet
The animations, the voiceover and the content are 🔥. Please keep posting.
Wow! This is without hyperbole the most beautiful video i've seen about molecular dynamics!
Thank you! :)
This guy put so much time and effort into this video. The content and video quality both are mind blowing. bestest video🛩🛩