I'm confused about the ability to place a vector wherever, and not just at the input point. This function creates this ordered fluid flow, but only if we place the vector at the input point. If we randomly place the vectors, the movement would be chaotic. Yet, we have functions for describing certain motions. Do they only work if we, by convention, place the vector at the input point?
This vector fluid method is just another way to visualize multivariate vector functions. If you'll place vector [5, 4] at point (1,2), it means, for (x, y) = (1, 2), the value of the vector function f(x, y) is [5, 4]. If you'll place vector [5, 4] at the origin, it means, for (x, y) = (0, 0), the value of the vector function f(x, y) is [5, 4]. This visualization is just a way to tell you the value of a function for a particular (x, y). Why shift that value to another (x, y)? In short, just follow the convention.
@@AdamJDuncan He does, on his RUclips channel, 3blue1brown. He's making a series called Essence of Differential Equations, and he's made beautifully animated series about Calculus and Linear Algebra.
He has a question for the same three-dimensional function, what is the derivative of this function, I would like to know df/? If anyone knows the answer, let me know
I'm not an expeter, but logically that would mean that the divergence has the opposite sign as when it all went outward. As a "physical interpretation" what the could mean: It coukld be a hole or some kind of storage for the "water"
Particles retain velocity, so each particle will keep going the direction it was going in before, up until it hits a new flow node. If all flow vector cells converge in a single point, the droplets will spin around in smaller and smaller circles
Imagine geniusness of the person who invented these concept without computer aid.
Ugh wait, this is the guy from 3b1b! 😁
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Priceless. Thank you!
I'm confused about the ability to place a vector wherever, and not just at the input point. This function creates this ordered fluid flow, but only if we place the vector at the input point. If we randomly place the vectors, the movement would be chaotic. Yet, we have functions for describing certain motions. Do they only work if we, by convention, place the vector at the input point?
This vector fluid method is just another way to visualize multivariate vector functions. If you'll place vector [5, 4] at point (1,2), it means, for (x, y) = (1, 2), the value of the vector function f(x, y) is [5, 4]. If you'll place vector [5, 4] at the origin, it means, for (x, y) = (0, 0), the value of the vector function f(x, y) is [5, 4]. This visualization is just a way to tell you the value of a function for a particular (x, y). Why shift that value to another (x, y)? In short, just follow the convention.
0:28 MY man's gonna solve the navier stokes
Marvellous💯
Great stuff!
thank your!
may i know what function of this vector?
Can you explain about vector field density
What kind of software is this?
is it commercial one?
He programs it by himself. I think he mentioned about the process in the linear algebra series
manim - github.com/3b1b/manim
Jesus... I hope this man gets paid well
@@AdamJDuncan He does, on his RUclips channel, 3blue1brown. He's making a series called Essence of Differential Equations, and he's made beautifully animated series about Calculus and Linear Algebra.
Hi what software/ programing language did you use to make the animations ??? They are amazing!!!!
He uses python in his own channel. So, I think he is using python.
He uses his own library for python call manim
thank you sir very much
He has a question for the same three-dimensional function, what is the derivative of this function, I would like to know df/? If anyone knows the answer, let me know
Wouldn’t most vector fields not make any sense as fluid flow since water is incompressible.
what will happen to the particles when they all diverge into a single point?
I mean where it will go.
I'm not an expeter, but logically that would mean that the divergence has the opposite sign as when it all went outward.
As a "physical interpretation" what the could mean: It coukld be a hole or some kind of storage for the "water"
You mean converge* into a single point.
Particles retain velocity, so each particle will keep going the direction it was going in before, up until it hits a new flow node. If all flow vector cells converge in a single point, the droplets will spin around in smaller and smaller circles
How do i repay 3b1b ever 😭😭😭
3B1B!!!!
Marvellous💯