![Pavel Rozhkov](/img/default-banner.jpg)
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Pavel Rozhkov
Приєднався 17 лют 2015
2D Schrodinger equation — double slit experiment
Color represents the phase of the wavefunction, brightness represents squared modulus of the wavefunction. Schrodinger equation is solved using finite difference method.
Переглядів: 2 025
Відео
Light passing by the Kerr black hole
Переглядів 171 тис.8 місяців тому
The white circle represents the outer event horizon, the gray circle represents the inner event horizon, and the dotted circle represents the ergosphere. The angular momentum of the black hole is perpendicular to the shown plane, and the black hole is rotating counter-clockwise. Particle trajectories are calculated using Hamiltonian mechanics. The Hamiltonian of a particle is the time component...
Circular orbits near Schwarzschild black hole
Переглядів 4 тис.9 місяців тому
Inner dotted line is the photon sphere, below which no orbits are possible, and the outer dotted line is the innermost stable circular orbit. At the start, particles are placed at circular orbits with a slight variation in speed. The passage of the particles' proper time is indicated by their blinking.
Black hole piercing through the dust cloud
Переглядів 3,4 тис.10 місяців тому
The white ellipse is the event horizon. The black hole moves at 76% of the speed of light. Particle trajectories are calculated using Hamiltonian mechanics. The Hamiltonian of a particle is the time component of its 4-momentum, derived from the length of 4-momentum (mass of the particle) in a given space-time metric as a function of canonical cooridantes and momenta.
Matter falling into Kerr black hole
Переглядів 4,2 тис.10 місяців тому
The white circle is the outer event horizon, the gray circle is the inner event horizon, the dotted circle is the ergosphere. Angular momentum of the black hole is perpendicular to the shown plane. Particle trajectories are calculated using Hamiltonian mechanics. The Hamiltonian of a particle is the time component of its 4-momentum, derived from the length of 4-momentum (mass of the particle) i...
Dust clouds near Schwarzschild black hole
Переглядів 3 тис.10 місяців тому
White circle is the event horizon. Particle trajectories are calculated using Hamiltonian mechanics. The Hamiltonian of a particle is the time component of its 4-momentum, derived from the length of 4-momentum (mass of the particle) in a given space-time metric as a function of canonical cooridantes and momenta.
Light passing by the Schwarzschild black hole
Переглядів 422 тис.11 місяців тому
White circle is the event horizon. Light trajectories are calculated using Hamiltonian mechanics. The Hamiltonian of a particle is the time component of its 4-momentum, derived from the length of 4-momentum in a given space-time metric (in case of light the length is zero) as a function of canonical cooridantes and momenta.
Rule 91r cellular automaton
Переглядів 876Рік тому
91r - reversible second-order cellular automaton. This cellular automaton creates structures similar in behavior to particles. They have inertia and interact with each other through direct contact - absolutely elastically repel, or exchange an analog of mass with each other. Particles with a large "mass" have a wide range of available velocities with which they can move. In addition, some form ...
Rule 77r cellular automaton
Переглядів 527Рік тому
77r - reversible second-order cellular automaton. This cellular automaton generates complex fractal-like structures that interact with each other and have inertia. Among other cellular automata with physical behavior, this one is distinguished by the asymmetry of the background mosaic, which is why structures of one kind can only move in one direction.
Rule 22r cellular automaton
Переглядів 442Рік тому
22r - reversible second-order cellular automaton. This cellular automaton, like 37r, generates stable structures similar in behavior to particles. Although they do not actively interact, they have some kind of Lorentz invariance in their structure. Also, under the influence of changes in the external mosaic, they are subject to Brownian motion.
Rule 37r cellular automaton
Переглядів 1,1 тис.Рік тому
37r - reversible second-order cellular automaton. A distinctive feature of this cellular automaton is the presence of configurations similar in behavior to particles. They have inertia and can interact with each other by absorption and radiation.
Stress tensor of the 2D sine-Gordon equation
Переглядів 400Рік тому
Сolor represents the field energy density, ellipses represent the elastic deformations under the action of a given stress in the field. Solitons in the 2D sine-Gordon equation behave like rubber bands due to the mechanical stress in the field along the length of the soliton. 0:00 scene 1 1:00 scene 2 1:30 scene 3 2:00 scene 4
Energy density and energy flow of the 2D sine-Gordon equation
Переглядів 331Рік тому
Сolor represents the field energy density, vectors show the energy flow. They are calculated from the sine-Gordon lagrangian as components of stress-energy tensor. The sine-Gordon equation in two dimensions is quite chaotic, which is why any interactions of solitons irreversibly produce a large amount of high-frequency waves that carry away energy. 0:00 scene 1 1:30 scene 2 2:10 scene 3
Stress tensor of the Klein-Gordon equation
Переглядів 245Рік тому
Сolor shows the amplitude of the field, ellipses represent the elastic deformations under the action of a given stress in the field. 0:00 - massive field 1:00 - massless field
Energy density and energy flow of the Klein-Gordon equation
Переглядів 314Рік тому
Сolor shows the field energy density, vectors show the energy flow. They are calculated from the Klein-Gordon field Lagrangian. 0:00 - massive field 1:00 - massless field
Interaction of solitons in the sine-Gordon equation
Переглядів 4072 роки тому
Interaction of solitons in the sine-Gordon equation
Interaction of solitons in the phi-4 theory
Переглядів 1522 роки тому
Interaction of solitons in the phi-4 theory
Interaction of solitons in the nonlinear Schrödinger equation
Переглядів 3332 роки тому
Interaction of solitons in the nonlinear Schrödinger equation
Pauli equation model - splitting of an electron in a magnetic field
Переглядів 2832 роки тому
Pauli equation model - splitting of an electron in a magnetic field
Gray-Scott reaction-diffusion equation model
Переглядів 1282 роки тому
Gray-Scott reaction-diffusion equation model
Energy density of the sine-Gordon equation
Переглядів 1492 роки тому
Energy density of the sine-Gordon equation
I thought the title said "Light child passing by the black hole"
Waths the game?
How many balls
I don't think this is a correct representation. The light will never cross the event horizon, so there should be a yellow ring around the black hole.
Hey, I enjoyed this visualization! I don't know what your exact intention is with uploading this video, but if it is along the lines of reaching more people, making the topic more understandable through visualization, maybe you could consider uploading this video to wikipedia commons and adding it to the "Klein-Gordon equation" article for example, that way it is an visual aid to anyone reading the article. That is just a suggestion, awsome work!
Another way to say black holes look black. 😊
and thats how you look into the past... just look near a black hole. not exactly time travel you cant go to the past but you can see into the past. jesus was here about 2000 years ago so you need to find a black hole about 4000 light years away and look near that but good luck zooming in far enough to see anything
1@81#
so if you look exactly at the right angle you can see stuff that happened in the past being reflected back at us? that is kinda great :)
Я хочу выразить свое восхищение исключительно мощной и успокаивающей природой этого видео. Объединение фортепиано, синтезатора и баса было создано с большой тщательностью, и я очень горжусь этим. Ваша постоянная приверженность созданию выдающихся видео действительно заслуживает похвалы. Я призываю вас продолжать вашу превосходную работу.
They've gone to plaid!
My favourite equation.....more especially the solitonic surfaces formed from these non linear pde
What happens if instead of (or in addition to) using 2 dimensional spatial coordinates, we make the field values 2 dimensional? If we sum the sines of the two field dimensions, we get a 2d lattice of potential minima.
If we just sum the cosines of the two field dimensions in the Lagrangian density, then their evolution would be independent of each other, which is rather boring. But if we take cosine of the modulus of field vector, then it would behave akin to the Higgs field, with rings of minimal potential energy.
@@pavelrozhkov3239 I guess that's true enough. It would be interesting to see what kind of results you'd get substituting various functions in for the mass term. Something like cos(abs(f))*abs(f) ? An attractive coulomb potential would do some crazy things. It would mean there would be absolutely no rest state of the field. It might also be interesting to explore weird kinetic terms. If we model the field as a vibrating string, this would correspond to the tension in the string responding weirdly when we pluck it. A coulomb kinetic term would make the coulomb mass term look sane. It would work in the discrete case, but would be mathematically ill-behaved in the continuous case.
@@JonBrase There is an interesting case of changing the Lagrangian, where one changes the first spatial derivative to the second spatial derivative in the Klein-Gordon Lagrangian. This field will behave like the Schrödinger equation (it will have the same dispersion relation), but at the same time it is still a scalar field.
What does it mean? Nothing passes inside Horizon? Are those dots that being thrown out redshift?
Nice video! I am curious that if this model is the physics origin of Xiao Hu's pseudospin(2015)?
Another good simulation but again you don't take into account time dilation. Keer is basically all BH, Schwarzschild only at the poles.
Great simulation Pavel. This is how I imagine interacting with Keer's BH. Obviosly without time dylatation.
What happens when you phase-conjugated it.
Um actually (joking around) nothing can escape a black hole, not even light 🤓🤓🤓
What is the music in this video? It's perfect for the visuals.
When is your next post?
I've been busy lately, but in the near future I will continue to post videos
@@pavelrozhkov3239 awesome
Why does the light at the ends seem to speed up relative to the light in the center?
Why does some of the light slow down until it basically stands still? Is this actually an acurate visualisation of space time and if so could someone explain why this happens?
Amazing to actually see them get "stuck" at the event horizon there. Good job
nice to know that ur still making videos C:
Why are those photons move slower when they are closer to the black hole? Aren't them suppose to be sucked into black holes?
Very cool. Would love to see a simulation going over the poles and comparing with vs against rotation. Could draw an einstein cross that way
Please share source code.
That is more realistic and what happens black holes are so dense that not even light can escape so it just gets sucked
Dude this is crazy
Keep up the good work. 👑
A particle in the 2D box?
kerr holes
Nice effort. Somehow I cannot accept it as an accurate simulation.
Does this mean you could see yourself if you were looking at the blackhole
If you could show the time-space fabric itself is spinning what would be great to see.
Amazing music choice. Never knew yt audio library had such good songs
This pianist is underrated.
Why the top rays move faster at the beginning? That is not right.
slingshot from a black hole
I kind of imagined the photons in the center would go forward a bit during the approach, and turn it into kind of a C shape, then the rest would follow.
I watch this now Knowing that in 100 years it will be proved otherwise
Why does some light slow at around 18s?
Nothing escapes a black hole so how did those outer edges of light get away?? Its incorrect
Mi amor NO TE ENTIENDO NA
Its missing the individual clocks for each object, its what most people don't understand when talking about black holes.
That is completely wrong.
So the things behind the black hole is never visible to us right?
Does this mean you can see the past?
Yes, but seeing is not enough! One has to risk it all by going past the event horizon and the dual singularity !
The music reminds me of those old miniclip flash games. Kids will google it, they can't know what I'm saying.
they say not even light can escape the balck hole, but it seems to me that it escaped.