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Cristal Medium Blue
Приєднався 21 лис 2013
Відео
Pattern formation by unbiased random walkers
Переглядів 3793 місяці тому
Thirty thousand unbiased random walkers forming clusters. Each random walker counts the total number of random walkers in its immediate neighborhood and then takes a random step in space. The maximum possible length of the step depends on the amount of neighbors within a radius. The random walkers take longer steps if they are either in a crowded region or in an uncrowded region. They take shor...
Clustering of unbiased random walkers
Переглядів 1,6 тис.3 місяці тому
Ten thousand unbiased random walkers forming clusters. Each random walker counts the total number of random walkers in its immediate neighborhood and then takes a random step in space. The maximum possible length of the step depends on the amount of neighbors within a radius. The random walkers take shorter steps if they are located in a crowded region, and they take longer steps if they are lo...
Random walkers are trapped on regions of space where maximum velocity is limited
Переглядів 3983 місяці тому
Unbiased random walkers form clusters in regions of space where the maximum possible step length is limited. The maximum possible step length a walker can take depends on the walker's location in space. The length of the step is a uniformly distributed random variable with mean zero: Step = D(R) * U(-1, 1) Where U(-1, 1) is the uniform distribution between -1 and 1. D(R) is the maximum possible...
Clustering of random walkers
Переглядів 1,4 тис.3 місяці тому
Ten thousand unbiased random walkers forming clusters. Each random walker counts the total number of random walkers in its immediate neighborhood and then takes a random step in space. The maximum possible length of the step depends on the amount of neighbors within a radius. The random walkers take shorter steps if they are located in a crowded region, and they take longer steps if they are lo...
Growing trees simulation (Diffusion-limited aggregation)
Переглядів 303 місяці тому
Growing trees simulation (Diffusion-limited aggregation)
Quadtree to efficiently check if two points are close to each other
Переглядів 245 місяців тому
Quadtree to efficiently check if two points are close to each other
Box2d.ts B. subtillis monolayer simulation
Переглядів 3710 місяців тому
Box2d.ts B. subtillis monolayer simulation
Bacteria Simulation of Nematic Alignment. Mosaic of micro-domains
Переглядів 5910 місяців тому
Bacteria Simulation of Nematic Alignment. Mosaic of micro-domains
I'm guessing that they have sort of collision system that causes them to get caught in "traffic jams
el logo himno de las bacterias mi canal favorito 😊
reminds me of a windows 95 screensaver 💾
Amazing 😊
Kind of reminds me of pug wrinkles or that one wrinkly cake.
Does anyone know why this happens? And are there any theoretical calculations on the possible implications of this on local non-uniformities in thermodynamic quantities such as pressure in a gas. I think it may be very intresting!
Intuitively, it takes fewer steps to enter a cluster from outside (since they travel greater distances) and more steps to exit a cluster (due to reduced travel distance). So even if the chances of joining a cluster are not biased, once you eventually enter a cluster, it's harder to leave. Easy entry, hard escape.
if they take shorter steps when in crowded reigon rhen obvuoulsy they create clusters>
I'm pretty sure it's a collision system that prevents them from going very far
Video has potential if you explain what's going on
I think there's a collision system which causes "traffic jams"
This is really cool! Could you share the code for this program?
github.com/CritalMediumBlue/Clustering.git
why is this happening?
So you call them unbiased walkers, despite the fact they are obviously biased by the number of neighbours.
They are unbiased in the sense that every direction the random walker can take has the same probability. In other words, the random walkers do not have any preferred direction to move. Which means, half of the time they will move left and half of the time they will move right. Half of the time they will move up, and half of the time they will move down. It seems to me that the clustering effect is not caused by a biased random walk, but rather, by a longer residence times in certain regions of space. In this simulation, it takes more time to explore certain regions of space because the maximum velocity that a particle can have depends on the number of neighboring particles. Edit: Does that make sense? (I am not an expert in the topic)
Well @CristalMediumBlue , you are an odd fellow, but I must say... you steam a good ham.
Interesting! To what extent is this effect dependent on Ito / Stratonovich / Isothermal convention for integrating the SDE, specifically the choice of whether D(R) is evaluated at the beginpoint or the endpoint of the random step?
In this simulation we evaluated D(R) at the beginning of each step. We haven't explored the effects of Stratonovich or Isothermal conventions in this particular study, but it's definitely an interesting question for further investigation. Thanks for this insight!
cool!
Is this used to model some specific natural phenomenon?
This particular simulation was made as an attempt to mimic protein clustering or bacteria agglomeration. But it is still unclear whether this is the right approach to describe these phenomena.
Almost looks like galaxy superclusters to me. The shorter steps are some similar to the gravity of the cluster pulling them in
@@CristalMediumBlue This simulation seems to be only 2D I would be careful generalizing from 2 to 3 dimensions as there are some neat theorems about ergodicity of random walkers in 2 vs 3+ dimensions. Notably 2D walkers are ergodic but 3D walkers are not.
oh thats actually surprisingly neat?
Very nice movie! Are these absorbing boundary conditions?
Thanks! Yes, bacteria get deleted from the simulation once they cross the boundary. PS: The simulations posted on your channel are very encouraging to me.
Very beautiful 💌