Timeline for The moose must flow, but how?
Current License: CC BY-SA 4.0
36 events
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| May 12, 2022 at 6:00 | history | tweeted | twitter.com/StackStats/status/1524630455982727168 | ||
| May 8, 2022 at 19:47 | comment | added | Galen | I have received a lot of valuable feedback on this question. Before I edit the question I would like a clarification. @PeterLeopold's suggestion building on whuber's comment sounds promising. Is it possible to model the mean field even without having any data related to time? | |
| May 8, 2022 at 3:59 | comment | added | Andris Birkmanis | Either moose are non-deterministic or the phase space is not limited to just the location (maybe include the bearing). | |
| May 7, 2022 at 9:00 | answer | added | nanoman | timeline score: 3 | |
| May 7, 2022 at 2:44 | answer | added | Daniel Wagner | timeline score: 1 | |
| May 6, 2022 at 20:07 | comment | added | Sextus Empiricus | "SextusEmpiricus suggested that a flux formulation is promising for..." More specifically a function of flux in multiple directions. For instance something like Latice Boltzmann methods which considers flow at the same point in multiple directions. (alternatively, if you want to stick with a vector field, then you might want to consider to add something like diffusion, or otherwise your moose that enter the region at some point will be modelled to exit in exactly one point instead at multiple according to some distribution). | |
| May 6, 2022 at 19:44 | comment | added | Sextus Empiricus | "The ultimate goal is to estimate likely paths that the moose are taking into and then out of the bounded region." You should specify this problem much more clearly. Currently you have created a vague question about a vector field with a lot of details while this might not be at all the path of solution to your ultimate goal. It is a bit of an xy problem. When you are considering the path of the moose as a sort of averaged velocity field then you are disregarding the individual paths. Is that something that you want for your final goal or not? | |
| May 6, 2022 at 10:37 | comment | added | TonyK | Here is a fluid dynamics paper that describes the Multiphysics Object Oriented Simulation Environment program (MOOSE for short). Also this article might be relevant. | |
| May 6, 2022 at 10:33 | answer | added | Cong Chen | timeline score: 2 | |
| May 6, 2022 at 5:56 | answer | added | Flounderer | timeline score: 4 | |
| May 5, 2022 at 17:49 | comment | added | Peter Leopold | It seems that all the answers so far respect the notion that there is a unique map $\Phi: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ to describe moose behavior. I suggest you consider @whuber's comment that the addition of time dependence $\Phi_t$ will in fact make your "map" a map, and then ask what is $\mathbb{E}_t[\Phi_t]$? The "mean field" behavior $\mathbb{E}_t[\Phi_t]$ gives you the first moment of a random field, where any data point in your dataset is an instance of that random field. The mean field would satisfy Laplace's equation. | |
| May 5, 2022 at 16:52 | answer | added | Hugh Nolan | timeline score: 3 | |
| May 5, 2022 at 16:00 | history | edited | Galen | CC BY-SA 4.0 |
added 9 characters in body
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| May 5, 2022 at 15:54 | history | edited | Galen | CC BY-SA 4.0 |
Responded to comment asking about how many moose are in the area.
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| May 5, 2022 at 15:42 | history | edited | Galen | CC BY-SA 4.0 |
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| May 5, 2022 at 15:42 | answer | added | Betterthan Kwora | timeline score: 2 | |
| May 5, 2022 at 15:35 | comment | added | Sextus Empiricus | Instead of a vector at each point $x,y$ you may want to have a function $f(\phi)$ giving the flux in every direction at the point $x,y$. This allows for crossing paths. Regarding a more definite complete answer to the question. This should also depend on what you want to do with the model. It is the application that helps to decide for a model and not just the thing that you want to model. | |
| May 5, 2022 at 14:29 | comment | added | jwimberley | Do you have a rough idea of how many moose there are in the bounded area at any single time? And do you have a rough idea of how old the moose tracks are (e.g. they are all < 1 day, 1 week, etc.)? I think this bears on whether the "continuous limit" makes sense. | |
| May 5, 2022 at 13:54 | comment | added | whuber♦ | Conceiving of these data as sampling a vector field might be an oversimplification: these tracks were laid down over time along specific paths. As such they really are the tangent vectors of some unknown map (or maps, for multiple animals) from a real interval (representing time) into the plane. This re-conception handles two major difficulties: (1) the vectors change over time. How would you deal with overlapping tracks made by the same animal? (2) The vectors are not defined everywhere in the plane; they are defined only in places where the animal has been. | |
| May 5, 2022 at 13:47 | answer | added | anjama | timeline score: 8 | |
| May 5, 2022 at 13:46 | answer | added | André LFS Bacci | timeline score: 9 | |
| May 5, 2022 at 13:06 | comment | added | anjama | Are you familiar with the subdiscipline of movement ecology? If not, you might find some inspiration there, although it's still a relatively young field and is focused heavily on GPS movements. | |
| May 5, 2022 at 11:37 | history | became hot network question | |||
| May 5, 2022 at 9:07 | answer | added | Tim | timeline score: 6 | |
| May 5, 2022 at 8:12 | review | Close votes | |||
| May 12, 2022 at 3:05 | |||||
| May 5, 2022 at 5:09 | history | edited | Galen | CC BY-SA 4.0 |
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| May 5, 2022 at 5:00 | history | edited | Galen | CC BY-SA 4.0 |
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| May 5, 2022 at 4:54 | comment | added | Galen | @PeterLeopold You have excellent ideas. I have edited the question to consider your recent comment. | |
| May 5, 2022 at 4:54 | history | edited | Galen | CC BY-SA 4.0 |
Added some responses to Franks answer
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| May 5, 2022 at 4:48 | answer | added | frank | timeline score: 14 | |
| May 5, 2022 at 4:20 | comment | added | Peter Leopold | Is your map single-valued? That is, is it a map? Is it possible for a moose to be at one point with two different bearings? Is the curl of the flow up or down? Or, to preserve symmetry, is the curl of the moose flow zero? A curl-less, sink-less, source-less flow is the solution of Laplace's equation. $\nabla^2 \psi =0.$ BUT REALLY, how about a random walk with some specific correlation features that keep the moose going more or less in one direction? | |
| May 5, 2022 at 4:06 | history | edited | Galen | CC BY-SA 4.0 |
Copyright.
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| May 5, 2022 at 3:58 | history | edited | Galen | CC BY-SA 4.0 |
Spelling
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| May 5, 2022 at 3:51 | history | edited | Galen | CC BY-SA 4.0 |
Added image.
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| May 5, 2022 at 3:42 | history | edited | Galen | CC BY-SA 4.0 |
I don't even have a choice of PDE yet.
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| May 5, 2022 at 3:33 | history | asked | Galen | CC BY-SA 4.0 |