Could you guys cooperate or something and write an intro Discussion or Main post on this for landlubbers? Pretty please?
I have glanced at a very brief introductory article on dim.an. in regards to Reynold’s number when I wondered whether I could model dissemination of fern’s spores within a ribbon-shaped population, or just simply read about such model, but it all seemed like so much trouble. And even worse, I had a weird feeling like ‘oh this has to be so noisy, how do they even know how the errors are combined in these new parameters? Surely they don’t just sum.’
(Um, a datapoint from a non-mathy person, I think I’m not alone in this.)
Sure, I’d be interested in writing an article on dimensional analysis and scaling in general. I might have time over my winter break. It’s also worth noting that I posted on dimensional analysis before. Dimensional analysis is not as popular as principal components analysis, despite being much easier, and I think this is unfortunate.
I don’t know what a “ribbon-shaped population” is, but I imagine that fern spores are blown off by wind and then dispersed by a combination of wind and turbulence. Turbulent dispersion of particles is essentially an entire field by itself. I have some experience in it from modeling water droplet trajectories for fire suppression, so I might be able to help you more, assuming I understand your problem correctly. Feel free to send me a message on here if you’d like help.
And even worse, I had a weird feeling like ‘oh this has to be so noisy, how do they even know how the errors are combined in these new parameters? Surely they don’t just sum.’
Could you explain this a little more? I’m not exactly following.
Because dimensional homogeneity is a requirement for physical models, any series of independent dimensionless variables you construct should be “correct” in a strict sense, but they are not unique, and consequently you might not naively pick “useful” variables. If this doesn’t make sense, then I could explain in more detail or differently.
Yes, I remember that post. It was ‘almost interesting’ to me, because it is beyond my actual knowledge. So, if you could just maybe make it less scary, we landlubbers would love you to bits. If you’d like.
I agree about the wind and the turbulence, which is somewhat “dampered” by the prolonged period of spore dissemination and the possibility (I don’t know how real) of re-dissemination of the ones that “didn’t stick” the first time. The thing I am (was) most interested in—how fertilization occurs in the new organisms growing from the spores—is further complicated by the motility of sperm and the relatively big window of opportunity (probably several seasons)… so I am not sure if modeling the dissemination has any value, but still. This part is at least above-ground. It’s really an example of looking for your keys under a lamplight.
re: errors. I mean that it seemed to me (probably wrongly) that if you measure a bunch of variables, and try to make a model from them, then realise you only want a few and the others can be screwed together into a dimensionless ‘thing’, then how do you know the, well, ‘bounds of correctness’ of the dimensionless thing? It was built from imperfect measurements that carried errors in them; where do the errors go when you combine variables into something new? (I mean, it is a silly question, but i haz it.)
(‘ribbon-shaped population’ was my clumsy way of describing a long and narrow, but relatively uninterrupted population of plants that stretches along a certain landscape feature, like a beach. I can’t recall the real word right now.)
Yes, I remember that post. It was ‘almost interesting’ to me, because it is beyond my actual knowledge. So, if you could just maybe make it less scary, we landlubbers would love you to bits. If you’d like.
If you don’t mind, could you highlight which parts you thought were too difficult?
Aside from adding more details, examples, and illustrations, I’m not sure what I could change. I will have to think about this more.
re: errors. I mean that it seemed to me (probably wrongly) that if you measure a bunch of variables, and try to make a model from them, then realise you only want a few and the others can be screwed together into a dimensionless ‘thing’, then how do you know the, well, ‘bounds of correctness’ of the dimensionless thing? It was built from imperfect measurements that carried errors in them; where do the errors go when you combine variables into something new? (I mean, it is a silly question, but i haz it.)
This is an important question to ask. After non-dimensionalizing the data and plotting it, if there aren’t large gaps in the coverage of any dimensionless independent variable, then you can just use the ranges of the dimensionless independent variables.
I could add some plots showing this more obviously in a discussion post.
Here are some example correlations from heat transfer. Engineers did heat transfer experiments in pipes and measured the heat flux as a function of different velocities. They then converted heat flux into the Nusselt number and the velocity/pipe diameter/viscosity into the Reynolds number, and had another term called the Prandtl number. There are plots of these experiments in the literature and you can see where the data for the correlation starts and ends. As you do not always have a clear idea of what happens outside the data (unless you have a theory), this usually is where the limits come from.
Could you guys cooperate or something and write an intro Discussion or Main post on this for landlubbers? Pretty please?
I have glanced at a very brief introductory article on dim.an. in regards to Reynold’s number when I wondered whether I could model dissemination of fern’s spores within a ribbon-shaped population, or just simply read about such model, but it all seemed like so much trouble. And even worse, I had a weird feeling like ‘oh this has to be so noisy, how do they even know how the errors are combined in these new parameters? Surely they don’t just sum.’
(Um, a datapoint from a non-mathy person, I think I’m not alone in this.)
Sure, I’d be interested in writing an article on dimensional analysis and scaling in general. I might have time over my winter break. It’s also worth noting that I posted on dimensional analysis before. Dimensional analysis is not as popular as principal components analysis, despite being much easier, and I think this is unfortunate.
I don’t know what a “ribbon-shaped population” is, but I imagine that fern spores are blown off by wind and then dispersed by a combination of wind and turbulence. Turbulent dispersion of particles is essentially an entire field by itself. I have some experience in it from modeling water droplet trajectories for fire suppression, so I might be able to help you more, assuming I understand your problem correctly. Feel free to send me a message on here if you’d like help.
Could you explain this a little more? I’m not exactly following.
Because dimensional homogeneity is a requirement for physical models, any series of independent dimensionless variables you construct should be “correct” in a strict sense, but they are not unique, and consequently you might not naively pick “useful” variables. If this doesn’t make sense, then I could explain in more detail or differently.
Yes, I remember that post. It was ‘almost interesting’ to me, because it is beyond my actual knowledge. So, if you could just maybe make it less scary, we landlubbers would love you to bits. If you’d like.
I agree about the wind and the turbulence, which is somewhat “dampered” by the prolonged period of spore dissemination and the possibility (I don’t know how real) of re-dissemination of the ones that “didn’t stick” the first time. The thing I am (was) most interested in—how fertilization occurs in the new organisms growing from the spores—is further complicated by the motility of sperm and the relatively big window of opportunity (probably several seasons)… so I am not sure if modeling the dissemination has any value, but still. This part is at least above-ground. It’s really an example of looking for your keys under a lamplight.
re: errors. I mean that it seemed to me (probably wrongly) that if you measure a bunch of variables, and try to make a model from them, then realise you only want a few and the others can be screwed together into a dimensionless ‘thing’, then how do you know the, well, ‘bounds of correctness’ of the dimensionless thing? It was built from imperfect measurements that carried errors in them; where do the errors go when you combine variables into something new? (I mean, it is a silly question, but i haz it.)
(‘ribbon-shaped population’ was my clumsy way of describing a long and narrow, but relatively uninterrupted population of plants that stretches along a certain landscape feature, like a beach. I can’t recall the real word right now.)
Romashka, I appreciate the reply.
If you don’t mind, could you highlight which parts you thought were too difficult?
Aside from adding more details, examples, and illustrations, I’m not sure what I could change. I will have to think about this more.
This is an important question to ask. After non-dimensionalizing the data and plotting it, if there aren’t large gaps in the coverage of any dimensionless independent variable, then you can just use the ranges of the dimensionless independent variables.
I could add some plots showing this more obviously in a discussion post.
Here are some example correlations from heat transfer. Engineers did heat transfer experiments in pipes and measured the heat flux as a function of different velocities. They then converted heat flux into the Nusselt number and the velocity/pipe diameter/viscosity into the Reynolds number, and had another term called the Prandtl number. There are plots of these experiments in the literature and you can see where the data for the correlation starts and ends. As you do not always have a clear idea of what happens outside the data (unless you have a theory), this usually is where the limits come from.