312 reputation
216
bio website tudelft.nl
location Delft, Netherlands
age 27
visits member for 1 year, 7 months
seen 4 hours ago

May
8
comment Integration and differentiation of an approximation to a function - order of approximation
So indeed the order of the approximation changes with integration/differentation?! Interesting, I wasn't expecting that!
Mar
13
comment Scaling a function with two 'asymptotes' of which one is non-constant
The slope would be fixed if that's what you mean. Essentially it will be the same as the graph in my question but with all curves having (all the same) slope $dy/dx\neq0$ at $x=0$ instead of the current case with $dy/dx=0$ at $x=0$
Mar
13
comment Scaling a function with two 'asymptotes' of which one is non-constant
Just a quick follow-up, if the lefthand asymptote is also a linear function instead of a constant, could I still apply a similar transformation?!
Mar
12
comment Scaling a function with two 'asymptotes' of which one is non-constant
I was indeed looking for a linear transformation. Sorry, forgot to mention that. Thanks for the answer! - Just for future reference: the choice of $t$ to map everything on the red curve in my case would be $t=(1-y_{as})/(y_0-y_{as})$ where $y_{as}$ is the value of the horizontal asymptote of the given function
Feb
6
comment Find the asymptote of an experimental dataset
Ok, good to know! Thanks!
Feb
4
comment Find the asymptote of an experimental dataset
@leftaroundabout , I am 100% sure the curve I am showing has an asymptote, because this is a stand-in for my experimental data and I created it with an asymptote: $y(x)=3/(x+1)+2+0.2rand()$. --- I would like to know whether there is any technique that doesn't involve fitting a function that would allow me to estimate this asymptote
Dec
4
comment Approximating $\tanh(B\sqrt{A} )$ for small $A$ and arbitrary $B$ by correcting for asymptotic behaviour of $\tanh$
I just found this question, I think that could be helpful for this particular case: math.stackexchange.com/questions/107292/…
Dec
4
comment Approximating $\tanh(B\sqrt{A} )$ for small $A$ and arbitrary $B$ by correcting for asymptotic behaviour of $\tanh$
How did you come up with $\tanh x \approx 1 - e^{-1.48x}$? If there is some strategy to that which I can also apply to the complete function which contains the $\tanh$ that would be perfect. Using the $\tanh$ itself is not an option because I need to solve an equation of the type $A + \tanh(B \sqrt{A})=1$ explicitly for $A$.
Dec
4
comment Approximating $\tanh(B\sqrt{A} )$ for small $A$ and arbitrary $B$ by correcting for asymptotic behaviour of $\tanh$
Strictly it can be anywhere between 0 and $\infty$, but the range I am interested in is roughly 0 to 50.
Nov
1
comment Why does the moment of approximation matter for the end result?
@AntonioVargas - I have tried the Newton's method approach for the full equation I am working on (the one here is just a minimal example to reproduce the behaviour) and it does indeed give a somewhat better approximation, although at the expense of having a significantly bigger equation. Thanks!
Oct
30
comment Why does the moment of approximation matter for the end result?
So would it be appropriate then to take again a Taylor series of (4) because this function is no longer linear in $a$? Because doing that would indeed result in the same answer as (3)
Oct
15
comment Approximations other than taylor series and pade approximation
Yes, I would like to have an approximate solution to get a feel for the way the result scales with $K_i$ and $Q_i$. Without having to scan a whole range of these parameters.
May
26
comment A Math function that draws water droplet shape?
@Henry, indeed, a falling liquid droplet will be close to spherical with a slightly flattened bottom part. The shape with the tail is something you will only see for a droplet running down a surface. In that case the tail forms due to a balance of capillary and viscous forces.
May
18
comment Existence and uniqueness of Stokes flow
@Qmechanic Ok! I have corrected the referencing.
May
18
comment Existence and uniqueness of Stokes flow
Don't pin me down on it, but I believe the situation is only unsolvable if the far-field is unbounded
May
3
comment Inaccuracy in numerical calculation of arclength of part of an ellipse
ok, this is pretty embarrassing. The mistake was in a function call where I had swapped the parameters of 2 ellipses. So I got the shape-plot for 1 ellipse (with b=2.5) while I got the integral for a different one (with b=0.52). Anyway, it's solved. Thanks for the effort and sorry about the dumb mistake
May
3
comment Inaccuracy in numerical calculation of arclength of part of an ellipse
Ah ok, so I am at least getting the same number. So maybe the error is already somewhere earlier: in the value of $\phi_s$. I will look into it and come back here when I sorted things out. Thanks for the help!! It's much appreciated
May
3
comment Inaccuracy in numerical calculation of arclength of part of an ellipse
You're right, they both are the same (I was missing a bracket), but still I get a much higher value. What I noticed by the way is that you use b=2.5 while I have b=0.52. What do you get with that smaller b?
May
3
comment Inaccuracy in numerical calculation of arclength of part of an ellipse
mmm that's odd. I found this for the integrand: $$a b \sqrt{\frac{b^4 \cos^2\phi+a^4 \sin^2\phi}{(b^2\cos^2\phi+a^2\sin^2\phi)^3}}$$ which is supposed to be the same according to ($\cos^2\phi+\sin^2\phi=1$) but apparently it is not????
May
3
comment Inaccuracy in numerical calculation of arclength of part of an ellipse
By the way: I agree that a different parametrization would be better. The thing is that I also need the polar angle so I will have to do a bit of work connecting the parametrization you suggest with the polar angle