Chemical engineer here. How do you make an equation to approximate

>Chemical engineer here.
>asks this question
yeah, nice try

>>7975092
so in otherwords you dont know either?

i should of not bothered asking apparently

>>7975084
0/10 bait

Might be more believable if you had posted "chemical engineering student," but you need a grad degree and licensure to work as an actual chemical engineer, and there's harder math than this on the test.

>>7975084
potentially future chemical engineer in training >here.

fixed that for you

i thought it would be obvious that i am just a student.

i just want to know how the researchers approximate their data like this.

its not a test, its just a graph from a research paper on wetting and contact angles.

i just want to know how they made that dashed line mathematically.

like they didn't just guess or make a random dashed line obviously, so howed they do it?

>>7975095
yes, you shouldn't have bothered
now get out

>>7975107
Then why did you claim to be an engineer. Also, consult your books.

>>7975084
http://mathworld.wolfram.com/LeastSquaresFittingPolynomial.html

wow so many cucks

no one knows the answer except for one guy but everyone has an insult

like anyone with an actual degree would be on this shithole at 2AM, it should be plainly obvious i am just a student

so since none of you failures know the answer, you just insult me instead to stroke your eggos

so can it be explained in a way for someone who isnt so math savvy what least squares is and how its used to make that curve?

>>7975084

>How do you make an equation to approximate a curve?

That's a very loaded question. There are many techniques for curve fitting and there is not necessarily one single method that is best for the job. In this case the curve looks like it was drawn with something (i.e. eyeballed) as opposed to generating it mathematically. If I were to do this myself, I would probably just go with a least squares fit with a second order polynomial for each half of the data. If I knew what the x-axis variable was I could maybe suggest a curve fit. Based on the number of data points I'd have to question whether fitting a curve is even worthwhile unless the underlying theory suggests the curve should have certain properties...

>>7975148
thanks for the detailed answer, thats what i was looking for

Everyone except this poster >>7975148 is an idiot that thinks you can just least square whatever you want. This isn't a baby math question, it's a valid conceptual question.

Also don't call yourself a ChemE when you're student, how fucking arrogant can you be? I'm a PhD student close to getting my PE and I don't refer to myself as a ChemE yet.

>>7975084
To understand modelling first realize there's no point to just fitting high order polynomials on everthing. You COULD make almost any data fit with very high order polynomials (including multivariate), but usually your "model" won't hold outside the data range. In fact where the theory weak a lot of software does exactly that (you can't use discreet data in design equations, but you can use an interpolation function or polynomial estimate). In general that is something that is only done as a last resort.

Now the golden standard of modelling is to find an fundamental theoretical model that can represent your data. A pure theoretical model is one where you can calculate all your parameters a-priori (without fitting data points).

Unfortunately theoretical models do not usually represent real world processes accurately or they are too computationally expensive to be used in practice. So the next step is to model what is called semi-empirical models as is the case in chemical kinetics/reaction engineering and most other meso-macro scientific and engineering fields. The semi part here refers to the fact that the general form of the equation is derived from a fundamental model, but the parameters are now allowed to vary to fit the data. That is the starting point where most researchers try to fit their parameters (there's no point to eye balling and guessing functions).

The actual parameter fitting is done by defining an objective function which will be specifically written for the problem to deal with non-linearity, discontinuity, singularities, higher weighting to important variables and so forth.

[cont.]

>>7975197
Now fitting the parameters can be a difficult problem especially with real functions (you will almost never be able to use least squares past undergrad). Optimisation is a massive field in its own right, but in general you will use some bounded global optimisation routine.

I would give a few examples to illustrate the importance and usefullness of semi-empirical models over pure empirical, but I'm on my phone so fuck TeXing on this shit.

cubic spline? lagrange polynomials? newtons method?

>>7975206
so amazing, ty

just proves most people here have inflated egos and confuse not explaining something with not being able to explain it

this was really helpful :)

>>7975225
This is the answer OP. Look up interpolation.

>>7975084

>>7975197 is correct, there is no perfect method that works for every curve. The best you can do is come up with a "theory" and use the math in the theory to come up with a model. Sometimes this involves using differential equations to determine what you think is changing and then adding up all the pieces. Once you have a model, you can just fit the curve using the arbitrary parameters around it.

>>7975092
You can use origin to make the fitting, dunno if the function as you expressed there can be fitted but I think it's possible to fit anything as long you propose the model (I remember fitting a certain model for rheology shear stress data).

>>7975324
>I think it's possible to fit anything
If only...

Try Quadratic Spline?

>>7975084
>Chemical engineer here.
>it should be plainly obvious i am just a student
If this board was decent you'd be banned.

>>7975357
Please don't think human decency is the sole responsibility of the moderators. You participate in the quality of content on this board just as much as anyone else does. Bans don't make good content, you do.

>>7975099
>grad degree and licensure to work as an actual chemical engineer
Is this true for america? In australia you just do a bachelors in a field of engineering and you can work as that an engineer of that field, then again we can just do medicine without pre-med.

>>7975364
No, most americans enter industry and get their PE directly after undergrad. Gradschool is really only for people who want to enter academia or research.

In Europe you need to do a masters because most of their bachelor programmes are a fucking joke.

t. Someone living in an impartial country.

>>7975368
>In Europe you need to do a masters because most of their bachelor programmes are a fucking joke
That's strange because I've always thought europe had a pretty excellent education system.

File: invert.png (5KB, 330x220px) Image search: [Google]

5KB, 330x220px

invert your graph
does this look familiar?
it should, it's Gaussian
the model follows

>>7975373
Their high-schools and pure science/math programmes are far superior. Their engineering programmes are outdated practically orientated shit that's closer to what know as a technologist degrees than Western engineer bachelor degrees.

I'm talking about continental Europe only of course.

>>7975405
it has finite endings tho

iss that make it still gausian?

the ends of graph are the end of the line too

>>7975419
Lrn2extended

>>7975422
is between 0 and 1 it cant be extended because 1 represents 100%

>>7975426
>is between 0 and 1
>>7975084
see the zero?
see the [math] \infty [/math]?
see how stupid you are?

>>7975570
infinity represents 1 as in 100%

>>7975573
>infinity represents 1
wat

>>7975620
your a bit slow huh

i will say this though

>>7975623
you are a bit 'tarded huh
I will say this though,
you are indeed 'tarded.

>>7975084
You shouldn't ask on this board, most of the people here are autists who never made it past calc 1

>>7975364
Yes, you have to pass a really long, like all day P.E. exam by ABET to get licensed.