/sci/ - Science & Math

[poly No.5732424]

Hey, YOU.
Engineering student in despair of understanding what your model represents.
Engineering student wanting to broaden your knowledge to other fields.

Ask your questions here and we try to answer them.

No fundamental physics here please (except maybe EM but still), I don't know much about relativity and only had an intro to QM atm so I won't be of much help.

pic related, it's a potential flow, using sources and wells just like positive and negatives charges.

[Anonymous No.5732441]

computational mechanics? how does FEA handle contact between two deformable bodies? how to derive circuit elements using least squares approximation? anyone?

[poly No.5732459]

>>5732441
you can handle contact between two deformable bodies by choosing a great number of nodes on the surface of the contact.
Boundary conditions are given by friction coefficient, local pressure, and large scale efforts (gravity for example)

let me think about the cricuit elements for a moment, I'll try to come up with an anwer

[poly No.5732467]

>>5732459
deformable are not so deformable if time is fixed

[Anonymous No.5732475]

Why are the Navier-Stokes equations difficult to solve?

[poly No.5732479]

>>5732467
if you want a time moving model, you can solve iteratively differential equations on the position of the nodes, then solve for the efforts at each iteration...

[Anonymous No.5732480]

>>5732475
Because mathematicians haven't yet come up with tools that can tackle PDFs well. T. Tao wrote up a good read on the subject
http://terrytao.wordpress.com/2007/03/18/why-global-regularity-for-navier-stokes-is-hard/

[poly No.5732486]

>>5732479

what >>5732480 said

you have to understand that most differential equations are unsolvable analytically, let alone when there are partial derivatives and quadratic forms...
But that's why we have good approximations for some cases: lubrification, potential flows, etc

[poly No.5732495]

bump with fourier optics for board's knowledge

[poly No.5732528]

bumping with particle diffusion

[poly No.5732671]

bumping with 4 bar linkages

I'm surprised no one has any questions.
Does everyone come to /sci/ only to ask if time travel is possible and to troll about how magnets work?

[Anonymous No.5732680]

What's the difference between H-infinity synthesis and mu-synthesis? I only know them in a MATLAB context, where the difference is H-infinity doesn't allow for uncertainty in the plant itself and mu-synthesis does.

Difficult to find elementary (well, "elementary") literature on robust control in general, so if anyone has good resources I'd appreciate it :)

[Anonymous No.5732707]

>>5732680
MATLAB master race reporting in

[Anonymous No.5732712]

>>5732480
>tackling PDFs

[Anonymous No.5732715]

>>5732671

This board is slow but I hope you hang around and check later.

Bumping for potential

[poly No.5732747]

>>5732680
H infinity requires you to model and know the parameters of your system, and deduces the best correction using that.
mu-synthesis uses a range of variation in the parameters.

If I could give an analogy, imagine you have a dataset;
H infinity could be seen as the linear regression assuming no error bars
mu-synthesis would take error bars into account and choose the best solution while remaining in the admissible error.
You can obviously get different solutions from the two methods!

[poly No.5732752]

>>5732441
Do you mean like: you're given a time response and you're supposed to find the elements of a circuit that could produce such a response?

in that case: without using a least squares approximation, you could use methods suggested here
http://www.facstaff.bucknell.edu/mastascu/econtrolhtml/Ident/Ident1.html

ask anything more precise maybe?

[Andi No.5732842]

I've sometimes wondered about the complex numbers and eigenmodes from the solution of differential equations, since in our engineering mathematics courses we're broadly taught how to use them and interpret them but not how they are what they are. They're kinda like a distant relative who you see occasionally at weddings and funerals who you are somehow related to, but never got round to enquiring about because they are just distant relatives.

[Andi No.5732856]

I've sometimes wondered about the complex numbers and eigenmodes from the solution of differential equations, since in our engineering mathematics courses we're broadly taught how to use them and interpret them but not how they are what they are. They're kinda like a distant relative who you see occasionally at weddings and funerals who you are somehow related to, but never got round to enquiring about because they are just distant relatives you'll probably never have to have much intimate knowledge of.

[poly No.5732869]

>>5732842
they mostly come from linearity, and second orders:
you know how to solve simple 1st order equations;
the solutions of the homogeneous equation are in the form x->A exp(ax).
Now, we want exp(ax) to be a solution of a second order equation.
Which is a problem because when the system is stable, you have a^2 < 0.
It's simply algebraic; but the way I see it is the following:
For second order systems, solutions are linear combinations of two basis functions, right? So in a certain way, your solutions are two-dimensional.
How do you represent two dimensions in one number? By using bidimensional vectors. Or complex numbers!

that's why we almost don't use them anymore when using state space representation: all the equations are matricial 1st order equations.

I hope I didn't confuse some things, but I must admit I never tried to ask myself about where they come from in physics.

[Anonymous No.5732872]

>>5732856

Not the same person from the rest of the thread, but

Your eigenstuffs are like a basis for a solution set (like x1, ..., xn in linear). You get eigenvectors that are actually functions by solving your DE and eigenvalues fall out accordingly.

The reason why you often don't have solutions look linear here (as you'd expect by finding a basis/taking combinations) is this step will often occur after a separation of variables, if appropriate, and then you put your solutions back together to get something non linear.

I hope that helped

[Andi No.5732898]

>>5732869
>>>
>For second order systems, solutions are linear combinations of two basis functions, right? So in a certain way, your solutions are two-dimensional.
How do you represent two dimensions in one number? By using bidimensional vectors. Or complex numbers!
Whoa. So that's how it is. Thanks OP!

[poly No.5732914]

>>5732898
no problem sir!

[poly No.5733086]

bumping with electric motor

[poly No.5733214]

bump to front page with PID block diagram

[Anonymous No.5733255]

Aerospace Engineering grad student here. I can probably answer a few questions too if OP doesn't mind. I like this thread.

>>5732480

This can handle PDF's no problem!

http://get.adobe.com/reader/

But seriously, the main reason NS and other such equations are so difficult is mainly due to the non-linear terms.

>>5732872

Seconding this.

For anyone who may know about it: I've done some wiki reading about Gauge theory/transformations and I was very surprised to learn that the vector potential in EM is actually a physically relevant thing and not just a mathematical "trick" or "artifact". Here is where I read this:

http://en.wikipedia.org/wiki/Introduction_to_gauge_theory#In_quantum_mechanics

Would anyone happen to know if other "potentials" (like the stress potential in stress analysis or potential flow theory in fluid mechanics) have physical significance as well?

[Anonymous No.5733283]

>>5733255
Well, of course non-linearity is the source of all nastiness. But non-linear ordinary diff. equations don't usually have such problems associated with them such as existence and/or regularity of solutions.

[Anonymous No.5733286]

AeroEfag here. What would be the procedure to find the altitude at which this nozzle operates, assuming I know To, Po, and knowing that a normal shockwave (OCN) is formed in that section. They tell me to assume international standard atmosphere.

[Anonymous No.5733317]

>>5733283

True. NS is the only one I know of that has that issue. Can any mathfags add to this??

>>5733286

If I remember how to do this right, if you know the inlet stagnation pressure, you can assume isentropic flow until the shock. Then use the area ratio of the shock to the throat to find the Mach number before the shock which you can use to get the stagnation pressure ratio across the shock from the normal shock tables. That tells you the stagnation pressure at the outlet since you can assume isentropic flow after the shock. Then use the area ratio of the exit to find the static to stagnation pressure ratio at the exit. The static pressure is the "receiver" pressure and should correspond to the atmospheric pressure. Then find the altitude.

[poly No.5733320]

>>5733286
oh god, I don't know just from that... do you have any equations you could use?
I assume the whole point is to make the right assumptions or reasoning that's why I ask

[Anonymous No.5733324]

>>5732424
I have a matrix equation of the form:
A*x=b
where if I find the eigenbasis of A, I discover there are some basis vectors that I do not want to exist. How can I project away these vectors and still find the inverse of A?

[poly No.5733334]

>>5733324
what's your matrix size?
I don't understand why you wouldn't want some basis vectors, please elaborate

[Anonymous No.5733347]

>>5733334
It is a very large matrix.
I am sort of simulating the motion of vertices on a surface and at least one of the eigenbasis vector directions corresponds to motion off of the surface.

[Anonymous No.5733374]

>>5733317

Very clear, thank you

[poly No.5733375]

>>5733347
let D be the "pseudo diagonal" matrix of size n such as:
the first k diagonal elements are those associated with the eigevectors you want to keep
and on the bottom right corner, you put a leftover submatrix M, that concerns the directions you don't want.

now A=P D P-1
and you can write

DP-1 X = P-1 B
now you just have to cut the leftover submatrix, and the last n-k coefficients of X P-1 X and P-1B

if A is invertible over R^n, the projection over a subspace is invertible over that subspace isn't it?

[Anonymous No.5733381]

>>5732424
Wave/Particle Model

[Anonymous No.5733382]

This is pretty off-topic but do you know any EE or CS? Can you explain how to design a circuit to execute a specific algorithm, say, Heron's square root algorithm

If not, do you know where I could find out?

[poly No.5733431]

>>5733382
yes I know some of both:
some algorithms can be executed by using synchronous components (an operation at each clock period), but that would mean we want a binary result.


let's try that then:
you want, given a number in binary form, find its square root using heron's algorithm.
That algorithm uses addition and division.

We can use D flip flops, JK or SR latches, registers, adders, (http://en.wikipedia.org/wiki/Adder_(electronics)), binary multipliers (http://en.wikipedia.org/wiki/Binary_multiplier))

Now, what is the first input? A, your number in binary form, and the first approximation, let's say N
What do you want to do with it?
you want to iterate (N<-(N+A/N)/2

So you need to keep the value of N and A/N(what component would you use?)
you need to divide by 2 (again, what procedure?)
you need to add (using the adder), store the result

You might also want to predefine a certain number of operations before stopping, so you can add a counter and a logic gate if you want

do you see the process?

[poly No.5733441]

>>5733431
and I might add that the whole point is that some outputs are linked to some other inputs. Just like in a flowchart

[Anonymous No.5733443]

>>5733375
to avoid confusion I am going to def: inv(P) := P-1
You are saying
D*inv(P)*X = inv(P)*B
which I agree with.
Then, you suggest to remove the last n-k elements from D*inv(P), X, and inv(P)*B which means only for the subspace do you have to find an inverse. Again, I agree, you can find this inverse. The problem is, there is no longer dynamic information for the n-k elements of X. I don't understand how this fixes the problem

[poly No.5733450]

>>5733443
well those dynamic elements imply movement on the wrong directions.
I assumed that since your surface is probably stable, if a particle of fluid descends, others will compensate, without any tangential movement of the node.

[Anonymous No.5733464]

>>5733450
The surface of constraint and X are not in the same basis. It is like I find equations that move in (r,phi,theta) but do not want radial motion but the problem is posed in Cartesian coordinates. I would break things if I just started ignoring the x in (x,y,z) representation.

[Anonymous No.5733478]

>>5732424
>engineering

Are you slow or just an underachiever?

[Anonymous No.5733481]

>>5732424
When did you come out of the closet?

[poly No.5733531]

>>5733464
I see... I have never thought about a similar problem before.
If anyone wants to contribute, please do so!
I'll try to think about it too, and if you come up with something smart, please post it so we can learn from it!

[poly No.5733539]

>>5733531
but why can't you still invert the matrix then get rid of what you don't want?

[poly No.5733546]

>>5733481
when your dad finally went back to work

[Anonymous No.5733578]

>>5733531
>>5733539
Well, we know that for an eigen decomposition of J,
J = a*b*inv(a) where b is a diagonal matrix of eigenvalues and a is a matrix of the eigenvectors.

Since b is diagonal, you can find its inverse by finding the inverse of each of its elements and using the fact that for 2 square matrices A,B their inverse product is:
inv(A*B) = inv(B)*inv(A)
we find the inverse of J:
inv(J) = a*inv(b)*inv(a)

So, for
J*x = B we have x = a*inv(b)*inv(a)*B
The question is if for I' (the truncated identity matrix that cuts off the eigenvectors that correspond to unphysical directions) is
I'*J*x = B'
going to give you the same x as in
x = a*I'*inv(b)*inv(a)*B'
We know that I' does not have an inverse, so, I do not see how it does

[Anonymous No.5733584]

>>5733578
>I'*J*x=B'
should be
a*I'*b*inv(a)*x = B'

[poly No.5733585]

>>5733578
actually I' is of size n-k and is invertible if A was invertible in the first place!

[Anonymous No.5733589]

>>5733585
In how I am writing it, it is still nxn but k of those n diagonal elements are 0 instead of 1. Otherwise, it cannot multiply these matrices

[poly No.5733715]

bump with an elligham diagram

[Anonymous No.5733731]

>>5733715
>engineering

[poly No.5733750]

>>5733731

[Anonymous No.5733759]

what is the difference between FFT, DTFT, DFT, DFCT, and the IFFT?

I can do them all but don't understand shit.

[Anonymous No.5733763]

>>5732424

I'm a chemical engineering student going in ot my final bachelors year after summer.

I've done well at all exams, but I really don't feel like I've developed intellectually. Maybe I'm a bit better at research and writing reports, stuff like that, but that's it.

I also think my mathematical ability will be overrated by anyone who thinks that engineers are good at maths. I'll be doing the MIT online maths course this summer (single variable calc, multi-variable, diff. equations and linear algebra, although some of it will obviously be religion).

Is this how everyone feels? I honestly feel barely any smarter than when I first came in to uni, although it doesn't help that I hate the subject.

[poly No.5733807]

>>5733759
discrete time fourier transform is the fourier the discrete fourier transform after sampling a continuous time signal.

what is dfct?
ifft simply allows you to go back to time domain.

What you have to understand is this:
Sometimes, you want to study a system, with retroactions. And even if it is linear, you cannot find the output given some input simply by using convolution.

For that reason, you can "travel" to the frequency domain via a fourier transform, work there (where convolution becomes multiplication), and then come back using a simple inverse fourier transform.

You can describe systems by their transfer function instead of their impulse response, which is quite more handy.

[poly No.5733816]

>>5733763
hello!
I really don't feel that way, I'm sorry for you bro...
Where I currently study, people go through 2 years of intense studying of maths and a large spectrum of physics and systems first, then some go specialize more, and others try to stay polyvalent.

I really encourage you to do those MIT courses, and maybe try to get interested in some other field of physics on your free time after that? (the mathematical tools are important)
My favorite ones are diffusion (particle/heat/momentum), fluid mechanics and fourier optics!

[poly No.5735042]

bump!
I'm back with antennas this time

[poly No.5735102]

don't hesitate!

[poly No.5735187]

[Anonymous No.5735190]

Elecfag here.
I know nothing of inductors, please help with the question (pic).

[poly No.5735198]

>>5735190
an ideal inductor has the following relation between <span class="math">v_L[/spoiler] and <span class="math">i_L[/spoiler]:

<span class="math"> v_L = L \frac{di_L}{dt} [/spoiler]

Now you know <span class="math">i_L[/spoiler] don't you? you just have to find <span class="math">\rac{di_L}{dt} [/spoiler]

[poly No.5735199]

>>5735198
the last sentence is
you just have to find <span class="math">\frac{di_L}{dt}[/spoiler]

[Anonymous No.5735206]

>>5735199
I'd like to first thank you for your help.
Sorry, but is iL 5 amps? Also could you explain how I get the derivative of i with only the variables given?

Sorry, I'm quite slow.

[poly No.5735208]

>>5735206
sure.
<span class="math">i_L[/spoiler] is a triangle wave of 5 amps peak to peak, with a frequency f = 5kHz.
what is of interest to us are the variations of the current.
At a certain moment <span class="math">t_0[/spoiler], the current reaches its lowest value <span class="math">i_{min}[/spoiler]
from <span class="math">t_0[/spoiler] to [matht_0+\frac{1}{f}, the current grows linearily to reach its maximum value <span class="math">i_{max} = i_{min}+5A [/spoiler] at time <span class="math">t_0 + \frac{1}{f}[/spoiler].

You basically have to find the slope of that line.

Again, from <span class="math">t_0 + \frac{1}{f}[/spoiler] to <span class="math">t_0 + \frac{2}{f}[/spoiler], the current diminishes linearily to reach its lowest value, etc.
At least try to draw the input to see what you're looking for.
Offset doesn't matter because we only care about the variations here!

[Anonymous No.5735243]

>>5735208
Thanks for the help.

[poly No.5735266]

>>5735208
well actually that was <span class="math">t_0 + \frac{1}{2f} [/spoiler] but the principle is the same

[Anonymous No.5735300]

is that in your pic a source + uniform current? or there is also a sink on the other side

[poly No.5735363]

>>5735300
yes indeed, it's a source superposed with a uniform current.
The red limit is the rankine half-body

[poly No.5735578]

bamp with thermodynamics

[Anonymous No.5735698]

Bumping with some aerospace engineering. This thread must not die!

[Anonymous No.5735704]

>>5735363
>>5735300

You can also make a Rankine oval if you put a sink behind the source. It's sometimes used in the study of compressible subsonic flow for finding critical Mach number as a function of aspect ratio.

[poly No.5735808]

>>5735704
Indeed! and even though Rankine bodies can look like mathematical manipulations,they eally amaze me!

[poly No.5736069]

bump with hysteresis

[Anonymous No.5736094]

Jesus, why is fluid mechanics so beautiful and awesome? I'm a second year AeroE and I would love to become a researcher in the field.

[poly No.5736100]

>>5736094
This is my project too... I feel kind of sorry for the people who couldn't try toying with fluid mechanics and don't know what they're missing!

[Anonymous No.5736102]

>>5736094
>>5736100

Mah niggas. How anyone can fail to appreciate fluid mechanics is beyond me.