/sci/ - Science & Math

first: there are many possible transfer functions, obviously.
secondly: did you try drawing a diagram?
tip: it's obviously a diagram with negative retroaction.

pic related

if you need more help, ask something more specific maybe?

Reflection or refraction come from a difference of impedence of mediums.

I don't know much about gravitational waves, but I guess we could show that space's impedence (with respect to this type of waves) is kind of homogeneous.

However, by googling it, I found that superconductors could reflect gravity waves.

the line crosses 2013 levels, in each of which it crosses at most 2 squares.
The case where it crosses no square is when it finds a vertex. And in that case, the number of squares is diminished by 2.

The number of vertices found by the line is simply gcd(2013,999)

I got it OP, wait a few minutes

>>5689722
what I mean is that each particular case can probably be simplified, depending on the flow you're considering, on the dimensions, on the speed, on the viscosity etc.
The simplest approximations are the assumption of a perfect fluid, of an incompressible flow or of an irrotational flow mostly (or a combination of these).
These allow you to cancel terms in your equations:
incompressible flow -> div(v)=0 or <span class="math">\frac{D\rho}{Dt}=0 [/spoiler]
perfect fluid -> <span class="math">\frac{\partial {\mathbf{v}}}{\partial t}[/spoiler]<span class="math"> + ({\mathbf{v}} \cdot \nabla) {\mathbf{v}} =[/spoiler]<span class="math"> - \frac{\nabla P}{\rho} + {\mathbf{f}}[/spoiler]
irrotational flow: rot(v)=0

Then there are more elaborate assumptions, like the lubrification approximation and so on and so forth.

Depending on the accuracy you need, you'll have to renounce to some of these though.

don't forget useful approximations, be it the perfect fluid approximation or the lubrification approximation or anything else...
Take advantage of potentiel flows, etc

>>5688950
During my second year of classe préparatoire (in France)

>>5688941
also <span class="math"> p(x,t)[/spoiler] is the variation in pressure.

>>5688941
sorry for the end:
<span class="math"> c^2 = \frac{1}{\rho_0 \chi_s}[/spoiler]

The speed of a wave can be derived from the wave-equation, right?

Which, in a unidimensional problem with no losses, is in the form of a d'Alembert equation:
<span class="math"> c^2 \frac{\partial p}{\partial x^2} - \frac{\partial p}{\partial t^2} = 0 [/spoiler], where <span class="math">c[/spoiler] has the dimension of a velocity.

Assuming small changes in pressure, volumic mass, and a small speed (compared to the speed we're looking for), we can write the developement:
<span class="math"> \rho(x,t) = \rho_0 + \mu (x,t), \mu << \rho_0[/spoiler]

Now, we also have: <span class="math">\rho(x,t)= \rho_0 + \frac{\partial \rho}{\partial p} p(x,t) [/spoiler] (it's the differential)
Physicists have hesitated between two interpretations of <span class="math">\frac{\partial \rho}{\partial p}[/spoiler]: is the process adiabatic or is it isothermal? (I think it was Laplace and Newton who didn't agree on that)
Turns out the adiabatic hypothesis describes the phonomenon more accurately.

Finally, when trying to find the wave equation, you have the term c^2 written as <span class="math">c^2 = \frac{1}{\rho_0 \chi_s [/spoiler], with <span class="math">\chi_s[/spoiler] the isentropic compressibility.

basically: sensory memory:

http://en.wikipedia.org/wiki/Sensory_memory

your point being?

>>5658525
care to post fig. 15.10?

somewhat, yes. Why?

>>5657474
oh ok. Well it's still better to know it exists at least!

>>5657464
>>5657464
for example, in the OP:

<span class="math">tan(x)(csc(x)-sin(x))= \frac{2t}{1-t^2}(\frac{1+t^2}{2t}- \frac{2t}{1+t^2})= \frac{(2t)(1+2t^2+t^4-4t^2)}{(1-t^2)(2t)(1+t^2)}[/spoiler]
so <span class="math">tan(x)(csc(x)-sin(x)) = \frac{1-t^2}{1+t^2}=cos(x) [/spoiler]

>>5657464
for example, in the OP:

<span class="math">tan(x)(csc(x)-sin(x))= \frac{2t}{1-t^2}(\frac{1+t^2}{2t}-\frac{2t}{1+t^2})= \frac{(2t)(1+2t^2+t^4-4t^2)}{(1-t^2)(2t)(1+t^2)}[/spoiler]
so <span class="math">tan(x)(csc(x)-sin(x)) = \frac{1-t^2}{1+t^2}=cos(x) [/spoiler]

>>5657448
you can also try other methods in combination with this:
I usually try to differentiate both side, maybe the differentials equality is easier to show.

You can also use: <span class="math">cos(x)=\frac{1-t^2}{1+t^2}, sin(x)=\frac{2t}{1+t^2}[/spoiler], and <span class="math"> tan(x)=\frac{2t}{1-t^2}[/spoiler], where <span class="math">t=tan(\frac{x}{2}) [/spoiler].
Trust me, it's very useful, and even more when you'll have to integrate stuff

>>5655247
and this yields <span class="math">c=2\sqrt{k.m}=2000 N.s/m[/spoiler]

hello
have you ever heard of critical damping?
you can model the fact of going over a bump or pothole by a rectangle function, which you can first assume to be a long enough rectangle (with respect to... something you have to find)

In that case, the minimum time is when you reach critical damping:
http://en.wikipedia.org/wiki/Damping#Critical_damping_.28.CE.B6_.3D_1.29

Why are you guys so afraid of doing the math yourself?
Like taking a piece of paper and a pen and trying to work it out?

>>5649144
that was supposed to say m=floor(r)

>>5649108
like <span class="math"> m=\floor{r} [/spoiler], then choose <span class="math"> n[/spoiler] small enough.

I'm currently testing something

>>5649067
I'm thinking about using either m or n to approximate r roughly, then use the other integer to get a more subtle approximation.