[ 3 / biz / cgl / ck / diy / fa / ic / jp / lit / sci / vr / vt ] [ index / top / reports ] [ become a patron ] [ status ]
2023-11: Warosu is now out of extended maintenance.

/sci/ - Science & Math

View post   
File: 119 KB, 579x552, sphere3.png [View same] [iqdb] [saucenao] [google]
9761415 No.9761415 [Reply] [Original]

Hello /sci/, I want to calculate how many interactions occur per second in my system.
Imagine a spherical space (red) filled with a fixed number of spherical objects (not in the graphic because they are too small).
The objects have a mean velocity and a density distribution.
Let's just assume the density goes with 1/r.

Now I want to know how many objects interact (in this context it just means enter) with a cone like space (green) per second.

>> No.9761422

>Statistics/Physics
not science or math

>> No.9761424

>>9761415
Probably really hard to do.
I think the only way is to run a simulation.

>> No.9761427

>>9761424
oh wait is the red thing supposed to be a perfect sphere?

>> No.9761429

>>9761427
Yeah

>> No.9761438

>>9761429
can you explain what you mean with "the density goes with 1/r"?

>> No.9761446

>>9761438
r is the distance from the middle point of the sphere. So the farther you move away from it the less dense it gets. So it'd be something like n(r)=n_0*1/r

>> No.9761448

>>9761446
That seems to imply there's some cohesive force keeping the particles like that, unless we're talking about initial conditions

What kind of interaction are you thinking about?

>> No.9761453

>>9761446
Wouldn't that make the density in the middle infinite?

>> No.9761456

>>9761415
First guess would be continuity equation, but your problem isnt continuous.
Maybe model it as a van der waals gas?

>> No.9761474

>>9761448
It's supposed to be in space and the force is gravity. Imagine that there's a heavy planet in the middle. This also solves this >>9761453
problem because it gives inner boundaries.

>> No.9761545

>>9761415
Do moving particles stay at the same radius? Otherwise how would the density distribution remain constant? What about particle size?

>> No.9761616

>>9761545
Yeah they stay at the same radius. Let's just consider the particles as points.

>> No.9761682

>>9761415
are you looking for the net flux in to and out of the cone? or just one way? also how are the particle velocities distributed (you only gave a mean). Is it a thermal distribution?

>> No.9761707

>>9761415
lets start with the simplification that the density is constant in the sphere.

in fact, lets just assume that we have a flat surface with area A and we want to know the particle flux in one direction across this surface

for a given constant particle density D of particles all moving at S meters per second, in one second half of those particles particles will move in a direction that brings them across the barrier, so the answer is

(D*S*A)/2 particles per second

for your cone shape, D is a function of r where D(r) = 1/r, so the flux at any point is F = (S*A)/(2*r)

all you need to do now is integrate F over the surface of the cone.

Assuming thermal distributions, etc, the approach is the same except you have to do some more integrations

>> No.9761787

>>9761707
well I guess technically it's

F = (S*dA)/(2*r)

but whatever

>> No.9761850
File: 18 KB, 480x377, hawking_pepe.jpg [View same] [iqdb] [saucenao] [google]
9761850

>>9761707
Thanks Anon. Your approach looks similar to mine. One thing I've had problems with is coming up with a solution for the units since (D*S*A)/2 is particles per second and I wanted to integrate it over the whole sphere which would make no sense unit wise.

Identifying the flux and integrating over the surface of the cone seems like a much more elegant approach.

>> No.9761980

Can someone PLEASE help me with basic stats?

Mean = 400
std = 50

What is the Probability that you get a value between 300-500?

My answer = 0,9544.

Is my answer correct?

>> No.9761982

>>9761980
Assuming it's a normal distribution, that's about right, yeah.

>> No.9761988

>>9761982
Yes, it's normal dis. Thank you very much anon. I got my exam back, and I was only short of 1,5 points from passing the exam. I'm trying to analyze my exam to see what I did wrong.

>> No.9762203

>>9761850
your welcome. ofc this involves a number of assumptions... I'm curious what the application of this model is supposed to be?

>> No.9762238

>>9761415
think of spreading your fucking balls evenly on your big ball, so that there is equal space between each ball. pretty much amount of small balls/volume of big ball.
Now calculate the volume of you cone and multiply with ratio of small balls per area of big ball. No matter how much time passes or how fast the balls are moving, on average the same amount of balls is going to be situated at that spot per unit time.
if you had asked "how many balls pass the cone boundary per second" then you could do more.

>> No.9762246

>>9762238
but he asked how many balls enter the cone per second, i.e. the inward flux across the boundary.

>> No.9762253

>>9762246
>Now I want to know how many objects interact (in this context it just means enter) with a cone like space (green) per second.
quote OP

>> No.9762257

>>9762253
> (in this context it just means enter)

your point?

>> No.9762259

>>9762257
my answer is still fucking valid tho

>> No.9762262

>>9762259
I mean I guess OP could have been more clear, and that the question can be interpreted as either NET flux, as you assume, or just flux in one direction across the boundary, which is what I'm assuming. Either way, you sound like a jackass

>> No.9762266
File: 360 KB, 1920x1280, bh_jet.jpg [View same] [iqdb] [saucenao] [google]
9762266

>>9762203
I want to calculate the interaction rate of gas clouds that move around a massive black hole with the black holes jet.

About the flux thing F = (S*A)/(2*r), the unit in this case would be m/s*m^2*1/m = m^2*1/s. Does this make sense or am I missing something?

>>9762238
>how many balls pass the cone boundary per second
This is what I want to calculate. Sorry for being unclear.

>> No.9762287

>>9762266
I understand your confusion but remember that while the function D(r) = 1/r, the unit of D is still N/m^3 (assuming N = number of particles)

so the unit of F is still D(r)*S*dA = (N/m^3)*(m/s)*(m^2) = N/s, i.e. particles per second.

When you integrate F you are integrating over dA, so the unit of the integral will remain N/s

>> No.9762290

>>9762266
>calculate the interaction rate of gas clouds that move around a massive black hole with the black holes jet

I'm not an astrophysics guy, but I'm doubtful that the clouds around a black hole act like an ideal gas... I'd expect a fair amount of anisotropy

>> No.9762477

>>9762290
It's not supposed to be a finished model.