Hi,
this is not a homework and my problem is much bigger for me to give full details here. I came across this integral
\mathcal{I}(\xi)=\int^{\xi_c}_{\xi}{\rm d}\xi^\prime\exp\left[\sqrt{2}\sigma\,{\rm Erf}^{-1}\left(1-\frac{8\pi}{3}{\xi^\prime}^3\right)\right]
where Erf^{-1} is the...
I have a MSc in astrophysics and I'm a last year PhD student. My project is not going anywhere, I haven't published any paper and I'm far from finishing. My advisor is very picky and won't let me publish anything and I'm terrified the last years have been a huge waste of time.
What do you think...
I have a very complicated stiff system, which can be expressed as:
x^{\prime}(t)=A(x,y)-B(x,y)
y^{\prime}(t)=C(x,y)-D(x,y)
I decided to solve it with the fixed-point iteration method (http://en.wikipedia.org/wiki/Fixed_point_iteration) but I also have to use adaptive time stepping to...
I work with a grid-based code, this means that all of my quantities are defined on a mesh. I need to compute, for every point of the mesh the divergence of the velocity field.
All I have is, for every cell of my mesh, the values of the 3-d velocity in his 26 neighbors.
I call neighbors the...
Homework Statement
I need to solve this differential equation numerically. I hope you can help me, it's not homework!
Homework Equations
This is the equation to be solved
x''=\dfrac{\alpha}{x}-\beta\dfrac{(x'-\gamma x)^2}{x}-\delta x - \dfrac{\varepsilon}{x^2}
The Attempt at a...
My question is not homework. I feel ashamed of having this doubts but I'm really stuck on this.
The problem is I have a reference frame xyz and here I define the COM \vec x{_{cm}} of the system.
Now I move the COM reference frame x'y'z':
\vec{x'}=\vec{x}-\vec x{_{cm}}
In this reference frame I...
I know this is rather trivial question but it's not homework!
I need this as part of a bigger project.
What I have to do is rotate my reference frame to another one. I want my new z-axis to be a vector Z=(Z1,Z2,Z3)
Following the notation of this wikipage...
We all know that for the gravitational field we can write the Poisson Equation:
\nabla^2\phi=-4\pi G\rho
But I was wondering if, mathematically, we can write the same equation for a scalar field which scale as r^{-2}.
Here is the thing. When you deal with gravity, the Poisson equation is...
I have a set of N data points defined over a periodic interval, 0\le x \le 1.
I made a discrete fast fourier transform of these data points and I get a discretized function in the Fuorier space. My question is what are the coordinate of these data points in the Fourier space?
I mean, in the real...
This might be a very stupid question but I can't come up with an answer, I hope you might help. So, I have two vector in a 3D space \vec x and \vec x^\prime. I know that a certain quantity \vec a is defined along the radial direction between the first vector with respect to the second. What are...
Homework Statement
I have to compute the average of A in all directions for a sphere of radius R.
For the direction r, A is defined as:
A=\int_0^R n(r)dr
where n(r) is the density profile of the sphere.
The answer should be
\langle A\rangle=\frac{4}{3}\left\langle n \right\rangle R
2. The...
I have a 3d data cube. For every point I measure the property A which is a gaussian variable of mean m and variance s and it's also a function of the density d at every point.
A(x,y,z)=f(d(x,y,z))e^(-(X-m)^2/(2\sigma^2))
X is a random number.
Now let's say I want to sample the...
Homework Statement
I need to infer the observed star formation efficiency of the Kennicutt Schimdt law starting from a volumetric SF law.
The KS law is a relationship between gas and stellar surface density that we can approximate as:
\frac{d\Sigma_*}{dt}=A\Sigma_{gas}^{1.5}
Where A...
Hi, this might be a stupid question, but I was wondering how to computer the gradient of a quantity on a grid. I mean I have a grid made of cells (not necessarily of the same size) where the variable \rho is defined at the center of every cell. How can I compute the gradient of this quantity?
It...
Hi,
I have a catalog of dark matter halos, which consists of their COM positions and their masses.
I need to determine the halo mass function. How can I do? I mean, it is easy to plot the number of halos between mass M and M+dM, but how can I have information on the volume? I don't get it...
Hi, I have a little problem, I'm using a code to run cosmological simulation and I have to recover the physical unities of every quantities. The problem is that there isn't a proper guide for this program. I try to explain.
All I have for every output/redshift is:
aexp
unit_l
unit_t
The...
Hi everyone,
I've derived a formula which computes a certain quantity. This is the equation:
f(x,t)=a(x,t)-\frac{1}{n}b(x)f(x,t)^{(1-n)/n}\frac{\partial f(x,t)}{\partial t}
I need to prove that f(x,t)\sim a(x,t).
All I have is that 0.5 < n < 2 , b(x) is a decreasing function of x...
Hi there,
I'm really ashamed of doing this stupid question but I really need help with this thing. And, even if it's simple, it's not homework.
I have a point P=(x,y,z) with velocity v=(vx,vy,vz)
how can I determine the radial component of the velocity?
My answer is that...
I need help with this PDE, it's not an homework, I need to solve it for my thesis and it has physical application...anyway the problem is:
\frac{dx}{dt}=f(t)g(r)+\frac{v}{r}\frac{d (Rx)}{dR}
f(t) and g(r) are known.
I can solve the equation with only the first or the second term ...
If I have this equation:
\int_0^{+\infty}{\frac{e^{-x}}{\int_{\Delta T}f(x,t)}f(x,t)xdx}=Ag(t)
I am interested to show that f(x,t) must be g(t). This condition must be necessary and sufficient. Is this possible to prove?
Can you help me solve this inequality for x?
\frac{1+(\gamma+x(r-\alpha)-1)t}{1+\frac{\gamma+x(r-\alpha)-1}{2}}>0
where \gamma>1, 0<t<1, 0<r<3\alpha, \alpha>0
I really don't know where to start ...
If I have
\int_0^{+\infty}h(x)g(x)dx=0
where h(x)>0 in [0,+\infty]. Can I conclude that g(x) might be zero or an odd function in such interval?
If the condition above is still valid and I add this request:
g(x)=(f(x)-q)
where f(x) is positive function in the interval. Can I say that...
Hi everyone,
here is this integral I can't find solution:
\int_0^\infty \frac{x e^{-x}}{A+Bx} dx
A and B are constants.
I'm going crazy, I don't think there is even an analytical solution.
Hi,
I noticed such a strange behavior in my code every time I add a threshold: little oscillation around the threshold value itself.
For example
f(x) = g(x), x > x_c
f(x) = 0, x <= x_c
\frac{dx}{dt}=f(x)
I solve the last equation and I find this oscillation. Can they be removed?
Hi everyone,
I've a little problem with my algorithm.
I have two grids: one for time and the other one for the radius.
I need to evaluate this equation:
\frac{d\beta(r,t)}{dt}=A\beta(r,t)^N
I try solving this with a simple Runge Kutta II method, but I'm not convinced at all that this works...