Recent content by Korbid

Well, i have reached to simplify enough the integral. Thank you. $$\int^{\infty}_0\int^{\infty}_0\int^{2\pi}_0 rv\exp\left(-\frac{v^2}{4T}\right)\exp\left(-\frac{E(\tau)}{T}\right)\;\mathrm{d}r\mathrm{d}v\mathrm{d}{\theta}$$ $$E(\tau)=\frac{k}{\tau^2}\exp\left(-\frac{\tau}{\tau_0}\right)$$...

stevendaryl, At first, thanks for answering me quickly. I'm sorry but i don't understand your method. if we do this change then we still have \vec{v2} in the first exponential.

I need to evaluate numerically this integral (second virial coefficient). At first, i want to simplify a bit, how could i do it? Now, i have a 8-dimensional integral and it's very horrible. T, k, tau0 and R are constants. r is the position and v is the velocity for two particles 1,2. r12 =...

I'm sorry, i forgot it. r12 is the relative position and v12 is the relative velocity $$ r_{12}=r_1-r_2$$ it's the same for v12

I'm trying to calculate the second virial coefficient for a potential E that depends on positions and velocities. The N particles are moving inside LxL square. $$\int^L_0\int^L_0\int^{\infty}_0\int^{\infty}_0{e^{-(\vec{v}^2_1+\vec{v}^2_2)}e^{-E(\tau)}}d\vec{r}_1d\vec{r}_2d\vec{v}_1d\vec{v}_2$$...

I'm trying to solve numerically this multiple integral. But i don't know how to calculate it with Mathamtica or Sage software. $$\int{e^{-(\vec{v}^2_1+\vec{v}^2_2)}e^{-E(\tau)}}d\vec{r}_1d\vec{r}_2d\vec{v}_1d\vec{v}_2$$ $$E(\tau)=\frac{k}{\tau^2}e^{-\tau/\tau_0}$$...

BvU, first thanks to answering me. i'm performing the same simulation with Python programming language. The radial distribution function has been determined by calculating the distance between all particle pairs and binning them into a histogram. The histogram is then normalized with respect...

Hi, i'm performing a simulation about this potential http://motion.cs.umn.edu/PowerLaw/ I calculated the radial distribution function succesfully but i don't know how these guys are normalized the other pair distribution function, as a function of time to collision. Could anyone help me? Thanks!

For a bidimensional system of N particles, the hamiltonian of pair-interaction is: H(\vec{q}_1,\vec{q}_2;\vec{p}_1,\vec{p}_2)=K(\vec{p}_1,\vec{p}_2)+U(\vec{q}_1,\vec{q}_2;\vec{p}_1,\vec{p}_2) where K is the kinetic (translational) energy and U is the potential energy i want to solve this...

vanhees71, Yeah, it's correct, I checked too with Matlab! I found it in this text, http://129.81.170.14/~vhm/papers_html/final22.pdf, equation (4.2) Thanks for your help!

Hi guys! I didn't give up! Finally, I found the solution of \rho_s \rho_s=\frac{g}{(2\pi)^3}\int \frac{m}{\omega}e^{-\omega/T}d\vec{k}=\frac{g}{(2\pi)^3}\int \frac{m}{\sqrt{m^2+k^2}}e^{-\frac{\sqrt{m^2+k^2}}{T}}d\vec{k}=\frac{mg}{(2\pi)^3}\int^{\infty}_0...

Well, i think the same thing...Thank you vanhees71!

Is there anyone who can tell me the solution of \rho_s? Please.

Sorry! I was wrong! \omega = \sqrt{m^2 + \vec{k}^2} However, i still can't solve it.

hi! i need to solve this integral: \rho_s=\int (m/\omega)e^{-\omega/T}d{\vec k} where \omega=\sqrt{m^2+{\vec k}} is the dispersion relation, T is the temperature of the system and m the mass of a particle Thank you!