Changes between Version 31 and Version 32 of GravoTurbulence

Timestamp:

12/12/11 13:46:31 (13 years ago)

Author:

Jonathan

Comment:

—

GravoTurbulence

@@ -20 +20 @@
 ||  Energy of a uniform 'sphere'  ||  [[latex($GM^2(\log(r/C)-1/4)$)]] ||  [[latex($-\frac{3 G M^2}{5 r}$)]]  ||
 
-Obviously to determine whether systems are 'bound' one needs a way to calculate the self-gravitational energy.  This requires determining an appropriate constant [[latex($C$)]]  
+Obviously to determine whether systems are 'bound' one needs a way to calculate the self-gravitational energy.  This requires determining an appropriate constant [[latex($C$)]].  Unfortunately the log potential does not go to some asymptotic value at infinity, so every system is 'bound'.  However, an arbitrary distance can be chosen that will mark an unbound system..  Currently we use [[latex($C=r_{square} e^{-1/2} \approx .6 r_{square}$)]] so that the potential goes to 1 at [[latex($r=r_{square}$)]] where [[latex($\pi r_{square}^2 = L_x \times L_y$)]].  '''Perhaps a better choice would be to set [[latex($C=r_{square}$)]] so that the potential goes to zero at [[latex($r=r_{square}$)]].'''  This is then roughly consistent with periodic boundary conditions for the gas potential where the freedom in additive constant is chosen to be zero.  This then sets the Energy of a uniform 'sphere' to be [[latex($GM^2(\log(r/r_{square}) + 1/4)$)]] '''with the above modification this would be [[latex($GM^2(\log(r/r_{square}) - 1/4)$)]] and would give a potential of [[latex($-\frac{GM^2}{4}$)]] for a sphere of radius [[latex($r_{square}$)]]'''
+
+Note the choice of the constant does not effect the force - but does effect the sink particle checks - and the calculation of the particle potential.
+
+
 
 == Density Perturbations ==
@@ -466 +470 @@
 ||  [[Image(2D_ss_rho0015.png, width=400)]]  ||
 ||  [attachment:2D_ss_rho.gif movie]  ||
+||  [[Image(2D_ss_energies.png, width=400)]]  ||
+||  [[Image(2D_ss_energy.png, width=400)]]  ||
+