task2 cleanup - final adjustments

nbody/presentation/main.typ

@@ -26,15 +26,6 @@
 // Finally - The real content
 = N-body forces and analytical solutions
 
-// == Objective
-// Implement naive N-body force computation and get an intuition of the challenges:
-// - accuracy
-// - computation time
-// - stability
-
-// $==>$ still useful to compute basic quantities of the system, but too limited for large systems or the dynamical evolution of the system
-
-
 == Overview - the system
 Get a feel for the particles and their distribution
 #columns(2)[
@@ -49,14 +40,6 @@ Get a feel for the particles and their distribution
   #footnote[Unit handling [#link(<task1:function_apply_units>)[code]]]
 ]
 
-// It is a small globular cluster with
-// - 5*10^4 stars => m in terms of msol
-// - radius - 10 pc
-// Densities are now expressed in M_sol / pc^3
-// Forces are now expressed 
-
-
-
 == Density
 Compare the computed density
 #footnote[Density sampling [#link(<task1:function_density_distribution>)[code]]]
@@ -79,8 +62,6 @@ with the analytical model provided by the _Hernquist_ model:
   ]
 )
 
-// Note that by construction, the first shell contains no particles
-// => the numerical density is zero there
 // Having more bins means to have shells that are nearly empty
 // => the error is large, NBINS = 30 is a good compromise
 
@@ -107,9 +88,6 @@ with the analytical model provided by the _Hernquist_ model:
   ]
 )
 
-// basic $N^2$ matches analytical solution without dropoff. but: noisy data from "bad" samples
-// $N^2$ with softening matches analytical solution but has a dropoff. No noisy data.
-// => softening $\approx 1 \varepsilon$ is a sweet spot since the dropoff is "late"
 
 
 == Relaxation
@@ -135,21 +113,6 @@ We find a relaxation of $approx 30 "Myr"$ ([#link(<task1:compute_relaxation_time
   ]
 )
 
-// The estimate for $n_{relax}$ comes from the contribution of each star-star encounter to the velocity dispersion. This depends on the perpendicular force
-
-// $\implies$ a bigger softening length leads to a smaller $\delta v$.
-
-// Using $n_{relax} = \frac{v^2}{\delta v^2}$, and knowing that the value of $v^2$ is derived from the Virial theorem (i.e. unaffected by the softening length), we can see that $n_{relax}$ should increase with $\varepsilon$.
-
-// === Effect
-// - The relaxation time **increases** with increasing softening length
-// - From the integration over all impact parameters $b$ even $b_{min}$ is chosen to be larger than $\varepsilon$ $\implies$ expect only a small effect on the relaxation time
-
-// **In other words:**
-// The softening dampens the change of velocity => time to relax is longer
-
-
-
 
 = Particle Mesh
 
@@ -191,20 +154,10 @@ We find a relaxation of $approx 30 "Myr"$ ([#link(<task1:compute_relaxation_time
   ]
 )
 
-// Some other comments:
-// - see the artifacts because of the even grid numbers (hence the switch to 75)
-// overdiscretization for large grids -> vertical spread even though r is constant
-// this becomes even more apparent when looking at the data without noise - the artifacts remain
-// 
-// We can not rely on the interparticle distance computation for a disk!
-// Given softening length 0.037 does not match the mean interparticle distance 0.0262396757880128
-// 
-// Discussion of the discrepancies
-// TODO
 
 
 #helpers.image_cell(t2, "plot_force_computation_time")
-// Computed for 10^4 particles => mesh will scale better for larger systems
+
 
 == Time integration
 *Integration step*
@@ -213,11 +166,9 @@ We find a relaxation of $approx 30 "Myr"$ ([#link(<task1:compute_relaxation_time
 *Timesteps*
 Chosen such that displacement is small (compared to the inter-particle distance) [#link(<task2:integration_timestep>)[code]]:
 $
-  op(d)t = 10^(-4) dot S / v_"part"
+  op(d)t = 10^(-3) dot S / v_"part"
 $
 
-// too large timesteps lead to instable systems <=> integration not accurate enough
-
 *Full integration*
 
 [#link(<task2:function_time_integration>)[code]]
@@ -244,7 +195,11 @@ $
 == Particle mesh solver
 #helpers.image_cell(t2, "plot_pm_solver_integration")
 
-#helpers.image_cell(t2, "plot_pm_solver_stability")
+#page(
+  columns: 2
+)[
+  #helpers.image_cell(t2, "plot_pm_solver_stability")
+]
 
 
 = Appendix - Code <appendix>

nbody/utils/forces_basic.py

@@ -40,7 +40,7 @@ def n_body_forces(particles: np.ndarray, G: float = 1, softening: float = 0):
         r_adjusted[i] = 1
         num[i] = 0
 
-        f = - np.sum((num.T / r_adjusted**1.5).T, axis=0) * m_current
+        f = np.sum((num.T / r_adjusted**1.5).T, axis=0) * m_current
         forces[i] = f
 
         if i!= 0 and i % 5000 == 0:

nbody/utils/forces_cache.py

@@ -40,10 +40,9 @@ def kwargs_to_str(kwargs: dict):
     """
     base_str = ""
     for k, v in kwargs.items():
-        print(type(v))
         if type(v) == float:
             base_str += f"{k}_{v:.3f}"
-        elif type(v) == callable:
+        elif callable(v):
             base_str += f"{k}_{v.__name__}"
         else:
             base_str += f"{k}_{v}"