updated some explanations

* started using jupyter Latex outputs

notebooks/single-voxel/voxel.ipynb

@@ -35,7 +35,8 @@
    "outputs": [],
    "source": [
     "from kosmatau3d import models\n",
-    "import numpy as np"
+    "import numpy as np\n",
+    "from IPython.display import display, Latex"
    ]
   },
   {
@@ -343,6 +344,22 @@
     "vox.get_model_mass() #mass of the clumps that have been modelled in M_sol. This is the mass of the voxel represented in clumps, which may differ from the input due to discretisation."
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Likewise for the ensemble-averaged density:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "vox.get_density()"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -524,7 +541,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "i_trans"
+    "#i_trans"
    ]
   },
   {
@@ -894,6 +911,15 @@
     "We must first ensure the voxel properties are correctly modelled."
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "models.masspoints.clump_log_density"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -2181,7 +2207,7 @@
     "              'ensemble_dispersion' : [2],\n",
     "              # 'volumeFactor' : [1.],\n",
     "              'ensemble_mass' : [1e3],\n",
-    "              'ensemble_density' : [1e6],\n",
+    "              'ensemble_density' : [10**6],\n",
     "              'fuv' : 1e4,\n",
     "              }\n",
     "\n",
@@ -2200,6 +2226,37 @@
    "source": [
     "Indeed the same intensity results are present in these two models. Since we do not change the model clumps, the voxel density, or FUV field, this should be expected by comparing the results of `ensemble.printEnsembleParameters()`. The volume-filling factor, however, changes by a factor of $10$, since we did not scale the mass with $\\Delta s^3$."
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "display(Latex(\"The surface densities $\\mathrm{log_{10}}(n_\\mathrm{s, cl})$ are \"\n",
+    "              + f\"${', '.join([f'{n:.3f}' for n in models.masspoints.clump_log_density[0][0]])}$ in the clumpy ensemble \"\n",
+    "              + f\"for clumps with masses ${', '.join([f'{10**m:.0f}' for m in models.constants.clump_log_mass[0][0]])}\\, M_\\odot$\"))\n",
+    "display(Latex(\"This is results in a clump-averaged density of $\\mathrm{log_{10}}(n_\\mathrm{ens})\\! =\\! \"\n",
+    "              + f\"{np.log10(vox.get_density()[0]):.1f}$.\"))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "display(Latex(\"The number of clumps, $N_\\mathrm{cl}$, in the ensemble are \"\n",
+    "              f\"${', '.join([f'{n:.0f}' for n in models.ensemble.clumpNj[0][0]])}$ \"\n",
+    "              f\"for clumps with masses ${', '.join([f'{10**m:.0f}' for m in models.constants.clump_log_mass[0][0]])}\\, M_\\odot$\"))"
+   ]
   }
  ],
  "metadata": {