fix equation numbering

module_intros/order.Nematic.ipynb

@@ -31,19 +31,19 @@
     "where $\\mathbf{m}$ is the $\\textit{molecular axis}$ (i.e. the vector tangent to a particle's principal axis) and $\\mathcal{B}$ is the unit hemisphere. 𝐐 is defined by the traceless tensor:\n",
     "\n",
     "$$\n",
-    "\\mathbf{Q} = \\mathbf{M} - \\frac{1}{3} \\mathbf{I} \\quad (3)\n",
+    "\\mathbf{Q} = \\mathbf{M} - \\frac{1}{3} \\mathbf{I} \\quad (2)\n",
     "$$\n",
     "\n",
     "where 𝐈 is the identity matrix. This shift by negative 𝐈 is to ensure that the value of the scalar parameter, defined below, is 0 for random orientations. For uniaxial systems, 𝐐 may also be written in terms of the $\\textit{nematic director}$ ($\\mathbf{n}$), which is the principal direction of alignment in the system. (For a more detailed account of the nematic tensor, and the extension of this to biaxial systems, see Section I of [Mottram and Newton](https://strathprints.strath.ac.uk/50668/1/1409.3542v2.pdf).)\n",
     "\n",
     "$$\n",
-    "\\mathbf{Q} = S (\\mathbf{n} \\otimes \\mathbf{n} - \\frac{1}{3} \\mathbf{I}) \\quad (4)\n",
+    "\\mathbf{Q} = S (\\mathbf{n} \\otimes \\mathbf{n} - \\frac{1}{3} \\mathbf{I}) \\quad (3)\n",
     "$$\n",
     "\n",
     "Here, the scalar order parameter, S, is defined as:\n",
     "\n",
     "$$\n",
-    "S = \\frac{1}{2} \\int_{\\mathcal{B}} (3\\cos^2 \\beta - 1) \\quad (5)\n",
+    "S = \\frac{1}{2} \\int_{\\mathcal{B}} (3\\cos^2 \\beta - 1) \\quad (4)\n",
     "$$\n",
     "\n",
     "where $\\beta$ is the angle between the molecular axis and nematic director. Whilst the nematic director is used to charaterise the direction of orientational order, S characterises its magnitude and varies from 0 to 1 during the isotropic to nematic phase transition. As noted in [Turzi](https://pubs.aip.org/aip/jmp/article/52/5/053517/232507/On-the-Cartesian-definition-of-orientational-order) the eigenvalues of $Q$ are $\\frac{2}{3}S$ which is associated with the eigenvector which is the nematic director $\\mathbf{n}$, and doubly degenerate eigenvalues $-\\frac{1}{3}S$, provided there is no biaxial phase. The values of interest, the nematic director $\\mathbf{n}$ and $S$, can be identified as the eigenvalue whose sign is different from other eigenvalues, or is the maximum eigenvalue, and it's eigenvector.\n",