more annotations

diffusion-equation.html

@@ -46,14 +46,15 @@
           </mfrac>
         </mrow>
         <mo>=</mo>
-        <mi mathvariant="normal">&#x2207;<!-- ∇ --></mi>
+        <mi mathvariant="normal" data-dref="nabla">&#x2207;<!-- ∇ --></mi>
         <mo>&#x22C5;<!-- ⋅ --></mo>
         <mrow class="MJX-TeXAtom-ORD">
           <mrow class="MJX-TeXAtom-ORD">
             <mo maxsize="1.2em" minsize="1.2em">[</mo>
           </mrow>
         </mrow>
-        <mi>D</mi>
+	<mrow data-dref="Dphir">
+          <mi data-dref="D">D</mi>
           <mo stretchy="false">(</mo>
           <mi>&#x03D5;<!-- ϕ --></mi>
           <mo>,</mo>
@@ -61,8 +62,9 @@
             <mi mathvariant="bold">r</mi>
           </mrow>
           <mo stretchy="false">)</mo>
+	</mrow>
         <mtext>&#xA0;</mtext>
-        <mi mathvariant="normal">&#x2207;<!-- ∇ --></mi>
+        <mi mathvariant="normal" data-dref="nabla">&#x2207;<!-- ∇ --></mi>
 	      <mrow data-dref="phirt">
 		<mi data-dref="phi">&#x03D5;<!-- ϕ --></mi>
 		<mo stretchy="false">(</mo>
@@ -92,8 +94,11 @@
 <p>where <span data-decl="phi"><i>ϕ</i>(<b>r</b>, <i>t</i>) is the <a href="/wiki/Density"
 title="Density">density</a> of the diffusing material <span  data-decl="r"> at location <b>r</b></span>
 and <span  data-decl="t"> time <i>t</i></span></span> and
-<span data-decl="Dphir"><i>D</i>(<i>ϕ</i>, <b>r</b>) is the collective <a href="/wiki/Diffusion_coefficient" class="mw-redirect" title="Diffusion coefficient">diffusion coefficient</a> for density <i>ϕ</i> at location <b>r</b></span>; and ∇ represents the vector <a href="/wiki/Differential_operator" title="Differential operator">differential operator</a> <a href="/wiki/Del" title="Del">del</a>. If the diffusion coefficient depends on the density then the equation is nonlinear, otherwise it is linear.</p>
-<p>More generally, when <i>D</i> is a symmetric <a href="/wiki/Positive_definite_matrix" class="mw-redirect" title="Positive definite matrix">positive definite matrix</a>, the equation describes <a href="/wiki/Anisotropy" title="Anisotropy">anisotropic</a> diffusion, which is written (for three dimensional diffusion) as:</p>
+<span data-decl="Dphir"><i>D</i>(<i>ϕ</i>, <b>r</b>) is the collective <a
+href="/wiki/Diffusion_coefficient" class="mw-redirect" title="Diffusion
+coefficient">diffusion coefficient</a> for density <i>ϕ</i> at location <b>r</b></span>;
+and <span data-decl="nabla">∇ represents the vector <a href="/wiki/Differential_operator" title="Differential operator">differential operator</a> <a href="/wiki/Del" title="Del">del</a></span>. If the diffusion coefficient depends on the density then the equation is nonlinear, otherwise it is linear.</p>
+<p>More generally, when <span data-decl="D"><i>D</i> is a symmetric <a href="/wiki/Positive_definite_matrix" class="mw-redirect" title="Positive definite matrix">positive definite matrix</a></span>, the equation describes <a href="/wiki/Anisotropy" title="Anisotropy">anisotropic</a> diffusion, which is written (for three dimensional diffusion) as:</p>
 <dl>
 <dd>
 <table cellpadding="5" style="border:2px solid #50C878;background: #ECFCF4; text-align: center;">
@@ -108,15 +113,17 @@ and <span  data-decl="t"> time <i>t</i></span></span> and
           <mfrac>
             <mrow>
               <mi mathvariant="normal">&#x2202;<!-- ∂ --></mi>
-              <mi>&#x03D5;<!-- ϕ --></mi>
+	      <mrow data-dref="phirt">
+		<mi data-dref="phi">&#x03D5;<!-- ϕ --></mi>
 		<mo stretchy="false">(</mo>
 		<mrow class="MJX-TeXAtom-ORD">
-                <mi mathvariant="bold">r</mi>
+                  <mi mathvariant="bold" data-dref="r">r</mi>
 		</mrow>
 		<mo>,</mo>
-              <mi>t</mi>
+		<mi data-dref="t">t</mi>
 		<mo stretchy="false">)</mo>
               </mrow>
+	    </mrow>
             <mrow>
 	      <mi mathvariant="normal">&#x2202;<!-- ∂ --></mi>
 	      <mi>t</mi>
@@ -163,7 +170,7 @@ and <span  data-decl="t"> time <i>t</i></span></span> and
         <mrow>
           <mo>[</mo>
           <mrow>
-            <msub>
+            <msub data-dref="D">
               <mi>D</mi>
               <mrow class="MJX-TeXAtom-ORD">
                 <mi>i</mi>
@@ -181,14 +188,16 @@ and <span  data-decl="t"> time <i>t</i></span></span> and
               <mfrac>
                 <mrow>
                   <mi mathvariant="normal">&#x2202;<!-- ∂ --></mi>
-                  <mi>&#x03D5;<!-- ϕ --></mi>
+	      <mrow data-dref="phirt">
+		<mi data-dref="phi">&#x03D5;<!-- ϕ --></mi>
 		<mo stretchy="false">(</mo>
 		<mrow class="MJX-TeXAtom-ORD">
-                    <mi mathvariant="bold">r</mi>
+                  <mi mathvariant="bold" data-dref="r">r</mi>
 		</mrow>
 		<mo>,</mo>
-                  <mi>t</mi>
+		<mi data-dref="t">t</mi>
 		<mo stretchy="false">)</mo>
+              </mrow>
                 </mrow>
                 <mrow>
                   <mi mathvariant="normal">&#x2202;<!-- ∂ --></mi>