- MaRDI portal

General

Display information for equation id:math.292.11 on revision:292

* Page found: Model for Electric Potential for Gate Electrodes in a Quantum Bus (eq math.292.11)

Occurrences on the following pages:

Model for Electric Potential for Gate Electrodes in a Quantum Bus Eq: math.292.11

Hash: 8be6d11d84661752d8db2b0ee94a927a

TeX (original user input):

\boldsymbol{n} \cdot \nabla \Phi(\boldsymbol{r},t)|_{\Gamma_N} = 0

TeX (checked):

{\boldsymbol {n}}\cdot \nabla \Phi ({\boldsymbol {r}},t)|_{\Gamma _{N}}=0

LaTeXML (experimental; uses MathML) rendering

MathML (4.039 KB / 912 B) :

{\displaystyle{\displaystyle\boldsymbol{n}\cdot\nabla\Phi(\boldsymbol{r},t)|_{% \Gamma_{N}}=0}}

<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\boldsymbol{n}\cdot\nabla\Phi(\boldsymbol{r},t)|_{%&#10;\Gamma_{N}}=0}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">
      <msub id="p1.1.m1.1.14.1.2" xref="p1.1.m1.1.14.1.1.cmml">
        <mrow id="p1.1.m1.1.14.1.2.3" xref="p1.1.m1.1.14.1.1.cmml">
          <mrow id="p1.1.m1.1.14.1.2.2" xref="p1.1.m1.1.14.1.2.2.cmml">
            <mrow id="p1.1.m1.1.14.1.2.2.2" xref="p1.1.m1.1.14.1.2.2.2.cmml">
              <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">𝒏</mi>
              <mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">⋅</mo>
              <mrow id="p1.1.m1.1.14.1.2.2.2.1" xref="p1.1.m1.1.14.1.2.2.2.1.cmml">
                <mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">∇</mo>
                <mo id="p1.1.m1.1.14.1.2.2.2.1a" xref="p1.1.m1.1.14.1.2.2.2.1.cmml">⁡</mo>
                <mi mathvariant="normal" id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">Φ</mi>
              </mrow>
            </mrow>
            <mo id="p1.1.m1.1.14.1.2.2.1" xref="p1.1.m1.1.14.1.2.2.1.cmml">⁢</mo>
            <mrow id="p1.1.m1.1.14.1.2.2.3" xref="p1.1.m1.1.14.1.2.2.3.1.cmml">
              <mo stretchy="false" id="p1.1.m1.1.5" xref="p1.1.m1.1.14.1.2.2.3.1.cmml">(</mo>
              <mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">𝒓</mi>
              <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.14.1.2.2.3.1.cmml">,</mo>
              <mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">t</mi>
              <mo stretchy="false" id="p1.1.m1.1.9" xref="p1.1.m1.1.14.1.2.2.3.1.cmml">)</mo>
            </mrow>
          </mrow>
          <mo fence="true" stretchy="false" id="p1.1.m1.1.10" xref="p1.1.m1.1.14.1.1.1.cmml">|</mo>
        </mrow>
        <msub id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">
          <mi mathvariant="normal" id="p1.1.m1.1.11.1.1" xref="p1.1.m1.1.11.1.1.cmml">Γ</mi>
          <mi id="p1.1.m1.1.11.1.2.1" xref="p1.1.m1.1.11.1.2.1.cmml">N</mi>
        </msub>
      </msub>
      <mo id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">=</mo>
      <mn id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">0</mn>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">
        <eq id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12"/>
        <apply id="p1.1.m1.1.14.1.1.cmml" xref="p1.1.m1.1.14.1.2">
          <csymbol cd="latexml" id="p1.1.m1.1.14.1.1.1.cmml" xref="p1.1.m1.1.10">evaluated-at</csymbol>
          <apply id="p1.1.m1.1.14.1.2.2.cmml" xref="p1.1.m1.1.14.1.2.2">
            <times id="p1.1.m1.1.14.1.2.2.1.cmml" xref="p1.1.m1.1.14.1.2.2.1"/>
            <apply id="p1.1.m1.1.14.1.2.2.2.cmml" xref="p1.1.m1.1.14.1.2.2.2">
              <ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">⋅</ci>
              <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝒏</ci>
              <apply id="p1.1.m1.1.14.1.2.2.2.1.cmml" xref="p1.1.m1.1.14.1.2.2.2.1">
                <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">∇</ci>
                <ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">Φ</ci>
              </apply>
            </apply>
            <interval closure="open" id="p1.1.m1.1.14.1.2.2.3.1.cmml" xref="p1.1.m1.1.14.1.2.2.3">
              <ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">𝒓</ci>
              <ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">𝑡</ci>
            </interval>
          </apply>
          <apply id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">
            <csymbol cd="ambiguous" id="p1.1.m1.1.11.1.3.cmml" xref="p1.1.m1.1.11.1">subscript</csymbol>
            <ci id="p1.1.m1.1.11.1.1.cmml" xref="p1.1.m1.1.11.1.1">Γ</ci>
            <ci id="p1.1.m1.1.11.1.2.1.cmml" xref="p1.1.m1.1.11.1.2.1">𝑁</ci>
          </apply>
        </apply>
        <cn type="integer" id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">0</cn>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle\boldsymbol{n}\cdot\nabla\Phi(\boldsymbol{r},t)|_{%
\Gamma_{N}}=0}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :

SVG (MathML can be enabled via browser plugin) rendering

MathML (1.325 KB / 465 B) :

{\boldsymbol {n}}\cdot \nabla \Phi ({\boldsymbol {r}},t)|_{\Gamma _{N}}=0

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\boldsymbol {n}}\cdot \nabla \Phi ({\boldsymbol {r}},t)|_{\Gamma _{N}}=0}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mrow class="MJX-TeXAtom-ORD">
          <mi mathvariant="bold-italic">n</mi>
        </mrow>
        <mo>&#x22C5;<!-- ⋅ --></mo>
        <mi mathvariant="normal">&#x2207;<!-- ∇ --></mi>
        <mi mathvariant="normal">&#x03A6;<!-- Φ --></mi>
        <mo stretchy="false">(</mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mi mathvariant="bold-italic">r</mi>
        </mrow>
        <mo>,</mo>
        <mi>t</mi>
        <mo stretchy="false">)</mo>
        <msub>
          <mrow class="MJX-TeXAtom-ORD">
            <mo stretchy="false">|</mo>
          </mrow>
          <mrow class="MJX-TeXAtom-ORD">
            <msub>
              <mi mathvariant="normal">&#x0393;<!-- Γ --></mi>
              <mrow class="MJX-TeXAtom-ORD">
                <mi>N</mi>
              </mrow>
            </msub>
          </mrow>
        </msub>
        <mo>=</mo>
        <mn>0</mn>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {n}}\cdot \nabla \Phi ({\boldsymbol {r}},t)|_{\Gamma _{N}}=0}</annotation>
  </semantics>
</math>

SVG (6.628 KB / 2.938 KB) :

MathML (experimental; no images) rendering

MathML (662 B / 277 B) :

n \cdot \nabla Φ (r, t) |_{Γ_{N}} = 0

<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">n</mi></mrow><mo>&#x22C5;</mo><mi mathvariant="normal">&#x2207;</mi><mi mathvariant="normal">&#x03A6;</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">r</mi></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><msub><mo>|</mo><mrow data-mjx-texclass="ORD"><msub><mi mathvariant="normal">&#x0393;</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub></mrow></msub><mo>=</mo><mn>0</mn></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

${\boldsymbol {n}}$

$\Phi$

${\boldsymbol {r}}$

$t$

$\Gamma _{N}$

MathML observations

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results