- MaRDI portal

General

Display information for equation id:math.292.1 on revision:292

* Page found: Model for Electric Potential for Gate Electrodes in a Quantum Bus (eq math.292.1)

Occurrences on the following pages:

Model for Electric Potential for Gate Electrodes in a Quantum Bus Eq: math.292.1

Hash: 24ccaf9fbd995aad7f8b73a8d12e7196

TeX (original user input):

-\nabla \cdot ( \varepsilon(\boldsymbol{r}) \nabla \Phi(\boldsymbol{r},t)) = 0

TeX (checked):

-\nabla \cdot (\varepsilon ({\boldsymbol {r}})\nabla \Phi ({\boldsymbol {r}},t))=0

LaTeXML (experimental; uses MathML) rendering

MathML (4.337 KB / 865 B) :

{\displaystyle{\displaystyle-\nabla\cdot(\varepsilon(\boldsymbol{r})\nabla\Phi% (\boldsymbol{r},t))=0}}

<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle-\nabla\cdot(\varepsilon(\boldsymbol{r})\nabla\Phi%&#10;(\boldsymbol{r},t))=0}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">
      <mrow id="p1.1.m1.1.19.1" xref="p1.1.m1.1.19.1.cmml">
        <mo id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">-</mo>
        <mrow id="p1.1.m1.1.19.1.1" xref="p1.1.m1.1.19.1.1.cmml">
          <mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">∇</mo>
          <mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">⋅</mo>
          <mrow id="p1.1.m1.1.19.1.1.1" xref="p1.1.m1.1.19.1.1.1.2.cmml">
            <mo stretchy="false" id="p1.1.m1.1.4" xref="p1.1.m1.1.19.1.1.1.2.cmml">(</mo>
            <mrow id="p1.1.m1.1.19.1.1.1.2" xref="p1.1.m1.1.19.1.1.1.2.cmml">
              <mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">ε</mi>
              <mo id="p1.1.m1.1.19.1.1.1.2.1" xref="p1.1.m1.1.19.1.1.1.2.1.cmml">⁢</mo>
              <mrow id="p1.1.m1.1.19.1.1.1.2.2" xref="p1.1.m1.1.19.1.1.1.2.cmml">
                <mo stretchy="false" id="p1.1.m1.1.6" xref="p1.1.m1.1.19.1.1.1.2.cmml">(</mo>
                <mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">𝒓</mi>
                <mo stretchy="false" id="p1.1.m1.1.8" xref="p1.1.m1.1.19.1.1.1.2.cmml">)</mo>
              </mrow>
              <mo id="p1.1.m1.1.19.1.1.1.2.1a" xref="p1.1.m1.1.19.1.1.1.2.1.cmml">⁢</mo>
              <mrow id="p1.1.m1.1.19.1.1.1.2.3" xref="p1.1.m1.1.19.1.1.1.2.3.cmml">
                <mo id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">∇</mo>
                <mo id="p1.1.m1.1.19.1.1.1.2.3a" xref="p1.1.m1.1.19.1.1.1.2.3.cmml">⁡</mo>
                <mi mathvariant="normal" id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">Φ</mi>
              </mrow>
              <mo id="p1.1.m1.1.19.1.1.1.2.1b" xref="p1.1.m1.1.19.1.1.1.2.1.cmml">⁢</mo>
              <mrow id="p1.1.m1.1.19.1.1.1.2.4" xref="p1.1.m1.1.19.1.1.1.2.4.1.cmml">
                <mo stretchy="false" id="p1.1.m1.1.11" xref="p1.1.m1.1.19.1.1.1.2.4.1.cmml">(</mo>
                <mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">𝒓</mi>
                <mo id="p1.1.m1.1.13" xref="p1.1.m1.1.19.1.1.1.2.4.1.cmml">,</mo>
                <mi id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">t</mi>
                <mo stretchy="false" id="p1.1.m1.1.15" xref="p1.1.m1.1.19.1.1.1.2.4.1.cmml">)</mo>
              </mrow>
            </mrow>
            <mo stretchy="false" id="p1.1.m1.1.16" xref="p1.1.m1.1.19.1.1.1.2.cmml">)</mo>
          </mrow>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">=</mo>
      <mn id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">0</mn>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">
        <eq id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17"/>
        <apply id="p1.1.m1.1.19.1.cmml" xref="p1.1.m1.1.19.1">
          <minus id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1"/>
          <apply id="p1.1.m1.1.19.1.1.cmml" xref="p1.1.m1.1.19.1.1">
            <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">⋅</ci>
            <ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">∇</ci>
            <apply id="p1.1.m1.1.19.1.1.1.2.cmml" xref="p1.1.m1.1.19.1.1.1">
              <times id="p1.1.m1.1.19.1.1.1.2.1.cmml" xref="p1.1.m1.1.19.1.1.1.2.1"/>
              <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">𝜀</ci>
              <ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">𝒓</ci>
              <apply id="p1.1.m1.1.19.1.1.1.2.3.cmml" xref="p1.1.m1.1.19.1.1.1.2.3">
                <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">∇</ci>
                <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">Φ</ci>
              </apply>
              <interval closure="open" id="p1.1.m1.1.19.1.1.1.2.4.1.cmml" xref="p1.1.m1.1.19.1.1.1.2.4">
                <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">𝒓</ci>
                <ci id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">𝑡</ci>
              </interval>
            </apply>
          </apply>
        </apply>
        <cn type="integer" id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">0</cn>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle-\nabla\cdot(\varepsilon(\boldsymbol{r})\nabla\Phi%
(\boldsymbol{r},t))=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 (1.237 KB / 435 B) :

-\nabla \cdot (\varepsilon ({\boldsymbol {r}})\nabla \Phi ({\boldsymbol {r}},t))=0

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle -\nabla \cdot (\varepsilon ({\boldsymbol {r}})\nabla \Phi ({\boldsymbol {r}},t))=0}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mo>&#x2212;<!-- − --></mo>
        <mi mathvariant="normal">&#x2207;<!-- ∇ --></mi>
        <mo>&#x22C5;<!-- ⋅ --></mo>
        <mo stretchy="false">(</mo>
        <mi>&#x03B5;<!-- ε --></mi>
        <mo stretchy="false">(</mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mi mathvariant="bold-italic">r</mi>
        </mrow>
        <mo stretchy="false">)</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>
        <mo stretchy="false">)</mo>
        <mo>=</mo>
        <mn>0</mn>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle -\nabla \cdot (\varepsilon ({\boldsymbol {r}})\nabla \Phi ({\boldsymbol {r}},t))=0}</annotation>
  </semantics>
</math>

SVG (5.627 KB / 2.36 KB) :

MathML (experimental; no images) rendering

MathML (684 B / 269 B) :

- \nabla \cdot (ε (r) \nabla Φ (r, t)) = 0

<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>&#x2212;</mo><mi mathvariant="normal">&#x2207;</mi><mo>&#x22C5;</mo><mo stretchy="false">(</mo><mi>&#x03B5;</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">r</mi></mrow><mo stretchy="false">)</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><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$\varepsilon$

${\boldsymbol {r}}$

$\Phi$

${\boldsymbol {r}}$

$t$

MathML observations

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results