An Analytic Analysis of the Diffusive-Heat-Flow Equation for Different Magnetic Field Profiles for a Single Magnetic Nanoparticle

<table>The absolute maximal temperature rise was plotted as a function of the number of harmonics summed, <svg height="10.325" id="M231" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 14.8375 10.325" width="14.8375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑁</tspan>
</text>
</g>
</g>
</svg>, and as a function of the core radius for a periodic pulse-shaped MFP having a pulsed width of <svg height="14.7125" id="M232" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 33.6875 14.7125" width="33.6875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.7125)">
<g transform="translate(72,-60.23)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">𝑇</tspan>
</text>
<text transform="matrix(1,0,0,-1,-49.44,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑠</tspan>
</text>
</g>
</g>
</svg>; the maximal summation value <svg height="10.325" id="M233" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 14.8375 10.325" width="14.8375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑁</tspan>
</text>
</g>
</g>
</svg> ranges from <svg height="10.6875" id="M234" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 40.625 10.6875" width="40.625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6875)">
<g transform="translate(72,-63.45)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑁</tspan>
<tspan style="font-size: 12.50px; " x="14.103384" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="26.143772" y="0">1</tspan>
</text>
</g>
</g>
</svg> to <svg height="10.9125" id="M235" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 56.262501 10.9125" width="56.262501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑁</tspan>
<tspan style="font-size: 12.50px; " x="14.103384" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="26.143772" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="32.395271" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="38.646774" y="0">0</tspan>
</text>
</g>
</g>
</svg>.</table>

Journal of Atomic and Molecular Physics

fig13

Figure 13

Figure 13: An Analytic Analysis of the Diffusive-Heat-Flow Equation for Different Magnetic Field Profiles for a Single Magnetic Nanoparticle 