Stash
This commit is contained in:
parent
6420a6bcd4
commit
e9b8aca97f
BIN
Phase-diag2.png
Normal file
BIN
Phase-diag2.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 93 KiB |
565
Phase-diag2.svg
Normal file
565
Phase-diag2.svg
Normal file
@ -0,0 +1,565 @@
|
||||
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
|
||||
<!-- Created with Inkscape (http://www.inkscape.org/) -->
|
||||
|
||||
<svg
|
||||
xmlns:dc="http://purl.org/dc/elements/1.1/"
|
||||
xmlns:cc="http://creativecommons.org/ns#"
|
||||
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
|
||||
xmlns:svg="http://www.w3.org/2000/svg"
|
||||
xmlns="http://www.w3.org/2000/svg"
|
||||
xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
|
||||
xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
|
||||
id="svg2"
|
||||
sodipodi:version="0.32"
|
||||
inkscape:version="0.48.4 r9939"
|
||||
width="530"
|
||||
height="443"
|
||||
sodipodi:docname="Phase-diag2 (noch eine Kopie).svg"
|
||||
version="1.0"
|
||||
inkscape:output_extension="org.inkscape.output.svg.inkscape">
|
||||
<metadata
|
||||
id="metadata7">
|
||||
<rdf:RDF>
|
||||
<cc:Work
|
||||
rdf:about="">
|
||||
<dc:format>image/svg+xml</dc:format>
|
||||
<dc:type
|
||||
rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
|
||||
</cc:Work>
|
||||
</rdf:RDF>
|
||||
</metadata>
|
||||
<defs
|
||||
id="defs5">
|
||||
<inkscape:perspective
|
||||
sodipodi:type="inkscape:persp3d"
|
||||
inkscape:vp_x="0 : 221.5 : 1"
|
||||
inkscape:vp_y="0 : 1000 : 0"
|
||||
inkscape:vp_z="575 : 221.5 : 1"
|
||||
inkscape:persp3d-origin="287.5 : 147.66667 : 1"
|
||||
id="perspective62" />
|
||||
<marker
|
||||
inkscape:stockid="Arrow2Mend"
|
||||
orient="auto"
|
||||
refY="0"
|
||||
refX="0"
|
||||
id="Arrow2Mend"
|
||||
style="overflow:visible">
|
||||
<path
|
||||
id="path2329"
|
||||
style="font-size:12px;fill-rule:evenodd;stroke-width:0.625;stroke-linejoin:round"
|
||||
d="M 8.7185878,4.0337352 -2.2072895,0.01601326 8.7185884,-4.0017078 c -1.7454984,2.3720609 -1.7354408,5.6174519 -6e-7,8.035443 z"
|
||||
transform="matrix(-0.6,0,0,-0.6,3,0)" />
|
||||
</marker>
|
||||
<marker
|
||||
inkscape:stockid="Arrow2Mstart"
|
||||
orient="auto"
|
||||
refY="0"
|
||||
refX="0"
|
||||
id="Arrow2Mstart"
|
||||
style="overflow:visible">
|
||||
<path
|
||||
id="path2332"
|
||||
style="font-size:12px;fill-rule:evenodd;stroke-width:0.625;stroke-linejoin:round"
|
||||
d="M 8.7185878,4.0337352 -2.2072895,0.01601326 8.7185884,-4.0017078 c -1.7454984,2.3720609 -1.7354408,5.6174519 -6e-7,8.035443 z"
|
||||
transform="matrix(0.6,0,0,0.6,-3,0)" />
|
||||
</marker>
|
||||
<marker
|
||||
inkscape:stockid="Arrow2Lstart"
|
||||
orient="auto"
|
||||
refY="0"
|
||||
refX="0"
|
||||
id="Arrow2Lstart"
|
||||
style="overflow:visible">
|
||||
<path
|
||||
id="path2338"
|
||||
style="font-size:12px;fill-rule:evenodd;stroke-width:0.625;stroke-linejoin:round"
|
||||
d="M 8.7185878,4.0337352 -2.2072895,0.01601326 8.7185884,-4.0017078 c -1.7454984,2.3720609 -1.7354408,5.6174519 -6e-7,8.035443 z"
|
||||
transform="matrix(1.1,0,0,1.1,-5.5,0)" />
|
||||
</marker>
|
||||
</defs>
|
||||
<sodipodi:namedview
|
||||
inkscape:window-height="1056"
|
||||
inkscape:window-width="1855"
|
||||
inkscape:pageshadow="2"
|
||||
inkscape:pageopacity="0.0"
|
||||
borderopacity="1.0"
|
||||
bordercolor="#666666"
|
||||
pagecolor="#ffffff"
|
||||
id="base"
|
||||
inkscape:zoom="1.7629797"
|
||||
inkscape:cx="265"
|
||||
inkscape:cy="221.5"
|
||||
inkscape:window-x="65"
|
||||
inkscape:window-y="24"
|
||||
inkscape:current-layer="switch50"
|
||||
inkscape:showpageshadow="false"
|
||||
height="443px"
|
||||
width="575px"
|
||||
showgrid="false"
|
||||
inkscape:window-maximized="1" />
|
||||
<path
|
||||
id="path3223"
|
||||
d="m 33.195464,306.23765 149.804556,0"
|
||||
style="fill:none;stroke:#dcdcdc;stroke-width:1.875;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:7.5, 7.5;stroke-dashoffset:0"
|
||||
sodipodi:nodetypes="cc" />
|
||||
<path
|
||||
id="path3225"
|
||||
d="m 183.61958,403.16968 0,-97.16968"
|
||||
style="fill:#dcdcdc;fill-opacity:0.75;fill-rule:evenodd;stroke:#dcdcdc;stroke-width:1.875;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:7.5, 7.5;stroke-dashoffset:0"
|
||||
sodipodi:nodetypes="cc" />
|
||||
<path
|
||||
style="fill:none;stroke:#000000;stroke-width:1.87499988;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none;marker-start:url(#Arrow2Mstart);marker-end:url(#Arrow2Mend)"
|
||||
d="m 32,23.332818 0,382.004652 478,0"
|
||||
id="path1308"
|
||||
sodipodi:nodetypes="ccc" />
|
||||
<path
|
||||
style="fill:none;stroke:#af0000;stroke-width:2.5;stroke-linecap:round;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none"
|
||||
d="m 32.944062,403.45421 c 0,0 93.791238,-8.96899 149.518348,-97.33085"
|
||||
id="path2371"
|
||||
sodipodi:nodetypes="cs" />
|
||||
<path
|
||||
style="fill:none;stroke:#0000af;stroke-width:2.5;stroke-linecap:round;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none"
|
||||
d="m 182.45365,306.13132 c 0,0 116.36276,1.75414 160.70482,-115.99705"
|
||||
id="path2373"
|
||||
sodipodi:nodetypes="cs" />
|
||||
<path
|
||||
sodipodi:nodetypes="css"
|
||||
id="path2377"
|
||||
d="m 182.45365,306.13132 c 0,0 10.49475,-8.71879 25.66658,-55.44449 26.90754,-82.86897 6.99995,-213.190839 79.66672,-216.683513"
|
||||
style="fill:none;stroke:#009600;stroke-width:2.5;stroke-linecap:round;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none" />
|
||||
<path
|
||||
style="fill:none;stroke:#009600;stroke-width:2.5;stroke-linecap:round;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:5, 5;stroke-dashoffset:0"
|
||||
d="m 183.1112,305.00524 c 0,0 0.78377,-169.1145 -12.22126,-275.141477"
|
||||
id="path2379"
|
||||
sodipodi:nodetypes="cs"
|
||||
inkscape:transform-center-x="-4.4196709" />
|
||||
<path
|
||||
style="fill:none;stroke:#000000;stroke-width:1.875;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:7.5, 7.5;stroke-dashoffset:0"
|
||||
d="m 344.00002,188.23765 172.41419,0"
|
||||
id="path3216" />
|
||||
<path
|
||||
style="fill:none;stroke:#dcdcdc;stroke-width:1.875;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:7.5, 7.5;stroke-dashoffset:0"
|
||||
d="m 33.195464,188.23765 310.804556,0"
|
||||
id="path2381" />
|
||||
<path
|
||||
style="fill:none;stroke:#000000;stroke-width:1.875;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:7.5, 7.5;stroke-dashoffset:0"
|
||||
d="m 343.61958,187 0,-109.078427"
|
||||
id="path2241" />
|
||||
<path
|
||||
style="fill:#dcdcdc;fill-opacity:0.75;fill-rule:evenodd;stroke:#dcdcdc;stroke-width:1.875;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:7.5, 7.5;stroke-dashoffset:0"
|
||||
d="m 343.61958,403.16968 0,-216.16968"
|
||||
id="path2383" />
|
||||
<path
|
||||
sodipodi:type="arc"
|
||||
style="fill:#af0000;fill-opacity:1;fill-rule:evenodd;stroke:#320000;stroke-width:3.06002283;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none;stroke-dashoffset:0"
|
||||
id="path2385"
|
||||
sodipodi:cx="243.06796"
|
||||
sodipodi:cy="235.59767"
|
||||
sodipodi:rx="7.601398"
|
||||
sodipodi:ry="7.601398"
|
||||
d="m 250.66936,235.59767 a 7.601398,7.601398 0 1 1 -15.2028,0 7.601398,7.601398 0 1 1 15.2028,0 z"
|
||||
transform="matrix(0.816987,0,0,0.816987,-15.511568,114.24268)" />
|
||||
<path
|
||||
sodipodi:type="arc"
|
||||
style="fill:#e10000;fill-opacity:1;fill-rule:evenodd;stroke:#640000;stroke-width:3.06002283;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none;stroke-dashoffset:0"
|
||||
id="path2387"
|
||||
sodipodi:cx="243.06796"
|
||||
sodipodi:cy="235.59767"
|
||||
sodipodi:rx="7.601398"
|
||||
sodipodi:ry="7.601398"
|
||||
d="m 250.66936,235.59767 a 7.601398,7.601398 0 1 1 -15.2028,0 7.601398,7.601398 0 1 1 15.2028,0 z"
|
||||
transform="matrix(0.816987,0,0,0.816987,145.00962,-3.567849)" />
|
||||
<switch
|
||||
id="switch26">
|
||||
<text
|
||||
systemLanguage="de"
|
||||
xml:space="preserve"
|
||||
style="font-size:18px;font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;text-align:end;line-height:125%;writing-mode:lr-tb;text-anchor:end;fill:#000000;fill-opacity:1;stroke:none;font-family:Arial"
|
||||
x="498"
|
||||
y="429"
|
||||
id="text2389"
|
||||
sodipodi:linespacing="125%"><tspan
|
||||
sodipodi:role="line"
|
||||
id="tspan2391"
|
||||
x="498"
|
||||
y="429">Temperatur</tspan></text>
|
||||
<text
|
||||
xml:space="preserve"
|
||||
style="font-size:18px;font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;text-align:end;line-height:125%;writing-mode:lr-tb;text-anchor:end;fill:#000000;fill-opacity:1;stroke:none;font-family:Arial"
|
||||
x="498"
|
||||
y="429"
|
||||
id="text30"
|
||||
sodipodi:linespacing="125%"><tspan
|
||||
sodipodi:role="line"
|
||||
id="tspan32"
|
||||
x="498"
|
||||
y="429">Temperature</tspan></text>
|
||||
</switch>
|
||||
<switch
|
||||
id="switch34">
|
||||
<text
|
||||
systemLanguage="de"
|
||||
xml:space="preserve"
|
||||
style="font-size:18px;font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;text-align:end;line-height:100%;writing-mode:lr-tb;text-anchor:end;fill:#000000;fill-opacity:1;stroke:none;font-family:Arial"
|
||||
x="-55.097656"
|
||||
y="19.722168"
|
||||
id="text2393"
|
||||
sodipodi:linespacing="100%"
|
||||
transform="matrix(0,-1,1,0,0,0)"><tspan
|
||||
sodipodi:role="line"
|
||||
id="tspan2395"
|
||||
x="-55.097656"
|
||||
y="19.722168">Druck</tspan></text>
|
||||
<text
|
||||
xml:space="preserve"
|
||||
style="font-size:18px;font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;text-align:end;line-height:100%;writing-mode:lr-tb;text-anchor:end;fill:#000000;fill-opacity:1;stroke:none;font-family:Arial"
|
||||
x="-55.097656"
|
||||
y="19.722168"
|
||||
id="text38"
|
||||
sodipodi:linespacing="100%"
|
||||
transform="matrix(0,-1,1,0,0,0)"><tspan
|
||||
sodipodi:role="line"
|
||||
id="tspan40"
|
||||
x="-55.097656"
|
||||
y="19.722168">Pressure</tspan></text>
|
||||
</switch>
|
||||
<switch
|
||||
id="switch42">
|
||||
<text
|
||||
systemLanguage="de"
|
||||
xml:space="preserve"
|
||||
style="font-size:22px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#af0000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
x="77.312576"
|
||||
y="293.41577"
|
||||
id="text2397"
|
||||
sodipodi:linespacing="125%"><tspan
|
||||
sodipodi:role="line"
|
||||
id="tspan2399"
|
||||
x="77.312576"
|
||||
y="293.41577">Tripelpunkt</tspan></text>
|
||||
<text
|
||||
xml:space="preserve"
|
||||
style="font-size:22px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#af0000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
x="77.312576"
|
||||
y="293.41577"
|
||||
id="text46"
|
||||
sodipodi:linespacing="125%"><tspan
|
||||
sodipodi:role="line"
|
||||
id="tspan48"
|
||||
x="77.312576"
|
||||
y="293.41577">triple point</tspan></text>
|
||||
</switch>
|
||||
<switch
|
||||
id="switch50">
|
||||
<text
|
||||
systemLanguage="de"
|
||||
xml:space="preserve"
|
||||
style="font-size:22px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#e10000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
x="349.69757"
|
||||
y="211.19748"
|
||||
id="text2401"
|
||||
sodipodi:linespacing="125%"><tspan
|
||||
sodipodi:role="line"
|
||||
id="tspan2403"
|
||||
x="349.69757"
|
||||
y="211.19748">kritischer Punkt</tspan></text>
|
||||
<text
|
||||
xml:space="preserve"
|
||||
style="font-size:22px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#e10000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
x="349.69757"
|
||||
y="211.19748"
|
||||
id="text54"
|
||||
sodipodi:linespacing="125%"><tspan
|
||||
sodipodi:role="line"
|
||||
id="tspan56"
|
||||
x="349.69757"
|
||||
y="211.19748">critical point</tspan></text>
|
||||
</switch>
|
||||
<switch
|
||||
id="switch58">
|
||||
<text
|
||||
systemLanguage="de"
|
||||
sodipodi:linespacing="125%"
|
||||
id="text2405"
|
||||
y="182.2061"
|
||||
x="35.985424"
|
||||
style="font-size:18px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
xml:space="preserve"><tspan
|
||||
y="182.2061"
|
||||
x="35.985424"
|
||||
id="tspan2407"
|
||||
sodipodi:role="line">kritischer Druck</tspan><tspan
|
||||
y="204.7061"
|
||||
x="35.985424"
|
||||
sodipodi:role="line"
|
||||
id="tspan3218">P<tspan
|
||||
style="font-size:12px"
|
||||
id="tspan2223">cr</tspan></tspan></text>
|
||||
<text
|
||||
sodipodi:linespacing="125%"
|
||||
id="text64"
|
||||
y="182.2061"
|
||||
x="35.985424"
|
||||
style="font-size:18px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
xml:space="preserve"><tspan
|
||||
y="182.2061"
|
||||
x="35.985424"
|
||||
id="tspan66"
|
||||
sodipodi:role="line">critical pressure</tspan><tspan
|
||||
y="204.7061"
|
||||
x="35.985424"
|
||||
sodipodi:role="line"
|
||||
id="tspan68">P<tspan
|
||||
style="font-size:12px"
|
||||
id="tspan70">cr</tspan></tspan></text>
|
||||
</switch>
|
||||
<switch
|
||||
id="switch72">
|
||||
<text
|
||||
systemLanguage="de"
|
||||
sodipodi:linespacing="100%"
|
||||
id="text2409"
|
||||
y="361.65479"
|
||||
x="349.69757"
|
||||
style="font-size:18px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:100%;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
xml:space="preserve"><tspan
|
||||
y="361.65479"
|
||||
x="349.69757"
|
||||
id="tspan2411"
|
||||
sodipodi:role="line">kritische</tspan><tspan
|
||||
y="379.65479"
|
||||
x="349.69757"
|
||||
sodipodi:role="line"
|
||||
id="tspan2413">Temperatur</tspan><tspan
|
||||
y="397.65479"
|
||||
x="349.69757"
|
||||
sodipodi:role="line"
|
||||
id="tspan2225">T<tspan
|
||||
style="font-size:12px"
|
||||
id="tspan2227">cr</tspan></tspan></text>
|
||||
<text
|
||||
sodipodi:linespacing="100%"
|
||||
id="text79"
|
||||
y="361.65479"
|
||||
x="349.69757"
|
||||
style="font-size:18px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:100%;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
xml:space="preserve"><tspan
|
||||
y="361.65479"
|
||||
x="349.69757"
|
||||
id="tspan81"
|
||||
sodipodi:role="line">critical</tspan><tspan
|
||||
y="379.65479"
|
||||
x="349.69757"
|
||||
sodipodi:role="line"
|
||||
id="tspan83">temperature</tspan><tspan
|
||||
y="397.65479"
|
||||
x="349.69757"
|
||||
sodipodi:role="line"
|
||||
id="tspan85">T<tspan
|
||||
style="font-size:12px"
|
||||
id="tspan87">cr</tspan></tspan></text>
|
||||
</switch>
|
||||
<switch
|
||||
id="switch89">
|
||||
<text
|
||||
systemLanguage="de"
|
||||
sodipodi:linespacing="125%"
|
||||
id="text2415"
|
||||
y="116.67241"
|
||||
x="76.885796"
|
||||
style="font-size:18px;font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
xml:space="preserve"><tspan
|
||||
y="116.67241"
|
||||
x="76.885796"
|
||||
id="tspan2417"
|
||||
sodipodi:role="line">feste Phase</tspan></text>
|
||||
<text
|
||||
sodipodi:linespacing="125%"
|
||||
id="text93"
|
||||
y="116.67241"
|
||||
x="76.885796"
|
||||
style="font-size:18px;font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
xml:space="preserve"><tspan
|
||||
y="116.67241"
|
||||
x="76.885796"
|
||||
id="tspan95"
|
||||
sodipodi:role="line">solid phase</tspan></text>
|
||||
</switch>
|
||||
<switch
|
||||
id="switch97">
|
||||
<text
|
||||
systemLanguage="de"
|
||||
sodipodi:linespacing="125%"
|
||||
id="text2419"
|
||||
y="221.38667"
|
||||
x="244.33746"
|
||||
style="font-size:18px;font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
xml:space="preserve"><tspan
|
||||
y="221.38667"
|
||||
x="244.33746"
|
||||
id="tspan2421"
|
||||
sodipodi:role="line">flüssige</tspan><tspan
|
||||
y="243.88667"
|
||||
x="244.33746"
|
||||
sodipodi:role="line"
|
||||
id="tspan2221">Phase</tspan></text>
|
||||
<text
|
||||
sodipodi:linespacing="125%"
|
||||
id="text102"
|
||||
y="221.38667"
|
||||
x="244.33746"
|
||||
style="font-size:18px;font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
xml:space="preserve"><tspan
|
||||
y="221.38667"
|
||||
x="244.33746"
|
||||
id="tspan104"
|
||||
sodipodi:role="line">liquid</tspan><tspan
|
||||
y="243.88667"
|
||||
x="244.33746"
|
||||
sodipodi:role="line"
|
||||
id="tspan106">phase</tspan></text>
|
||||
</switch>
|
||||
<switch
|
||||
id="switch108">
|
||||
<text
|
||||
systemLanguage="de"
|
||||
sodipodi:linespacing="125%"
|
||||
id="text2423"
|
||||
y="291.66678"
|
||||
x="389.11276"
|
||||
style="font-size:18px;font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
xml:space="preserve"><tspan
|
||||
y="291.66678"
|
||||
x="389.11276"
|
||||
id="tspan2425"
|
||||
sodipodi:role="line">Gasphase</tspan></text>
|
||||
<text
|
||||
sodipodi:linespacing="125%"
|
||||
id="text112"
|
||||
y="291.66678"
|
||||
x="389.11276"
|
||||
style="font-size:18px;font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
xml:space="preserve"><tspan
|
||||
y="291.66678"
|
||||
x="389.11276"
|
||||
id="tspan114"
|
||||
sodipodi:role="line">gaseous phase</tspan></text>
|
||||
</switch>
|
||||
<switch
|
||||
id="switch116">
|
||||
<text
|
||||
systemLanguage="de"
|
||||
sodipodi:linespacing="125%"
|
||||
id="text2229"
|
||||
y="128.31366"
|
||||
x="283.71512"
|
||||
style="font-size:18px;font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:center;line-height:125%;writing-mode:lr-tb;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
xml:space="preserve"><tspan
|
||||
y="128.31366"
|
||||
x="283.71512"
|
||||
sodipodi:role="line"
|
||||
id="tspan2233">kompressible</tspan><tspan
|
||||
y="150.81366"
|
||||
x="283.71512"
|
||||
sodipodi:role="line"
|
||||
id="tspan2237">Flüssigkeit</tspan></text>
|
||||
<text
|
||||
sodipodi:linespacing="125%"
|
||||
id="text121"
|
||||
y="128.31366"
|
||||
x="283.71512"
|
||||
style="font-size:18px;font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:center;line-height:125%;writing-mode:lr-tb;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
xml:space="preserve"><tspan
|
||||
y="128.31366"
|
||||
x="283.71512"
|
||||
sodipodi:role="line"
|
||||
id="tspan123">compressible</tspan><tspan
|
||||
y="150.81366"
|
||||
x="283.71512"
|
||||
sodipodi:role="line"
|
||||
id="tspan125">liquid</tspan></text>
|
||||
</switch>
|
||||
<text
|
||||
xml:space="preserve"
|
||||
style="font-size:18px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
x="35.985424"
|
||||
y="301.20612"
|
||||
id="text3235"
|
||||
sodipodi:linespacing="125%"><tspan
|
||||
id="tspan3239"
|
||||
sodipodi:role="line"
|
||||
x="35.985424"
|
||||
y="301.20612">P<tspan
|
||||
id="tspan3241"
|
||||
style="font-size:12px">tp</tspan></tspan></text>
|
||||
<text
|
||||
sodipodi:linespacing="100%"
|
||||
id="text3245"
|
||||
y="396.16699"
|
||||
x="190.18408"
|
||||
style="font-size:18px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:100%;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
xml:space="preserve"><tspan
|
||||
y="396.16699"
|
||||
x="190.18408"
|
||||
sodipodi:role="line"
|
||||
id="tspan3251">T<tspan
|
||||
style="font-size:12px"
|
||||
id="tspan3253">tp</tspan></tspan></text>
|
||||
<switch
|
||||
id="switch133">
|
||||
<text
|
||||
systemLanguage="de"
|
||||
sodipodi:linespacing="125%"
|
||||
id="text3259"
|
||||
y="332.50381"
|
||||
x="271.46863"
|
||||
style="font-size:18px;font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:center;line-height:125%;writing-mode:lr-tb;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
xml:space="preserve"><tspan
|
||||
y="332.50381"
|
||||
x="271.46863"
|
||||
sodipodi:role="line"
|
||||
id="tspan2868">Dampf</tspan></text>
|
||||
<text
|
||||
sodipodi:linespacing="125%"
|
||||
id="text137"
|
||||
y="332.50381"
|
||||
x="271.46863"
|
||||
style="font-size:18px;font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:center;line-height:125%;writing-mode:lr-tb;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
xml:space="preserve"><tspan
|
||||
y="332.50381"
|
||||
x="271.46863"
|
||||
sodipodi:role="line"
|
||||
id="tspan139">vapour</tspan></text>
|
||||
</switch>
|
||||
<switch
|
||||
id="switch141">
|
||||
<text
|
||||
systemLanguage="de"
|
||||
sodipodi:linespacing="125%"
|
||||
id="text3263"
|
||||
y="132.32422"
|
||||
x="376.2373"
|
||||
style="font-size:18px;font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
xml:space="preserve"><tspan
|
||||
y="132.32422"
|
||||
x="376.2373"
|
||||
id="tspan3265"
|
||||
sodipodi:role="line">überkritische</tspan><tspan
|
||||
y="132.32422"
|
||||
x="376.2373"
|
||||
dy="1em"
|
||||
id="tspan145"
|
||||
sodipodi:role="line">Flüssigkeit</tspan></text>
|
||||
<text
|
||||
sodipodi:linespacing="125%"
|
||||
id="text147"
|
||||
y="132.32422"
|
||||
x="376.2373"
|
||||
style="font-size:18px;font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman"
|
||||
xml:space="preserve"><tspan
|
||||
y="132.32422"
|
||||
x="376.2373"
|
||||
id="tspan149"
|
||||
sodipodi:role="line">supercritical fluid</tspan></text>
|
||||
</switch>
|
||||
</svg>
|
||||
|
After Width: | Height: | Size: 23 KiB |
@ -8,13 +8,19 @@
|
||||
|
||||
\section*{Introduction}
|
||||
|
||||
In statistical mechanics phase transitions occur when there is a discontinuity singularity in the free energy or one of its derivatives, such as specific heat capacity, density, or other thermodynamic observables. Examples include the liquid-gas transition, the appearance super conductors (\TKK CHECK), or ferromagnetic materials at the Curie Temperature $T_C$ (\TKK cite and check this is $T_C$). An example of this can be seen in Figure \TKK.
|
||||
\begin{figure}[hbt]
|
||||
\label{eg-phase-diagram}
|
||||
\includegraphics[width=\columnwidth]{Phase-diag2.png}
|
||||
\caption{An example phase diagram of water showing different phase transitions and phases separating them. The critical point a the end of the liquid-gaseous phase is clearly shown, beyond this point a supercritical fluid is observed and the thermodynamic variables can be varied without a corresponding discontinuity in a state function. Source \parencite{wiki:phase-digram-eg}}
|
||||
\end{figure}
|
||||
|
||||
\TKK something about critical points.
|
||||
In statistical mechanics phase transitions occur when there is a discontinuity singularity in the free energy or one of its derivatives, such as specific heat capacity, density, or other thermodynamic observables. Examples include the liquid-gas transition, the appearance super conductors, or ferromagnetic materials at the Curie Temperature $T_C$. Phase diagrams such as the one shown in Figure \ref{eg-phase-diagram} are used to represent these transitions, with the lines representing where discontinuities are present.
|
||||
|
||||
Of these transitions one of the easiest to model is that of ferromagnets at their Curie Temperature. This involves heating a ferromagnetic material up, possibly in the presence of an external magnetic field $H$, and observing the innate magnetisation of the material $M$, the order parameter of the system. All phase transitions occur when $H = 0$ due to the symmetry of the system to sign reversal of the external magnetic field, making this a useful model for exploring critical points themselves.
|
||||
As the magnitude of the discontinuity varies across the extent of the phase transition, it will often reach a point such that it becomes $0$ and thus the phase transition line abruptly ends. Beyond this point one can continuously transition between different phases without crossing the now terminated phase transition line.
|
||||
|
||||
This has birthed a number of models for ferromagnetic materials around their critical point including: the Ising Model which models the magnetic as a lattice of interacting magnetic spin sites\fnmark{ising-model-generalisations}; Mean Field Theory which models interactions of spins with a hypothetical mean field of all other spins in the material; and Renormalisation Group Theory which is a general mathematical framework for understanding systems which can exhibit scale invariance.
|
||||
Of these transitions one of the easiest to model is that of ferromagnets at their Curie Temperature. This involves heating a ferromagnetic material up, possibly in the presence of an external magnetic field $H$, and observing the magnetisation $M$ of the material itself, the order parameter of the system. All phase transitions occur when $H = 0$ due to the symmetry of the system to sign reversal of the external magnetic field, making this a useful model for exploring critical points themselves.
|
||||
|
||||
This has birthed a number of models for ferromagnetic materials around their critical point including: the Ising Model which models the magnetic as a lattice of interacting magnetic spin sites\fnmark{ising-model-generalisations}; Mean Field Theory which models interactions of spins with a hypothetical mean field of all other spins in the material; and Renormalisation Group Theory which is a more general mathematical framework for understanding systems which can exhibit scale invariance.
|
||||
|
||||
\fntext{ising-model-generalisations}{
|
||||
There are a number of generalisations of the Ising Model including the Heisenberg Model, XY model, Potts Model, among others which increase the possible states of spins. These however are not discussed in this paper.
|
||||
@ -28,7 +34,7 @@ There are a number of generalisations of the Ising Model including the Heisenber
|
||||
|
||||
Of these we will focus most on the Ising Model, which we will use to model ferromagnetic materials under various conditions, comparing it to Mean Field Theory. (\TKK will we mention renormalisation), with the aim of extracting quantitative data (\TKK we are not mentioning critical) about the behaviour of systems at their critical points (\TKK Do we want to mention universality classes? Is that a thing which we can?).
|
||||
|
||||
In the discussion we will explore the theory behind the models discussed, as well as phase transitions (\TKK is this a hyphenated word or not?) and critical points themselves. This will be followed by a brief discussion of the Monte-Carlo (\TKK do I need to mention this before) method employed in the simulation and relevant statistical methods. Finally we will present data from these simulations, comparing it to the result from theory and concluding on the effectiveness of our model in desired exploration.
|
||||
In the discussion we will explore the theory behind the models discussed, as well as phase transitions and critical points themselves. This will be followed by a brief discussion of the Monte-Carlo (\TKK do I need to mention this before) method employed in the simulation and relevant statistical methods. Finally we will present data from these simulations, comparing it to the result from theory and concluding on the effectiveness of our model in desired exploration.
|
||||
|
||||
|
||||
|
||||
@ -63,37 +69,41 @@ Here we will discuss the theory behind the different models mentioned as well as
|
||||
\caption{The relationship between the partition function and various thermodynamic observables. From \parencite{yeomansStatisticalMechanicsPhase1992}}
|
||||
\end{figure}
|
||||
|
||||
Whichever model we use standard Statistical Mechanics gives us relations between the partition function, itself derived from the energy of the system, and other thermodynamic observables. This relationship can be seen in Figure \ref{thermodynamic-variables}, from \cite[p. 17]{yeomansStatisticalMechanicsPhase1992}.
|
||||
Whichever model we apply standard statistical mechanics to give us relations between the partition function, itself derived from the energy of the system, and other thermodynamic observables. These relationships can be seen in Figure \ref{thermodynamic-variables}, from \cite[p. 17]{yeomansStatisticalMechanicsPhase1992}.
|
||||
|
||||
We obtain the magnetisation and energy from our chosen model, relying on statistical mechanics for the specific heat capacity, and magnetic susceptibility (labeled as \enquote{Isothermal susceptibility} in the diagram), given by
|
||||
We obtain the magnetisation and energy from our chosen model, deriving the specific heat capacity, and magnetic susceptibility (labeled as \enquote{Isothermal susceptibility} in the diagram) from these base quantities by the equations,
|
||||
|
||||
\begin{align}
|
||||
c &= \frac{\p}{\p T} \left\langle\frac{E}{N}\right\rangle \\
|
||||
\chi &= \frac{\p}{\p h} \left\langle M \right\rangle.
|
||||
\chi &= \frac{\p}{\p h} \left\langle\frac{M}{N}\right\rangle.
|
||||
\end{align}
|
||||
|
||||
\TKK define E and M
|
||||
where $E$ is the total energy of the system, $M$ is total magnetisation of the system and then $N$ is the number of cells in the Ising Model. For convenience we write $m = \frac MN$.
|
||||
|
||||
To these we can apply the Fluctuation-dissipation theorem \cite{???} \TKK to transform the derivatives in these equations to expressions about the thermodynamic variance of the property at equilibrium. These are much more useful for the purposes of simulation and are given by,
|
||||
We can then apply the Fluctuation-dissipation theorem \cite{???} to transform the derivatives in these equations into expressions about the thermodynamic variance of the property at equilibrium. These are much more useful for the purposes of simulation and are given by,
|
||||
|
||||
\begin{align}
|
||||
c &= \frac{1}{N k_B T^2} \Var(E) \\
|
||||
\chi &= \frac{N}{k_B T} \Var(M).
|
||||
\chi &= \frac{N}{k_B T} \Var(m).
|
||||
\end{align}
|
||||
|
||||
Which in terms of our dimensionless energy gives us \TKK.
|
||||
|
||||
\subsection*{The Ising Model}
|
||||
|
||||
%The Ising model was invented by the physicist Wilhelm Lenz (1920), who gave it as a problem to his student Ernst Ising. The one-dimensional Ising model was solved by Ising (1925) alone in his 1924 thesis;[2] it has no phase transition. The two-dimensional square-lattice Ising model is much harder and was only given an analytic description much later, by Lars Onsager (1944). It is usually solved by a transfer-matrix method, although there exist different approaches, more related to quantum field theory.
|
||||
|
||||
The Ising Model will be the main model used to explore the behaviour of our system. It was developed by \TKK in \TKK for \TKK.
|
||||
|
||||
It is comprised of a grid of spin-sites which can take a value of either $+1$ or $-1$, representing up or down spins respectively. These spins interact in a local manner, with their nearest neighbours in the grid, having an interaction energy equal to,
|
||||
It is comprised of a grid of spin-sites which can take a value of either $+1$ or $-1$, representing up or down spins respectively. These spins interact in a local manner with their nearest neighbours in the grid. We write the interaction energy as,
|
||||
|
||||
\begin{equation}
|
||||
E = -J\sum_{\ip{ij}} s_i s_j
|
||||
\end{equation}
|
||||
|
||||
where $J > 0$ is the strength of the \todo{what are the units?} interaction, and $i, j$ are specific sites in the grid\fnmark{sites}. We can see trivially that this energy expression preferences same spin neighbours having $(\pm 1)^2 = 1 \implies E_i < 0$.
|
||||
where $J > 0$ is the strength of the interaction, $\sum_{\ip{ij}}$ represents a sum over all pairs of nearest neighbours, with the neighbours being written as sites $i, j$\fnmark{sites}. We can see trivially that this energy expression preferences same spin neighbours having $(\pm 1)^2 = 1 \implies E_i < 0$.
|
||||
|
||||
\fntext{sites}{When performing a calculation a \emph{site} is mapped to two integers $(x, y) \in \N$ representing the location of this site in the overall grid, however in mathematics we abstract this to a single index for conceptual ease.}
|
||||
\fntext{sites}{When performing a calculation a \emph{site} is mapped to two integers $(x, y) \in \N^2$ representing the location of this site in the overall grid, however in mathematics we abstract this to a single index for conceptual ease.}
|
||||
|
||||
In the fully general model this adds to energy from the the externally imposed magnetic field $H$ giving a total energy of,
|
||||
|
||||
@ -107,37 +117,39 @@ From these expressions we can obtain the partition function, in the standard man
|
||||
Z(T) = \sum_{\omega \in \Omega} \exp\left(\frac{E(\omega)}{k_B T}\right)
|
||||
\end{equation}
|
||||
|
||||
where $\omega \in \Omega$ is a particular microstate, corresponding to a particular set of choices for $s_i \in \set{\pm 1}$. This has a total phase space of $\Omega = \set{1, -1}^N$ where $N$ is the number of cells in the grid.
|
||||
where $\omega \in \Omega$ is a particular micro-state, corresponding to a particular set of choices for $s_i \in \set{\pm 1}$. This has a total phase space of $\Omega = \set{1, -1}^N$ where $N$ is the number of cells in the grid.
|
||||
|
||||
\subsection*{Mean Field Theory}
|
||||
|
||||
Whereas the Ising Model restrict interactions of spins to nearest-neighbours, Mean Field Theory, also known as Curie-Weiss theory (\TKK consistent capitalisation of terms), instead chooses to average the effect that each other site on the cell has on a chosen site. In this sense a site interacts with a \enquote{mean field}, representing all other sites in the lattice.
|
||||
|
||||
\TKK
|
||||
Taking this spin to be $s_0 = \pm 1$ we can determine its energy as
|
||||
|
||||
\begin{equation}
|
||||
E(s_0) = -s_0\left(J\sum_{\ip{s_0 s_j}} s_j + H \right)
|
||||
E(s_0) = -s_0\left(J\sum_{\ip{0 j}} s_j + H \right)
|
||||
\end{equation}
|
||||
|
||||
where $\ip{s_0 s_j}$ represents the nearest-neighbours to some fixed $s_0$. By counting noting that the number of neighbours to any given site, $q$, is constant with a value of $q = 4$ we can obtain,
|
||||
where this time one site, $0$, is fixed in our nearest neighbour sum. On a square 2D grid this sum has a constant number of terms, $q = 4$ which allows us to re-write this expression as,
|
||||
|
||||
\begin{equation}
|
||||
E(s_0) = -s_0(qJm + H) - Js_0 \sum_j(s_j - m)
|
||||
E(s_0) = -s_0(qJm + H) - Js_0 \sum_{\ip{0 j}}(s_j - m)
|
||||
\end{equation}
|
||||
|
||||
where $s_j - m$ is the effect of the variation of site $s_j$ from the overall mean on the energy of $s_0$. If we take this to be $0$ for all $s_j$ then we obtain,
|
||||
where $s_j - m$ is the effect of the variation of site $s_j$ from the overall mean on the energy of $s_0$. If we take this variation to be $0$ for all $s_j$ then we obtain,
|
||||
|
||||
\begin{equation}
|
||||
E(s_0) = -s_0(qJm + H)
|
||||
\end{equation}
|
||||
|
||||
which is an expression containing no cross terms and hence allows for treatment as a non-interacting thermodynamic system and hence,
|
||||
which is an expression containing no cross terms and hence allows for treatment as a non-interacting thermodynamic system with
|
||||
|
||||
\begin{align}
|
||||
\begin{equation}
|
||||
\begin{split}
|
||||
Z_1(s_0) &= \sum_{s \in \set{\pm 1}} \exp(-\beta E(s)) \\
|
||||
&= 2\cosh({(\beta(qJm + H))}) \\
|
||||
&= 2\cosh({\beta_0(qm + H)})
|
||||
\end{align}
|
||||
\end{split}
|
||||
\end{equation}
|
||||
|
||||
where $\beta_0$ is the dimensionless $\beta$ discussed in \TKK.
|
||||
|
||||
@ -145,19 +157,16 @@ where $\beta_0$ is the dimensionless $\beta$ discussed in \TKK.
|
||||
Z = (Z_1(s_0))^N
|
||||
\end{equation}
|
||||
|
||||
where $N$ is the number of sites in the system. Applying the identities seen in Figure \ref{thermodynamic-identities-graph} we obtain an expression for the magnetisation as,
|
||||
where $N$ is the number of sites in the system. Applying the identities seen in Figure \ref{thermodynamic-variables} we obtain an expression for the magnetisation as,
|
||||
|
||||
\begin{equation}
|
||||
m = \tanh(\beta(qJm + H))
|
||||
m = \tanh(\beta_0(qJm + H))
|
||||
\end{equation}
|
||||
|
||||
which must be solved to find a self consistent value of $m$ for a given $H, \beta_0$.
|
||||
|
||||
\subsection*{Phase transitions and Critical Points}
|
||||
|
||||
%The Ising model (German pronunciation: [ˈiːzɪŋ]) (or Lenz-Ising model or Ising-Lenz model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic "spins" that can be in one of two states (+1 or −1). The spins are arranged in a graph, usually a lattice (where the local structure repeats periodically in all directions), allowing each spin to interact with its neighbors. Neighboring spins that agree have a lower energy than those that disagree; the system tends to the lowest energy but heat disturbs this tendency, thus creating the possibility of different structural phases. The model allows the identification of phase transitions as a simplified model of reality. The two-dimensional square-lattice Ising model is one of the simplest statistical models to show a phase transition.[1]
|
||||
%
|
||||
%The Ising model was invented by the physicist Wilhelm Lenz (1920), who gave it as a problem to his student Ernst Ising. The one-dimensional Ising model was solved by Ising (1925) alone in his 1924 thesis;[2] it has no phase transition. The two-dimensional square-lattice Ising model is much harder and was only given an analytic description much later, by Lars Onsager (1944). It is usually solved by a transfer-matrix method, although there exist different approaches, more related to quantum field theory.
|
||||
%
|
||||
%In dimensions greater than four, the phase transition of the Ising model is described by mean-field theory. The Ising model for greater dimensions was also explored with respect to various tree topologies in the late 1970’s, culminating in an exact solution of the zero-field, time-independent Barth (1981) model for closed Cayley trees of arbitrary branching ratio, and thereby, arbitrarily large dimensionality within tree branches. The solution to this model exhibited a new, unusual phase transition behavior, along with non-vanishing long-range and nearest-neighbor spin-spin correlations, deemed relevant to large neural networks as one of its possible applications.
|
||||
%
|
||||
|
||||
@ -65,6 +65,7 @@
|
||||
\setlength{\marginparwidth}{1.2cm}
|
||||
|
||||
\usepackage{csquotes}
|
||||
\usepackage{url}
|
||||
\usepackage{refcount}% http://ctan.org/pkg/refcount
|
||||
\newcounter{fncntr}
|
||||
\newcommand{\fnmark}[1]{\refstepcounter{fncntr}\label{#1}\footnotemark[\getrefnumber{#1}]}
|
||||
|
||||
@ -3,6 +3,7 @@
|
||||
|
||||
\input prelude.tex
|
||||
\addbibresource{references.bib}
|
||||
\addbibresource{static.bib}
|
||||
\setlength{\marginparwidth}{1.2cm}
|
||||
|
||||
\title{\textbf{Comparison of Models for Ferromagnetic Systems near the Critical Point}}
|
||||
|
||||
@ -34,4 +34,6 @@ Using this data to extract steady state information we are able to determine val
|
||||
\subsection*{Critical Exponents}
|
||||
|
||||
|
||||
|
||||
|
||||
\section*{Conclusion}
|
||||
|
||||
28
static.bib
28
static.bib
@ -1,20 +1,8 @@
|
||||
@article{GNUParallel,
|
||||
title = {GNU Parallel - The Command-Line Power Tool},
|
||||
author = {O. Tange},
|
||||
address = {Frederiksberg, Denmark},
|
||||
journal = {;login: The USENIX Magazine},
|
||||
month = {Feb},
|
||||
number = {1},
|
||||
volume = {36},
|
||||
url = {http://www.gnu.org/s/parallel},
|
||||
year = {2011},
|
||||
pages = {42-47}
|
||||
}
|
||||
|
||||
@online{IPC,
|
||||
author = {Various Physics Lecturers},
|
||||
title = {{Initially Provided DLA Code Model}},
|
||||
url = {https://moodle.bath.ac.uk/course/view.php?id=1876§ion=3},
|
||||
urldate = {2023-03-14}
|
||||
}
|
||||
|
||||
@misc{wiki:phase-digram-eg,
|
||||
author = "Wikimedia Commons",
|
||||
title = "File:Phase-diag2.svg --- Wikimedia Commons{,} the free media repository",
|
||||
year = "2022",
|
||||
url = "\url{https://commons.wikimedia.org/w/index.php?title=File:Phase-diag2.svg&oldid=667966844}",
|
||||
note = "[Online; accessed 28-May-2023]"
|
||||
}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user