{"id":1735,"date":"2022-02-04T14:27:07","date_gmt":"2022-02-04T05:27:07","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=1735"},"modified":"2023-02-03T11:20:04","modified_gmt":"2023-02-03T02:20:04","slug":"%e8%a3%9c%e8%b6%b3%ef%bc%9agnuplot-%e3%81%a7%e5%ae%87%e5%ae%99%e5%b9%b4%e9%bd%a2%e3%81%ae%e3%82%b0%e3%83%a9%e3%83%95%e3%82%92%e6%8f%8f%e3%81%8f","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e4%b8%80%e8%88%ac%e7%9b%b8%e5%af%be%e8%ab%96%e7%9a%84%e5%ae%87%e5%ae%99%e8%ab%96\/%e5%ae%87%e5%ae%99%e8%ab%96%e3%83%91%e3%83%a9%e3%83%a1%e3%83%bc%e3%82%bf%e3%81%a8%e5%ae%87%e5%ae%99%e5%b9%b4%e9%bd%a2\/%e8%a3%9c%e8%b6%b3%ef%bc%9agnuplot-%e3%81%a7%e5%ae%87%e5%ae%99%e5%b9%b4%e9%bd%a2%e3%81%ae%e3%82%b0%e3%83%a9%e3%83%95%e3%82%92%e6%8f%8f%e3%81%8f\/","title":{"rendered":"\u88dc\u8db3\uff1agnuplot \u3067\u5b87\u5b99\u5e74\u9f62\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f"},"content":{"rendered":"<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5b87\u5b99\u5e74\u9f62\u306e\u8868\u5f0f\u306e\u5c0e\u51fa\u306b\u3064\u3044\u3066\u306f\uff0c\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u3092\u53c2\u7167\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e4%b8%80%e8%88%ac%e7%9b%b8%e5%af%be%e8%ab%96%e7%9a%84%e5%ae%87%e5%ae%99%e8%ab%96\/%e5%ae%87%e5%ae%99%e8%ab%96%e3%83%91%e3%83%a9%e3%83%a1%e3%83%bc%e3%82%bf%e3%81%a8%e5%ae%87%e5%ae%99%e5%b9%b4%e9%bd%a2\/\">\u5b87\u5b99\u8ad6\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u5b87\u5b99\u5e74\u9f62<\/a><\/li>\n<\/ul>\n<p>\u3053\u3053\u3067\u306f\uff0cgnuplot \u3092\u4f7f\u3063\u3066\u5b87\u5b99\u5e74\u9f62\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u3044\u3066\u307f\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p><!--more--><\/p>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[1]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-gnuplot\">\n<pre><span class=\"err\">%gnu<\/span><span class=\"k\">plot<\/span> <span class=\"n\">inline<\/span> <span class=\"n\">svg<\/span> <span class=\"n\">size<\/span> <span class=\"mi\">600<\/span><span class=\"o\">,<\/span><span class=\"mi\">450<\/span> <span class=\"n\">font<\/span> <span class=\"s\">\"Arial, 14\"<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"$\\Omega_{\\Lambda}-=-0$-\u306e\u5834\u5408\">$\\Omega_{\\Lambda} = 0$ \u306e\u5834\u5408<\/h3>\n<p>$$H_0 t_0 = -\\frac{1}{\\Omega_{\\rm m} -1}+\\frac{\\Omega_{\\rm m}}{(\\Omega_{\\rm m}-1)^{\\frac{3}{2}} }<br \/>\n\\tan^{-1}\\sqrt{\\Omega_{\\rm m}-1} \\quad \\mbox{for}\\ \\ \\Omega_{\\rm m} &gt; 1$$$$H_0 t_0 = \\frac{1}{1-\\Omega_{\\rm m}}-\\frac{\\Omega_{\\rm m}}{(1-\\Omega_{\\rm m})^{\\frac{3}{2}} }<br \/>\n\\tanh^{-1}\\sqrt{1-\\Omega_{\\rm m}} \\quad \\mbox{for}\\ \\ \\Omega_{\\rm m} &lt; 1$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-gnuplot\">\n<pre><span class=\"c\"># Omega &gt; 1<\/span>\r\n<span class=\"nf\">t1<\/span>(Om) <span class=\"o\">=<\/span> <span class=\"mi\">-1<\/span><span class=\"o\">.\/<\/span><span class=\"p\">(<\/span><span class=\"n\">Om<\/span><span class=\"mi\">-1<\/span><span class=\"p\">)<\/span> <span class=\"o\">+<\/span> <span class=\"n\">Om<\/span><span class=\"o\">\/<\/span><span class=\"p\">((<\/span><span class=\"n\">Om<\/span><span class=\"mi\">-1<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">Om<\/span><span class=\"mi\">-1<\/span><span class=\"p\">))<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">atan<\/span><span class=\"p\">(<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">Om<\/span><span class=\"mi\">-1<\/span><span class=\"p\">))<\/span>\r\n<span class=\"c\"># Omega &lt; 1<\/span>\r\n<span class=\"nf\">t2<\/span>(Om) <span class=\"o\">=<\/span> <span class=\"mf\">1.<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">Om<\/span><span class=\"p\">)<\/span> <span class=\"o\">-<\/span> <span class=\"n\">Om<\/span><span class=\"o\">\/<\/span><span class=\"p\">((<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">Om<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">Om<\/span><span class=\"p\">))<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">atanh<\/span><span class=\"p\">(<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">Om<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"c\"># \u4e09\u9805\u6f14\u7b97\u5b50\u3092\u4f7f\u3063\u305f\u95a2\u6570\u5b9a\u7fa9\u3002Om = 1 \u306e\u3068\u304d\u304c\u3061\u3087\u3063\u3068\u4e0d\u5b89<\/span>\r\n<span class=\"nf\">t<\/span>(Om) <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"n\">Om<\/span> <span class=\"o\">&gt;<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">?<\/span> <span class=\"nf\">t1<\/span><span class=\"p\">(<\/span><span class=\"n\">Om<\/span><span class=\"p\">)<\/span> <span class=\"o\">:<\/span> <span class=\"nf\">t2<\/span><span class=\"p\">(<\/span><span class=\"n\">Om<\/span><span class=\"p\">))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"$k-=-0$-\u306e\u5834\u5408\">$k = 0$ \u306e\u5834\u5408<\/h3>\n<p>$$H_0 t_0 = \\frac{2}{3\\sqrt{\\Omega_{\\rm m} -1}}\\tan^{-1} \\sqrt{\\Omega_{\\rm m} -1} \\quad \\mbox{for}\\ \\ \\Omega_{\\rm m} &gt; 1$$$$H_0 t_0 = \\frac{2}{3\\sqrt{1-\\Omega_{\\rm m} }}\\tanh^{-1} \\sqrt{1-\\Omega_{\\rm m} } \\quad \\mbox{for}\\ \\ \\Omega_{\\rm m} &lt; 1$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[3]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-gnuplot\">\n<pre><span class=\"c\"># Omega &gt; 1<\/span>\r\n<span class=\"nf\">T1<\/span>(Om) <span class=\"o\">=<\/span> <span class=\"mf\">2.<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"mi\">3<\/span><span class=\"o\">*<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">Om<\/span><span class=\"mi\">-1<\/span><span class=\"p\">))<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">atan<\/span><span class=\"p\">(<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">Om<\/span><span class=\"mi\">-1<\/span><span class=\"p\">))<\/span>\r\n<span class=\"c\"># Omega &lt; 1<\/span>\r\n<span class=\"nf\">T2<\/span>(Om) <span class=\"o\">=<\/span> <span class=\"mf\">2.<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"mi\">3<\/span><span class=\"o\">*<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">Om<\/span><span class=\"p\">))<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">atanh<\/span><span class=\"p\">(<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">Om<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"c\"># \u4e09\u9805\u6f14\u7b97\u5b50\u3092\u4f7f\u3063\u305f\u95a2\u6570\u5b9a\u7fa9\u3002Om = 1 \u306e\u3068\u304d\u304c\u3061\u3087\u3063\u3068\u4e0d\u5b89<\/span>\r\n<span class=\"nf\">T<\/span>(Om) <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"n\">Om<\/span> <span class=\"o\">&gt;<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">?<\/span> <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"n\">Om<\/span><span class=\"p\">)<\/span> <span class=\"o\">:<\/span> <span class=\"nf\">T2<\/span><span class=\"p\">(<\/span><span class=\"n\">Om<\/span><span class=\"p\">))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[4]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-gnuplot\">\n<pre><span class=\"k\">set<\/span> <span class=\"nb\">samples<\/span> <span class=\"mi\">200<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">title<\/span> <span class=\"s\">\"\u5b87\u5b99\u5e74\u9f62\u306e\u5bc6\u5ea6\u30d1\u30e9\u30e1\u30fc\u30bf\u4f9d\u5b58\u6027\"<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">xlabel<\/span> <span class=\"s\">\"{\/Times \u03a9_m}\"<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">ylabel<\/span> <span class=\"s\">\"{\/jsMath-cmti10=16 H}_0 {\/jsMath-cmti10=16 t}_0\"<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">xtics<\/span> <span class=\"mf\">0.2<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">mxtics<\/span> <span class=\"mi\">2<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">ytics<\/span> <span class=\"mf\">0.1<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">mytics<\/span> <span class=\"mi\">2<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">grid<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">yrange<\/span> <span class=\"p\">[<\/span><span class=\"mf\">0.5<\/span><span class=\"o\">:<\/span><span class=\"mf\">1.5<\/span><span class=\"p\">]<\/span>\r\n\r\n<span class=\"k\">plot<\/span> <span class=\"p\">[<\/span><span class=\"n\">Om<\/span><span class=\"o\">=<\/span><span class=\"mi\">0<\/span><span class=\"o\">:<\/span><span class=\"mi\">2<\/span><span class=\"p\">]<\/span> \\\r\n<span class=\"nf\">T<\/span><span class=\"p\">(<\/span><span class=\"n\">Om<\/span><span class=\"p\">)<\/span> <span class=\"n\">lc<\/span> <span class=\"s\">\"red\"<\/span> <span class=\"n\">lw<\/span> <span class=\"mi\">2<\/span> <span class=\"nb\">title<\/span> <span class=\"s\">\"{\/Times \u03a9_\u039b = 1 - \u03a9_m}\"<\/span><span class=\"o\">,<\/span> \\\r\n<span class=\"nb\">t<\/span><span class=\"p\">(<\/span><span class=\"n\">Om<\/span><span class=\"p\">)<\/span> <span class=\"n\">lc<\/span> <span class=\"s\">\"black\"<\/span> <span class=\"n\">lw<\/span> <span class=\"mi\">2<\/span> <span class=\"nb\">title<\/span> <span class=\"s\">\"{\/Times \u03a9_\u039b = 0}\"<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-5304\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/gt-fig1A.svg\" alt=\"\" width=\"600\" height=\"450\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5b87\u5b99\u5e74\u9f62\u306e\u8868\u5f0f\u306e\u5c0e\u51fa\u306b\u3064\u3044\u3066\u306f\uff0c\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u3092\u53c2\u7167\u3002<\/p>\n<ul>\n<li>\u5b87\u5b99\u8ad6\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u5b87\u5b99\u5e74\u9f62<\/li>\n<\/ul>\n<p>\u3053\u3053\u3067\u306f\uff0cgnuplot \u3092\u4f7f\u3063\u3066\u5b87\u5b99\u5e74\u9f62\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u3044\u3066\u307f\u308b\u3002<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e4%b8%80%e8%88%ac%e7%9b%b8%e5%af%be%e8%ab%96%e7%9a%84%e5%ae%87%e5%ae%99%e8%ab%96\/%e5%ae%87%e5%ae%99%e8%ab%96%e3%83%91%e3%83%a9%e3%83%a1%e3%83%bc%e3%82%bf%e3%81%a8%e5%ae%87%e5%ae%99%e5%b9%b4%e9%bd%a2\/%e8%a3%9c%e8%b6%b3%ef%bc%9agnuplot-%e3%81%a7%e5%ae%87%e5%ae%99%e5%b9%b4%e9%bd%a2%e3%81%ae%e3%82%b0%e3%83%a9%e3%83%95%e3%82%92%e6%8f%8f%e3%81%8f\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"parent":1483,"menu_order":20,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-1735","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/1735","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/users\/33"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=1735"}],"version-history":[{"count":5,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/1735\/revisions"}],"predecessor-version":[{"id":5305,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/1735\/revisions\/5305"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/1483"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=1735"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}