Now using spline interpolation as the default for all specific heats, entropies.

1 files changed, 1666 insertions, 1925 deletions

diff --git a/tempering_analysis.nb b/tempering_analysis.nb
index 80e02b2..b5de990 100644
--- a/tempering_analysis.nb
+++ b/tempering_analysis.nb
@@ -10,10 +10,10 @@
 NotebookFileLineBreakTest
 NotebookFileLineBreakTest
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-NotebookOptionsPosition[    372668,       7302]
-NotebookOutlinePosition[    373035,       7318]
-CellTagsIndexPosition[    372992,       7315]
+NotebookDataLength[    364620,       7161]
+NotebookOptionsPosition[    358256,       7055]
+NotebookOutlinePosition[    358619,       7071]
+CellTagsIndexPosition[    358576,       7068]
 WindowFrame->Normal*)
 
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-     RowBox[{"Prepend", "[", 
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-         RowBox[{
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+    RowBox[{
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+      RowBox[{"Prepend", "[", 
+       RowBox[{
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-       ",", 
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           "]]}, 
-        Annotation[#, "Charting`Private`Tag$67707#3"]& ]}}, {}}, {
+        Annotation[#, "Charting`Private`Tag$114440#5"]& ]}}, {}}, {
     DisplayFunction -> Identity, Ticks -> {Automatic, Automatic}, 
-     AxesOrigin -> {Automatic, Automatic}, FrameTicks -> {{Automatic, 
+     AxesOrigin -> {Automatic, 0}, FrameTicks -> {{Automatic, 
         Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic, 
         Charting`ScaledFrameTicks[{Identity, Identity}]}}, 
      GridLines -> {None, None}, DisplayFunction -> Identity, 
      PlotRangePadding -> {{
         Scaled[0.02], 
-        Scaled[0.02]}, {
-        Scaled[0.05], 
-        Scaled[0.05]}}, PlotRangeClipping -> True, ImagePadding -> All, 
-     DisplayFunction -> Identity, AspectRatio -> 
+        Scaled[0.02]}, {0, 0}}, PlotRangeClipping -> True, ImagePadding -> 
+     All, DisplayFunction -> Identity, AspectRatio -> 
      NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True}, 
      AxesLabel -> {
        FormBox["\[Beta]", TraditionalForm], 
@@ -1551,11 +1577,15 @@ vrCP3Q==
            (Identity[#]& )[
             Part[#, 1]], 
            (Identity[#]& )[
-            Part[#, 2]]}& )}}, PlotRange -> {All, All}, PlotRangeClipping -> 
+            Part[#, 2]]}& )}}, PlotRange -> {All, {0, 2}}, PlotRangeClipping -> 
      True, PlotRangePadding -> {{Automatic, Automatic}, {
        Automatic, Automatic}}, Ticks -> {Automatic, Automatic}}],FormBox[
     FormBox[
      TemplateBox[{
+      "\"High-\\!\\(\\*StyleBox[\\\"T\\\",FontSlant->\\\"Italic\\\"]\\) \
+expansion\"", 
+       "\"Low-\\!\\(\\*StyleBox[\\\"T\\\",FontSlant->\\\"Italic\\\"]\\)\\!\\(\
+\\*StyleBox[\\\" \\\",FontSlant->\\\"Italic\\\"]\\)expansion\"", 
        RowBox[{"n", "\[LongEqual]", "8"}], 
        RowBox[{"n", "\[LongEqual]", "12"}], 
        RowBox[{"n", "\[LongEqual]", "16"}]}, "LineLegend", 
@@ -1575,9 +1605,9 @@ vrCP3Q==
                     GrayLevel[0]]], 
                     PointSize[0.5], 
                     Opacity[1.], 
-                    RGBColor[0.368417, 0.506779, 0.709798], 
-                    AbsoluteThickness[1.6]], {
-                    LineBox[{{0, 10}, {20, 10}}]}}, {
+                    AbsoluteThickness[1.6], 
+                    GrayLevel[0]], {
+                    LineBox[{{0, 10}, {40, 10}}]}}, {
                     Directive[
                     EdgeForm[
                     Directive[
@@ -1585,9 +1615,9 @@ vrCP3Q==
                     GrayLevel[0]]], 
                     PointSize[0.5], 
                     Opacity[1.], 
-                    RGBColor[0.368417, 0.506779, 0.709798], 
-                    AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, 
-                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
+                    AbsoluteThickness[1.6], 
+                    GrayLevel[0]], {}}}, AspectRatio -> Full, 
+                    ImageSize -> {40, 10}, PlotRangePadding -> None, 
                     ImagePadding -> Automatic, 
                     BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
                    GraphicsBox[{{
@@ -1598,9 +1628,10 @@ vrCP3Q==
                     GrayLevel[0]]], 
                     PointSize[0.5], 
                     Opacity[1.], 
-                    RGBColor[0.880722, 0.611041, 0.142051], 
-                    AbsoluteThickness[1.6]], {
-                    LineBox[{{0, 10}, {20, 10}}]}}, {
+                    AbsoluteThickness[1.6], 
+                    GrayLevel[0], 
+                    Dashing[{Small, Small}]], {
+                    LineBox[{{0, 10}, {40, 10}}]}}, {
                     Directive[
                     EdgeForm[
                     Directive[
@@ -1608,9 +1639,10 @@ vrCP3Q==
                     GrayLevel[0]]], 
                     PointSize[0.5], 
                     Opacity[1.], 
-                    RGBColor[0.880722, 0.611041, 0.142051], 
-                    AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, 
-                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
+                    AbsoluteThickness[1.6], 
+                    GrayLevel[0], 
+                    Dashing[{Small, Small}]], {}}}, AspectRatio -> Full, 
+                    ImageSize -> {40, 10}, PlotRangePadding -> None, 
                     ImagePadding -> Automatic, 
                     BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, {
                    GraphicsBox[{{
@@ -1621,9 +1653,9 @@ vrCP3Q==
                     GrayLevel[0]]], 
                     PointSize[0.5], 
                     Opacity[1.], 
-                    RGBColor[0.560181, 0.691569, 0.194885], 
-                    AbsoluteThickness[1.6]], {
-                    LineBox[{{0, 10}, {20, 10}}]}}, {
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.368417, 0.506779, 0.709798]], {
+                    LineBox[{{0, 10}, {40, 10}}]}}, {
                     Directive[
                     EdgeForm[
                     Directive[
@@ -1631,11 +1663,57 @@ vrCP3Q==
                     GrayLevel[0]]], 
                     PointSize[0.5], 
                     Opacity[1.], 
-                    RGBColor[0.560181, 0.691569, 0.194885], 
-                    AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, 
-                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
-                    ImagePadding -> Automatic, 
-                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}}, 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.368417, 0.506779, 0.709798]], {}}}, 
+                    AspectRatio -> Full, ImageSize -> {40, 10}, 
+                    PlotRangePadding -> None, ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}, {
+                   GraphicsBox[{{
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    Opacity[1.], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.880722, 0.611041, 0.142051]], {
+                    LineBox[{{0, 10}, {40, 10}}]}}, {
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    Opacity[1.], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.880722, 0.611041, 0.142051]], {}}}, 
+                    AspectRatio -> Full, ImageSize -> {40, 10}, 
+                    PlotRangePadding -> None, ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}, {
+                   GraphicsBox[{{
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    Opacity[1.], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.560181, 0.691569, 0.194885]], {
+                    LineBox[{{0, 10}, {40, 10}}]}}, {
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    Opacity[1.], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.560181, 0.691569, 0.194885]], {}}}, 
+                    AspectRatio -> Full, ImageSize -> {40, 10}, 
+                    PlotRangePadding -> None, ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #5}}, 
                  GridBoxAlignment -> {
                   "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, 
                  AutoDelete -> False, 
@@ -1661,6 +1739,97 @@ vrCP3Q==
                RowBox[{"Directive", "[", 
                  RowBox[{
                    RowBox[{"Opacity", "[", "1.`", "]"}], ",", 
+                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
+                   InterpretationBox[
+                    ButtonBox[
+                    TooltipBox[
+                    GraphicsBox[{{
+                    GrayLevel[0], 
+                    RectangleBox[{0, 0}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{1, -1}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
+                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
+                    FrameStyle -> GrayLevel[0.], FrameTicks -> None, 
+                    PlotRangePadding -> None, ImageSize -> 
+                    Dynamic[{
+                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
+                    AbsoluteCurrentValue[Magnification]}]], 
+                    StyleBox[
+                    RowBox[{"GrayLevel", "[", "0", "]"}], NumberMarks -> 
+                    False]], Appearance -> None, BaseStyle -> {}, 
+                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
+                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
+                    If[
+                    Not[
+                    AbsoluteCurrentValue["Deployed"]], 
+                    SelectionMove[Typeset`box$, All, Expression]; 
+                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
+                    FrontEnd`Private`$ColorSelectorInitialColor = 
+                    GrayLevel[0]; 
+                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
+                    MathLink`CallFrontEnd[
+                    FrontEnd`AttachCell[Typeset`box$, 
+                    FrontEndResource["GrayLevelColorValueSelector"], {
+                    0, {Left, Bottom}}, {Left, Top}, 
+                    "ClosingActions" -> {
+                    "SelectionDeparture", "ParentChanged", 
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           "]]}, 
-        Annotation[#, "Charting`Private`Tag$77931#4"]& ]}}, {}}, {
+        Annotation[#, "Charting`Private`Tag$113748#5"]& ]}}, {}}, {
     DisplayFunction -> Identity, 
      Method -> {
       "DefaultBoundaryStyle" -> Automatic, 
@@ -2243,7 +2417,7 @@ TJXndPgf1VQfRw==
      Ticks -> {Quiet[
         Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& , Quiet[
         Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& }, 
-     AxesOrigin -> {-11.512925464970229`, -14.619668330378314`}, 
+     AxesOrigin -> {-11.512925150175361`, -14.619668378205503`}, 
      FrameTicks -> {{Quiet[
          Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& , 
         Charting`ScaledFrameTicks[{Log, Exp}]}, {Quiet[
@@ -2252,8 +2426,7 @@ TJXndPgf1VQfRw==
      DisplayFunction -> Identity, PlotRangePadding -> {{
         Scaled[0.02], 
         Scaled[0.02]}, {
-        Scaled[0.05], 
-        Scaled[0.05]}}, PlotRangeClipping -> True, ImagePadding -> All, 
+        Scaled[0.05], 0}}, PlotRangeClipping -> True, ImagePadding -> All, 
      DisplayFunction -> Identity, 
      Method -> {
       "DefaultBoundaryStyle" -> Automatic, 
@@ -2265,13 +2438,12 @@ TJXndPgf1VQfRw==
             "freeformCursorMode" -> True, 
              "placement" -> {"x" -> "All", "y" -> "None"}}}}, 
        "DefaultMeshStyle" -> AbsolutePointSize[6], "ScalingFunctions" -> None,
-        "ClippingRange" -> {{{-11.512925164321222`, 
-        3.2188755242191944`}, {-14.619668330378314`, 
-        0.11934465787337491`}}, {{-11.512925164321222`, 
-        3.2188755242191944`}, {-14.619668330378314`, 0.11934465787337491`}}}},
-      DisplayFunction -> Identity, AspectRatio -> 
-     NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True}, 
-     AxesLabel -> {
+        "ClippingRange" -> {{{-11.512925150175361`, 
+        3.9120226906332793`}, {-14.619668378205503`, 
+        10.12663078905547}}, {{-11.512925150175361`, 
+        3.9120226906332793`}, {-14.619668378205503`, 0.}}}}, DisplayFunction -> 
+     Identity, AspectRatio -> NCache[GoldenRatio^(-1), 0.6180339887498948], 
+     Axes -> {True, True}, AxesLabel -> {
        FormBox["\[Beta]", TraditionalForm], 
        FormBox["\"c(\[Beta]) / \[Beta]\"", TraditionalForm]}, 
      AxesOrigin -> {0, 0}, CoordinatesToolOptions -> {"DisplayFunction" -> ({
@@ -2298,19 +2470,16 @@ TJXndPgf1VQfRw==
             "freeformCursorMode" -> True, 
              "placement" -> {"x" -> "All", "y" -> "None"}}}}, 
        "DefaultMeshStyle" -> AbsolutePointSize[6], "ScalingFunctions" -> 
-       None}, PlotRange -> NCache[{{-11.512925464970229`, 
-         Log[25]}, {-14.619668330378314`, 
-        0.11934465787337491`}}, {{-11.512925464970229`, 
-       3.2188758248682006`}, {-14.619668330378314`, 0.11934465787337491`}}], 
-     PlotRangeClipping -> True, PlotRangePadding -> {{
-        Scaled[0.02], 
-        Scaled[0.02]}, {
-        Scaled[0.02], 
-        Scaled[0.02]}}, Ticks -> {Automatic, Automatic}}],FormBox[
+       None}, PlotRange -> {All, {-14.619668378205503`, 0}}, 
+     PlotRangeClipping -> True, 
+     PlotRangePadding -> {{Automatic, Automatic}, {
+        Scaled[0.02], Automatic}}, Ticks -> {Automatic, Automatic}}],FormBox[
     FormBox[
      TemplateBox[{
       "\"High-\\!\\(\\*StyleBox[\\\"T\\\",FontSlant->\\\"Italic\\\"]\\) \
 expansion\"", 
+       "\"Low-\\!\\(\\*StyleBox[\\\"T\\\",FontSlant->\\\"Italic\\\"]\\)\\!\\(\
+\\*StyleBox[\\\" \\\",FontSlant->\\\"Italic\\\"]\\)expansion\"", 
        RowBox[{"n", "\[LongEqual]", "8"}], 
        RowBox[{"n", "\[LongEqual]", "12"}], 
        RowBox[{"n", "\[LongEqual]", "16"}]}, "LineLegend", 
@@ -2332,7 +2501,7 @@ expansion\"",
                     Opacity[1.], 
                     AbsoluteThickness[1.6], 
                     GrayLevel[0]], {
-                    LineBox[{{0, 10}, {20, 10}}]}}, {
+                    LineBox[{{0, 10}, {40, 10}}]}}, {
                     Directive[
                     EdgeForm[
                     Directive[
@@ -2342,7 +2511,7 @@ expansion\"",
                     Opacity[1.], 
                     AbsoluteThickness[1.6], 
                     GrayLevel[0]], {}}}, AspectRatio -> Full, 
-                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
+                    ImageSize -> {40, 10}, PlotRangePadding -> None, 
                     ImagePadding -> Automatic, 
                     BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
                    GraphicsBox[{{
@@ -2354,8 +2523,33 @@ expansion\"",
                     PointSize[0.5], 
                     Opacity[1.], 
                     AbsoluteThickness[1.6], 
+                    GrayLevel[0], 
+                    Dashing[{Small, Small}]], {
+                    LineBox[{{0, 10}, {40, 10}}]}}, {
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    Opacity[1.], 
+                    AbsoluteThickness[1.6], 
+                    GrayLevel[0], 
+                    Dashing[{Small, Small}]], {}}}, AspectRatio -> Full, 
+                    ImageSize -> {40, 10}, PlotRangePadding -> None, 
+                    ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, {
+                   GraphicsBox[{{
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    Opacity[1.], 
+                    AbsoluteThickness[1.6], 
                     RGBColor[0.368417, 0.506779, 0.709798]], {
-                    LineBox[{{0, 10}, {20, 10}}]}}, {
+                    LineBox[{{0, 10}, {40, 10}}]}}, {
                     Directive[
                     EdgeForm[
                     Directive[
@@ -2365,9 +2559,9 @@ expansion\"",
                     Opacity[1.], 
                     AbsoluteThickness[1.6], 
                     RGBColor[0.368417, 0.506779, 0.709798]], {}}}, 
-                    AspectRatio -> Full, ImageSize -> {20, 10}, 
+                    AspectRatio -> Full, ImageSize -> {40, 10}, 
                     PlotRangePadding -> None, ImagePadding -> Automatic, 
-                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, {
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}, {
                    GraphicsBox[{{
                     Directive[
                     EdgeForm[
@@ -2378,7 +2572,7 @@ expansion\"",
                     Opacity[1.], 
                     AbsoluteThickness[1.6], 
                     RGBColor[0.880722, 0.611041, 0.142051]], {
-                    LineBox[{{0, 10}, {20, 10}}]}}, {
+                    LineBox[{{0, 10}, {40, 10}}]}}, {
                     Directive[
                     EdgeForm[
                     Directive[
@@ -2388,9 +2582,9 @@ expansion\"",
                     Opacity[1.], 
                     AbsoluteThickness[1.6], 
                     RGBColor[0.880722, 0.611041, 0.142051]], {}}}, 
-                    AspectRatio -> Full, ImageSize -> {20, 10}, 
+                    AspectRatio -> Full, ImageSize -> {40, 10}, 
                     PlotRangePadding -> None, ImagePadding -> Automatic, 
-                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}, {
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}, {
                    GraphicsBox[{{
                     Directive[
                     EdgeForm[
@@ -2401,7 +2595,7 @@ expansion\"",
                     Opacity[1.], 
                     AbsoluteThickness[1.6], 
                     RGBColor[0.560181, 0.691569, 0.194885]], {
-                    LineBox[{{0, 10}, {20, 10}}]}}, {
+                    LineBox[{{0, 10}, {40, 10}}]}}, {
                     Directive[
                     EdgeForm[
                     Directive[
@@ -2411,9 +2605,9 @@ expansion\"",
                     Opacity[1.], 
                     AbsoluteThickness[1.6], 
                     RGBColor[0.560181, 0.691569, 0.194885]], {}}}, 
-                    AspectRatio -> Full, ImageSize -> {20, 10}, 
+                    AspectRatio -> Full, ImageSize -> {40, 10}, 
                     PlotRangePadding -> None, ImagePadding -> Automatic, 
-                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}}, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #5}}, 
                  GridBoxAlignment -> {
                   "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, 
                  AutoDelete -> False, 
@@ -2491,6 +2685,53 @@ expansion\"",
                     RectangleBox[{0, 0}]}, {
                     GrayLevel[0], 
                     RectangleBox[{1, -1}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
+                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
+                    FrameStyle -> GrayLevel[0.], FrameTicks -> None, 
+                    PlotRangePadding -> None, ImageSize -> 
+                    Dynamic[{
+                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
+                    AbsoluteCurrentValue[Magnification]}]], 
+                    StyleBox[
+                    RowBox[{"GrayLevel", "[", "0", "]"}], NumberMarks -> 
+                    False]], Appearance -> None, BaseStyle -> {}, 
+                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
+                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
+                    If[
+                    Not[
+                    AbsoluteCurrentValue["Deployed"]], 
+                    SelectionMove[Typeset`box$, All, Expression]; 
+                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
+                    FrontEnd`Private`$ColorSelectorInitialColor = 
+                    GrayLevel[0]; 
+                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
+                    MathLink`CallFrontEnd[
+                    FrontEnd`AttachCell[Typeset`box$, 
+                    FrontEndResource["GrayLevelColorValueSelector"], {
+                    0, {Left, Bottom}}, {Left, Top}, 
+                    "ClosingActions" -> {
+                    "SelectionDeparture", "ParentChanged", 
+                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
+                    Automatic, Method -> "Preemptive"], 
+                    GrayLevel[0], Editable -> False, Selectable -> False], 
+                   ",", 
+                   RowBox[{"Dashing", "[", 
+                    RowBox[{"{", 
+                    RowBox[{"Small", ",", "Small"}], "}"}], "]"}]}], "]"}], 
+               ",", 
+               RowBox[{"Directive", "[", 
+                 RowBox[{
+                   RowBox[{"Opacity", "[", "1.`", "]"}], ",", 
+                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
+                   InterpretationBox[
+                    ButtonBox[
+                    TooltipBox[
+                    GraphicsBox[{{
+                    GrayLevel[0], 
+                    RectangleBox[{0, 0}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{1, -1}]}, {
                     RGBColor[0.368417, 0.506779, 0.709798], 
                     RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                     "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
@@ -2622,7 +2863,7 @@ expansion\"",
                     RGBColor[0.560181, 0.691569, 0.194885], Editable -> False,
                      Selectable -> False]}], "]"}]}], "}"}], ",", 
            RowBox[{"{", 
-             RowBox[{#, ",", #2, ",", #3, ",", #4}], "}"}], ",", 
+             RowBox[{#, ",", #2, ",", #3, ",", #4, ",", #5}], "}"}], ",", 
            RowBox[{"LegendMarkers", "\[Rule]", "None"}], ",", 
            RowBox[{"LabelStyle", "\[Rule]", 
              RowBox[{"{", "}"}]}], ",", 
@@ -2650,9 +2891,10 @@ expansion\"",
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    3.790680768133603*^9, {3.790681247430805*^9, 3.7906812623349133`*^9}, 
    3.79068130990163*^9, 3.7906856024308653`*^9, 3.7906857162813396`*^9, {
-   3.790686478844146*^9, 3.7906865357958193`*^9}, 3.790687109731969*^9},
- CellLabel->
-  "Out[303]=",ExpressionUUID->"8e44c7c9-5ce5-472b-9910-b5854ac7e6dc"]
+   3.790686478844146*^9, 3.7906865357958193`*^9}, 3.790687109731969*^9, 
+   3.7908818555386677`*^9, {3.790882251610034*^9, 3.79088230753218*^9}, 
+   3.79088233976814*^9, 3.790882410673272*^9, 3.790882481813483*^9},
+ CellLabel->"Out[80]=",ExpressionUUID->"927dd89d-4b73-4120-a692-bfd5bafde5d0"]
 }, Open  ]],
 
 Cell[BoxData[{
@@ -2681,8 +2923,7 @@ Cell[BoxData[{
   3.7898320553038607`*^9}, {3.789864943007975*^9, 3.7898649514318943`*^9}, {
   3.789892831115396*^9, 3.789892831435464*^9}, {3.789896963511537*^9, 
   3.7898969690204773`*^9}},
- CellLabel->
-  "In[271]:=",ExpressionUUID->"09f155dc-a270-465f-83b4-5452a9d3c6a6"],
+ CellLabel->"In[39]:=",ExpressionUUID->"09f155dc-a270-465f-83b4-5452a9d3c6a6"],
 
 Cell[BoxData[{
  RowBox[{
@@ -2708,8 +2949,7 @@ Cell[BoxData[{
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   3.789892842756661*^9}, {3.789896975455278*^9, 3.789896979805492*^9}},
- CellLabel->
-  "In[294]:=",ExpressionUUID->"faf27222-05ad-48db-b551-d6176fd5d567"],
+ CellLabel->"In[43]:=",ExpressionUUID->"faf27222-05ad-48db-b551-d6176fd5d567"],
 
 Cell[CellGroupData[{
 
@@ -2753,7 +2993,7 @@ Cell[BoxData[
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         RowBox[{"[", "1", "]"}], "]"}]}]}], "}"}], "]"}], ",", 
    RowBox[{"{", 
-    RowBox[{"x", ",", "1", ",", "25"}], "}"}], ",", 
+    RowBox[{"x", ",", "1", ",", "10"}], "}"}], ",", 
    RowBox[{"AxesLabel", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{"\[Beta]", ",", 
@@ -2762,12 +3002,22 @@ Cell[BoxData[
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         RowBox[{"s", "[", "\[Beta]", "]"}]}], ")"}]}], "}"}]}], ",", 
    RowBox[{"PlotStyle", "\[Rule]", 
-    RowBox[{
-     RowBox[{"ColorData", "[", "97", "]"}], "/@", 
-     RowBox[{"Riffle", "[", 
+    RowBox[{"Thread", "[", 
+     RowBox[{"{", 
       RowBox[{
-       RowBox[{"Range", "[", "3", "]"}], ",", 
-       RowBox[{"Range", "[", "3", "]"}]}], "]"}]}]}], ",", 
+       RowBox[{"Flatten", "[", 
+        RowBox[{"ConstantArray", "[", 
+         RowBox[{
+          RowBox[{"{", 
+           RowBox[{"None", ",", "Dashed"}], "}"}], ",", "3"}], "]"}], "]"}], 
+       ",", 
+       RowBox[{
+        RowBox[{"ColorData", "[", "97", "]"}], "/@", 
+        RowBox[{"Riffle", "[", 
+         RowBox[{
+          RowBox[{"Range", "[", "3", "]"}], ",", 
+          RowBox[{"Range", "[", "3", "]"}]}], "]"}]}]}], "}"}], "]"}]}], ",", 
+   
    RowBox[{"PlotLegends", "\[Rule]", 
     RowBox[{"{", 
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@@ -2786,9 +3036,10 @@ Cell[BoxData[
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+   3.790883013839507*^9}},
+ CellLabel->"In[85]:=",ExpressionUUID->"511fd1ec-10b6-4e80-beb1-748a7f18c95e"],
 
 Cell[BoxData[
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