SchoolKias/PartonShowersCkkw: KIASschool.m

File KIASschool.m, 355.2 KB (added by GrishaKirilin, 9 years ago)

the Mathematica package needed for the first lecture

Line 
1(* ::Package:: *)
2
3(************************************************************************)
4(* This file was generated automatically by the Mathematica front end.  *)
5(* It contains Initialization cells from a Notebook file, which         *)
6(* typically will have the same name as this file except ending in      *)
7(* ".nb" instead of ".m".                                               *)
8(*                                                                      *)
9(* This file is intended to be loaded into the Mathematica kernel using *)
10(* the package loading commands Get or Needs.  Doing so is equivalent   *)
11(* to using the Evaluate Initialization Cells menu command in the front *)
12(* end.                                                                 *)
13(*                                                                      *)
14(* DO NOT EDIT THIS FILE.  This entire file is regenerated              *)
15(* automatically each time the parent Notebook file is saved in the     *)
16(* Mathematica front end.  Any changes you make to this file will be    *)
17(* overwritten.                                                         *)
18(************************************************************************)
19
20
21
22(* Grisha Kirilin 2011 *)
23
24
25BeginPackage["KIAS`KIASschool`" ]
26
27
28movingCharge::usage="runs the manitulation dialog for moving cgarge electric field demonstration"
29demonstration::usage="runs the manitulation dialog for n-prong antenna"
30show3Dpattern::usage="auxilary function for the dialog for n-prong antenna"
31
32
33Begin["`Private`"]
34
35
36\[Beta]List=Range[0.19,0.99,0.1];
37
38
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56812PYff/wxVgcAWLUMlqICddle8bn4dIgpXWOmWB0AYK0w6EbfpwkAAAAAAAAA
5682AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
5683AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
5684AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
5685AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
5686AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
5687AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACwSvn/71qo
5688vg==
5689"], {{0, 0}, {360., 358.56}}, {0, 255}, ColorFunction -> RGBColor], ImageSize -> {360., 358.56}, PlotRange -> {{0, 360.}, {0, 358.56}}]};
5690
5691
5692demonstration[0]=Manipulate[rasterPlots[[\[Beta]]],{{\[Beta],1,"Speed of charge"},1,Length[\[Beta]List],1}];
5693
5694
5695pmax[\[Mu]_]=1/2 Sqrt[(1-9\[Mu]^2)(1-\[Mu]^2)];
5696pzmax[p_,\[Mu]_]=With[{\[Epsilon]=1-Sqrt[p^2+\[Mu]^2]},1/2 (p+\[Epsilon] Sqrt[1-(4\[Mu]^2)/(\[Epsilon]^2-p^2)])];
5697pzmin[p_,\[Mu]_]=With[{\[Epsilon]=1-Sqrt[p^2+\[Mu]^2]},1/2 (p-\[Epsilon] Sqrt[1-(4\[Mu]^2)/(\[Epsilon]^2-p^2)])];
5698
5699
5700kT[p_,pz_,\[Mu]_]=With[{\[Epsilon]=1-Sqrt[p^2+\[Mu]^2]},(1/4 (\[Epsilon]+(pz^2-(p-pz)^2)/\[Epsilon])^2-\[Mu]^2-pz^2)^(1/2)];
5701
5702
5703\[Epsilon][1,p_,pz_,\[Mu]_]=Sqrt[p^2+\[Mu]^2];
5704\[Epsilon][2,p_,pz_,\[Mu]_]=Sqrt[pz^2+kT[p,pz,\[Mu]]^2+\[Mu]^2];
5705\[Epsilon][3,p_,pz_,\[Mu]_]=Sqrt[(p-pz)^2+kT[p,pz,\[Mu]]^2+\[Mu]^2];
5706
5707
5708prongs[p_,pz_,\[Mu]_]={{-p,0},{pz,kT[p,pz,\[Mu]]},{p-pz,-kT[p,pz,\[Mu]]}};
5709
5710
5711prongs[\[Theta]_]={{1,0},RotationMatrix[\[Theta]].{1,0}};
5712
5713
5714singlePattern[q_,v_,n_]:=q Cross[v,n]/(1-v.n);
5715
5716
5717nProngPattern[vList_,eList_,n_]:=#.#&[Total[Table[singlePattern[eList[[i]],vList[[i]],n] ,{i,1,Length[vList]}]]];
5718
5719
5720TwoProng2D[{v_,\[Theta]_},\[Eta]_]=nProngPattern[{v{1,0,0},v Append[RotationMatrix[\[Theta]].{1,0},0]},{1,-1},{Cos[\[Eta]],Sin[\[Eta]],0}];
5721
5722
5723TwoProng3D[{v_,\[Theta]_},{\[Eta]_,\[Phi]_}]=nProngPattern[{v{1,0,0},v Append[RotationMatrix[\[Theta]].{1,0},0]},{1,-1},{Cos[\[Eta]],Sin[\[Eta]]Cos[\[Phi]],Sin[\[Eta]]Sin[\[Phi]]}];
5724
5725
5726ThreeProng2D[{p_,pz_,\[Mu]_},\[CapitalTheta]_]=nProngPattern[{{-p,0,0}/\[Epsilon][1,p,pz,\[Mu]],{pz,kT[p,pz,\[Mu]],0}/\[Epsilon][2,p,pz,\[Mu]],{p-pz,-kT[p,pz,\[Mu]],0}/\[Epsilon][3,p,pz,\[Mu]]},{1,-N[GoldenRatio],-1+N[GoldenRatio]},{Cos[\[Theta]],Sin[\[Theta]],0}];
5727
5728
5729ThreeProng3D[{p_,pz_,\[Mu]_},{\[CapitalTheta]_,\[Phi]_}]=nProngPattern[{{-p,0,0}/\[Epsilon][1,p,pz,\[Mu]],{pz,kT[p,pz,\[Mu]],0}/\[Epsilon][2,p,pz,\[Mu]],{p-pz,-kT[p,pz,\[Mu]],0}/\[Epsilon][3,p,pz,\[Mu]]},{1,-N[GoldenRatio],-1+N[GoldenRatio]},{Cos[\[Theta]],Sin[\[Theta]]Cos[\[Phi]],Sin[\[Theta]]Sin[\[Phi]]}];
5730
5731
5732prongStyle={Red,Blue,Darker[Green]};
5733
5734
5735pdemo[p_,\[Mu]_]=p pmax[\[Mu]];
5736pzdemo[p_,pz_,\[Mu]_]=pzmin[p pmax[\[Mu]],\[Mu]]+pz(pzmax[p pmax[\[Mu]],\[Mu]]-pzmin[p pmax[\[Mu]],\[Mu]]);
5737
5738
5739epilog[True,\[Theta]_]:=With[{cPoint=ImageScaled[{.5,.5}]},{
5740(* particle momenta *)
5741MapIndexed[{Opacity[.35],Thickness[0.015],prongStyle[[First@#2]],Line[{cPoint,ImageScaled[{.5,.5}+#1/2]}]}&,prongs[\[Theta]]],
5742(* paricles *)
5743MapIndexed[{prongStyle[[First@#2]],EdgeForm[Darker[prongStyle[[First@#2]]]],Disk[ImageScaled[{.5,.5}+#1/2],ImageScaled[0.01]]}&,prongs[\[Theta]]],
5744(* arc demonstration *)
5745{Gray,Line[{cPoint,ImageScaled[{1,.5}]}]},
5746{Gray,Circle[cPoint,ImageScaled[0.3],{0,\[Theta]}]},
5747(* point in the center *)
5748{Black,PointSize-> Medium,Point[{0,0}]}
5749}];
5750
5751
5752epilog[False,\[Theta]_]:=With[{cPoint=ImageScaled[{.5,.5}]},{
5753(* particle momenta *)
5754MapIndexed[{Opacity[.35],Thickness[0.015],prongStyle[[First@#2]],Line[{cPoint,ImageScaled[{.5,.5}+#1/2]}]}&,prongs[\[Theta]]],
5755(* paricles *)
5756MapIndexed[{prongStyle[[First@#2]],EdgeForm[Darker[prongStyle[[First@#2]]]],Disk[ImageScaled[{.5,.5}+#1/2],ImageScaled[0.01]]}&,prongs[\[Theta]]],
5757(* point in the center *)
5758{Black,PointSize-> Medium,Point[{0,0}]}
5759}];
5760
5761
5762epilog[True,p_,pz_,\[Mu]_]:=With[{cPoint=ImageScaled[{.5,.5}]},{
5763(* particle momenta *)
5764MapIndexed[{Opacity[.35],Thickness[0.015],prongStyle[[First@#2]],Line[{cPoint,ImageScaled[{.5,.5}+#1/(2pmax[\[Mu]])]}]}&,prongs[pdemo[p,\[Mu]],pzdemo[p,pz,\[Mu]],\[Mu]]],
5765(* paricles *)
5766MapIndexed[{prongStyle[[First@#2]],EdgeForm[Darker[prongStyle[[First@#2]]]],Disk[ImageScaled[{.5,.5}+#1/(2pmax[\[Mu]])],ImageScaled[0.01]]}&,prongs[pdemo[p,\[Mu]],pzdemo[p,pz,\[Mu]],\[Mu]]],
5767(* reference circle *)
5768{Gray,Circle[cPoint,ImageScaled[0.5]]},
5769(* pz projection line *)
5770{Dashed,Gray,Line[ImageScaled[{.5,.5}+#/(2pmax[\[Mu]])]&/@{{pzdemo[p,pz,\[Mu]],0},{pzdemo[p,pz,\[Mu]],kT[pdemo[p,\[Mu]],pzdemo[p,pz,\[Mu]],\[Mu]]}}]},
5771{Gray,Line[ImageScaled[{.5,.5}+#/(2pmax[\[Mu]])]&/@{{pzdemo[p,pz,\[Mu]],0},{0,0}}]},
5772(* point in the center *)
5773{Black,PointSize-> Medium,Point[{0,0}]}
5774}];
5775
5776epilog[False,p_,pz_,\[Mu]_]:=With[{cPoint=ImageScaled[{.5,.5}]},{
5777(* particle momenta *)
5778MapIndexed[{Opacity[.35],Thickness[0.015],prongStyle[[First@#2]],Line[{cPoint,ImageScaled[{.5,.5}+#1/(2pmax[\[Mu]])]}]}&,prongs[pdemo[p,\[Mu]],pzdemo[p,pz,\[Mu]],\[Mu]]],
5779(* paricles *)
5780MapIndexed[{prongStyle[[First@#2]],EdgeForm[Darker[prongStyle[[First@#2]]]],Disk[ImageScaled[{.5,.5}+#1/(2pmax[\[Mu]])],ImageScaled[0.01]]}&,prongs[pdemo[p,\[Mu]],pzdemo[p,pz,\[Mu]],\[Mu]]],
5781(* reference circle *)
5782{Gray,Circle[cPoint,ImageScaled[0.5]]},
5783(* point in the center *)
5784{Black,PointSize-> Medium,Point[{0,0}]}
5785}];
5786
5787
5788picture2prong2D[{True,showArc_},{\[Theta]_,v_}]:=PolarPlot[{TwoProng2D[{v,\[Theta]},\[Eta]]},{\[Eta],0,2\[Pi]},
5789PlotRange-> All,
5790Axes->False,
5791ImageSize->400,
5792PlotStyle->{Thickness[0.004],Black},
5793Epilog->epilog[showArc,\[Theta]]];
5794
5795picture2prong2D[{False,showArc_},{\[Theta]_,v_}]:=Graphics[epilog[showArc,\[Theta]],ImageSize->400];
5796
5797
5798picture3prong2D[{True,showPZ_},p\[Beta]_,pz\[Beta]_,\[Mu]\[Beta]_]:=PolarPlot[{ThreeProng2D[{pdemo[p\[Beta],Exp[-\[Mu]\[Beta]]],pzdemo[p\[Beta],pz\[Beta],Exp[-\[Mu]\[Beta]]],Exp[-\[Mu]\[Beta]]},\[Theta]]},{\[Theta],0,2\[Pi]},
5799PlotRange-> All,
5800Axes->False,
5801ImageSize->400,
5802PlotStyle->{Thickness[0.004],Black},
5803Epilog->epilog[showPZ,p\[Beta],pz\[Beta],Exp[-\[Mu]\[Beta]]]];
5804
5805picture3prong2D[{False,showPZ_},p\[Beta]_,pz\[Beta]_,\[Mu]\[Beta]_]:=Graphics[epilog[showPZ,p\[Beta],pz\[Beta],Exp[-\[Mu]\[Beta]]],ImageSize->400];
5806
5807
5808picture2prong3D[{{points3D_,mesh_},{\[Theta]_,v_}}]:=SphericalPlot3D[TwoProng3D[{v,\[Theta]},{\[Eta],\[Phi]}],{\[Eta],0,\[Pi]},{\[Phi],0,2\[Pi]},
5809PlotRange->All,
5810Axes->False,
5811Mesh-> mesh,
5812MeshStyle-> Directive[ColorData[6,"ColorList"][[6]] ,Opacity[0.3],Dashed],
5813Boxed->False,
5814PlotStyle->Directive[Green,Opacity[0.7]],
5815SphericalRegion->True,
5816ImageSize->300,
5817PlotPoints->points3D]
5818
5819
5820picture3prong3D[{{points3D_,mesh_},{p\[Gamma]_,pz\[Gamma]_,\[Mu]\[Gamma]_}}]:=SphericalPlot3D[ThreeProng3D[{pdemo[p\[Gamma],Exp[-\[Mu]\[Gamma]]],pzdemo[p\[Gamma],pz\[Gamma],Exp[-\[Mu]\[Gamma]]],Exp[-\[Mu]\[Gamma]]},{\[Theta],\[Phi]}],{\[Theta],0,\[Pi]},{\[Phi],0,2\[Pi]},
5821PlotRange->All,
5822Axes->False,
5823Mesh-> mesh,
5824MeshStyle-> Directive[ColorData[6,"ColorList"][[6]] ,Opacity[0.3],Dashed],
5825Boxed->False,
5826PlotStyle->Directive[Green,Opacity[0.7]],
5827SphericalRegion->True,
5828ImageSize->300,
5829PlotPoints->points3D]
5830
5831
5832show3Dpattern[flag_,obj_]:=If[flag,obj,Graphics3D[]];
5833
5834
5835\[Delta]=N[10^-8];
5836
5837demonstration[1]=Module[{v\[Alpha]=Log[1-0.1],\[Theta]\[Alpha]=Log[N[\[Pi]/4]],showRP=False,showArc=False,show3D=False,mesh=5,box=False,points3D=10,object3D=Graphics3D[],arguments={{Automatic,5,True},{0.5,0.5,0.3}}},
5838Panel[
5839Grid[
5840{{"Log[1-v] ",Slider[Dynamic[v\[Alpha]],{Log[1-\[Delta]],Log[\[Delta]]}],"Show 2D pattern",Checkbox[Dynamic[showRP]],Row[{"Mesh:  ",Checkbox[Dynamic[mesh],{None,5}],"     Box:  ",Checkbox[Dynamic[box]]}],SpanFromLeft},
5841{"Log[\[Theta]] ",Slider[Dynamic[\[Theta]\[Alpha]],{Log[\[Delta]] ,Log[2\[Pi]-\[Delta]]}],"Show arc",Checkbox[Dynamic[showArc]],"3D quality:",RadioButtonBar[Dynamic[points3D],{10,30,50,70,100}]},
5842{" "," ","Show 3D pattern",Checkbox[Dynamic[show3D]],Button["Refresh 3D",showRP=False;object3D=picture2prong3D[{{points3D,mesh},{Exp[\[Theta]\[Alpha]],1-Exp[v\[Alpha]]}}];showRP=True;,ImageSize->Medium,Method->"Queued"]," "},
5843{Dynamic[picture2prong2D[{showRP,showArc},{Exp[\[Theta]\[Alpha]],1-Exp[v\[Alpha]]}]],SpanFromLeft,SpanFromLeft,SpanFromLeft,Dynamic[Show[show3Dpattern[show3D,object3D],Boxed->box]],SpanFromLeft}},
5844Alignment->Left,
5845Frame->{None,None,{{{1,3},{1,2}}->True,{{1,3},{3,4}}->True,{{4,4},{1,4}}->True,{{1,3},{5,6}}->True,{{5,4},{5,6}}->box}},
5846FrameStyle->LightGray,
5847Spacings->{{1,1,3,1,3,1,1},{1,1,1,3,1}}]
5848]];
5849
5850
5851\[Delta]=N[10^-5];
5852
5853demonstration[2]=Module[{p\[Alpha]=0.5,pz\[Alpha]=0.5,\[Mu]\[Alpha]=-Log[0.3],showRP=False,showPZ=False,show3D=False,mesh=5,box=False,points3D=10,object3D=Graphics3D[],arguments={{Automatic,5,True},{0.5,0.5,0.3}}},
5854Panel[
5855Grid[
5856{{"ln\!\(\*FractionBox[\(Q\), \(m\)]\) ",Slider[Dynamic[\[Mu]\[Alpha]],{-Log[\[Delta]],-Log[1/3-\[Delta]]}],"Show 2D pattern",Checkbox[Dynamic[showRP]],Row[{"Mesh:  ",Checkbox[Dynamic[mesh],{None,5}],"     Box:  ",Checkbox[Dynamic[box]]}],SpanFromLeft},
5857{"p ",Slider[Dynamic[p\[Alpha]],{\[Delta] 10^-3,1-\[Delta]}],"Show \!\(\*SubscriptBox[\(p\), \(z\)]\) projection",Checkbox[Dynamic[showPZ]],"3D quality:",RadioButtonBar[Dynamic[points3D],{10,30,50,70,100}]},
5858{"\!\(\*SubscriptBox[\(p\), \(z\)]\) ",Slider[Dynamic[pz\[Alpha]],{\[Delta] 10^-3,1-\[Delta] 10^-3}],"Show 3D pattern",Checkbox[Dynamic[show3D]],Button["Refresh 3D",showRP=False;object3D=picture3prong3D[{{points3D,mesh},{p\[Alpha],pz\[Alpha],\[Mu]\[Alpha]}}];showRP=True;,ImageSize->Medium,Method->"Queued"]," "},
5859{Dynamic[picture3prong2D[{showRP,showPZ},p\[Alpha],pz\[Alpha],\[Mu]\[Alpha]]],SpanFromLeft,SpanFromLeft,SpanFromLeft,Dynamic[Show[show3Dpattern[show3D,object3D],Boxed->box]],SpanFromLeft}},
5860Alignment->Left,
5861Frame->{None,None,{{{1,3},{1,2}}->True,{{1,3},{3,4}}->True,{{4,4},{1,4}}->True,{{1,3},{5,6}}->True,{{5,4},{5,6}}->box}},
5862FrameStyle->LightGray,
5863Spacings->{{1,1,3,1,3,1,1},{1,1,1,3,1}}]
5864]];
5865
5866
5867\[Delta]2=\[Pi] 10^-5;
5868doublePattern[\[Phi]_,\[Chi]_]=With[{n={Cos[\[Chi]],Sin[\[Chi]],0},np={1,0,0},nm={Cos[\[Phi]],Sin[\[Phi]],0}},(2(1-nm.np))/((1-n.np+\[Delta]2^2)(1-n.nm)+\[Delta]2^2)];
5869plusPattern[\[Phi]_,\[Chi]_]=With[{n={Cos[\[Chi]],Sin[\[Chi]],0},np={1,0,0},nm={Cos[\[Phi]],Sin[\[Phi]],0}},(2(1-nm.np))/((1-n.np+\[Delta]2^2)(2-n.(nm+np)+\[Delta]2^2))];
5870minusPattern[\[Phi]_,\[Chi]_]=With[{n={Cos[\[Chi]],Sin[\[Chi]],0},np={1,0,0},nm={Cos[\[Phi]],Sin[\[Phi]],0}},(2(1-nm.np))/((1-n.nm+\[Delta]2^2)(2-n.(nm+np)+\[Delta]2^2))];
5871
5872
5873doubleZoom[{\[Phi]_,\[Chi]_},rmax_]:=If[#2>rmax #1,rmax #1,#2]&[doublePattern[\[Phi],\[Phi]/2],doublePattern[\[Phi],\[Chi]]];
5874plusZoom[{\[Phi]_,\[Chi]_},rmax_]:=If[#2>rmax #1,rmax #1,#2]&[doublePattern[\[Phi],\[Phi]/2],plusPattern[\[Phi],\[Chi]]];
5875minusZoom[{\[Phi]_,\[Chi]_},rmax_]:=If[#2>rmax #1,rmax #1,#2]&[doublePattern[\[Phi],\[Phi]/2],minusPattern[\[Phi],\[Chi]]];
5876
5877
5878cP={0.0,0.0};
5879vectors[\[Phi]_,r_]:={
5880{PointSize->Large,Point[cP]},
5881{PointSize->Large,Red,Point[r{1,0}]},
5882{PointSize->Large,Blue,Point[r RotationMatrix[{{Cos[\[Phi]],-Sin[\[Phi]]},{1,0}}].{1,0}]},
5883{Opacity[.35],Thickness[0.0125],Red,Line[{cP,cP+r{1,0}}]},
5884{Opacity[.35],Thickness[0.0125],Blue,Line[{cP,cP+r RotationMatrix[{{Cos[\[Phi]],-Sin[\[Phi]]},{1,0}}].{1,0}}]}}
5885
5886
5887polar[\[Phi]_,rmax_]:=PolarPlot[
5888{rmax doublePattern[\[Phi],\[Phi]/2],doubleZoom[{\[Phi],\[Chi]},rmax],plusZoom[{\[Phi],\[Chi]},rmax],minusZoom[{\[Phi],\[Chi]},rmax]},{\[Chi],0,2Pi},
5889Frame->True,
5890PlotRange->1.1rmax doublePattern[\[Phi],\[Phi]/2]{{-1,1},{-1,1}},
5891Epilog->vectors[\[Phi],1.1rmax doublePattern[\[Phi],\[Phi]/2]],
5892PlotPoints->50,
5893Axes->False,
5894ImageSize->500];
5895
5896
5897demonstration[3]=Manipulate[polar[\[Theta],rmax],{{\[Theta],\[Pi]/4,"\[Theta]"},\[Delta]2,\[Pi]-\[Delta]2},{{rmax,10,"Zoom out"},0.1,20}];
5898
5899
5900End[]
5901
5902
5903EndPackage[]