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Manual - Florence Theory Group

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1. section for Glauber MonteCarlo initial conditions NCONF 500 number of nuclear configurat NBCOLL 20 number of impact parameters ss EV START 28 identifies the event from wh EV_STOP 31 identifies the event at whic KAPPA 37 0 model parameters taken from SIG 0 6 smearing parameter COLLISION 1 kind of collision 1 AA 2 d section for freezout hypersurface computation HYP_COMPU 0 0 disable 1 enable hypersu FREEZKIND 0 0 freezout based on temperat FREEZEVAL 140 freezeout threshold tempera HYPSURFTI 0 1 time interval between hypers section for initialization with an energy or entropy de IN_D_FILE ed dat name of the file with the ta section for simulations with tilted initial energy de ETAM TILT 1 eta_m to produce initial en UETA_COEF 0 for tests with initial u eta 16 FARR RG RG RG I Hk ak ak 74 Printed variables in the output files please select 1 density 1 7A TX aga 1 VY ice E EE 1 76 VZ ees 1 vz obviously means veta when pressure 1 74 ene dens 1 temper 1 sq entr dens 1 bulk visc 1 bulk viscosity active only 82 pi tt 1 tt component of shear viscos pi tx 1 tx component of shear viscos 84 pi ty 1 ty component of shear viscos pi tz 1 tz component of shear viscos sd pi xy 1 xy component of shear viscos pi xz 1 xz component of shear viscos sd pi yz
2. where the np flag sets up the number of processors to be used to be more precise the number of processes but usually the best choice is to insert the number of CPUs available Please note that the minimum allowed number of cells along x is the number of processors divided by 3 The output files are stored in the outr0001 subdirectory The output directory can be changed passing the o flag to ECHO QGP echo exe o new name The name of the output directory must be 8 characters long When performing Glauber Monte Carlo simulations the suffix numbers of output directories are automatically assigned they will be equal to the index numbers identifying the selected events for example if the users chooses 11 to run events with id 113 and 114 in the sequence generated by ECHO QGP then the output directories will be outr0113 and outr0114 When correctly executed ECHO QGP prints a summary of the grid the parameters and the algorithms employed and then a short message each time the output is written and a final message about time elapsed You can see an example of a successful running output up to the second time step in the listing 2 1 ECHO QGP STARTED nrk 2 q Settings and parameters j Test O optical geometrical Glauber initial Using Bjorken coordinates g This is a viscous simulation Bulk viscosity is neglected ij This simulation uses MPI and the number 4 Evolved shear viscous tensor
3. 0 0001 F 1e 05 pt GeV Figure 6 8 Test A I pr y 0 of particles Red color means that viscous corrections to thermal distribution have been taken into account blue color means not else if init type eq SHOCK TUBE 2D then if yCiy lt x ix then vv kpr 25 401411 else vv kpr 20 337588 end if 52 vily Figure 6 9 0 Vo pr Y Test A Directed flow of x particles Red color means that viscous corrections to thermal distribution have been taken into account blue color means not pt GeV Figure 6 10 Test A Elliptic flow of particles Red color means that viscous corrections to thermal distribution have been taken into account blue color means not After compiling ECHO QGB we run ECHO QGP a few times using different values for s changing the ETA S parameter into param dat We can also execute an inviscid simulation setting the parameter VISCOUS 0 Please take care to not overwrite the results of the various simulations either renam ing the output directory after the end of each simulation or using the o flag when launching the program e g echo exe o out 2Dtest First we check if the initial conditions are correct We copy the tools readvar pro gdl script into the output directory e g outr0001 but it could have a different name and then we use it 53 cd outr0001 gdl GDL gt readvar 0001
4. if 0 is 2 pi ybox 00 0 upper limit for mc box HISTOGRAM RELATED mxv_pt 3 0 max value for pt mnv_pt 0 0 min value for pt mxv_ang 6 28318 max value for phi mnv_ang 0 0 min value for phi mxv_y 0 0 max value for y mnv_y 0 0 min value for y binpt 50 binphi 1 binrap 1 6 28318530718 we can compute the thermal spectra of z A and A taking into account the viscous corrections to the distribution function Please remember to create the outr0001 spectra directory before running the tool After executing the program thermal exe we can enter into outr0001 spectra and make some plots gnuplot plot_pionplus_spectra gp The plot files can be quickly converted from EPS to PDF with for i in eps do ps2pdf dEPSCrop i done See figures 6 7 6 8 6 9 6 10 6 2 2D shock tube test B This is a simple test of a 2D shock wave The param dat files of this test can be found into the tests testB directory The initial state is simply costitued by a sharp jump in pressure when crossing the y z locus whose values can be adjusted editing the init f90 file a few lines after the condition 51 Figure 6 7 Test A dNdy of particles Red color means that viscous corrections to thermal distribution have been taken into account blue color means not 0 0 1 F Pr y 0 01 F 0 001 F X
5. where eo is assigned with the parameter ECENTER and the total weight function W x y is defined as e a W x y 1 TT a npc r y W z y n 1 a Wy 0 0 0 ango 0 0 where a is the AH parameter and lt 2 Ho ew i 9 A I ml na n where no 0 if the parameter ETAM TILT gt 0 tilted initial energy profile otherwise Er In 1 Bo no 5 io where p Ile ae ea 29 Viscous tensor components are initialized as a ji q mz qm es E eni TO All other components are set to 0 4 2 Initialization 1 2D shock tube Initial condition is a constant pressure profile p for y lt z and p otherwise All other variables are set to O The inital values of the variables can be changed only editing the init f90 file and recompiling ECHO QGP 4 3 Initialization 2 1D viscous shear flow These initial conditions are designed to perform the 1 1 D test in Minkowski Cartesian coordinates described in 6 and 11 Pressure and density have constant values density p 1 and pressure p 0 25 so that using ideal equation of state energy density e 3p 0 75 and e p 1 and v v0 erf ian where the constant v0 amp c t s and t is time with this choice of the various parameters t should be 1 at the beginning of the simulation 4 4 Initialization 3 Glauber MonteCarlo This initialization is based on a simple Glauber MonteCarlo model designe
6. 1 yz component of shear viscos pi xx 1 xx component of shear viscos od pi yy 71 yy component of shear viscos pi zz 1 zz component of shear viscos 94 gamma 1 dutdt 0 94 duxdx 0 duydy 0 oq duzdz 0 theta 0 9 Vorticity 0 prints the derivatives of va flows 0 prints directed and elliptic Kok k k k k ok ok k ck ok ck k k k ok k ok oe k oe oe ck oe oe ck KOK k k OK KOK OK e e KKK k 104 Essential parameters for some nuclei Please add custom nucleus parameters paying attention 104 When echo qgp is launched it will select the parameter 10d Au projmass 197 radius 6 38 fm delta 0 5 Pb projmass 208 radius 6 62 fm delta 0 5 10d XxO00 projmass 280 radius 8 76 fm delta 0 7 Au000 projmass 197 radius 6 37 fm delta 0 5 Listing 3 1 Example of param dat 3 2 Kind of initialization This section is devoted to the pre hydro modules and it can set up the initial energy density or entropy density profile in such a way that it reproduces a known test or situation See chapters 4 and 6 for the various initializations that can be reproduced with ECHO QGP 17 INIT_TYPE integer flag It is the flag selecting among different initial profiles for a variety of cases The allowed possibilities are see next chapter 4 0 Glauber geometric initialization 2D shock tube test 1D viscous shear flow test Glauber Monte
7. 10 10 and a plot like that in Fig 6 1 will appear on a separate window actually here we show a postscript figure created with a couple of additional commands see further in this text plots on the screen usually have b w colors inverted If we didn t plot the x array together with the en slice then gdl on the x axis would have used only the index numbers of the elements of the slice of the en array Let s see now how the energy density profile looks like moving along the 7 direction at x y 0 Fig 6 2 43 20 we 15 QUU e t x gt x v 2 x D 10 E E x D a x x g e D g x x x x x x x fm Figure 6 1 Plot of energy density in GeV fm at r 1 fm cfory n 0 GDL gt plot z en 50 50 xtitle eta ytitle Energy density GeV fm 3 xrange 10 10 20 Energy density GeV fm 3 0 10 9 0 5 10 eta Figure 6 2 Plot of energy density in GeV fm atr 1 fm cfor x y 0 Now let s make a surface plot of the energy density along the x 7 plane for y 0 Fig 6 3 GDL gt surface reform en 50 x z xtitle x fm ytitle eta ztitle En dens GeV fm 3 xrange 10 10 yrange 10 10 44 n dens Ge tm iw 3 M A NS SW x im Figure 6 3 Surface plot of energy density in GeV fm at T 1 fm c for y 0 Let s replot the same quantities
8. The minimum value for z or 7 ZMAX real value The maximum value for z or 7 3 5 Time parameters The simulation starts at a given proper time and can be terminated by two different criteria when it reaches a threshold temperature or at a given proper time TSTART real value Proper time at which the simulation starts ro in fm c TSTOP real value Proper time at which the simulation ends in fm c TEMP END real flag and cutoff The simulation ends when the maximum temperature in GeV reaches a value less than TEMP END If this pa rameter is set to O then this feature is turned off 3 6 Output parameters This section specifies the output frequency and criteria DTLOG real value Proper time interval between log updating it should be greater than MAXDT DTOUT real value Proper time interval between output printings it should be greater than MAXDT OUTP PREC integer flag The user can choose between 4 single or 8 double bytes precision when printing output values Note that in the particle production tools this choice is made at build time MAXDT real value Maximum time step allowed for the time integration RESTART integer flag Enables 1 or disables 0 the possibility to restart a simulation from the last output file If enabled it forces the frequency of output printing and freeze out hypersurface computation to be done at the same time 19 3 7 Algorithm parameters CFL real value The Couran
9. We can make a sketchy plot simply typing GDL gt plot x pr 100 This is fine to make a simple check but if we wish to prepare a better quality plot we can export the data to a file and then use it another tool e g gnuplot grace and many others To perform this task we can use the fortran postprocessing tools or gdl itself preparaing for example a script like file tests testB tofile pro openw 12 initial pressure testB dat please change the for cycle interval accordingly with your grid remind that array indexes in gnudatalanguage start from 0 for example if you have a 201x201 grid initial and final values are 0 and 200 and if the grid is symmetric respect to the origin the index corresponding to O is 100 for i 0 200 do begin printf 12 x i pr i 100 endfor free lun 12 END If we run the script with GDL gt r tofile we should get an ascii file called initial pressure testB dat which we can plot using another program 6 11 Assuming to have executed four simulations one inviscid and the other three with 7 s 0 001 0 01 0 1 after compiling the fortran tools and copying them into the output directory we can extract the data at the end of the run 7 4 fm c with readx exe 31 31 54 Pressure GeV tm x fm Figure 6 11 Test B Initial pressure profile at T 1 f m c for y 0 followed by
10. into the postproc readx directory fromecho exe EPS0031 dat enO 1 dat x 1 201 101 101 1 1 fromecho exe VX0031 dat vxO0 1 dat x 1 201 101 101 1 1 In the previous example the name of the output files refer to energy density and Vz of the run with 7 s 0 1 In the tests testB directory there is a simple gnuplot script to plot the results after gathering them in a common directory Fig 6 12 and 6 13 0 35 Inviscid T s 0 001 pm 0 3 F ws 0 01 qs 0 1 eee 0 25 Q 02 5 2 i 70045 j i 0 1 0 05 0 i ki 5 4 3 2 1 0 2 3 4 5 x fm Figure 6 12 Test B Comparison of V profiles at T 4 fm c for y 0 55 Tnviscid 20 F n s 0 001 J n s 0 01 amp 18r 1 S20 1 E ES 16 o 14 g 10 8 5 8r LLI 6 4 E 2 1 5 4 3 2 1 0 1 2 3 4 5 x fm Figure 6 13 Test B Comparison of energy density profiles at r 4 fm c for y 0 6 3 1D viscous shear flow test test C This is merely the execution of the test described in section 4 3 and 6 The file param dat to set up the simulation can be found in tests testC The results can be examined with the usual tools following the procedures already shown in the previous examples readx exe 91 91 fromecho exe VY0091 dat vy dat x 1 301 111 1 A simple gnuplot script plotiD gp
11. v 20 or 4 8 v or v 21 a or n 9 p 22 x or n 10 dV or dv 23 n or 7 11 dv 24 T or 27 12 dv 25 e p T 13 dV or dv the variables are computed interpolating linearly using a weight w F F w _ Ba The volume element in the bjorken case is defined as dV 7 s rAxrAyAn fm dV s rArAyAn fm T E dV29 s rATrAcAn fm uM am om dvtn SATArAy fm dV 68 note that currently for most cells just one of the dV component is not vanish ing The above described array is printed in the file hypersuface txt in the output folder This file contains as a first row the selected switch namely FREEZKIND the temperature in GeV of the hypersuface and its energy density GeVfm After the first row it contains a block for each time step The block head is an integer it is the number of frozen cells contained which corresponds to the amount of lines to be read before finding another block Each one of these lines is a frozen cell where the column index refers to the array hypersurface described above For the ideal case the columns are 13 for the viscous one the columns are 25 7 2 Particle spectra routines All the spectra routines are contained in the folder analisi There are four separate programs thermal which can be build with the command make thermal utils therm which can be build with the command make utils_them MCgen which can be build wit
12. Carlo initialization viscous Gubser s fluid test ua A N e Initialization with a tabulated energy or entropy density profile 3 3 Kind of simulation This section is devoted the set up of the simulation such as choosing the coordinates see also 4 COORD integer flag It sets the metric used 1 Minkowski coordinate system with metric diag 1 1 1 1 2 Bjorken coordinate system with metric diag 1 1 1 77 VISCOUS integer flag Enables 1 or disables 0 the viscous correction to the evolution equations BULK integer flag Enables 1 or disables 0 the bulk viscosity contri bution In the first case the parameter 27 1 3 cs in the last 107 NS integer flag If set to 1 it imposes the use of Navier Stokes formalism instead of the I S second order theory CUT_TEMP real flag and cutoff If gt 0 then under the temperature CUT_VALUE the viscous tensor components are smoothed i e their magnitude is reduced This section is devoted the set up of the lattice 3 4 Grid parameters NX integer value The number of cells along x direction NY integer value The number of cells along y direction NZ integer value The number of cells along eta direction To set up 2D 1 simulations just impose NZ 1 XMIN real value The minimum value for x 18 XMAX real value The maximum value for x YMIN real value The minimum value for y YMAX real value The maximum value for y ZMIN real value
13. IDL GDL script that reads the output files of echo qgp containing data about variable derivatives at fixed 7 The files grid summary dat and param dat must be in the same directory with data where this script is launched ce pro IDL GDL script that for the inviscid case and Bjorken coordinates only computes the total energy Etot and the total angular momentum J along the y direction over the computational grid using the formulas Etot roost T9 sinh T dndaxdy JS re n zI9 T sinhg zT zT dndxdy 34 Since the energy density value defined by the ENEZERO parameter is added to each cells of the grid at the beginning of each run with Glauber initial conditions the values of these basement energy density and the corresponding pressure can be assigned to the limit_en and limit_pr variables in the first lines of the script before running the script so that they will be subtracted These values of limit_en and limit_pr variables are printend to the standard output by ECHO QGP at the beginning of each run Please note that this utility is based on a raw summation of the values inside the cells and depending on what are the grid dimensions the grid resolution and the value of ENEZERO it may give inaccurate or even wrong results You are invited to always check the results changing grid dimensions grid resolution and the value of ENEZERO 5 2 Fortran utilities readx f90 this small program ca
14. characters 3 15 Section for simulations with tilted initial en ergy density profile ETAM TILT real value Parameter to produce a tilting in the initial energy distribution as in ref 8 if the parameter is set to a negative number no tilting is introduced 24 UETA_COEF Parameter used for tests with initial conditions different from the BIC u u u 0 Here u 0 and u r UETA COEF x the impact parameter b lies on the zx axis 3 16 Printed variables in the output files This section simply contains a list of all the fields that the simulation can print in the output files The user can enable 1 or disable 0 the output of any variable The computational time also depends on how many variables are printed They all are real flags with the precision defined by the flag OUTP_PREC density baryon charge density vx v contravariant vy v contravariant vz v Or v contravariant pressure p expressed in GeV fm ene dens e energy density expressed in GeV fm temper T temperature expressed in GeV entr dens s entropy density expressed in fm bulk visc II bulk viscosity only active when VISCOUS parameter is set to 1 pitt 7 component of shear viscous tensor active only when VISCOUS pa rameter is set to 1 pitx 7 component of shear viscous tensor active only when VISCOUS pa rameter is set to 1 pity 7 component of shear viscous tensor active only when VISCOUS
15. charge density in m Please note that in the current version this parameter does not have any physical meaning it is exploited as a tracer i e as a mathematical trick to simplify the evolution equations of shear viscous tensor components In order to perform viscous simulations RHOCENTER must be different from zero 20 DETA real value Shift of the pp rapidity distribution fq in equation 4 1 SIGETA real value Width of the pp rapidity distribution c in equation 4 1 3 10 Viscosity parameters These parameters are only considered when the flag VISCOSITY 1 ETA S real value It is the shear viscosity coefficient divided by the entropy density 7 s in natural units It is employed in the calculation of the shear viscous tensor where s is the entropy density In the Navier Stokes formulation this value is simply assigned to 7 TAU PI C real value The parameter which controls the 7 the relaxation time in the formula 7 TAU PI C BTA where T is the temper ature TRACE_IMP character flag Discriminates the equation used to close the system It can assume two different values TRACE_IMP no The components 7 144 777 774 477 nY of the shear viscous tensor are evolved while the 7 1 5 5 components are retrieved imposing the orthogonality condition TRACE IMP zz the 7 component is obtained imposing the trace lessness condition in addition to the orthogonality condition 3 11 Equation of State
16. components xx yy ZZ Xy xz if tt tx ty tz and zz are obtained imposing orth and null trace 18 Grid parameters x y and z or eta number of cells 51 51 51 17 x range fm 9 000 9 000 y range fm 9 000 9 000 1 z or eta range fm 9 000 9 000 step x y eta fm 0 353 0 353 0 353 Time parameters 23 starting time 1 000 ending time 1 400 29 ending temeperature MeV 130 000 maximum timestep 0 005 eta s parameter for shear viscosity tens 0 080 29 Temperature limit for smoothing viscosit 0 095 eq of state 3 3 numerical derivatives with anal eos 0 33 Nucleus parameters proj mass 197 000 3g radius fm 6 380 W S width fm 0 535 12 6 6 63 69 79 oo 8d sqrt s GeV Y b cross section mb impact parameter fm initial hardness parameter central energy density GeV fm 3 enezero GeV fm 3 przero GeV fm 3 central density pp rapidity distribution shift deta e pp rapidity distribution width sigeta p ueta A coeff so that u eta A x Computing freeze out hypersurface Hypersurface computation based on temper Freezeout threshold MeV time interval between hypersurfaces comp Other numerical parameters Courant Fr Lew condition parameter Reconstruction algorithm Limiter z step thickness function fm r step thickness function fm integration accuracy Output parameters interval between log updating i
17. file is read during the execution of the program Instead if the analytical Equation of State EoS is modified then it becomes compulsory to issue the command make clean before compiling ECHO QGP again because the files containing the analytical EoS are included with the include state ments thus they are not automatically considered by the make command An example of param dat is reported in the paragraph 3 1 This file has different sections for different subsets of parameters used by different modules of the program We are going to see them in detail in this section following the file sections Once again it is very important NOT TO ALTER the structure of the file number of columns before the symbol or before the symbol kind of initialization 3 INIT_TYPE 0 0 Geometric Glauber 1 2D sh kind of simulation 4 COORD 2 system coordinates i Minkow VISCOUS 0 it takes into account viscou q BULK 0 if O it cuts off bulk viscos IN Si uus ks 0 if 0 it uses I S second orde g CUT_TEMP 0 08 if gt 0 it fixes the temperat grid parameters i NX 101 number of cells along x dire NYa eas 101 number of cells along y dire 13 NZ 101 number of cells along z Min XMIN 2 12 minimum value for x 14 XMAX 12 maximum value for x YMIN 2 12 minimum value for y 15 24 6 64 64 6 6 YMAX 12 maximum v
18. for speeding up computations in system with multicore processors with shared memory and of course with OpenMP installed To take advantage of OpenMB you have to edit the makefile adding the compilation flag fopenmp and execute the make command you just have to comment uncomment a couple of lines at the beginning of the makefile If 37 compilation is successfull export the environment variables used by OpenMP unless they have already been set up in advance e g for a 4 cores cpu export OMP NUM THREADS 4 export OMP SCHEDULE GUIDED 4 At the end of the compilation stage you ll get an executable named thermal exe When OpenMP is used if thermal exe is the only relevant running application the common top utility will report for thermal exe a CPU usage almost equal to OMP NUM THREADS times 100 The configuration file is settings txt The output directory where the pro gram stores the results must be created before launching it For a much more detailed description of this tool please read chapter 7 38 Chapter 6 Tutorials In this chapter we will give some examples of how to use the code The tutorials will not cover all the features of ECHO QGP nevertheless they should give to the user a working knowledge sufficient to perform many basic tasks Usage examples of external programs like gnuplot or the gnudatalanguage will be provided too hoping that they will be useful to young students and to other
19. gt tar gz OK For any other return state the user should download again the package 2 2 20 Uncompress the folder To unpack the compressed archive containing the sources just issue the command tar xzf ECHO QGP version gt tar gz The uncompressed folder will contain some sub directories for utilities and post hydro programs some text files and all the files building ECHO QGP itself In detail the bundle is composed as follows analysis folder Contains the post hydro tools for the particle spectra produc tion see 7 doc folder Contains the latest version of this manual and the BIEX sources to build it eos data folder Contains some essential files to run the simulations equation of state particle list chemical potential temperature definition LICENSE TXT text file License under wich ECHO QGP is released makefile The instructions to build the program using GNU Make param dat text file Configuration file of ECHO QGP random seed dat An integer number to provide an initial seed for the Ran dom Number Generator used with Glauber Monte Carlo initial condi tions see 4 4 tests folder Contains the essential informations and data to reproduce the examples described in the tutorials chapter see 6 of this manual tools folder Contains some tools to analyze the results of the simulations see 5 The remaining files included are the Fortran files containing the modules of ECHO QGP We give here
20. hypersufsce f90 in FCHO OGP och bee ee n ome 7 2 Particle spectra routines uuu ack vex Re cR gw we Be wl 7 3 How to configure the particle production 7 3 1 ECHO QGP related parameters 7 3 2 Particle related parameters 7 4 InputOuput iosa llle 7 5 Parameters for the Monte Carlo production 7 6 Examples of particles subset l l 7 6 1 Producing all available particles 1istorseq 0 7 6 2 Producing an interval of listed particles listorseq 1 7 6 3 Producing a detailed list of particles 1listorseq 2 7 6 4 Producing the standard subset of particleslistorseq 3 References 34 34 35 37 75 76 T7 Chapter 1 Introduction 1 1 What is ECHO QGP ECHO QGP is a program used to model heavy ions collisions It solves numer ically the viscous hydrodinamic equations in the Israel Stewart theoretical frame 1 2 in 2 1D or 3 1D in Bjorken coordinates from the formation of quark gluon plasma up to the freeze out stage The user can set up different initial conditions Optical and Monte Carlo Glauber as well as custom initial energy density profile and he she can also choose between both analytic and tabulated equations of state The programming language chosen for ECHO QGP is FORTRAN 2008 1 2 The ECHO QGP team At the time of release 1 0 00 22 05 2015 the ECHO QGP team is composed by Francesco Becattini Univ of Florence INFN Sect of Floren
21. of the output and manipulate them interactively First we check if initialization was correct so we read the first output file GDL gt readvar 0001 96 Compiled module READVAR This program reads the output of echo qgp Reading grid summary dat nx 101 ny 101 nz 101 xstep 0 277228 ystep 0 277228 zstep 0 277228 xmin 14 0000 ymin 14 0000 zmin 14 0000 xmax 14 0000 ymax 14 0000 zmax 14 0000 Reading grid dat Compiled module SKIP LUN Run with viscosity Output has 8 bytes precision Variables to be read density vx vy VZ pressure energy density temperature entropy density bulk viscosity pi tt pi tx pi ty pi tz pi xy pi xz pi yz pi xx 41 pi yy pi zz gamma Number of variables is 20 Reading file out0001 dat time 1 00000000 time or tau is stored into variable t 1 0000000 Arrays available x y and z of type double with 101 101 101 elements Arrays available with their maximum mean and minimum values 96 Compiled module MEAN rho 0 10000000 0 10000000 0 10000000 Vx 0 0000000 0 0000000 0 0000000 vy 0 0000000 0 0000000 0 0000000 vZ 0 0000000 0 0000000 0 0000000 pr 3 9807911 0 030049485 6 1038367e 05 en 15 303008 0 13728677 0 00030000000 temp 0 30648078 0 057427603 0 047645369 entropy 62 920094 0 69550263 0 0075776172 bu 0 0000000 0 0000000 0 0000000 tt 0 0000000 0 0000000 0 0000000 tx 0 0000000 0 00
22. parameters EOS integer flag Discriminates the Equation of State used by ECHO QGP The options are 1 A barotropic analytic equation of state is used of the kind P P p e The relations among the pressure P the charge density p and energy density e are explicitly written in the files de f contained in the folder eos data pressure vs rh en def Dependence of the pressure P GeV fm on the energy density e GeV fm temperature def Dependence of the temperature T GeV on the energy density e GeV fm energy den def Optional only if NUM DER 0 the dependence of energy density on pressure dprdrh def Optional only if NUM DER 0 the partial deriva tive of pressure respect to density 21 dprden def Optional only if NUM_DER 0 the partial deriva tive of pressure respect to energy density The files in the bundle contain the ideal ultrarelativistic EoS P e 3 More precisely grr 3 1 P 32 e3 soy STP where g 37 for a non interacting QGP with 3 light flavors All the def files in the eos data folder can be edited as the user wishes as long as the variable and parameters names are preserved Any change in these files requires to issue again the command make 2 A complete analytic equation of state with the pressure as a function of temperature T and chemical potential u is used P P T u This feature is not yet implemented in the current version of the code 3 ECHO QGP uses a
23. people not familiar with them The tests directory contains the configurations files and some plots together with related datafiles of the results of the numerical simulations presented in this chapter 6 1 A3D 1 simulation with Glauber model test A Unpack the code with tar xf echo qgp lt version gt tar gz Then enter into the code directory cd echo qgp lt version gt If you wish you can modify the makefile to best exploit the capabilities of your processor or for debugging purposes Default optimization flag O2 should fit well for most cases If your cpu has only one core or if you wish to run ECHO QGP serially to compile just issue make 39 otherwise with a multi core machine with MPI installed issue make par Now open the file param dat with your favorite text editor e g vim emacs gedit geany kwrite kate Let s assume that we wish to run a 3D 1 simulation of the hydrodynamical evolution of the QGP after the collision of two gold nuclei at an s NN 200 GeV using Geometrical Glauber Initial conditions with an impact param eter of 7 fm taking into account shear viscosity effects with an 7 s 0 08 We choose 140 MeV as freeze out temperature The details of ECHO QGP con figuration are all written into the param dat file inside the folder tests testA Assuming that we have got a two core computer we ll use mpirun np 2 echo
24. same as pce dat but with an additional entry for T 0 NUM DER integer flag Enables or disables the automatic computation of the derivatives for the thermodynamic variables in case of an analytic EoS Works with EOS 1 or EOS 2 ECHO QGP computes numerical derivatives to find other physical quantities Theuser must provide explicit derivatives in the files energy den def and part der pr vs rh en def 3 12 Glauber Monte Carlo initial conditions parame ters NCONF integer value Number of nuclear configurations NBCOLL integer value Number of impact parameters per configuration EV START integer ID ID number of the event from which to start among the generated events EV STOP integer ID ID number of the event from which to stop among the generated events KAPPA real value Value of the K parameter in K Npart ag 2 e 7 x 5 4 l a X e S n Nooi x t a gt exp aoe For further details see 6 7 SIG real value Value of the o smearing parameter in the above equation For further details see 6 7 COLLISION integer flag Discriminates the kind of collision 1 AA nucleus nucleus 2 dA deuton nucleus e 3 pA proton nucleus 23 3 13 Decoupling hypersurface parameters The task of the routine hypersuface f90 included in ECHO QGP is to find store and print the coordinates of the hypersurface detected during the hydrodinamic evolution HYP COMPU integer flag Disables 0 or e
25. to the produced particle and not the fluid The decomposition of the particle four momentum must be consistent with the Milne coordinates mr cosh y ns mr mic pp pee Pr cos pr p2 p 7 3 pr sing i E p ae i 7 sinh y ns y 3 n G2 The current version of the particle spectra production routines only works in Milne Bjorken coordinates 7 1 hypersuface f90 in ECHO QGP The task of the routine hypersuface f90 included in ECHO QGP is to find store and print the coordinates of the hypersurface detected during the hydrodinamic evolution The user can choose the hypersuface to be isothermal or constant energy using the switch HYP COMPU in the param dat file 67 The routine checks in every space time direction if two adjacent cells are one above and one below the criterion Let US refer to the cells with the index i being the direction positive with crescent i es r gt 2 and Fi F41 F respectively the selected field temperature or energy density in the adjacent cells and of the constant hypersuface Then we know that the hypersuface lies between the considered cells if Fi F F F gt 0 When this happens we store all the needed information namely in the ideal case in the viscous case an array with 13 entries In addition to the ideal case an other array with 12 entries 1 tort 14 bulk 2520 15 7 3 y 16 n or 17 4 norz 17 7 or 74 5 p 18 6 v 19 TY 7
26. 00000 0 0000000 ty 0 0000000 0 0000000 0 0000000 tz 0 0000000 0 0000000 0 0000000 xy 0 0000000 0 0000000 0 0000000 XZ 0 0000000 0 0000000 0 0000000 yz 0 0000000 0 0000000 0 0000000 Xx 0 66217778 0 0073195439 7 9747652e 05 yy 0 66217778 0 0073195439 7 9747652e 05 zz 0 00015949530 0 014639088 1 3243556 v0 1 0000000 1 0000000 1 0000000 It is usually a wise practice not only to check what ECHO QGP prints to the standard output but also that the simulation has been properly initialized and the gdl scripts offer a good method to test it We can easily check for example grid dimensions grid resolution and what variables will be printed into the output files Also we can check that initial velocities are all O and that the minimum value of 7 is twice the maximum value of 7 and 7 with changed sign while other shear viscous tensor components are 0 It is beyond the scope of this tutorial to teach how to use gdl or IDL however we ll give some additional basic information to show how to make some sketchy plots Further informations can be easily found on the web Using gdl it possible to store the data as multidimensional arrays into the RAM of the computer and then extract print and plot some sections of them See for example http www ita uni heidelberg de dullemond lectures num_fluid_2009 App_B pdf or http www sgeier net tools GDL intro pdf 42 In gdl array indexes start from 0 and interv
27. 00000000000002 time 4 7999999999999998 Now we copy the utility fromecho exe into the new created postproc readx directory and then we enter into it cp fromecho exe postproc readx cd postproc readx Calling fromecho exe without any arguments prints an help message 46 fromecho exe Synopsis To extract data from the left to the right border of the grid along x y or z direction fromecho input file output file x y z To extract data using a specific range along one direction and fixing the other ones at a point fromecho input file output file x y z x indx start x indx end y indx start y indx end z indx start z indx end Please note that starting and ending indexes of the fixed directions must be equal Usage example fromecho prova input prova output y 33 33 2 150 44 44 This extracts data from file prova inputs and write the values along y direction from point with index 2 to point with index 150 fixing x at index 33 and z at index 44 We extract the value of temperature at 7 10 f m c along the x axis for y n 0 fromecho exe T0091 dat temperature_x_tau_10 0 dat x Now extract the value of temperature at r 10 fm c along the axis for x y 0 for all the 7 range reminding that now indexes go from 1 to 101 fromecho exe T0091 dat temperature z tau 10 0 dat z 51 51 51 51 1 101 All the files created by fromecho exe consists of
28. 3 20 15 10 5 0 5 10 15 20 x fm Figure 6 18 Test F Initial energy density distribution at r 1 fm c with Glauber MonteCarlo initialization x y 0 Fig 6 19 fromecho exe EPS0001 dat energy_vs_eta_taul dat z 56 56 56 56 1 81 gnuplot plot_en_vs_eta gp Now we plot the initial energy distribution on the 7 0 x y plane at T 10 22 fm c last output frame before the end of the simulation i e when the maximum temperature on the grid was less than 137 MeV Fig 6 20 63 15 10 5 0 5 10 15 Figure 6 19 Test F Initial energy density vs n at T 1fm cand x y 0 Glauber MonteCarlo initialization fromecho2d exe EPS0094 dat en out94 dat x y gnuplot contour_out94 gp 6 7 Run with tilted initial conditions test G In this example we run a simulation with Geometric Glauber initial conditions without viscous effects but with a tilted energy density distribution The files related to this example can be found into the tests testG directory Using the same procedure shown in the previous example test F we draw a contour plot of the initial energy distribution to visually verify the effect of tilting Fig 6 21 Now since this is a simulation without viscosity effects we use the GDL postprocessing utilities to verify the conservation of total energy and angular momentum during the fluid evolution So after cop
29. 6 15 Test D Comparison between the semianalytical solution and ECHO QGP results at T 4 fm c Into the tests testD directory there are a few more plots of other variables obtained with the same procedure 6 5 Initialization with a tabulated file test E In this kind of initialization the initial entropy density distribution is provided with an ascii tabulated file Changing the IENENTR parameter from 1 to 0 it is also possible to initialize ECHO QGP using an energy density distribution The name of the input file can be chosen with the IN D FILE parameter The input file for this example is created with a short python script 3nit tab py that computes a simple gaussian distribution The script and the param dat file to configure ECHO QGP are into the tests testE directory See figures 6 16 and 6 17 60 Enegy density GeV fm3 6 1 8 1 6 4 1 4 2 12 3 1 0 gt 0 8 2 0 6 0 4 4 0 2 6 0 6 4 2 0 2 4 6 x fm Figure 6 16 Test E Initial energy density distribution at T 1 fm c 6 0 8 07 4 0 6 2 0 5 p 0 4 P 0 3 2 0 2 4 0 1 6 Enegy density GeV fm3 6 4 2 0 2 4 6 Figure 6 17 Test E Energy density distribution at T 5 fm c 61 6 6 Glauber Monte Carlo initialization test F In the tests testF directory can be found a param dat file to initialize a Glabuer Monte Carlo simulation The random seed determines what will be the sequence of events so using the same rando
30. D_start 211 ID stop 10213 part_list 0 antibar 1 chempot 1 xs INPUT inputdir out001 ioutdir out001 spectra mcoutdir out001 mc001 file out seed 0 ptbox 3 0 phibox 0 ybox 6 0 oversmpl 1 0 x HISTOGRAM RELATED mxv_pt 4 0 mnv_pt 0 0 mxv ang 6 28318 mnv_ang 0 0 mxv_y 3 0 mnv_y 3 0 binpt 10 binphi 1 binrap 11 6 28318530718 Listing 7 1 Example of settings txt for the routine 1 1 viscosity co Evaluate vor total number points for t min transver max transver points for t min polar an max polar an points for t min rapidity max rapidity 0 all ID of first e ID of last p particles in 1 on O off hypersurface output paren output child name of the if O generat upper limit if 0 is 2 pi upper limit e Should be 1 max value fo min max value fo min max value fo min 21931 3 Is it a visc 1 se value fo value fo value fo Despite all programs read the settings file not all the variables are being used in each 70 7 3 1 ECHO QGP related parameters This section contains the parametrs and the flags related to the hydrodynamic part of the simulation such as the dim integer flag Sets the dimensionality of the ECHO QGP simulation Allowed values are 2 or 3 for 1 2 D and 3 1 D simulati
31. ECHO QGP manual Version 1 0 00 The ECHO QGP developers team 22 05 2015 Contents 1 Introduction 3 1 1 WhatisECHO OGP i ok oe ww dome Rex Box ROSSO ROUX we 3 1 2 The ECHO QGP team ssaa aaa 3 MS LICENSE s so ence RR MU Gee aae Ge ee ws sms Pere debe amp 4 IM P ndine A PEPTIDE 5 1 5 Main limitations what the code cannot do 5 2 How to set up and run simulations 7 2 1 Requirements l l y 2 1 1 Parallel run requirements coke om RR 8 2 2 Download of ECHO QGP 0 20000 eee 8 2 2 1 Check of the integrity of the file 8 2 2 2 Uncompress the folder 2 04444 0 8 244 Rn 9 2 3 Configure EGHO QGP 2 6446 408444 48a ab bee eS 10 2 4 How to build and run ECHO QGP 10 2 4 1 Build and run on multi processors architectures 11 3 ECHO QGP configuration 15 3 1 The param dat file aaa aaa poe Ke en 15 3 2 Kind of initialization uua X Rok aaa a EAA RR 17 3 3 Kind of simulation uuo aa aaa a HE ERA 18 3 4 Grid parameters zoo o oo a RRS 18 3 5 Time parameters o oo e 19 3 6 Output parameters oo a 19 3 7 Algorithm parameters a oa aa o oo 9o dees 20 3 8 Collision parameters uou qoo 978 9C S99 ES DL Sd 20 3 9 Initial conditions parameters 20 3 10 Viscosity parameters leere 21 3 11 Equation of State parameters 2l 3 12 Glauber Monte Carlo initial conditions parameters 23 3 13 Decoupling hyper
32. als are denoted by colons the arguments of the functions are separated by commas So for example to print to print the first four values of the x array GDL gt print x 0 3 13 861386 13 584158 13 306931 13 029703 To make things faster you can move across the history of commands using the keyboard arrows and re edit the commands Dimensions inside multi dimensional arrays are separated by commas The asterisk means all elements contained into that dimension We can assign the values of a slice of an already existing array to a new array for example the following energy for z O array contains the value of energy density for 7 0 GDL gt energy for z O reform en 50 GDL gt help energy for z O ENERGY FOR Z 0 DOUBLE Array 101 101 The help command tells what kind of values its argument is please remind that gdl is case insensitive i e a and A are the same variable Here we used reform to cut off the dimension with only 1 element In this particular case actually it was not needed but it is recommended to always use it when you wish to cut slices with less dimensions to avoid to get 3D objects instead as 2D as in this case GDL gt energy try en 50 GDL gt help energy try ENERGY TRY DOUBLE Array 101 1 101 To make a plot we can type GDL gt plot x energy for z 0 50 xtitle x fm ytitle Energy density GeV fm 3 psym 2 xrange
33. alue for y ZMIN 12 minimum value for z Minkows ZMAX 212 maximum value for z Minkows time parameters TSTART 1 0 start simulation proper time TSTOP 10 stop simulation proper time TEMP_END 135 simulation ends when maximum output parameters DTL0G 0 05 proper time interval between DTOUT 0 1 proper time interval between OUTP_PREC 8 output precision it can be MAXDT 0 01 maximum timestep RESTART 1 restart possibilities O nev algorithm parameters OPE ees 0 2 Courant Fr Lew condition beam parameters NUCLEUS Au symbol of the colliding ions RADS 200 sqrt s NN GeV SIGMA IN 42 total inelastic cross sectio Bu vds 7 impact parameter fm initial conditions IENENTR 0 initial condition 0 energy T ede 0 15 initial hardness ECENTER 20 energy dens or entropy dens ENEZERO0 0 0000001 minimum value of energy dens RHOCENTER 0 1 charge density at the origin DET Aes 1 0 shift of the pp rapidity dis SIGETA 1 5 width of the pp rapidity dis viscosity parameters active only when VISCOUS paramete ETA_S 0 08 leta entropy dens parameter TAU PI C 3 relaxation time coefficient TRACE IMP zz shear viscous tensor compone equation of state EOS t 1 analytic eos pr rh en 2 TAB EOS FILE qcdIEO0380 dat name of the file containing NUM DER 0 i with an eos it uses num d
34. an extremely synthetic description of each one of them common f90 contains all the global variables and some utility functions echo f90 main file eos f90 handles the Equation of State and the interplay among the thermo dynamic variables evolve f90 Computes the time evolution of the quark gluon plasma glaubermc f90 Prepares the initial state for the hydro evolution with the Glauber Monte Carlo model holib f90 Library with high order reconstruction algorithms hypersurface f90 Computes the thermal freezeout hypersurface init f90 Initialization file out f90 Handles the output parallel_mpi f90 Handles the parallelization parallel_nompi f90 Dummy file for the serial run system f90 Prepares the lattice and the metrics handles the conversions between primitive and conserved variables viscous f90 Computes the viscous corrections work f90 Riemann solver and interfaces to high order libraries 2 3 Configure ECHO QGP The configuration file param dat can be edited with any text editor e g vim gedit geany kate but itis very important NOT TO ALTER the structure of the file number of columns before the symbol or before the symbol The change in the parameters in param dat are read at runtime so it is not necessary to compile again the program There are some parameters that as for now are not configurable from the param dat file as they are declared in the Fortran files and their modification requires to recompile
35. but using a contour plot Fig 6 5 GDL gt set_plot ps GDL gt device filename plot4 ps GDL gt contour reform en 50 x z xtitle x fm ytitle eta xrange 6 6 yrange 5 5 LEVELS 0 0 2 5 5 7 5 10 12 5 15 17 5 20 C LABEIS 1 0 1 0 1 O 1 0 1 GDL gt device close Now let s have a look at what is the situation at a later time using the fortran utilities Output data are written into binary files the readx exe utility extracts these data into separate files for each variable in ascii format Calling readx exe without any argument prints an help message readx exe Please insert the range of echo qgp output files from which you want to extract values Optionally you can also write the name of the directory where the output files will be written default postproc readx If we are interested only in output at 7 10 0 f m c we can look at the time dat file and after reading that corresponding output data number is 91 we can type 45 6 7 mr eta o C gl aaa d aaa d aaa d acacacd Pau 6 4 2 0 2 4 6 x fm Figure 6 4 Contour plot of energy density in GeV f m at r 1 f m c for y 0 readx exe 91 91 time 9 9999999999999822 If we wished to extract all output data from 7 4 5 fm cto T 4 8 f m c we would use readx exe 36 39 time 4 5000000000000009 time 4 6000000000000005 time 4 70
36. ce Project coordinator becattini fi infn it Andrea Beraudo INFN Sect of Turin Glauber Monte Carlo initialization testing postprocessing routines beraudo to infn it Luca Del Zanna Univ of Florence INAE Arcetri Obs INFN Sect of Florence Author of the original ECHO code http www astro unifi it echo from which ECHO QGP has been derived delzanna unifi it Arturo De Pace INFN Sect of Turin Geometric Glauber initialization testing depace to infn it Alessandro Drago Univ of Ferrara INFN Sect of Ferrara Consultant drago fe infn it Gabriele Inghirami FIAS Goethe Universitat Frankfurt am Main Maintainer of the hydrodynamical evolution part of the code inghirami fias uni frankfurt de Marzia Nardi INFN Sect of Turin Consultant testing nardi to infn it Giuseppe Pagliara INFN Sect of Ferrara Consultant pagliara fe infn it Valentina Rolando INFN Sect of Ferrara Maintainer of the freeze out and particle spectra computation part of the code rolando fe infn it Past collaborators Vinod Chandra Consultant for the second order viscous corrections We would like to thank also P Cea J Rizzo L Cosmai R Tripiccione for their help in building up the very first implementation of ECHO QGB A Palmese A M Marin Garcia V Gonzalez D Piagneri for their feedback as first users of the pre release versions of the code G Denicol for useful inputs about the Gubser s vis
37. chempot 1 Listing 7 2 Example of the section in settings txt producing all the available particles 7 6 2 Producing an interval of listed particles listorseq 1 Let s assume that the user wants to produce all the particle listed in pdglist txt between two given IDs say 7 with ID 211 and 7 with ID 221 which are t 7 0 K K K0 K0 n The fastest way to configure settings txt is to set listorseq 1 ID start 211 and ID stop 221 Here we provide an 75 example setup for a simulation producing such ensemble without the produc tion of antibaryons and with the appropriate chemical potential Please note that still there is NO line after the part_list line and the variable part_list itself is set to 0 PARTICLE RELATED npt 41 ptmin 0 0 ptmax 4 0 nphi 36 phimin 0 0 phimax 6 28318530718 nrap 41 4 rapmin 4 0 rapmax 4 0 listorseq 1 ID start 211 3 ID stop 221 part_list 0 g antibar 0 chempot 16 points for t min transver max transver points for t min polar an max polar an points for t min rapidity max rapidity O all 1 se ID of first ID of last p particles in 1 on O off Listing 7 3 Example of the section in settings txt producing a custom sequence of particles 7 6 3 Producing a detailed list of particles listorseq 2 Within this configuration the user can pick any lis
38. cous flow test 1 3 License The code is released under the GPL v 2 0 please read the file LICENSE TXT contained into the source directory or have a look at https www gnu org licenses gpl 2 0 html 1 4 Funding The development of ECHO QGP has been supported by the Italian Ministry of Education and Research grant PRIN 2009 Il Quark Gluon Plasma e le collisioni nucleari di alta energia by the INFN project RM31 and by funding from HIC for FAIR 1 5 Main limitations what the code cannot do The main limitations of the code are The code can describe one fluid only expanding in vacuum see next point about the vacuum term The code needs a minimum baseline for the value of the energy density of the order of 1 KeV for the inviscid case and 0 1 1 MeV for the viscous case The time derivatives have a limited first order accuracy Baryon charge evolution is properly treated only in the inviscid case in the viscous case it only plays a numerical role but it doesn t have a physical meaning since there are some missing terms in the equations describing its evolution To ensure the stability of the program it is necessary to switch off the viscosity effects under a certain temperature usually less than 100MeV i e well below the freezeout temperature where the hydrodynamical description is not valid anymore If initial conditions are not very smooth the program may crash before reac
39. d as follows 7 6 A Woods Saxon distribution is sampled to create an initial nuclear configuration The transverse positions of the nucleons of the two colliding nuclei are reshuffled into their center of mass frame e For each configuration a random impact parameter bc 0 bmaz is x tracted from the distribution dP 2rbdb A collision happens if the positions x of the nucleon i from nucleus A and v of nuclean j from nucleus B are such that z 2 F yi yj lt onn 7 The param eter min participants contained into file glaubermc f90 establishes the minimum number of particpant nucleons to accept or reject the 30 event The user with the parameter NCONE can choose how many configurations to compute e To each participant and collision is associated an energy density distribu tion described by a gaussian function with variance o these distributions are then summed together Npart NR part 2 Neoil r gell 2 e T0 A a a e 7 eese i 1 Ono 29 29 i 1 The profile e 79 x is then multiplied by 0 Ini beam UE f n exp 3z T flat lt Ini lt Ybeam 1 In lt niat where n nfiat 2 Nflat is given in param dat by the DETA VSNN TUN parameter c by SIGETA and yream log Viscous tensor components are initialized as in initialization 0 We advice that at the time of the release of ECHO QGP 1 0 00 initializations with p A and d A collisions hav
40. d case The definition we used for the spatial eccentricity ecO files is H f dzdy x zo y yo EelN const r m f dxdy a m x0 M y yo the definition for the df0 files with average flow in x direction is _ J dadyyuze Uz n f dedyye while the definition 9 for the momentum eccentricity epO files is J dady e p o v v J dady c 9 v2 v2 2 p p Uf eanabw 26 where is the energy density 7 is the Lorentz factor and p is the pressure 3 17 Essential parameters for projectile nuclei In this section it is possible to choose the parameters for specific nuclei and or to give the essential parameters i e mass in a m u radius in fm Wood Saxon width in fm and normal nuclaer density in fm If a new projectile nucleus is wanted it is sufficient to type or copy and paste a new line where the 5 characters at the beginning are reserved for the name and the rest of the line structure is preserved 27 Chapter 4 Available initialization alternatives As its hydrodynamic starting point ECHO QGP can set up different initial energy density or entropy density profiles based on various widespread models or on some of the most common numerical tests The ones currently available in the code are listed below and they are selected through the parameter INIT_TYPE in the configuration file param dat 4 1 Initialization 0 Geometric Glauber Here we compute t
41. default real 8 fromecho f90 The synopsis of the program is fromecho input file output file x y z The program takes as input one of the output files of readx and select the values of the given variables along the x y or z direction from the 0 up to the right border printing them into output file For example fromecho exe PROOO1 dat pressure txt x it will print into the file pressure txt the values of pressure along x from O up to the border of the grid The ouput file is a two column ascii file in the first column there are the coordinate values and in the second column the variable values fromecho2d f90 this utility extracts a 2D slice parallel to one of the coordi nate axis from a 3D set of data It can be individually compiled with the command gfortran o fromecho2D exe fdefault real 8 fromecho2D f90 and its synopsis is fromecho input output x y z x y z optional x y z value default is 0 where input is one of the files containing single variable data produced by readx Usage example fromecho prova input prova output x y This extracts data from file prova inputs and writes into file output file the values on the x y plane for z 0 Usage example fromecho prova input prova output zx 5 This extracts data from file prova inputs and writes into file output file the values on the z x plane for y 5 For the optional 5th argument actually it is selected the grid value which is closest to the chosen value i e no interpo
42. der eos data must be present the file pdglist txt which lists all the particle which can be included in the computation one can see a human readable table in the Appendix The code uses such table to read the particles features The first integer number is the ID number of the particle which we use in the settings file to identify it listorseq can assume following values 0 Uses ALL the particle listed in the file pdglist txt 1 Uses a the particles included in the list between the ID correspond ing to ID START and the ID corresponding to ID STOP 2 Uses a list of particles which IDs must be listed in the settings file just after the part list line 72 For the sake of clearness we show in this section three examples of the using of these options in the subsection 7 6 ID start integer particle ID Only used if 1istorseq 1 is the first particle in the range the user wants to used ID stop integer particle ID Only used if listorseq 1 is the last particle in the range the user wants to used part list integer value Only used if listorseq 2 is the total number of particles listed in the settings file which must correspond to the lines with the IDs after this parameter antibar integer flag Since in the pdglist txt file there is no antibaryon listed this switch enables 1 or disables 0 the production of the antibaryons corresponding to the listed baryons chempot integer flag If set to O it force
43. e not been properly tested 4 5 Initialization 4 Viscous Gubser Flow Viscous Gubser flow with initial values provided by a tabulated file named Initial Profile GubserFlow dat contained into the main ECHO QGP source tree This is a 2D 1 test in Bjorken coordinates See the proper section 6 3 in the tutorials chapter for further informations 4 6 Initialization 5 tabulated initial energy or en tropy density profile This is a 2D 1 initialization Inital energy density profile if parameter IENENTR is set to 0 or entropy density profile if parameter IENENTR is set to 1 are read from file named IN D FILE Viscous tensor components are initialized as in initialization 0 31 4 7 Other parameters inside the code The user can change some parameters included inside the code After changing one of these parameters the user has to recompile the code before using the program If the user changes files with definitions like eos_data temperature def which are inserted into other source files by an include directive he she has also to clean the source tree with make clean or make cleanall before recompiling the program with make or make par option algo Parameter located into system 90 inside the subroutine sys tem cons2prim it changes the algorithm for obtaining primitive vari ables starting from the evolved conservative ones The best choice is usually 1 lambdaO lambda1 lambda2 Parameters located into system 90 inside t
44. exe or if we have got only a single core machine and so obviously we didn t choose to use mpi echo exe If we wish to run the program even after we log out from the computer very common situation when we use an ssh connection we may use nohup nohup mpirun np 2 echo exe amp With nohup the messages printed by echo qgp on the screen will be written into a file named nohup out The output data files will be written into the outr0001 directory inside that directory a log file showing the progress of the computation will be updated every DTLOG 7 intervals in this example run each 0 01 fm c Let s suppose now that the run ended and we wish to analyze the results First we need to compile the fortran postprocessing utility with the command make tools and then we have to copy the produced executable files with the exe exten sion and the GDL scripts into the output directory cp tools exe tools pro outr0001 40 Now let s move into the output directory cd outr0001 If you have installed IDL or its free clone named gnudatalanguage at least version 0 9 3 its website is http gnudatalanguage sourceforge net you can use some scripts to make some sketchy but quick plots Let s see how First launch gdl gdl You ll get an interactive shell With the script readvar pro you will be able to read the variables
45. h the command make MCgen utils histogram which can be build with the command make utils_histogram Issuing just the make command just thermal and MCgen are produced thermal produces the averaged spectra of the selected particle specie whereas MCgen produces a ramdom sample of such particles This last program needs some of the output files of the former but since the computational load for thermal is heavy the user can exploit utils_therm to produce just the files needed by the Monte Carlo generator saving time utils histogram instead allows the user to re arrange in different binnings the histogram produced by MCgen All these programs need the file settings txt to be carefully filled in 7 3 How to configure the particle production All the programs contained in the folder analisi use as configuration file settings txt although not all parameters are effectively used in each pro gram In the listing 7 1 an example of the configuration file is provided As we did in ECHO QGP configuration file also this settings txt is divided into sections and most important needs its structure not to be altered 69 RI 2d This is the file containg the settings x ECHO RELATED visco hyd 1 visco spe 1 vorticity 1 nout 0 PARTICLE RELATED npt 41 ptmin 0 0 ptmax 4 0 nphi 36 phimin 0 0 phimax 6 28318530718 nrap 41 rapmin 4 0 rapmax 4 0 listorseq 0 I
46. he initial state for the energy density profile in the Optical Glauber Model frame 10 We define the usual thickness function as T z y I at dz ge ee sg 5 where po 6 and r are the normal nuclear density the Wood Saxon width and the radius of the nucleus all of them defined at the end of param dat file Then we define T4 xr T xr b 2 T_ xr T xr b 2 where xp x y is the vector of the transverse plane coordinates and b is the impact parameter vector connecting the centers of the two nuclei In our conventional cartesian reference frame the b vector is oriented along the positive x axis and the two nuclei have initial momentum along the z axis whence the reaction plane is the xz plane b is assigned with the B parameter Given c as the total nucleon nucleon inelastic cross section corresponding 28 to the parameter SIGMA IN m as the mass number of the colling nuclei and T x y as the thickness function we define Ti z y T 1 T 1 7 T z y T 1 while the number of binary collisions is npo z y eT x y Te x y We define the wounded nucleons weight function Wy as Wy z y n 2 Tila y f n ud To x y f n where 1 7 lt Nm n f n 4 aE Nm 0 N gt Nm and 0 n lt Thm 7 7 f n 2 m Nm N m Nm 1 N gt Nm Finally the initial proper energy density distribution is assumed to be e x y n co W z y n H n
47. he subroutine system sources they enable if set to 1 or disable if set to 0 the contributions to the source terms of viscous tensor components of the mq 0 term the second order terms the vorticity terms iseed Parameter saved into the file random seed dat When using Glauber MC initialization procedure if ECHO QGP finds this file it reads the integer value it contains for seeding the random number generator thus reproducing the last energy density profile If the user removes this file ECHO QGP uses the integer value obtained from a system clock call as the new random seed iseed and it saves its value inside the file random seed dat REC Choice of reconstruction algorithm also used for computing spatial derivatives of velocities for obtaining shear viscous tensor components Possibile choices are TVD2 CENO3 WENO3 WENOS PPM4 MPE3 MPES5 MPE7 This parameter is located inside common 90 limiters The tvd2 ceno3 and ppm4 reconstruction algorithms may use MM2 or MC2 as possible limiters The pre defined algorithm is MM2 but the user can change it to MC2 commenting uncommenting just a few lines inside holib f90 following the instructions inserted into the code If the user wishes to change how the values of viscous tensor are initialized he she has to modify the final part of the subroutine viscous initio contained into file viscous f90 If the user wishes to change the initial u velocity field he she has t
48. hing the freezeout temperature unfortunately currently this happens quite often with Glauber Monte Carlo initial conditions The correct parsing of the configuration parameters requires not to alter the structure of the files param dat and settings txt The hypersurface computation always runs over a single core it is not parallelized The grid partitioning in runs exploiting MPI is limited to the x axis only and the user can exploit a number of CPUs not exceeding one third of the cells along the x axis O actions are performed by only a single processor The code does not yet take into account a post hydro after burner any transport code or resonance decayer rescatterings etc Chapter 2 How to set up and run simulations 2 1 Requirements Some requirements are assumed in order to use ECHO QGP v1 0 a working GNU Linux environment a fortran 2008 compiler the make utility the tar utility the gzip utility The current version was developed and tested with Debian 7 0 x86 64 equipped with the GCC 4 7 2 compiler Ubuntu 14 04 amd64 equipped with the GCC 4 8 2 compiler The makefile provided within the package contains some of the most frequent flags used for specific architectures so that an expert user can modify it at pleasure Additionally some the optional postprocessing tools require GDL http www gnudatalanguage org or IDL by EXELIS VIS to be installed Root access is not needed to co
49. ity Output has 8 bytes precision Variables to be read density Vx vy VZ pressure energy density temperature entropy density bulk viscosity pi tt pi tx pi ty pi tz gamma Number of variables is 20 Reading file out0031 dat time 4 00000000 time or tau is stored into variable t 4 0000000 Arrays available x y and z of type double with 401 401 1 elements Arrays available with their maximum mean and minimum values 96 Compiled module MEAN rho 0 21052070 0 12870059 0 0034551016 VX 0 97009619 8 2463097e 16 0 97009619 vy 0 97009619 6 2895014e 15 0 97009619 vz 0 0000000 0 0000000 0 0000000 pr 0 0074253124 0 0010125367 1 0013452e 05 en 0 022275937 0 0030376102 3 0040355e 05 temp 0 059237610 0 027047653 0 011351802 58 entropy 0 50139177 0 088629927 0 0035284097 bu 0 0000000 0 0000000 0 0000000 tt 0 0000000 0 0011994727 0 0089583879 tx 0 0093095075 3 2743781e 18 0 0093095075 ty 0 0093095075 6 1862789e 18 0 0093095075 tz 0 0000000 0 0000000 0 0000000 xy 0 0044716459 1 7072896e 18 0 0044716459 XZ 0 0000000 0 0000000 0 0000000 yz 0 0000000 0 0000000 0 0000000 XX 1 1768752e 05 yy 1 1768752e 05 ZZ 0 00010049364 vO 4 1203721 0 00081962219 0 00081962219 2 7411661e 05 1 9250202 0 0096843503 0 0096843503 3 8899064e 07 1 0000000 Now we read the tabulated file with the solutions computed by Maple using
50. lations are made The ascii output file contains the coordinate value on the first axis the coordinate values on the second axis and the variable value in that point of the slice Assuming that these values are x y and f x y the output file is written in this way 36 x 1 y 1 x 1 y 1 x 1 y 2 x 1 y 2 x 1 y 3 x 1 y 3 x 1 yay f x 1 y ny blank line x 2 y 1 x 2 y x 2 y 2 f0x 20 y C2 x 2 y ny x 2 y ny blank line x 3 y 1 x 32 y 02 x 3 y 2 x 3 y 2 x nx 1 y ny f x nx 1 y ny x nx y ny x nx y ny The blank lines are inserted to make easier to plot the output file with gnuplot timev f90 this small program can be individually compiled with the com mand gfortran o timev exe fdefault real 8 timev f90 Usage example timev exe T 1 137 51 40 37 pippo It prints into the file named pippo two columns of values the first one contains the time the second one the values of the variable usually T stands for temperature at cell of indexes x 51 y 40 and z 37 stored in the files from TO001 dat to TO137 dat search sh This very small and very simple bash script searches and highlights a given string inside all source code files Example search sh allocate 5 3 The particle spectra production tool The tool for producing particle spectra is contained into the analysis direc tory and can be compiled simply with the make command This program is able to use OpenMP
51. lice of the grid for example fromecho2d exe T0091 dat tempxz91 dat x z Then we can use a gnuplot script like the following to plot the data Set terminal and output set terminal pngcairo size 900 900 enhanced font Helvetica 22 set encoding utf8 set output contour91xz png 48 Set plot properties set size square set pm3d unset surface set view map set key outside set pm3d interpolate 0 0 interpolate the color Set the color palette set palette model RGB defined O black 1 blue 2 cyan 3 green 4 yellow 5 red 6 purple Se the axes set xlabel x fm set ylabel Symbol h set cblabel Temperature MeV Draw the plot splot tempxz91 dat u 1 2 3 1000 notitle 15 160 10 140 1205 5 E 100 9 c o 2 80 2 5 60 15 20 Figure 6 6 Test A Contour of temperature MeV at rT 10 fm c for y 0 A copy of the plotted datafile tempxz91 dat can be found in tests testA Now let s see how to compute the thermal particle spectra From the ECHO QGP main directory of sources we enter the analysis subdi rectory and we compile the tools 49 make We remind that to make use of OPENMP the user has to edit the makefile and export some environment variable see 5 3 for more details Using the following configuration file settings txt This is the file containg the setting
52. line with comment GUBSERCHECKS Since in this test we wish to compare the evolution of some variables with the semianalytical solutions obtained numerically with some external code we need also these solutions In the tests testD directory we provide the solutions computed with Maple 12 at 7 4 fm c the Maple worksheet can be reused with only minor changes to compute the solutions at different times and or with different grid resolutions After the end of the run we can check the results There are many ways to do it here we ll use gdl and gnuplot cd outr0001 gdl We can use the shell commands inside gnudatalanguage adding a dollar sign before issuing the command For example to list the files inside the current directory to check if the script readvar pro is there we can type GDL gt ls 1 grep readvar rw r r 1 gg 12562 mag 9 02 42 readvar pro 57 Now we read the output at 7 4 fm c please remind that you can look at time dat to see what is the output number corresponding to that time GDL gt readvar 0031 96 Compiled module READVAR This program reads the output of echo qgp Reading grid summary dat nx 401 ny i 401 nz 1 xstep 0 0500000 ystep 0 0500000 zstep 2 00000 xmin 10 0250 ymin 10 0250 zmin 1 00000 xmax 10 0250 ymax 10 0250 zmax 1 00000 Reading grid dat Compiled module SKIP_LUN Run with viscos
53. m seed saved into the file random_seed dat it is possible to reproduce the same initial series of events Other parameters can be ajdusted editing the first lines of glaubermc f90 In this example we try to produce a series of events from a sequence of 500 nuclear configurations each with 20 different impact parameters getting 1881 events which satisfy our selection criteria i e a minimum of 18 partici pants as specified with the option min_participants 18 at the beginning of file glaubermc f 90 The results are stored into the file partcoll dat From this list we select the event with id 67 but we can choose a sequence of events instead of a single one Now we plot the initial energy density distribution The procedure for each plot is the same apart obviously for the names of the files For the event with id 67 we compile the fortran prostprocessing tools make tools cp tools readx exe outr0067 cd outr0067 We are interested in the first and last output files so readx 1 1 readx 94 94 cp tools fromecho exe postproc readx cd postproc readx 62 fromecho2d exe EPS0001 dat en outl dat x y gnuplot contour outl gp The Fig 6 18 shows the initial energy distribution on the 7 0 x y plane at 7 1 fm c Now we look at the energy density profile as a function of 7 for Energy density GeV fm
54. mpile or run the program 2 1 1 Parallel run requirements To execute parallel runs of ECHO QGP on multiple cores machines an MPI library is also needed The code has been tested using only the OpenMPI implementation of the Message Passing Interface MPI standard version 1 6 5 all versions from 1 3 x to 1 8 x should also work but they were not tested 2 2 Download of ECHO QGP The latest version is downloadable from the official ECHO QGP website http theory fi infn it echoggp From now on lt version gt occurences refer to the version of the code on which we are working on e g ECHO QGP version tar gz could be ECHO QGP 1 0 03 or ECHO QGP 1 5 11 The version id is composed by three numbers a change in the first number will correspond to deep changes in the structure of the code or in the physics that it handles a change in the second number will reflect significant im provements or minor new features changes in the third number are reserved to bug fixes only Only bug fixing versions will not introduce incompatibilities with previous versions while first and second digit new versions probably it will 2 2 1 Check of the integrity of the file It is possible to check the source code tarball integrity it is sufficient to download the corresponding md5sum checksum file and issue the command md5sum c ECHO QGP lt version gt tar gz md5sum which returns on positive match ECHO QGP version
55. n be individually compiled with the com mand gfortran o readx exe fdefault real 8 readx f03 The synopsys of the program is readx exe number of start frame number of end frame If selected in the param dat file and for viscous tensor components if we run a simulation with viscosity there will be the following output files nnnn refers to the four digits number identifying the frame EPSnnnn dat the energy density PRnnnn dat the pressure VXnnnn dat the velocity along x direction VYnnnn dat the velocity along y direction e VZnnnn dat the velocity along 7 direction RHOnnnn dat the charge density Snnnn dat the entropy density Tnnnn dat the temperature bulknnnn dat the bulk viscosity ttnnnn dat the 7 shear viscous tensor component txnnnn dat the shear viscous tensor component e tynnnn dat the 7 shear viscous tensor component e tznnnn dat the 7 shear viscous tensor component e xynnnn dat the 7 shear viscous tensor component e xznnnn dat the 7 shear viscous tensor component 35 e yznnnn dat the 7 shear viscous tensor component e xxnnnn dat the 7 shear viscous tensor component e yynnnn dat the 7 shear viscous tensor component e zznnnn dat the 7 shear viscous tensor component x dat y dat eta dat tau dat the grid coordinates fromecho f90 this small program can be individually compiled with the command gfortran o fromecho exe f
56. nables 1 the computation of the decoupling hypersurface If set to 0 it saves computational time but it does not perform any decoupling technique FREEZKIND integer flag Criterion for the detection of the hypersurface 0 Isothermal hypersuface Uses a threshold temperature FREEZE VAL Tyo GeV 1 Constant energy density hypersuface Uses a threshold energy density FREEZEVAL efo GeV fm FREEZEVAL Decoupling field threshold temperature GeV or energy den sity GeV fm HYPSURFTI real value Time interval in fm c of the grid passed to the hypersurface finding routine Sometimes to treat shocks it is useful to set a very dense grid but in order to compute the hypersurface a lesser dense grid is needed so it would be a waste of computing time to perform the check at every hydro step 3 14 Initialization with a custom energy or entropy density profile ECHO QGP can use as a starting profile r 79 a custom 2D energy density or entropy density profile at mid rapidity with the field values at any cell center The structure of the file must be x coordinate y coordinate energy density value in GeV fm or entropy density value in fm The field values of the tabulated file will be interpolated on the grid chosen in param dat if the grid on which they lie does not match with the grid of ECHO QGP IN D FILE character max 18 characters Name of the file with the tabu lated energy or entropy density distribution max 18
57. ng from a uniform distribution of the polar angle 4 If set to 0 the upper limit is automatically set to 27 ybox real value Upper limit for the random sampling from a uniform distribution of the rapidity y The user must be careful in the choice of ptbox phibox and ybox given three random numbers rj r2 r3 0 1 the momentum is sampled with the formula pp 71 ptbox 7 4 r3 phibox 7 5 y r3 2 ybox ybox 7 6 so a bad choice of the upper limits can lead either to a wrong sampling ensable or a bottleneck in the code oversmpl real flag and value This parameter allows the user to perform an oversampled if the parameter is greater than 1 simulation as well as an undersampled if the parameter is less than 1 simulation The histograms computation automatically takes care of this param eter renormalizing them This parameter is mainly useful during the debugging stage Histogram related parameters When the Monte Carlo production of the particles is terminated some his tograms are automatically calculated in order to be compared with the averaged spectra Such histograms calculation can also be performed indepen dently with the program utils_histogram This section specifies the binning of such histograms mxv pt real value Maximum value in the transverse momentum histogram mnv_pt real value Minimum value in the transverse momentum histogram mxv_ang real value Maximum value in the polar a
58. ngle histogram mnv ang real value Minimum value in the polar angle histogram mxv y real value Maximum value in the particle rapidity histogram mnv y real value Minimum value in the particle rapidity histogram 74 binpt integer value Number of bins in the transverse momentum his togram binphi integer value Number of bins in the polar angle histogram binrap integer value Number of bins in the particle rapidity histogram 7 6 Examples of particles subset The IDs of the particles are listed into the file eos data pdglist txt 7 6 1 Producing all available particles listorseq 0 We provide here an example of the particle section in the setup file for a sim ulation including ALL the particles comprehensive of antibaryons We also set as active in the computation the appropriate and the chemical potential in settings txt Please note in 7 2 that there is NO line after the part list line and the variable part list itself is set to O x PARTICLE RELATED i1 listorseq 0 O all i se ID_start 0 34 ID stop 0 part_list 0 ID of first ID of last p particles in nptkes 41 points for t ptmin 0 0 min transver ptmax 4 0 max transver nphi 36 points for t phimin 0 0 min polar an phimax 6 28318530718 max polar an nrap 41 points for t 4 rapmin 4 0 min rapidity rapmax 4 0 max rapidity id antibar 1 1 on O off
59. nterval between output printing output precision Variables printed in the output files density vx Xx vz pressure energy density temperature entropy density bulk viscosity pi tt pi tx pi ty pi tz pi xy pi xz pi yz pi xx pi yy pi zz u0 or gamma Lorentz factor 13 200 000 5 361 4 200 5 000 0 150 20 000 0 10E 02 0 22E 03 0 100 1 000 1 500 0 000 140 000 0 050 0 200 0 001 0 001 0 10E 06 0 010 0 050 double MPE5 MM2 8 bytes 91 9g og dutdt duxdx duydy duzdz theta or expansion rate vorticities will also be printed into separated output files Calculating thickness function check nucleus mass 196 94642 Done k k k 2k k k ak k RR k k k k RUN NUMBER 1 RUN 1 OF 1 Initializations done mkdir outr0001 Grid computed Files for hypersurface computation written Summary of variables written Time 1 00000000 out0001 dat 1 61100000 secs Copying param dat into the output directory Pressure treshold GeV fm 3 2 9468165948506055E 003 Energy density treshold Gev fm 3 1 3051308079431541 E 002 Time 1 05000000 out0002 dat 1 01000000 secs Listing 2 1 Output of ECHO QGP 14 Chapter 3 ECHO QGP configuration 3 1 The param dat file The param dat file contains several parameters used by the program and that the user can modify Changing a parameter in such file does not imply to compile again ECHO QGP because the
60. o modify the subroutine calc vel long nz ueta contained into the file init f90 The parameter 7 as defined into 4 1 can also be changed editing the function H of eta into the file init f90 32 4 8 Arguments passing ECHO QGP accepts some arguments passed when calling it Currently they are v version it prints version information and exits h help it prints usage information this message and exits m maxdt maximum timestep allowed r restart it restarts from last saved frame t tstop n it ends at proper time tstop 0 outdir name it changes the name of output directory 33 Chapter 5 Post processing tools Inside the tools directory there are several utilities to manipulate the results to make easy to visualize them using programs like grace IDL gdl or gnuplot 5 1 IDL GDL scripts readvar pro IDL GDL script that reads the output of echo qgp and stores the variables it into 3 dimensional arrays the grid data into 3 arrays x y and z The files grid summary dat and param dat must be in the same directory with data where this script is launched readvartime IDL GDL script that reads the output files of echo qgp and the values of a chosen variable at a chosen point on the grid in a chosen range of output files are printed into a chosen file togheter with the time at which they refer The files grid summary dat and param dat must be in the same directory with data where this script is launched readder pro
61. ons re spectively If the cross check with the output with ECHO QGP gives a different dimensionality the code quits with en error message visco hyd integer flag Passes to the program the information about the ECHO QGP simulation must be 1 if the simulation was a viscous one 0 if it was ideal Note that the file containing the hypersurface information and the array listed in section 7 1 are allocated accordingly visco spe integer flag Enables 1 or disables 0 the viscous contributions to the distribution function in the spectra computation It can only be activated when visco hyd 1 vorticity integer flag Enables 1 or disables 0 the computation of ther mal vorticity over the decoupling hypersurface It needs the file hyper surf derivtxt produced by ECHO QGP in the same directory containing hypersurface txt nout integer flag It is the number of time steps to be taken into account If set to 0 the program reads all the time steps produced by ECHO QGB if not the program asks the user if the number of output is correct and wants a Y N answer from the keyboard followed by the return command to continue This variable is very useful for debugging 7 3 2 Particle related parameters This section contains the parametrs related to the produced particles such as the species and the momentum The programs in this section use concatenated loops over the momen tum components where we refer to the momentum components referring to eq
62. pa rameter is set to 1 pitz 7 component of shear viscous tensor active only when VISCOUS pa rameter is set to 1 pixy 7 component of shear viscous tensor active only when VISCOUS parameter is set to 1 pixz 7 component of shear viscous tensor active only when VISCOUS parameter is set to 1 25 piyz 7 component of shear viscous tensor active only when VISCOUS parameter is set to 1 pixx 7 component of shear viscous tensor active only when VISCOUS parameter is set to 1 piyy 7 component of shear viscous tensor active only when VISCOUS parameter is set to 1 pizz 7 component of shear viscous tensor active only when VISCOUS parameter is set to 1 gamma y Lorentz factor also v v dutdt 7 duxdx ave duydy oe Ovz duzdz 32 Ot Ox additional term ue with Milne coordinates theta 0 9v Qe zx Qe with Minkowski coordinates and the derivativ Prints the derivatives of velocities and temperature vs 7 2 y and 7 at 7 intervals given by parameter DTOUT into separate output ASCII files der0001 dat der0002 dat and if the computation of f o hypersurface is active also on o hypersurface producing the file hypersurf deriv txt flows Prints the hydrodynamical eccentricities on the transverse plane vs 7 at 7 intervals given by parameter DTOUT into separate output ASCII files df0001 dat epO0001 dat ecO0001 dat df0002 dat ep0002 dat ec0002 dat The computations are valid only in the invisci
63. s for the routine producing the spectra ECHO RELATED dim 141 2 1 341 dimension for the simulation visco_hyd 1 Is it a viscous hydro simulation O no l yes visco spe 1 viscosity corrections to the distribution function 0 no 1 yes vorticity 0 Evaluate vorticity on hypersurface nout 0 total number of outputs if O reads all available PARTICLE RELATED npt 40 points for the transverse momentum ptmin 0 0 min transverse momentum ptmax 4 0 max transverse momentum nphi 36 points for the polar angle phimin 0 0 min polar angle phimax 6 28318530718 max polar angle nrap 41 points for the particle rapidity rapmin 4 0 min rapidity rapmax 4 0 max rapidity listorseq 2 0 all 1 sequence ID start ID stop 2 list 3 stable ID start 211 ID of first particle to be considered ID stop 10213 ID of last particle to be considered part list 2 particles in the list 211 3122 antibar 1 1 on O off chempot 1 read chemical potential from eos_data chemical_potential txt 0 ste mu 0 INPUT inputdir outr0001 input directory ioutdir outr0001 spectra output directory filg out name of the ECHO outout file 50 RANDOM SEED saved anyway seed if O generates random seed otherwise use that ptbox 3 0 upper limit for mc box phibox 0
64. s the chemical potentials of all considered particles to be 0 If set to 1 the program reads the chemical potential corresponding to the the given temperature from the file chemical potential txt contained in the eos data folder 7 4 Input Ouput The section of the file settings txt dedicated to the input output addresses simply contains paths and names inputdir character 64 path Path ofthe folder containing the file hypersurface txt ioutdir character 64 path Path in which all the files produced by thermal and by utils_therm are stored The same path also contains the info used by MCgen If the folder exists already the content is replaced while if the folder does not exist a new one is created mcoutdir character 64 path Path in which all the files produced by MCgen and by utils histogram are stored If the folder exists already the content is replaced while if the folder does not exist a new one is created 7 5 Parameters for the Monte Carlo production In this section the user can find all the parameters for the Monte Carlo generation of particles seed integer flag and value If 0 is given the seed is automatically gen erated and stored in the file report MCgen txt placed in the folder specified by the path mcoutdir 73 ptbox real value Upper limit for the random sampling from a uniform distribution of the transverse momentum pr GeV phibox real flag and value Upper limit for the random sampli
65. surface parameters 24 3 14 Initialization with a custom energy or entropy density profile 24 3 15 Section for simulations with tilted initial energy density profile 24 4 6 7 3 16 Printed variables in the output files 3 17 Essential parameters for projectile nuclei Available initialization alternatives 4 1 Initialization 0 Geometric Glauber 4 2 Initialization 1 2D shock tube 4 3 Initialization 2 1D viscous shear flow 4 4 Initialization 3 Glauber MonteCarlo 4 5 Initialization 4 Viscous Gubser Flow 4 6 Initialization 5 tabulated initial energy or entropy density PONE Soc alge eB pha ace debe dst Qe qoe By ee t 4 7 Other parameters inside the code 4 8 Arguments passing leen Post processing tools 5 1 IDL GDLscripts 0 202 000 5 2 Fortra utilities cuyo ck QE e Red Sw LR do eo 5 3 The particle spectra production tool Tutorials 6 1 A3D 1 simulation with Glauber model testA 6 2 2Dshocktube testB llle 6 3 1D viscous shear flow test testC 6 4 Gubser flowtest testD 0 2 000 6 5 Initialization with a tabulated file testE 6 6 Glauber Monte Carlo initialization testF 6 7 Run with tilted initial conditions test G Particle spectra production 7 1
66. t Friedrichs Lewy condition 3 8 Collision parameters In this section ECHO QGP reads all the parameters characterizing the collision the specie of the nuclei the beam energy NUCLEUS character flag It sets the specie of colliding nuclei and it corre sponds to the symbol of the atom e g Au or Pb At the end of the file param dat the essential parameters corresponding to each nucleus are written i e mass in a m u radius in fm Wood Saxon width in fm and normal nuclear density in fm The user can add other species simply appending other data with the same format at the end of the file RADS real value Total energy per nucleon in the center of mass frame G SNN in GeV SIGMA IN real value The total inelastic nucleon nucleon cross section in mb B real value The impact parameter b expressed in fm 3 9 Initial conditions parameters IENENTR integer flag Allows to use either energy 0 or entropy 1 density for the profile used in the initial stage modeling AH real value Hardness parameter opc 0 1 in equation 4 1 ECENTER real value Central x y z b 0 value for the field used in the initial profile i e For IENENTR 0 ECENTER is the energy density in GeV fm For IENENTR 1 ECENTER is the entropy density in fm ENEZERO real value Minimum allowed value for the energy density in GeV fm at program starting RHOCENTER real value Central x y z b 0 value for the baryon
67. t of particles to produce and specify their ID in any order Let s assume that the user wants to produce a ID 211 K ID 321 p ID 113 w ID 223 p ID 2212 and p not listed for a total amount of 5 listed particle and 1 anti baryon In the settings txt file the variable part list must contain the numeber of listed particles part list 5 and the IDs of the particles must be placed one per line just after this parameter as shown in the listings 7 4 PARTICLE RELATED npt 41 ptmin 0 0 ptmax 4 0 nphi 36 phimin 0 0 phimax 6 28318530718 nrap 41 4 rapmin 4 0 rapmax 4 0 listorseq 2 ID start 211 3 ID stop 221 part_list 5 3 211 76 points for t min transver max transver points for t min polar an max polar an points for t min rapidity max rapidity O all 1 se ID of first E ID of last p particles in 321 17 113 223 19 2212 antibar 0 1 0on O off 21 chempot 16 Listing 7 4 Example of the section in settings txt producing a custom list of particles 7 6 4 Producing the standard subset of particleslistorseq 3 Example setup for a simulation including the standard subset of particles T TO T K n Ke RC N W p N A M 59 m ES E Please note that still there is NO line after the part list line and the variable part list itself is set to O PARTICLE RELATED Anpt 41 poin
68. tabulated equation of state specified in the file TAB EOS FILE 4 ECHO QGP builds a tabulated equation of state and then uses it Feature not yet implemented in this version of the code TAB EOS FILE character max 15 characters Name of the file containing the tabulated EoS if EOS 3 to be located in the eos data directory ECHO QGP allows the use of any tabulated EoS of this kind if provided by the user in the following format The first row containing the number N of entries of the file N rows each one containing the temperature T in GeV the energy density in GeV T the pressure in GeV T the square speed of sound c dP de all separated by white spaces In the bundle there are four available tabulated EoS files qcdIEOS dat EoS of ref 3 arising from a weak coupling QCD calcu lation with realistic quark masses qcdIEOSO dat Nearly identical to qcdIEOS dat except for the first entry for T 0 added to solve some stability problems at low temperatures far below the temperature range of existence of the quark gluon plasma pce dat EoS of ref 4 based on partial chemical equilibrium obtained by matching a Hadron Resonance Gas EoS HRG EoS at low tem perature with the continuum extrapolated lattice QCD results by 22 the Budapest Wuppertal collaboration 5 The HRG EoS was ob tained by summing the contributions of all hadrons and resonances in the PDG up to a mass of 2 GeV P 9 P pceO dat The
69. the program See section 4 7 for further details 2 4 How to build and run ECHO QGP To build the program enter the source directory and issue the command make The command make reads the instructions on how to compile from the file makefile The make command can be invoked with five different targets make to build the program for serial runs on a single processor make par to build the program parallel runs on multi cores systems using the MPI library 10 make tools to build the post processing utilities contained into the tools directory make clean to remove the files produced during a previous compilation executable object files modules and so on make cleanall to remove both the files produced by the compiler and the files produced by an ECHO QGP run An expert user can edit the makefile to change or choose a proper compiling option suitable for its own compiler and architecture On a successful build the executable file echo exe can be found in the directory To run the program simply issue echo exe 2 4 1 Build and run on multi processors architectures If the user has a computer with many CPUs and the MPI library installed he she can speed up the simulations launching parallel runs In order to compile ECHO QGP with MPI just issue the command make par and then to run ECHO QGP mpirun np lt number of processors gt echo exe e g mpirun np 4 echo exe
70. the script read M12 pro in the tests testD directory GDL gt r read M12 96 Compiled module MAIN mx12 my12 mtemp12 mux12 muy12 mpixx12 mpiyy12 mipxy12 mpitt12 mpitx12 mpity12 mpizz12 The script reads the file maple gub full y eq x tau 4 0 the user can eas ily modify the worksheet to read other files with the same structure Now we prepare the data for plotting We are interested in the values with coordinates x y so first we declare an array to store these values GDL gt a dblarr 401 Then we fill the array in this example with the values of u yv GDL gt for i 0 400 do a i v0O i i vx i i And now we print the values to compare into the file ux comparison dat GDL gt openw 12 ux comparison dat GDL gt for i 0 400 do printf 12 x i a i mux12 i GDL gt free lun 12 Now we can make the plot with gnuplot set term pos eps col enh font Helvetica 22 set out ux eps set xlabel x fm set ylabel u x c units set key top left box 59 plot ux comparison dat u 1 2 w 1 1t 1 le 3 Iw 3 title ECHO QGP ux comparison dat u 1 3 w 1 It 3 le 4 Iw 3 title Semianalytic The commands are gathered into the plot ux gp script under tests testD which can be executed with gnuplot plot ux gp ECHO QGP Semianalytic u c units x fm Figure
71. tivistic viscous hydrodynamics for heavy ion collisions with ECHO QGP Eur Phys J vol C73 p 2524 2013 H Holopainen H Niemi and K J Eskola Event by event hydrodynam ics and elliptic flow from fluctuating initial state Phys Rev vol C83 p 034901 2011 E Becattini G Inghirami V Rolando A Beraudo L Del Zanna et al A study of vorticity formation in high energy nuclear collisions 2015 P Boek and I Wyskiel Directed flow in ultrarelativistic heavy ion collisions Phys Rev C vol 81 p 054902 May 2010 R Glauber Lectures in Theoretical Physics vol 1 WE Brittin and LG Dunham Eds Interscience 1959 M Takamoto and S Inutsuka A fast numerical scheme for causal relativistic hydrodynamics with dissipation J Comput Phys vol 230 no 18 pp 7002 7017 2011 78 12 H Marrochio J Noronha G S Denicol M Luzum S Jeon et al So lutions of Conformal Israel Stewart Relativistic Viscous Fluid Dynamics 2013 13 E Cooper and G Frye Single particle distribution in the hydrodynamic and statistical thermodynamic models of multiparticle production Phys Rev D vol 10 pp 186 189 Jul 1974 79
72. to plot the results is also included 6 4 Gubser flow test test D The description of this test can be found on 12 8 here we ll simply sum marize what do to perform it First we need a set of initial values which can be found into the tests testD directory This file named Initial Profile GubserFlow dat has been pro duced with Maple 12 executing the worksheet initial conditions maplei2 mw contained into the same directory The settings inside param dat must match those of the tabulated initial conditions e g the grid and also 7 7 s and the relation between temperature and energy density must correspond to what chosen for computing the input file with initial conditions The file tests testD param dat works with the provided intial conditions To complete the setup the user has to comment uncomment the temperature 56 0 01 0 008 r 0 006 0 004 0 002 r gt 0r 0 002 0 004 0 006 0 008 0 01 ECHO QGP Analytic 1 5 i 0 5 0 0 5 1 1 5 Figure 6 14 Test C Comparison between the analytical solution and ECHO QGP at T 10 fm c relation with energy density inside the eos data temperature def file clean the sources with make clean and recompile ECHO QGP If the grid used for computing the initial conditions is changed then it is required to change not only the lines defining the grid into param dat but also the checks contained into init f90 after the
73. ts for t ptmin 0 0 min transver 4 ptmax 4 0 max transver nphi 36 points for t phimin 0 0 min polar an phimax 6 28318530718 max polar an nrap 41 points for t rapmin 4 0 min rapidity id rapmax 4 0 max rapidity listorseq 0 0 all 1 se 14 ID start 0 ID of first E ID_stop 0 ID of last p 14 part_list 0 particles in antibar 1 1 on O off id chempot 0 Listing 7 5 Example of settings txt producing the standard subset of particles 77 Bibliography 1 2 3 4 5 6 7 8 9 10 11 W Israel and J Stewart Transient relativistic thermodynamics and kinetic theory Annals of Physics vol 118 no 2 pp 341 372 1979 W Israel Nonstationary irreversible thermodynamics A causal rel ativistic theory Annals of Physics vol 100 no 1 2 pp 310 331 1976 M Laine and Y Schroder Quark mass thresholds in QCD thermody namics Phys Rev vol D73 p 085009 2006 M Bluhm P Alba W Alberico A Beraudo and C Ratti Lattice QCD based equations of state at vanishing net baryon density Nucl Phys vol A929 pp 157 168 2014 S Borsanyi G Endrodi Z Fodor A Jakovac S D Katz et al The QCD equation of state with dynamical quarks JHEP vol 1011 p 077 2010 L Del Zanna V Chandra G Inghirami V Rolando A Beraudo et al Rela
74. two columns the first one is the coordinate position the second one the value of the variable This data format can be easily read by many plotting software For example using gnuplot Fig 6 5 gnuplot GNUPLOT Version 4 6 patchlevel O last modified 2012 03 04 Build System Linux x86 64 Copyright C 1986 1993 1998 2004 2007 2012 Thomas Williams Colin Kelley and many others gnuplot home http www gnuplot info faq bugs etc type help FAQ immediate help type help plot window hit h Terminal type set to wxt gnuplot gt set term pos eps col enh font Helvetica 22 Terminal type set to postscript 47 Options are eps enhanced defaultplex leveldefault color colortext dashed dashlength 1 0 linewidth 1 0 butt noclip nobackground palfuncparam 2000 0 003 Helvetica 22 fontscale 1 0 gnuplot set out temperature eps gnuplot set ylabel Temperature GeV gnuplot gt set xlabel Symbol hj gnuplot gt plot temperature z tau 10 0 dat with linespoints lt 7 linecolor 3 notitle We remind that the image files in Encapsulated Postscript eps format can be converted into Portable Document Format pdf with the utility ps2pdf e g ps2pdf dEPSCrop temperature eps Temperature GeV Figure 6 5 Test A Temperature profile at r 10 fm c for y 0 We can use the utility fromecho2d exe to extract values for a 2D s
75. uations 7 3 and using the transverse momentum pr the polar angle and the particle rapidity y as the indipendent variables The three dimensional grid in momentum is thus composed by nptxnphixnrap Npr x Ng x Ny The points in each one of the three components are computed following the simple scheme 71 dphi phimax phimin nphi i dpt ptmax ptmin npt lege ve aped ed P phi i phimin i 1 0 m f dphi oo ee dpt 4 we would like start with 0 end do The particle rapidity initialization is very similar to the ones listed above except the fact that the code checks whether the range is symmetric and tries to adjust Ny adding a point to have the value 0 too npt integer value Number of transverse momentum pr points ptmin real value Minimum of the range in transverse momentum pr yin GeV ptmax real value Maximum of the range in transverse momentum PT max GeV nphi integer value Number of polar angle 6 points phimin real value Minimum of the range in polar angle min phimax real value Maximum of the range in polar angle max nrap integer value Number of rapidity y points rapmin real value Minimum of the range in rapidity ymin rapmax real value Maximum of the range in rapidity Ymax listorseq integer flag It is the switch that allows the user to change the set of particles to be used All the programs can use three different sets of particles In the fol
76. ying from the tools directory into the outr0001 directory the readvar pro and ce pro scripts we launch gdl and we run them GDL gt readvar 0001 GDL gt ce 64 0 14 0 12 oa 01 gt oj 0 08 2 Oo 0 06 amp E 5 0 04 2 t LL 0 02 0 Figure 6 20 Test F Initial energy density distribution at r 10 22 fm c with Glauber MonteCarlo initialization 16 4 14 T 12 2 gt 108 gt cQ 8 o 6 o 2 5 4 2 0 4 2 0 2 4 x fm Figure 6 21 Test G Initial energy density distribution at r 1 fm c getting for tau 1 fm c Total energy 12400 207 65 J y 5838 3068 then to see what are the total energy and the angular momentum J at T 11 imc readvar 0101 ce getting Total energy 12371 264 J y 5834 8883 So in this run total energy was conserved within a 0 2 while for J within a 0 06 66 Chapter 7 Particle spectra production We always refer to the Minkowski and Bjorken metrics respectively as 1 1 n l 1 Iu zd g E 7 1 1 d We convert the description from hydro to particles using the Cooper Frye prescription Referring directly to the article by Cooper and Frye 13 d Nj d Nj gi Peo exp E dp dyprdprd 2x E c 7 2 The index i refers to the nature of the particle Note that this time the rapidity y refers

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