The Multi Module Model for Ultra-Relativistic Heavy Ion Collisions at RHIC
and LHC energies is presented. It uses the Effective String Rope Model for the
calculation of the initial stages of the reaction; the output of this model is
used as the initial state for the subsequent one-fluid calculations. It is
shown that such an initial state leads to the creation of the third flow
component. The hydrodynamical evolution of the energy density distribution is
also presented.Comment: Talk given at the New Trend in High-Energy Physics, Yalta, Crimea,
  Ukraine, September 22-29, 2001. To be published in the Proceedings. 8 pages,
  2 figures The Fig. 2 has been update

Csernai, L. P.

Magas, V. K.

Strottman, D.

English

arXiv

The Multi Module Model for Ultra-Relativistic Heavy Ion Collisioiis at RHIC and LHC energies is presented. It uses the Effective String Rope Model for the calculation of the initial stages of the reaction; the output of this model is used as the initial state for the subsequent one-fluid calculations. It is shown that such an initial state leads to the creation of the third flow component. The hydrodynainical evolution of the energy density distribution is also presented

Magas, V.

Csernai, L. P. (László P.)

UNT Digital Library

Approved forpublic releasu: distribution is unlimited. Title Authorfs) Submitted to Multi-Module Model for Ultra-Relativistic Heavy Ion Collisions V. Magas, L. P. Csernai, D. D. Strottman Proceedings of the New Trend in High-Energy Physics Yalta, Crimea, Ukraine September 22-29, 2001 Los Alamos N AT I 0 N A L LAB 0 RAT0 RY Los Alamos National Laboratory. an affirmative action/equal opportunity employer, is operated by the University of California for the US. Department of Energy under contract W-7405-ENG-36. By acceptance of this article, the publisher recognizes that the US. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or to allow others to do so, for US. Government purposes. Los Alamos National Laboratory requests that the publisher identify this article as work performed under the auspices of the US.  Department of Energy. Los Alamos National Laboratory strongly supports academic freedom and a researcher’s right to publish; as an institution, however, the Laboratory does not endorse the viewpoint of a publication or guarantee its technical correctness. Form 836 (8/00) Multi Module Model for Ultra-Relativistic Heavy Ion Collisions -~ V. M a g a ~ ~ , ~ : ~ ,  L.P. Cseriiai3l4 and D. Strottman’ CFIF, Instituto Superior Tecnico Av. Rovisco Pais, 1049-001 Lisbon, Portugal Bogolyubov Institute for Theoretical Physics Metrolohich,na str. 14 b, 01 143 Kiev, Ukraine Section for Theoretical and Computational Physics University of Bergen, Allegaten 55, 5007 Bergen, Norway KFKI Research Institute for Particle and Nuclear Physics P. 0.Box 49, 1525 Budapest, Hungary Theoretical Division, Los Alarnos National Laboratory Los Alamos, NM) 87454) USA October 25, 2001 Abstract The Multi Module Model for Ultra-Relativistic Heavy Ion Collisioiis at RHIC and LHC energies is presented. I t  uses the Effective String Rope Model for the calculation of the initial stages of the reaction; the output of this model is used as the initial state for the subsequent one-fluid cal- culations. It is shown that such an initial state leads to the creation of the third flow component. The hydrody- 1 nainical evolution of the energy density distribution is also presented. A realistic and detailed description of an energetic heavy ion re- action requires a Addti Module Model, wherein the different stages of the reaction are each described with a suitable theoretical ap- proach. It is important that these Modules are coupled to each other correctly: on the interface, which is a three dimensional hyper-surface in space-time, all conservation laws should be satis- fied and entropy should not decrease. These matching conditions were worked out and studied for the correct matching at FO in detail in Refs. [l]. Fluid dynamical models are widely used to describe ultra- relativistic heavy ioii collisions. Their advantage is that one can vary flexibly the Equation of State (EoS) of the matter and test its consequences on the reaction dynamics and the outcome. For ex- ample, the oiily models which may handle the supercooled QGP are hydrodynamical models with a corresponding EoS. In ener- getic collisions of large heavy ions, especially if a Quark-Gluon Plasma (QGP) is formed in the collision, one-fluid dynamics is a valid and good description for the intermediate stages of the re- action. Here, interactions are strong and frequent, so that other models, (e.g. transport models, string models, etc., that assume binary collisions, with free propagation of constituents between collisions) have limited validity. On the other hand, the initial and final, Fkeeze-Out (FO), stages of the reaction are outside the domain of applicability of the fluid dynamical model. After hadronization and FO, the mat- ter is already dilute and can be described well with kinetic models. The initial stages are the most problematic. Non of the theoreti- cal models on the physics market can unambiguously describe the initial stages (see for example [2, 31 for discussion). Thus, since we can not unambiguously describe the initial stages of relativistic heavy ion collisions in microscopic models, we have to use some phenomeiiological models. There are two phe- nomenological models, which are most frequently discussed in the 2 literature - the Landau and the Bjorken scenarios. These models describe two extreme cases - complete stopping or complete trans- parency, respectively. Nowadays, experiments have entered the region where the Bjorken model is expected to be applicable, but there is no clear and unambiguous confirmation that experiments follow this scenario. The preliminary experimental results from RHIC do not show transparency - most particle multiplicities (ex- cept maybe the most central collisions) do not show a dip in the rapidity spectra, but rather a plateau around mid rapidity [G, 71, which is a sign of strong stopping. Furthermore, very strong ellip- tic flow has been measured, whjch shows a clear peak around mid rapidity [G, 81. To build such a strong elliptic flow, strong stopping and momentum equilibration are required. Also the p / p  ratio at mid rapidity measured at RHIC [9, 101 (preliminary) is still far from 1, which tells us that the middle region is not baryonfree. Our goal is to build a Multi Module Model for ultra-relativistic heavy ion collisions valid for RHIC and LHC energies, and maybe for the most energetic SPS collisions. In the present work only the first step is done - a Two Module Model [3, 41 - but a very important one, since the Effective String Rope Model (ESRM) [2, 31 has been developed for the most problematic module - the niodule describing the initial st ages of collisions. We describe the initial state with the ESRM; then the hydro- dynamical evolution with a QGP EoS is used for the intermediate state. The hydrodymanical calculations are performed with the Los Alamos Particle-in-Cell (PIC) one fluid code [la, 131. The hy- dro evolution stops at the FO hypersurface. We present a version of the code assuming that FO (simultaneous chemical and ther- mal) happens on the simplified toothed hypersurface, where it’s normal vector, du+, is parallel to the flow velocity for every cell. On average this hypersurface approximates the constant time hy- persurface. Therefore the flow velocity does not change during the FO process, and the calculations can be done in local rest frame of the matter. Such a surface is also completely timelike; this al- lows us to avoid the problems discussed in Refs. [I]. The more 3 a,dvanced description of the FO process is planned to be separated into the Third Module. The statistical production model will be applied for production of the all hadronic species. The EoS presently used in the code was used and presented in Ref. [ 121. This phenonienological phase transition model A) takes the phenomenological EoS for hadronic matter in a simple form, which nevertheless allows one to check different parameterizations discussed in the literature; B) uses the Bag model EoS to describe QGP; C) creates a complete EoS, containing pure phases and a region where they coexist, by the Maxwell construction. The reader may notice that the model is still in a formative stage and a lot of further work remains necessary. We are not yet ready to present the quantitative calculations to be compared with data. Nevertheless we present some preliminary results. First of all, the flow component, VI,  as a function of rapidity, y, is pre- sented in Fig. 1 , to show that our expectation that the model will generate a third flow component (Refs. [2]) is reasonable [3 ,  47. Our initial state generated by the ESRM indeed produces a strong antiflow in semi-central collisioiis. The directed 211 component ap- pears to be very small, as expected for RHIC energies. The peaks in 211 (actually us) around y =: k0.3 look very high, but this is typical for calculations without thermal sniearing [ 141. Including thermal smearing will lead to smaller and wider peaks. We also present in Fig. 2 the evolution of the energy density distribution, e( T ,  t )  , during the hydrodynamic expansion (notice that t = 0 corresponds to the moment then we start the hydro description, i.e. 3.5 fn2/c after the collision). We can see the development of the small but very dense, shock-like domains at the intermediate stages. This effect, at least to  some extent, is due to numerical artifacts. The PIC method has a well-known defect called 'ringing' or marker-clustering [15]. It is called this way because early calculations in two dimensions resulted in density distributions that looked similar to the vibration patterns in sound vibrations - areas of higher and lower densities [15]. Advanced algorithms thnt mitigate this effect are being implemented in the 4 code. Another reason which may cause the development of the nu- merical artifacts is a step-like in beam direction initial energy den- sity distribution (output of ESRM): it has a jump from e(z,y) = const inside the matter to 0 in the outside vacuum. In order to avoid (or at least to suppress) tlie effect of this we are planning to smooth over initial energy density distribution, for example by a Gaussian shape, as proposed in Ref. [16]. Thus it is plausible that the development of the shock-like domains in the simulation is not a physical effect, although we can not rule out other possibilities. Refer en ces [I] Cs. Anderlik et al., Phys. Rev. C 59 (1999) 388, (nucl-tli/9808024); Phys. Rev. C 59 (1999) 3309, (nucl- th/9806004); Phys. Lett. B 459 (1999) 33, (nucl-th/9905054); V.K. Magas et  al., Heavy Ion Phys. 9 (1999) 193, (nucl- th/9903045); Nucl. Phys. A 661 (1999) 596, (nucl- th/0001049). [2] V. Magas, L.P. Csernai, D. Strottmczn, Phys. Rev. C 64 (2001) 014901, (hep-ph/0010307); Proceedings of the New ‘Trends in High-Energy Physics, Yalta (Crimea) , Ukraine, May 27 - June 4, 2000, p. 93, (nucl-th/0009049); Proceedings of the ISMD 2000, Tihany, Lake Balaton, Hungary, October 9-15, 2000, p. 523, (hep-ph/0101125); L.P. Csernai, Cs. An- derlik, V.K. Magas, Proceedings of the Symposium on Funda- mental Issues in Elementary Matter, Bad Honiief, Germany, September 25-29, 2000, p. 77, (nucl-th/0010023). 131 V.K. Magas, PhD Thesis, Aug 2001, University of Bergen, Norway. [4] L.P. Csernai, Cs. Anderlik, V.K. Magas and D. Strottman, presented at the Jnternational Workshop 011 The Physics of The Quark Gluon Plasma, September 4-7, 2001, Palaiseau, 5 Paris, France - in press, http://polywww.in2p3.fr/CIPPQG/trans/Csernai.ppt [5] M. Gyulassy, L.P. Csernai, Nucl. Phys. A 460 (1986) 723. 161 P. Steinberg, n~icl-ex/0104006; R.' Snellings, A. Drees, talks at  the Quark Matter 2001, Stoiiy Brook, NY, USA, Jaiiyary 15-20, 2001. [7] STAR Collaboration, Phys. Rev. Lett. 87 (2001) 112303, (nucl-ex/0106004). [SI PHENIX Collaboration, nucl-ex/0105003; PHOBOS Collab- oration, n~icl-ex/0105015; STAR Collaboration, Phys. Rev. Lett. 86 (2001) 401, (nucl-ex/0009011); nucl-ex/0107003. [9] F. Videbaek, talk at the Quark Matter 2001, Stoiiy Brook, NY, USA, Januaxy 15-20, 2001. [lo] C. Adler, et al., (STAR Collaboration),Phys. Rev. Lett. 86 (2001) 4778. (nucl-ex/0104022) [II] L.P. Csernai, D. Roliricb, Phys. Lett. B 458 (1999) 454. (11~~1- t h /99 0 80 3 4) [12] A.K. Holme, E.F. Staubo, L.P. Cseriiai, E. Osnes, D. Strottman, Phys.1lev. D 40 (1989) 3735. [13] E.F. Staubo et al., Phys. Lett. B 229 (1989) 351; Phys. Scripta T 32 (1990) 190; N.S. Amelin et al., Phys. Lett. B 261 (1991) 352; Phys. Rev. Lett. 67 (1991) 1523; Nucl. Phys. A 544 (1992) 463; L.V. Braviiia et al., Nucl. Phys. A 566 (1994) 461; Phys. Rev. C 50 (1994) 2161. [14] H. Stocker et al., Phys. Rev. Lett. 47 (1981) 1807, [15] J. U. Brackbill, J .  Compwt. Phys. 75, (1988) 469 [16] T. Hiram, nucl-th/0108004. G Figure 1: Preliminary results of Two Module Model calculations for v1 vs rapidity, y. Au+Au collision at E O  = 65 GeV/nucZ for different impact parameters. Initial state was generated with A = 0.065, r = 3.5 fm/c (see [2, 31 for details). 7 Figure 2: Preliminary results of Two Module Model calculations for energy density distribution in the reaction plane. Au+Au col- lision. at c0 = 65 GeVlnucZ, b = 0.1 - ~ R A ,  for different moments of time; initial state was generated with A = 0.08, r = 3.5 fm/c  (see r2, 31 for details). 8 -0.5 -1 1 0.5 0 -0.5 -1 + +  + + + + + + + + +  -I" ++ -1. -1 - .5 Y i 1.5 + +  -I- + + + + + + + +  ++ + + + 3 u -1 I a - 3 4 5 6 T 3 4 5 6 30 30 25 25 20 20 15 3 4 5 6 7 1 3 4 5 G 7 30 25 20 15 10 5 6 T 1 2 3 4 5 6 7 3 4 

Multi-module model for ultra-relativistic heavy ion collisions.

The Multi Module Model for Ultra-Relativistic Heavy Ion Collisions at RHIC and LHC energies is presented. It uses the Effective String Rope Model for the calculation of the initial stages of the reaction; the output of this model is used as the initial state for the subsequent one-fluid calculations. It is shown that such an initial state leads to the creation of the third flow component. The hydrodynamical evolution of the energy density distribution is also presented

Magas, V K

Csernai, László P

Strottman, D D

CERN Document Server

Multi Module Model forUltra-Relativistic Heavy IonCollisionsV. Magas1,2,3∗, L.P. Csernai3,4 and D. Strottman51 CFIF, Instituto Superior TecnicoAv. Rovisco Pais, 1049-001 Lisbon, Portugal2 Bogolyubov Institute for Theoretical PhysicsMetrolohichna str. 14b, 01143 Kiev, Ukraine3 Section for Theoretical and Computational PhysicsUniversity of Bergen, Allegaten 55, 5007 Bergen, Norway4 KFKI Research Institute for Particle and Nuclear PhysicsP.O.Box 49, 1525 Budapest, Hungary5 Theoretical Division, Los Alamos National LaboratoryLos Alamos, NM, 87454, USAOctober 29, 2001AbstractThe Multi Module Model for Ultra-Relativistic Heavy Ion Colli-sions at RHIC and LHC energies is presented. It uses the EectiveString Rope Model for the calculation of the initial stages of thereaction; the output of this model is used as the initial state forthe subsequent one-fluid calculations. It is shown that such an ini-tial state leads to the creation of the third flow component. Thehydrodynamical evolution of the energy density distribution is alsopresented.∗Talk given at the New Trend in High-Energy Physics, Yalta, Crimea, Ukraine,September 22-29, 2001.11 IntroductionA realistic and detailed description of an energetic heavy ion reaction re-quires a Multi Module Model, wherein the dierent stages of the reactionare each described with a suitable theoretical approach. It is importantthat these Modules are coupled to each other correctly: on the interface,which is a three dimensional hyper-surface in space-time, all conservationlaws should be satised and entropy should not decrease. These matchingconditions were worked out and studied for the correct matching at FO indetail in Refs. [1].Fluid dynamical models are widely used to describe ultra-relativisticheavy ion collisions. Their advantage is that one can vary flexibly theEquation of State (EoS) of the matter and test its consequences on thereaction dynamics and the outcome. For example, the only models whichmay handle the supercooled QGP are hydrodynamical models with a cor-responding EoS. In energetic collisions of large heavy ions, especially if aQuark-Gluon Plasma (QGP) is formed in the collision, one-fluid dynamicsis a valid and good description for the intermediate stages of the reaction.Here, interactions are strong and frequent, so that other models, (e.g.transport models, string models, etc., that assume binary collisions, withfree propagation of constituents between collisions) have limited validity.On the other hand, the initial and nal, Freeze-Out (FO), stages ofthe reaction are outside the domain of applicability of the fluid dynami-cal model. After hadronization and FO, the matter is already dilute andcan be described well with kinetic models. The initial stages are the mostproblematic. Non of the theoretical models on the physics market canunambiguously describe the initial stages (see for example [2, 3] for discus-sion).Thus, since we can not unambiguously describe the initial stages of rela-tivistic heavy ion collisions in microscopic models, we have to use some phe-nomenological models. There are two phenomenological models, which aremost frequently discussed in the literature - the Landau and the Bjorkenscenarios. These models describe two extreme cases - complete stoppingor complete transparency, respectively. Nowadays, experiments have en-tered the region where the Bjorken model is expected to be applicable, butthere is no clear and unambiguous conrmation that experiments followthis scenario. The preliminary experimental results from RHIC do notshow transparency - most particle multiplicities (except maybe the most2central collisions) do not show a dip in the rapidity spectra, but rathera plateau around mid rapidity [6, 7], which is a sign of strong stopping.Furthermore, very strong elliptic flow has been measured, which shows aclear peak around mid rapidity [6, 9]. To build such a strong elliptic flow,strong stopping and momentum equilibration are required. Also the p/pratio at mid rapidity measured at RHIC [10, 11] (preliminary) is still farfrom 1, which tells us that the middle region is not baryonfree.2 Two Module ModelOur goal is to build a Multi Module Model for ultra-relativistic heavy ioncollisions valid for RHIC and LHC energies, and maybe for the most ener-getic SPS collisions. In the present work only the rst step is done - a TwoModule Model [3, 4] - but a very important one, since the Eective StringRope Model (ESRM) [2, 3] has been developed for the most problematicmodule - the module describing the initial stages of collisions.We describe the initial state with the ESRM; then the hydrodynam-ical evolution with a QGP EoS is used for the intermediate state. Thehydrodymanical calculations are performed with the Los Alamos Particle-in-Cell (PIC) one fluid code [13, 14]. The hydro evolution stops at theFO hypersurface. We present a version of the code assuming that FO(simultaneous chemical and thermal) happens on the simplied toothedhypersurface, where it’s normal vector, dσµ, is parallel to the flow velocityfor every cell. On average this hypersurface approximates the constanttime hypersurface. Therefore the flow velocity does not change during theFO process, and the calculations can be done in local rest frame of thematter. Such a surface is also completely timelike; this allows us to avoidthe problems discussed in Refs. [1]. The more advanced description of theFO process is planned to be separated into the Third Module.The EoS presently used in the code was used and presented in Ref.[13]. This phenomenological phase transition modelA) takes the phenomenological EoS for hadronic matter in a simple form,which nevertheless allows one to check dierent parameterizations dis-cussed in the literature;B) uses the Bag model EoS to describe QGP;C) creates a complete EoS, containing pure phases and a region where theycoexist, by the Maxwell construction.The reader may notice that the model is still in a formative stage and3a lot of further work remains necessary. We are not yet ready to presentthe quantitative calculations to be compared with data. Nevertheless wepresent some preliminary results. First of all, the flow component, v1, as afunction of rapidity, y, is presented in Fig. 1, to show that our expectationthat the model will generate a third flow component (Refs. [2]) is reason-able [3, 4]. Our initial state generated by the ESRM indeed produces astrong antiflow in semi-central collisions. The directed v1 component ap-pears to be very small, as expected for RHIC energies (for example [8]).The peaks in v1 (actually v3) around y = ±0.3 look very high, but this istypical for calculations without thermal smearing [15]. Including thermalsmearing will lead to smaller and wider peaks.We also present in Fig. 2 the evolution of the energy density distribu-tion, e(r, t), during the hydrodynamic expansion (notice that t = 0 corre-sponds to the moment then we start the hydro description, i.e. 3.5 fm/cafter the collision). We can see the development of the small but verydense, shock-like domains at the intermediate stages. This eect, at leastto some extent, is due to numerical artifacts. The PIC method has a well-known defect called ’ringing’ or marker-clustering [16]. It is called this waybecause early calculations in two dimensions resulted in density distribu-tions that looked similar to the vibration patterns in sound vibrations -areas of higher and lower densities [16]. Advanced algorithms that mitigatethis eect are being implemented in the code.Another reason which may cause the development of the numericalartifacts is a step-like in beam direction initial energy density distribution(output of ESRM): it has a jump from e(x, y) = const inside the matterto 0 in the outside vacuum. In order to avoid (or at least to suppress)the eect of this we are planning to smooth over initial energy densitydistribution, for example by a Gaussian shape, as proposed in Ref. [17].Thus it is plausible that the development of the shock-like domains in thesimulation is not a physical eect, although we can not rule out otherpossibilities.To evaluate the observables a third, FO module is going to be at-tached to the model. Here the widely used Cooper-Frye model shouldbe essentially improved and modied. First of all conservation laws andthe requirement of increasing entropy should be enforced in the module.In addition, particularly for FO across space-like hypersurfaces, realistic,non-equilibrium post FO phase space distributions will have to be used toavoid negative contributions occuring in the naive use of the Cooper-Frye4model [1, 3].References[1] Cs. Anderlik et al., Phys. Rev. C 59 (1999) 388, (nucl-th/9808024);Phys. Rev. C 59 (1999) 3309, (nucl-th/9806004); Phys. Lett. B 459(1999) 33, (nucl-th/9905054); V.K. Magas et al., Heavy Ion Phys.9 (1999) 193, (nucl-th/9903045); Nucl. Phys. A 661 (1999) 596,(nucl-th/0001049).[2] V. Magas, L.P. Csernai, D. Strottman, Phys. Rev. C 64 (2001)014901, (hep-ph/0010307); Proceedings of the New Trends in High-Energy Physics, Yalta (Crimea), Ukraine, May 27 - June 4, 2000, p.93, (nucl-th/0009049); Proceedings of the ISMD 2000, Tihany, LakeBalaton, Hungary, October 9-15, 2000, p. 523, (hep-ph/0101125); L.P.Csernai, Cs. Anderlik, V.K. Magas, Proceedings of the Symposiumon Fundamental Issues in Elementary Matter, Bad Honnef, Germany,September 25-29, 2000, p. 77, (nucl-th/0010023).[3] V.K. Magas, PhD Thesis, Aug 2001, University of Bergen, Norway.[4] L.P. Csernai, Cs. Anderlik, V.K. Magas and D. Strottman, presentedat the International Workshop On The Physics of The Quark GluonPlasma, September 4-7, 2001, Palaiseau, Paris, France - in press,http://polywww.in2p3.fr/CIPPQG/trans/Csernai.ppt[5] M. Gyulassy, L.P. Csernai, Nucl. Phys. A 460 (1986) 723.[6] P. Steinberg, nucl-ex/0104006; R. Snellings, A. Drees, talks at theQuark Matter 2001, Stony Brook, NY, USA, Janyary 15-20, 2001.[7] STAR Collaboration, Phys. Rev. Lett. 87 (2001) 112303, (nucl-ex/0106004).[8] P. Huovinen, talk at the School on Relativistic Heavy Ion Physics& Hard Probes Collaboration Meeting, Copenhagen, Denmark, May14-18, 2001.[9] PHENIX Collaboration, nucl-ex/0105003; PHOBOS Collaboration,nucl-ex/0105015; STAR Collaboration, Phys. Rev. Lett. 86 (2001)401, (nucl-ex/0009011); nucl-ex/0107003.5[10] F. Videbaek, talk at the Quark Matter 2001, Stony Brook, NY, USA,January 15-20, 2001.[11] C. Adler, et al., (STAR Collaboration),Phys. Rev. Lett. 86 (2001)4778. (nucl-ex/0104022)[12] L.P. Csernai, D. Ro¨hrich, Phys. Lett. B 458 (1999) 454. (nucl-th/9908034)[13] A.K. Holme, E.F. Staubo, L.P. Csernai, E. Osnes, D. Strottman,Phys.Rev. D 40 (1989) 3735.[14] E.F. Staubo et al., Phys. Lett. B 229 (1989) 351; Phys. Scripta T32 (1990) 190; N.S. Amelin et al., Phys. Lett. B 261 (1991) 352;Phys. Rev. Lett. 67 (1991) 1523; Nucl. Phys. A 544 (1992) 463; L.V.Bravina et al., Nucl. Phys.A 566 (1994) 461; Phys. Rev.C 50 (1994)2161.[15] H. Sto¨cker et al., Phys. Rev. Lett. 47 (1981) 1807.[16] J. U. Brackbill, J. Comput. Phys. 75, (1988) 469.[17] T. Hirano, nucl-th/0108004.6−1 −0.5 0 0.5 1 1.5−1−0.500.51yv 1 −1.5 −1 −0.5 0 0.5 1 1.5−1−0.500.51yv 1 −2 −1 0 1 2−1−0.500.51yv 1 b=0.1*2Rb=0.25*2RAuAub=0.5*2RAuFigure 1: Preliminary results of Two Module Model calculations for v1 vsrapidity, y. Au+Au collision at ε0 = 65 GeV/nucl for dierent impactparameters. Initial state was generated with A = 0.065, τ = 3.5 fm/c (see[2, 3] for details).7z, fmt=0 fm t=1.9 fmt=3.8 fm t=5.7 fmt=7.6 fm t=9.5 fmx, fmFigure 2: Preliminary results of Two Module Model calculations forenergy density distribution in the reaction plane. Au+Au collision atε0 = 65 GeV/nucl, b = 0.1 · 2RAu for dierent moments of time; initialstate was generated with A = 0.08, τ = 3.5 fm/c (see [2, 3] for details).8

Multi module model for ultra-relativistic heavy ion collisions

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Multi Module Model for Ultra-Relativistic Heavy Ion Collisions

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