相对论重离子碰撞的逐个事例流体力学模拟
|
摘要
美国布鲁克海文国家实验室的相对论重离子碰撞机以及欧洲核子中心的大强子碰撞机是当今碰撞能量最高的两个高能物理实验设备,目的是把重离子加速到相对论速度,并使它们发生碰撞。物理学家试图使用这种核碰撞设备产生高温高密的夸克胶子等离子体(QGP)并研究这种新物质形态的性质。因为量子色动力学的渐近自由属性,最初人们认为形成的夸克胶子等离子体是弱耦合的夸克胶子气体,后来通过相对论粘滞流体力学模拟以及与实验结果的比较,人们发现相对论重离子碰撞机产生的夸克胶子等离子体的剪切粘滞系数与熵密度之比非常小,表现的更像强耦合流体,所以称之为强耦合夸克胶子等离子体(sQGP)。
在核子模型中,相对论重离子碰撞可以看作是两个来自核子的部分子束流或夸克胶子束流之间的碰撞。根据能标和时间尺度的不同,相对论重离子碰撞实验的物理可以分为硬部分和软部分。高横动量转移的硬散射或非相干散射发生在碰撞的早期并在末态产生高能部分子喷注。根据不确定性原理,低横动量转移和纵向动量转移的碰撞,相干时间可比或大于原子核的大小。软部分子主要是胶子会在大的纵向距离上产生关联,并连结着互相穿越的两个重离子的领头价夸克和双夸克。这些关联的软胶子可以描述为低横动量,演化时间尺度远大于领头夸克的纵向色流管。这些色流管密度很高,因为占据的相空间相互重叠而形成一种凝聚态物质。在相对论重离子碰撞中,这种凝聚态物质也被称作色玻璃凝聚(CGC)。
实验数据显示这些色流管在短于1fm/c的时间内实现了快速热化及局域热平衡,其机制仍然是个谜。目前人们认为有两种可能的机制：第一种是色流管先通过经典的场辐射或量子的对产生变成部分子碎片,这些部分子在2->2和2->3的散射过程中实现快速热化。第二种是非阿贝尔等离子体的不稳定性可以使系统快速达到局域各向同性,其散射率远大于部分子的微扰散射率。对于早期热化,既可以用部分子级联散射的输运模型也可以用基于Yang-Mills经典理论的胶子等离子体演化来描述相对论重离子碰撞后到1fm/c之前的预平衡阶段。达到局域热平衡之后的夸克胶子等离子体演化可以用理想或粘滞相对论流体力学模拟,在系统膨胀的晚期,夸克胶子等离子体温度降低到色禁闭的临界温度,部分子通过融合形成强子共振气体。这样的强子化过程可以通过流体力学模拟中的状态方程来描述,在演化的晚期当强子平均自由程很大的时候,系统远离局域热平衡,流体力学将不再适用。强子输运模型如超相对论量子分子动力学模型(URQMD)可以被用来描述系统接下来的演化。
光滑初始条件的理想及粘滞流体力学模拟以及强子的级联散射被广泛用来研究相对论重离子碰撞末态中低横动量强子的动量谱及椭圆流。通过流体力学模拟结果与实验数据的比较,人们试图确定相对论重离子碰撞产生的夸克胶子等离子体的剪切粘滞。人们需要提供能量密度以及流体速度分布作为流体力学模拟的初始条件。在真实的相对论重离子碰撞实验中,碰撞几何,核子在原子核内的相空间分布,部分子在核子内的相空间分布,色核的分布都是有涨落的。这些初始条件中的涨落对描述高阶尤其是奇次谐振流和双强子关联至关重要。因此人们借助涨落的初始条件,做逐个事例的流体力学模拟来描述相对论重离子碰撞实验的数据。比较实验得到的高阶谐振流与使用有横向与纵向涨落的初始条件,得到的逐个事例流体力学模拟结果,可以为确定夸克胶子等离子体的输运系数带来更严格的限制。
除了可以用相对论流体力学描述的低能部分子系统的膨胀,早期产生的高能部分子喷注也会参与早期热化,夸克胶子等离子体演化和强子气体膨胀的整个阶段,并与膨胀系统中的软部分子发生相互作用。这种相互作用会导致高能部分子的能量损失,又称作喷注淬灭。高能部分子喷注淬灭强烈依赖于局域温度,可以作为探针来研究相对论重离子碰撞系统膨胀的各个阶段。另一方面,膨胀系统的介质也会受到喷注淬灭所沉积的能量的影响。在有涨落的膨胀介质中和光滑的介质背景中,高能部分子的能量损失是大不相同的。因此使用有涨落的初始条件做逐个事例流体力学模拟对于研究高能部分子喷注淬灭也是至关重要的。一个完整的模拟需要在相对论重离子碰撞的各个阶段既包含硬过程物理也包含软过程的物理。为了比较现实的模拟相对论重离子碰撞,我们必须全面考虑基于微扰量子色动力学的高能部分子喷注产生过程,低能部分子早期热化以及后期流体演化过程,高能部分子能量损失以及对两者的修正,碎裂强子化过程,部分子融合强子化过程以及强子共振气体散射过程。
本论文聚焦于相对论重离子碰撞实验中的逐个事例相对论流体力学模拟。论文回顾目前国际上各组逐个事例流体力学模拟的初始条件,模拟程序以及大致结果,然后介绍我们编写的3+1维理想流体力学程序,使用多相输运模型(AMPT)得到有涨落的初始条件和我们发明的计算3+1维冷却超曲面的投影算法。在AMPT模型中,来自于迷你喷注的硬部分子和来自于弦碎裂的软部分子参与部分子级联散射,以期实现早期热化。经过预平衡阶段短暂的部分子级联散射,我们得到了同时拥有横平面涨落与纵向涨落的能量密度与速度分布,并用作逐个事例相对论流体力学模拟的初始条件。我们用逐个事例相对论流体力学模拟了200GeV的金核金核对撞以及2.76TeV的铅核铅核对撞,验证了横向涨落效应,并首先发现纵向涨落可以显著压低椭圆流。我们使用逐个事例相对论流体力学模拟得到双强子方位角关联并与实验数据比较,并研究了初始速度和纵向涨落效应对双强子方位角关联的影响。使用(AMPT)的初始条件,我们的逐个事例相对论流体力学模拟自然给出对心碰撞时双强子方位角关联在快度方向的长程关联,迷你喷注产生的同向关联峰,以及由涨落引起的背向关联双峰结构。我们介绍了3+1维理想流体力学程序数值实现的细节,以及使用格点玻尔兹曼方法解有粘滞的3+1维流体力学方面的研究进展及部分结果。
The Relativistic Heavy Ion Collider (RHIC) at the Brookhaven National Lab-oratory and the Larger Hadron Collider (LHC) at the European Organization for Nuclear Research (CERN) are two large high-energy physics facilities where heavy ions are accelerated to relativistic speed and collide with each other. Physicists attempt to produce a form of hot and dense matter called quark gluon plasma (QGP) and study its properties in these nuclear collisions. The QGP was orig-inally expected to be a system of weakly coupled quark and gluon gas due to the asymptotic freedom of Quantum Chromodynamic (QCD). Comparisons be-tween experimental data and relativistic viscous hydrodynamic simulations indi-cate, however, that the QGP formed in heavy-ion collisions at RHIC and LHC behaves like a strongly coupled fluid with extremely small values of shear viscosity to entropy ratio. It is therefore termed as strongly coupled quark gluon plasma (sQGP).
In a parton model, relativistic heavy ion collisions can be considered as col-lisions between two beams of quarks and gluons, generally referred to as partons, from inside the nucleons. The collisions between partons can be divided into hard and soft process according to the energy and time scales involved. Hard and incoherent scatterings with large transverse momentum transfer happen at very early time and produce energetic partons or jets in the final state. For collisions with small transverse and longitudinal momentum transfer, the coherence time can become comparable or larger than the nuclear size according to the uncer-tainty principle. The produced soft partons, mainly gluons, become coherent over large longitudinal distance between the leading valence quarks and diquarks of the colliding nucleons. These coherence soft partons can be effectively described as longitudinal color flux tubes which have small transverse momentum and evolve slowly at a time scale that is much longer than that of their color source or va-lence quarks and diquarks. These gluons are so dense and their phase space may overlap to form a condensed matter. Such a picture is also referred to as the Color Glass Condensate (CGC) model of heavy-ion collisions.
How these color flux tubes evolve into a dense matter with local equilibrium in less than1fm/c, as indicated by the experimental data, is still not well under-stood. Currently two possible scenarios have been proposed. In the first scenario, color flux tubes break into partons by quantum pair production and the produced partons achieve fast thermalization via2->2elastic and2->3inelastic processes. An alternative scenario is that the non-Abelian plasma instabilities can drive the flux tubes to isotropization with a scattering rate much faster than that given by perturbative parton scattering. The classical Yang-Mills theory, parton cascade and lattice gauge transport all have been used to study the early time evolution in relativistic heavy ion collisions. The subsequent evolution of the quark gluon plasma can be described by ideal or viscous hydrodynamic simulation. At the late stage of the evolution of the expanding system, when the energy density becomes smaller than the critical value for color confinement, hadrons can form via parton combination. Such hadronization can be described through an effective equation of state (EoS) in hydrodynamic simulations. In the later stage of the evolution when the mean free path is too large, system will be far from local thermalization and hydrodynamic description will fail. From this point on, hadron transportation models such as the Ultra Relativistic Quantum Molecular Dynamics (URQMD) model can be be used to describe further evolution of the system.
The ideal and viscous hydrodynamic models with smoothed initial condition and hadron cascade in the late stage were widely used to study the momentum spectra and elliptic flow of final particles in relativistic heavy ion collisions. They were used to extract shear viscosity from fitting to experimental data. In these hydrodynamic simulations, one has to provide the initial condition on density and flow velocity distributions. In real relativistic heavy ion collisions, there will also be fluctuations in initial conditions which can be introduced by collision geome-try, nucleon distribution in nucleus, parton distribution in nucleon and quantum fluctuation. These fluctuating initial conditions are critical to describe higher, es-pecially odd order harmonic flows and di-hadron correlation. One therefore has to resort to event-by-event simulation to describe experimental data. Comparisons between experimental data on higher harmonic flows and hydrodynamic simula-tions with the transverse and longitudinal fluctuations in the initial conditions can provide more stringent constraint on extracting transport coefficients.
In addition to the soft bulk matter whose evolution can be described by rela-tivistic hydrodynamic model, high energy jets produced in the early time will also interact with partons in the expanding medium, from the pre-equilibrium stage, to the hydrodynamic evolution of QGP and Hadron Resonance Gas (HRS) phases. Such interaction will lead to parton energy loss or jet quenching. Jet Quench-ing can be used as hard probes to stud the properties of the expanding medium since it strongly depends on the local temperature. On the other hand, the bulk medium is also affected by the energy deposited by jet quenching. Energy loss of an energetic jet behaves quite differently in a fluctuating expanding medium than a smoothed background. Therefore, event by event hydrodynamic simulations with fluctuating initial conditions are needed for the study of jet quenching. A full simulation of relativistic heavy ion collisions should include both hard and soft physics in each stage of the evolution. These include the initial production of high energy jets based on pQCD, early time thermalization and late time hy-drodynamic evolution of soft partons, jet quenching and the modification to both hard and soft parton spectra, hadronization from jet fragmentation and parton coalescence and the cascading of hadron resonance gas.
This thesis focuses on event-by-event hydrodynamic simulations with fluctu-ating initial conditions. I will start with a review on existing event-by-event hy-drodynamic simulations with different initial conditions, different hydrodynamic algorithms and their results. Then I will describe the3+1D ideal hydrodynamic model that we developed, with the fluctuating initial condition obtained from AMPT(A Multiple Phase Transportation) model and our new projection method for calculation of the freeze out hyper surface. The harden partons from mini-jet and soft partons from string fragmentation all take part in parton cascade dur-ing the pre-equilibrium stage in AMPT. The fluctuating energy density and flow velocity in both transverse and longitudinal direction from AMPT model after a short initial period of time are then used as the initial conditions for event-by-event hydrodynamic simulations. We have studied both AuAu collisions at the RHIC energy of (?)=200GeV/nucleon and PbPb collisions at the LHC energy (?)=2.76TeV/nucleon with our event-by-event3+1D relativistic hydrodynamic simulations. We illustrate the effect of the transverse fluctuation and discovered the effect of the longitudinal fluctuation which suppresses elliptic flow noticeably. We also calculate di-hadron correlation and compare to the experimental data. We also study the effect of flow velocity and longitudinal fluctuations on the di-hadron correlation. By using AMPT initial conditions, our event-by-event3+1D hydrodynamic simulations of central heavy-ion collisions naturally give rise to a long range correlation in rapidity, near-side peak from mini-jets and away side double peaks structure from superposition of all hadronic flows. We will provide a description of the numerical implementation for the3+1D ideal hydrodynamic simulation and present the progresses and some results in solving3+1D viscous hydrodynamics with Relativistic Lattice Boltzmann Method.
在核子模型中,相对论重离子碰撞可以看作是两个来自核子的部分子束流或夸克胶子束流之间的碰撞。根据能标和时间尺度的不同,相对论重离子碰撞实验的物理可以分为硬部分和软部分。高横动量转移的硬散射或非相干散射发生在碰撞的早期并在末态产生高能部分子喷注。根据不确定性原理,低横动量转移和纵向动量转移的碰撞,相干时间可比或大于原子核的大小。软部分子主要是胶子会在大的纵向距离上产生关联,并连结着互相穿越的两个重离子的领头价夸克和双夸克。这些关联的软胶子可以描述为低横动量,演化时间尺度远大于领头夸克的纵向色流管。这些色流管密度很高,因为占据的相空间相互重叠而形成一种凝聚态物质。在相对论重离子碰撞中,这种凝聚态物质也被称作色玻璃凝聚(CGC)。
实验数据显示这些色流管在短于1fm/c的时间内实现了快速热化及局域热平衡,其机制仍然是个谜。目前人们认为有两种可能的机制：第一种是色流管先通过经典的场辐射或量子的对产生变成部分子碎片,这些部分子在2->2和2->3的散射过程中实现快速热化。第二种是非阿贝尔等离子体的不稳定性可以使系统快速达到局域各向同性,其散射率远大于部分子的微扰散射率。对于早期热化,既可以用部分子级联散射的输运模型也可以用基于Yang-Mills经典理论的胶子等离子体演化来描述相对论重离子碰撞后到1fm/c之前的预平衡阶段。达到局域热平衡之后的夸克胶子等离子体演化可以用理想或粘滞相对论流体力学模拟,在系统膨胀的晚期,夸克胶子等离子体温度降低到色禁闭的临界温度,部分子通过融合形成强子共振气体。这样的强子化过程可以通过流体力学模拟中的状态方程来描述,在演化的晚期当强子平均自由程很大的时候,系统远离局域热平衡,流体力学将不再适用。强子输运模型如超相对论量子分子动力学模型(URQMD)可以被用来描述系统接下来的演化。
光滑初始条件的理想及粘滞流体力学模拟以及强子的级联散射被广泛用来研究相对论重离子碰撞末态中低横动量强子的动量谱及椭圆流。通过流体力学模拟结果与实验数据的比较,人们试图确定相对论重离子碰撞产生的夸克胶子等离子体的剪切粘滞。人们需要提供能量密度以及流体速度分布作为流体力学模拟的初始条件。在真实的相对论重离子碰撞实验中,碰撞几何,核子在原子核内的相空间分布,部分子在核子内的相空间分布,色核的分布都是有涨落的。这些初始条件中的涨落对描述高阶尤其是奇次谐振流和双强子关联至关重要。因此人们借助涨落的初始条件,做逐个事例的流体力学模拟来描述相对论重离子碰撞实验的数据。比较实验得到的高阶谐振流与使用有横向与纵向涨落的初始条件,得到的逐个事例流体力学模拟结果,可以为确定夸克胶子等离子体的输运系数带来更严格的限制。
除了可以用相对论流体力学描述的低能部分子系统的膨胀,早期产生的高能部分子喷注也会参与早期热化,夸克胶子等离子体演化和强子气体膨胀的整个阶段,并与膨胀系统中的软部分子发生相互作用。这种相互作用会导致高能部分子的能量损失,又称作喷注淬灭。高能部分子喷注淬灭强烈依赖于局域温度,可以作为探针来研究相对论重离子碰撞系统膨胀的各个阶段。另一方面,膨胀系统的介质也会受到喷注淬灭所沉积的能量的影响。在有涨落的膨胀介质中和光滑的介质背景中,高能部分子的能量损失是大不相同的。因此使用有涨落的初始条件做逐个事例流体力学模拟对于研究高能部分子喷注淬灭也是至关重要的。一个完整的模拟需要在相对论重离子碰撞的各个阶段既包含硬过程物理也包含软过程的物理。为了比较现实的模拟相对论重离子碰撞,我们必须全面考虑基于微扰量子色动力学的高能部分子喷注产生过程,低能部分子早期热化以及后期流体演化过程,高能部分子能量损失以及对两者的修正,碎裂强子化过程,部分子融合强子化过程以及强子共振气体散射过程。
本论文聚焦于相对论重离子碰撞实验中的逐个事例相对论流体力学模拟。论文回顾目前国际上各组逐个事例流体力学模拟的初始条件,模拟程序以及大致结果,然后介绍我们编写的3+1维理想流体力学程序,使用多相输运模型(AMPT)得到有涨落的初始条件和我们发明的计算3+1维冷却超曲面的投影算法。在AMPT模型中,来自于迷你喷注的硬部分子和来自于弦碎裂的软部分子参与部分子级联散射,以期实现早期热化。经过预平衡阶段短暂的部分子级联散射,我们得到了同时拥有横平面涨落与纵向涨落的能量密度与速度分布,并用作逐个事例相对论流体力学模拟的初始条件。我们用逐个事例相对论流体力学模拟了200GeV的金核金核对撞以及2.76TeV的铅核铅核对撞,验证了横向涨落效应,并首先发现纵向涨落可以显著压低椭圆流。我们使用逐个事例相对论流体力学模拟得到双强子方位角关联并与实验数据比较,并研究了初始速度和纵向涨落效应对双强子方位角关联的影响。使用(AMPT)的初始条件,我们的逐个事例相对论流体力学模拟自然给出对心碰撞时双强子方位角关联在快度方向的长程关联,迷你喷注产生的同向关联峰,以及由涨落引起的背向关联双峰结构。我们介绍了3+1维理想流体力学程序数值实现的细节,以及使用格点玻尔兹曼方法解有粘滞的3+1维流体力学方面的研究进展及部分结果。
The Relativistic Heavy Ion Collider (RHIC) at the Brookhaven National Lab-oratory and the Larger Hadron Collider (LHC) at the European Organization for Nuclear Research (CERN) are two large high-energy physics facilities where heavy ions are accelerated to relativistic speed and collide with each other. Physicists attempt to produce a form of hot and dense matter called quark gluon plasma (QGP) and study its properties in these nuclear collisions. The QGP was orig-inally expected to be a system of weakly coupled quark and gluon gas due to the asymptotic freedom of Quantum Chromodynamic (QCD). Comparisons be-tween experimental data and relativistic viscous hydrodynamic simulations indi-cate, however, that the QGP formed in heavy-ion collisions at RHIC and LHC behaves like a strongly coupled fluid with extremely small values of shear viscosity to entropy ratio. It is therefore termed as strongly coupled quark gluon plasma (sQGP).
In a parton model, relativistic heavy ion collisions can be considered as col-lisions between two beams of quarks and gluons, generally referred to as partons, from inside the nucleons. The collisions between partons can be divided into hard and soft process according to the energy and time scales involved. Hard and incoherent scatterings with large transverse momentum transfer happen at very early time and produce energetic partons or jets in the final state. For collisions with small transverse and longitudinal momentum transfer, the coherence time can become comparable or larger than the nuclear size according to the uncer-tainty principle. The produced soft partons, mainly gluons, become coherent over large longitudinal distance between the leading valence quarks and diquarks of the colliding nucleons. These coherence soft partons can be effectively described as longitudinal color flux tubes which have small transverse momentum and evolve slowly at a time scale that is much longer than that of their color source or va-lence quarks and diquarks. These gluons are so dense and their phase space may overlap to form a condensed matter. Such a picture is also referred to as the Color Glass Condensate (CGC) model of heavy-ion collisions.
How these color flux tubes evolve into a dense matter with local equilibrium in less than1fm/c, as indicated by the experimental data, is still not well under-stood. Currently two possible scenarios have been proposed. In the first scenario, color flux tubes break into partons by quantum pair production and the produced partons achieve fast thermalization via2->2elastic and2->3inelastic processes. An alternative scenario is that the non-Abelian plasma instabilities can drive the flux tubes to isotropization with a scattering rate much faster than that given by perturbative parton scattering. The classical Yang-Mills theory, parton cascade and lattice gauge transport all have been used to study the early time evolution in relativistic heavy ion collisions. The subsequent evolution of the quark gluon plasma can be described by ideal or viscous hydrodynamic simulation. At the late stage of the evolution of the expanding system, when the energy density becomes smaller than the critical value for color confinement, hadrons can form via parton combination. Such hadronization can be described through an effective equation of state (EoS) in hydrodynamic simulations. In the later stage of the evolution when the mean free path is too large, system will be far from local thermalization and hydrodynamic description will fail. From this point on, hadron transportation models such as the Ultra Relativistic Quantum Molecular Dynamics (URQMD) model can be be used to describe further evolution of the system.
The ideal and viscous hydrodynamic models with smoothed initial condition and hadron cascade in the late stage were widely used to study the momentum spectra and elliptic flow of final particles in relativistic heavy ion collisions. They were used to extract shear viscosity from fitting to experimental data. In these hydrodynamic simulations, one has to provide the initial condition on density and flow velocity distributions. In real relativistic heavy ion collisions, there will also be fluctuations in initial conditions which can be introduced by collision geome-try, nucleon distribution in nucleus, parton distribution in nucleon and quantum fluctuation. These fluctuating initial conditions are critical to describe higher, es-pecially odd order harmonic flows and di-hadron correlation. One therefore has to resort to event-by-event simulation to describe experimental data. Comparisons between experimental data on higher harmonic flows and hydrodynamic simula-tions with the transverse and longitudinal fluctuations in the initial conditions can provide more stringent constraint on extracting transport coefficients.
In addition to the soft bulk matter whose evolution can be described by rela-tivistic hydrodynamic model, high energy jets produced in the early time will also interact with partons in the expanding medium, from the pre-equilibrium stage, to the hydrodynamic evolution of QGP and Hadron Resonance Gas (HRS) phases. Such interaction will lead to parton energy loss or jet quenching. Jet Quench-ing can be used as hard probes to stud the properties of the expanding medium since it strongly depends on the local temperature. On the other hand, the bulk medium is also affected by the energy deposited by jet quenching. Energy loss of an energetic jet behaves quite differently in a fluctuating expanding medium than a smoothed background. Therefore, event by event hydrodynamic simulations with fluctuating initial conditions are needed for the study of jet quenching. A full simulation of relativistic heavy ion collisions should include both hard and soft physics in each stage of the evolution. These include the initial production of high energy jets based on pQCD, early time thermalization and late time hy-drodynamic evolution of soft partons, jet quenching and the modification to both hard and soft parton spectra, hadronization from jet fragmentation and parton coalescence and the cascading of hadron resonance gas.
This thesis focuses on event-by-event hydrodynamic simulations with fluctu-ating initial conditions. I will start with a review on existing event-by-event hy-drodynamic simulations with different initial conditions, different hydrodynamic algorithms and their results. Then I will describe the3+1D ideal hydrodynamic model that we developed, with the fluctuating initial condition obtained from AMPT(A Multiple Phase Transportation) model and our new projection method for calculation of the freeze out hyper surface. The harden partons from mini-jet and soft partons from string fragmentation all take part in parton cascade dur-ing the pre-equilibrium stage in AMPT. The fluctuating energy density and flow velocity in both transverse and longitudinal direction from AMPT model after a short initial period of time are then used as the initial conditions for event-by-event hydrodynamic simulations. We have studied both AuAu collisions at the RHIC energy of (?)=200GeV/nucleon and PbPb collisions at the LHC energy (?)=2.76TeV/nucleon with our event-by-event3+1D relativistic hydrodynamic simulations. We illustrate the effect of the transverse fluctuation and discovered the effect of the longitudinal fluctuation which suppresses elliptic flow noticeably. We also calculate di-hadron correlation and compare to the experimental data. We also study the effect of flow velocity and longitudinal fluctuations on the di-hadron correlation. By using AMPT initial conditions, our event-by-event3+1D hydrodynamic simulations of central heavy-ion collisions naturally give rise to a long range correlation in rapidity, near-side peak from mini-jets and away side double peaks structure from superposition of all hadronic flows. We will provide a description of the numerical implementation for the3+1D ideal hydrodynamic simulation and present the progresses and some results in solving3+1D viscous hydrodynamics with Relativistic Lattice Boltzmann Method.
引文
[1]N C R, G G. The Experimental Foundations of Particle Physics. Cambridge:Cambridge University Press,1989.
[2]GellMann M. Symmetries of baryons and mesons. Phys.Rev.,1962,125:1067-1084.
[3]Ne'eman Y. Derivation of strong interactions from a gauge invariance. Nucl.Phys.,1961, 26:222-229.
[4]Barnes V, Connolly P, Crennell D, et al. Observation of a Hyperon with Strangeness-3. Phys.Rev.Lett.,1964,12:204-206.
[5]D P H. Phys. Rev,1973, Lett.3:1346-1349.
[6]Gross D, Wilczek F. Ultraviolet Behavior of Nonabelian Gauge Theories. Phys.Rev.Lett.,1973, 30:1343-1346.
[7]Bethke S. alphas at Zinnowitz 2004. Nucl.Phys.Proc.Suppl,2004,135:345-352.
[8]Bjorken J. Asymptotic Sum Rules at Infinite Momentum. Phys.Rev.,1969,179:1547-1553.
[9]Chekanov S, et al. A ZEUS next-to-leading-order QCD analysis of data on deep inelastic scattering. Phys.Rev.,2003, D67:012007.
[10]Breidenbach M, Friedman J I, Kendall H W, et al. Observed Behavior of Highly Inelastic electron-Proton Scattering. Phys.Rev.Lett.,1969,23:935-939.
[11]Lee T, Wick G. Vacuum Stability and Vacuum Excitation in a Spin 0 Field Theory. Phys.Rev, 1974, D9:2291.
[12]HOOFT G. Renormalizable Lagrangians for massive Yang-Mills fields. Nucl. Phys.,1971, B35:167-188..
[13]Maldacena J M. The Large N limit of superconformal field theories and supergravity. Adv.Theor.Math.Phys.,1998,2:231-252.
[14]Gubser S, Klebanov I R, Polyakov A M. Gauge theory correlators from noncritical string theory. Phys.Lett.,1998, B428:105-114.
[15]Witten E. Anti-de Sitter space and holography. Adv.Theor.Math.Phys.,1998,2:253-291.
[16]Pisarski R D. Scattering Amplitudes in Hot Gauge Theories. Phys.Rev.Lett.,1989,63:1129.
[17]Weinberg S. Phenomenological Lagrangians. Physica,1979, A96:327.
[18]Nambu Y, Jona-Lasinio G. Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity.1. Phys.Rev.,1961,122:345-358.
[19]Nambu Y, Jona-Lasinio G. DYNAMICAL MODEL OF ELEMENTARY PARTICLES BASED ON AN ANALOGY WITH SUPERCONDUCTIVITY. II. Phys.Rev.,1961,124:246-254.
[20]Wilson K G. Nonlagrangian models of current algebra. Phys.Rev.,1969,179:1499-1512.
[21]Collins J C, Soper D E, Sterman G F. Factorization for Short Distance Hadron-Hadron Scattering. Nucl.Phys.,1985, B261:104.
[22]Mueller A H. Perturbative QCD at High-Energies. Phys.Rept.,1981,73:237.
[23]Collins J C, Soper D E. Back-To-Back Jets in QCD. Nucl.Phys.,1981, B193:381.
[24]Collins J C, Frankfurt L, Strikman M. Diffractive hard scattering with a coherent pomeron. Phys.Lett.,1993, B307:161-168.
[25]Collins J C, Heppelmann S F, Ladinsky G A. Measuring transversity densities in singly polarized hadron hadron and lepton-hadron collisions. Nucl.Phys.,1994, B420:565-582.
[26]Sterman G F, Weinberg S. Jets from Quantum Chromodynamics. Phys.Rev.Lett.,1977,39:1436.
[27]Basham C, Brown L, Ellis S, et al. Energy Correlations in electron-Positron Annihilation in Quan-tum Chromodynamics:Asymptotically Free Perturbation Theory. Phys.Rev.,1979, D19:2018.
[28]Adcox K, et al. Suppression of hadrons with large transverse momentum in central Au+Au collisions at(?)=130-GeV. Phys.Rev.Lett.,2002,88:022301.
[29]Adler C, et al. Disappearance of back-to-back high pT hadron correlations in central Au+Au collisions at sNN**1/2= 200-GeV. Phys.Rev.Lett.,2003,90:082302.
[30]Adams J, et al. Evidence from d+Au measurements for final state suppression of high p(T) hadrons in Au+Au collisions at RHIC. Phys.Rev.Lett.,2003,91:072304.
[31]Nagamiya S, Gyulassy M. High-energy nuclear collisions. Adv.Nucl.Phys.,1984,13:201-315.
[32]Ritter H, Gutbrod H, Kampert K, et al. Collective flow measured with the plastic ball.1989..
[33]PKienlr. The SIS/ESR Project of GSI,. GSI-report,1985, GST R5-:16.
[34]Harris J W, Muller B. The Search for the quark-gluon plasma. Ann.Rev.Nucl.Part.Sci.,1996, 46:71-107.
[35]Arsene I, et al. Quark gluon plasma and color glass condensate at RHIC? The Perspective from the BRAHMS experiment. Nucl.Phys.,2005, A757:1-27.
[36]Back B, Baker M, Ballintijn M, et al. The PHOBOS perspective on discoveries at RHIC. Nucl.Phys.,2005, A757:28-101.
[37]Adams J, et al. Experimental and theoretical challenges in the search for the quark gluon plasma: The STAR Collaboration's critical assessment of the evidence from RHIC collisions. Nucl.Phys., 2005, A757:102-183.
[38]Adcox K, et al. Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC:Experimental evaluation by the PHENIX collaboration. Nucl.Phys.,2005, A757:184-283.
[39]Armesto e, Borghini e, Jeon e, et al. Heavy Ion Collisions at the LHC-Last Call for Predictions. J.Phys.G,2008, G35:054001.
[40]Gyulassy M. The QGP discovered at RHIC.2004.159-182.
[41]Aoki Y, Endrodi G, Fodor Z, et al. The Order of the quantum chromodynamics transition predicted by the standard model of particle physics. Nature,2006,443:675-678.
[42]Aoki Y, Fodor Z, Katz S, et al. The QCD transition temperature:Results with physical masses in the continuum limit. Phys.Lett.,2006, B643:46-54.
[43]Davidson S, Descotes-Genon S. Minimal Flavour Violation for Leptoquarks. JHEP,2010,1011:073.
[44]Abelev B, et al. Identified particle production, azimuthal anisotropy, and interferometry mea-surements in Au+Au collisions at s(NN)**(1/2)= 9.2-GeV. Phys.Rev.,2010, C81:024911.
[45]Gyulassy M, McLerran L. New forms of QCD matter discovered at RHIC. Nucl.Phys.,2005, A750:30-63.
[46]Karsch F. Lattice QCD at high temperature and density. Lect.Notes Phys.,2002,583:209-249.
[47]Armesto N. Nuclear shadowing. J.Phys.G,2006, G32:R367-R394.
[48]Kharzeev D, Levin E, McLerran L. Parton saturation and N(part) scaling of semihard processes in QCD. Phys.Lett.,2003, B561:93-101.
[49]Adams J, et al. Transverse momentum and collision energy dependence of high p(T) hadron suppression in Au+Au collisions at ultrarelativistic energies. Phys.Rev.Lett.,2003,91:172302.
[50]Kolb P, Huovinen P, Heinz U W, et al. Elliptic flow at SPS and RHIC:From kinetic transport to hydrodynamics. Phys.Lett.,2001, B500:232-240.
[51]Adare A, et al. Scaling properties of azimuthal anisotropy in Au+Au and Cu+Cu collisions at s(NN)= 200-GeV. Phys.Rev.Lett.,2007,98:162301.
[52]Teaney D, Lauret J, Shuryak E V. Flow at the SPS and RHIC as a quark gluon plasma signature. Phys.Rev.Lett.,2001,86:4783-4786.
[53]Huovinen P, Kolb P, Heinz U W, et al. Radial and elliptic flow at RHIC:Further predictions. Phys.Lett.,2001, B503:58-64.
[54]Hirano T, Tsuda K. Collective flow and two pion correlations from a relativistic hydrodynamic model with early chemical freezeout. Phys.Rev.,2002, C66:054905.
[55]Tannenbaum M. Recent results in relativistic heavy ion collisions:From'a new state of matter' to'the perfect fluid'. Rept.Prog.Phys.,2006,69:2005-2060.
[56]Romatschke P, Romatschke U. Viscosity Information from Relativistic Nuclear Collisions:How Perfect is the Fluid Observed at RHIC? Phys.Rev.Lett.,2007,99:172301.
[57]Song H, Heinz U W. Causal viscous hydrodynamics in 2+1 dimensions for relativistic heavy-ion collisions. Phys.Rev.,2008, C77:064901.
[58]Shuryak E V, Zahed I. Rethinking the properties of the quark gluon plasma at T approximately T(c). Phys.Rev.,2004, C70:021901.
[59]Ipp A, Kajantie K, Rebhan A, et al. Unified description of deconfined QCD equation of state. J.Phys.G,2007, G34:S631-S634.
[60]Schenke B, Jeon S, Gale C. Elliptic and triangular flow in event-by-event (3+1)D viscous hydro-dynamics. Phys.Rev.Lett.,2011,106:042301.
[61]Huovinen P, Petreczky P. QCD Equation of State and Hadron Resonance Gas. Nucl.Phys.,2010, A837:26-53.
[62]Huovinen P, Petreczky P. Equation of state at finite baryon density based on lattice QCD. J.Phys.G,2011, G38:124103.
[63]Schenke B, Tribedy P, Venugopalan R. Fluctuating Glasma initial conditions and flow in heavy ion collisions. Phys.Rev.Lett.,2012,108:252301.
[64]Baier R, Mueller A H, Schiff D, et al. Does parton saturation at high density explain hadron multiplicities at RHIC? Phys.Lett.,2002, B539:46-52.
[65]Molnar D, Gyulassy M. Saturation of elliptic flow and the transport opacity of the gluon plasma at RHIC. Nucl.Phys.,2002, A697:495-520.
[66]Mrowczynski S. Streame instabilities of the quark-gluon plasma. Phys.Lett.,1988, B214:587.
[67]Romatschke P, Strickland M. Collective modes of an anisotropic quark gluon plasma. Phys.Rev., 2003, D68:036004.
[68]Arnold P B, Lenaghan J. The Abelianization of QCD plasma instabilities. Phys.Rev.,2004, D70:114007.
[69]Xu Z, Greiner C. Thermalization of gluons in ultrarelativistic heavy ion collisions by including three-body interactions in a parton cascade. Phys.Rev.,2005, C71:064901.
[70]Alver B, Roland G. Collision geometry fluctuations and triangular flow in heavy-ion collisions. Phys.Rev.,2010, C81:054905.
[71]Adler S, et al. Dense-Medium Modifications to Jet-Induced Hadron Pair Distributions in Au+Au Collisions at s(NN)**(1/2)= 200-GeV. Phys.Rev.Lett.,2006,97:052301.
[72]Adare A, et al. Dihadron azimuthal correlations in Au+Au collisions at s(NN)**(1/2)= 200-GeV. Phys.Rev.,2008, C78:014901.
[73]Abelev B, et al. Indications of Conical Emission of Charged Hadrons at RHIC. Phys.Rev.Lett., 2009,102:052302.
[74]Agakishiev H, et al. Measurements of Dihadron Correlations Relative to the Event Plane in Au+Au Collisions at s**1/2= 200 GeV.2010..
[75]Alver B, et al. High transverse momentum triggered correlations over a large pseudorapidity acceptance in Au+Au collisions at s(NN)**1/2= 200 GeV. Phys.Rev.Lett.,2010,104:062301.
[76]Aamodt K, et al. Higher harmonic anisotropic flow measurements of charged particles in Pb-Pb collisions at s**1/2= 2.76 TeV. Phys.Rev.Lett.,2011,107:032301.
[77]Aad G, et al. Measurement of the azimuthal anisotropy for charged particle production in sqrt(sNN)= 2.76 TeV lead-lead collisions with the ATLAS detector. Phys.Rev.,2012, C86:014907.
[78]Romatschke P, Venugopalan R. A Weibel instability in the melting color glass condensate. Eur.Phys.J.,2006, A29:71-75.
[79]Ackermann K, et al. Elliptic flow in Au+Au collisions at (S(NN))**(1/2)= 130 GeV. Phys.Rev.Lett.,2001,86:402-407.
[80]Adams J, et al. Azimuthal anisotropy in Au+Au collisions at s(NN)**(1/2)= 200-GeV. Phys.Rev., 2005, C72:014904.
[81]Adler S, et al. Elliptic flow of identified hadrons in Au+Au collisions at s(NN)**(1/2)= 200-GeV. Phys.Rev.Lett.,2003,91:182301.
[82]Afanasiev S, et al. Systematic Studies of Elliptic Flow Measurements in Au+Au Collisions at s**(1/2)= 200-GeV. Phys.Rev.,2009, C80:024909.
[83]Back B, et al. Centrality and pseudorapidity dependence of elliptic flow for charged hadrons in Au+Au collisions at s(NN)**(1/2)= 200-GeV. Phys.Rev.,2005, C72:051901.
[84]Aamodt K, et al. Elliptic flow of charged particles in Pb-Pb collisions at 2.76 TeV. Phys.Rev.Lett., 2010,105:252302.
[85]Jia J. Measurement of elliptic and higher order flow from ATLAS experiment at the LHC. J. Phys.,2011, G 38:124012.
[86]Ollitrault J Y. Anisotropy as a signature of transverse collective flow. Phys.Rev.,1992, D46:229-245.
[87]Voloshin S, Zhang Y. Flow study in relativistic nuclear collisions by Fourier expansion of Azimuthal particle distributions. Z.Phys.,1996, C70:665-672.
[88]Kolb P F, Sollfrank J, Heinz U W. Anisotropic transverse flow and the quark hadron phase transition. Phys.Rev.,2000, C62:054909.
[89]Heinz U W, Kolb P F. Early thermalization at RHIC. Nucl.Phys.,2002, A702:269-280.
[90]Jacobs P, Wang X N. Matter in extremis:Ultrarelativistic nuclear collisions at RHIC. Prog.Part.Nucl.Phys.,2005,54:443-534.
[91]Muller B, Nagle J L. Results from the relativistic heavy ion collider. Ann.Rev.Nucl.Part.Sci., 2006,56:93-135.
[92]Shuryak E. Physics of Strongly coupled Quark-Gluon Plasma. Prog.Part.Nucl.Phys.,2009, 62:48-101.
[93]Heinz U W. The Strongly coupled quark-gluon plasma created at RHIC. J.Phys.A,2009, A42:214003.
[94]Teaney D. The Effects of viscosity on spectra, elliptic flow, and HBT radii. Phys.Rev.,2003, C68:034913.
[95]Dusling K, Teaney D. Simulating elliptic flow with viscous hydrodynamics. Phys.Rev.,2008, C77:034905.
[96]Song H, Bass S A, Heinz U, et al.200 A GeV Au+Au collisions serve a nearly perfect quark-gluon liquid. Phys.Rev.Lett.,2011,106:192301.
[97]Hirano T, Heinz U W, Kharzeev D, et al. Hadronic dissipative effects on elliptic flow in ultrarel-ativistic heavy-ion collisions. Phys.Lett.,2006, B636:299-304.
[98]Steinheimer J, Bleicher M, Petersen H, et al. (3+1)-dimensional hydrodynamic expansion with a critical point from realistic initial conditions. Phys.Rev.,2008, C77:034901.
[99]Werner K, Karpenko I, Pierog T, et al. Event-by-Event Simulation of the Three-Dimensional Hy-drodynamic Evolution from Flux Tube Initial Conditions in Ultrarelativistic Heavy Ion Collisions. Phys.Rev.,2010, C82:044904.
[100]Andrade R P G, Grassi F, Hama Y, et al. Temporal evolution of tubular initial conditions and their influence on two-particle correlations in relativistic nuclear collisions. Phys.Lett.,2012, B712:226-230.
[101]Petersen H, Qin G Y, Bass S A, et al. Triangular flow in event-by-event ideal hydrodynamics in Au+Au collisions at (sNN)**1/2= 200 A GeV. Phys.Rev.,2010, C82:041901.
[102]Holopainen H, Niemi H, Eskola K J. Event-by-event hydrodynamics and elliptic flow from fluctu-ating initial state. Phys.Rev.,2011, C83:034901.
[103]Albacete J L, Dumitru A, Nara Y. CGC initial conditions at RHIC and LHC. J.Phys.Conf.Ser., 2011,316:012011.
[104]Schenke B, Jeon S, Gale C. Higher flow harmonics from (3+1)D event-by-event viscous hydrody-namics. Phys.Rev.,2012, C85:024901.
[105]Qiu Z, Heinz U W. Event-by-event shape and flow fluctuations of relativistic heavy-ion collision fireballs. Phys.Rev.,2011, C84:024911.
[106]Qiu Z, Shen C, Heinz U. Hydrodynamic elliptic and triangular flow in Pb-Pb collisions at sqrt(s)=2.76ATeV. Phys.Lett.,2012, B707:151-155.
[107]Gardim F G, Grassi F, Luzum M, et al. Anisotropic flow in event-by-event ideal hydrodynamic simulations of s**1/2=200 GeV Au+Au collisions.2012..
[108]Ma G L, Wang X N. Jets, Mach cone, hot spots, ridges, harmonic flow, dihadron and gamma-hadron correlation in high-energy heavy-ion collisions. Phys.Rev.Lett.,2011,106:162301.
[109]Adams J, et al. Minijet deformation and charge-independent angular correlations on momentum subspace (eta, phi) in Au-Au collisions at s(NN)**(1/2)= 130-GeV. Phys.Rev.,2006, C73:064907.
[110]Putschke J. Intra-jet correlations of high-p(t) hadrons from STAR. J.Phys.G,2007, G34:S679-684.
[111]Abelev B, et al. Long range rapidity correlations and jet production in high energy nuclear collisions. Phys.Rev.,2009, C80:064912.
[112]Takahashi J, Tavares B, Qian W, et al. Topology studies of hydrodynamics using two particle correlation analysis. Phys.Rev.Lett.,2009,103:242301.
[113]Werner K, Karpenko I, Mikhailov K, et al. Ridges and Soft Jet Components in Untriggered Di-hadron Correlations in Pb+Pb Collisions at 2.76 TeV.2011..
[114]Xu J, Ko C M. Triangular flow in heavy ion collisions in a multiphase transport model. Phys.Rev., 2011, C84:014903.
[115]Chaudhuri A. Influence of shear viscosity on the correlation between the triangular flow and initial spatial triangularity. Phys.Lett.,2012, B713:91-94.
[116]Miller M L, Reygers K, Sanders S J, et al. Glauber modeling in high energy nuclear collisions. Ann.Rev.Nucl.Part.Sci.,2007,57:205-243.
[117]Drescher H J, Dumitru A, Hayashigaki A, et al. The Eccentricity in heavy-ion collisions from color glass condensate initial conditions. Phys.Rev.,2006, C74:044905.
[118]Drescher H J, Nara Y. Effects of fluctuations on the initial eccentricity from the Color Glass Condensate in heavy ion collisions. Phys.Rev.,2007, C75:034905.
[119]Kharzeev D, Levin E, Nardi M. QCD saturation and deuteron nucleus collisions. Nucl.Phys., 2004, A730:448-459.
[120]Kharzeev D, Levin E, Nardi M. Color glass condensate at the LHC:Hadron multiplicities in pp, pA and AA collisions. Nucl.Phys.,2005, A747:609-629.
[121]Wang X N, Gyulassy M. HIJING:A Monte Carlo model for multiple jet production in p p, p A and A A collisions. Phys.Rev.,1991, D44:3501-3516.
[122]Gyulassy M, Wang X N. HIJING 1.0:A Monte Carlo program for parton and particle production in high-energy hadronic and nuclear collisions. Comput.Phys.Commun.,1994,83:307.
[123]Deng W t, Wang X N. Multiple Parton Scattering in Nuclei:Modified DGLAP Evolution for Fragmentation Functions. Phys.Rev.,2010, C81:024902.
[124]Pratt S, Schindel D. Is HBT really puzzling? AIP Conf.Proc.,2006,828:430-435.
[125]Florchinger S, Wiedemann U A. Fluctuations around Bjorken Flow and the onset of turbulent phenomena. JHEP,2011,1111:100.
[126]Kapusta J, Muller B, Stephanov M. Relativistic Theory of Hydrodynamic Fluctuations with Applications to Heavy Ion Collisions. Phys.Rev.,2012, C85:054906.
[127]Luzum M, Romatschke P. Conformal Relativistic Viscous Hydrodynamics:Applications to RHIC results at s(NN)**(1/2)-200-GeV. Phys.Rev.,2008, C78:034915.
[128]Esumi S. Collective Flow Measurements from the PHENIX Experiment. J.Phys.G,2011, G38:124010.
[129]Geiger K, Muller B. Dynamics of parton cascades in highly relativistic nuclear collisions. Nucl.Phys.,1992, B369:600-654.
[130]Chen J W, Deng J, Dong H, et al. Shear and Bulk Viscosities of a Gluon Plasma in Perturbative QCD:Comparison of Different Treatments for the gg<->ggg Process.2011.
[131]Pang L, Wang Q, Wang X N. Effects of initial flow velocity fluctuation in event-by-event (3+l)D hydrodynamics. Phys.Rev.,2012, C86:024911.
[132]Petersen H, Steinheimer J, Burau G, et al. A Fully Integrated Transport Approach to Heavy Ion Reactions with an Intermediate Hydrodynamic Stage. Phys.Rev.,2008, C78:044901.
[133]Drescher H, Hladik M, Ostapchenko S, et al. A Unified treatment of high-energy interactions. J.Phys.G,1999, G25:L91-L96.
[134]Drescher H, Ostapchenko S, Pierog T, et al. Initial condition for QGP evolution from NEXUS. Phys.Rev.,2002, C65:054902.
[135]Karsch F, Laermann E. Thermodynamics and in medium hadron properties from lattice QCD. 2003..
[136]Cooper F, Frye G. Comment on the Single Particle Distribution in the Hydrodynamic and Sta-tistical Thermodynamic Models of Multiparticle Production. Phys.Rev.,1974, D10:186.
[137]Hirano T. Is early thermalization achieved only near mid-rapidity at RHIC? Phys.Rev.,2002, C65:011901.
[138]Huovinen P, Petersen H. Particlization in hybrid models.2012..
[139]Heinz U W, Shen C, Song H. The viscosity of quark-gluon plasma at RHIC and the LHC. AIP Conf.Proc.,2012,1441:766-770.
[140]Demir N, Bass S A. Shear-Viscosity to Entropy-Density Ratio of a Relativistic Hadron Gas. Phys.Rev.Lett.,2009,102:172302.
[141]Bozek P. Flow and interferometry in 3+1 dimensional viscous hydrodynamics. Phys.Rev.,2012, C85:034901.
[142]Mendoza M, Boghosian B, Herrmann H, et al. Fast Lattice Boltzmann Solver for Relativistic Hydrodynamics. Phys.Rev.Lett.,2010,105:014502.
[143]Romatschke P. New Developments in Relativistic Viscous Hydrodynamics. Int.J.Mod.Phys.,2010, E19:1-53.
[144]Romatschke P, Mendoza M, Succi S. A fully relativistic lattice Boltzmann algorithm. Phys.Rev., 2011, C84:034903.
[145]Romatschke P. Relativistic (Lattice) Boltzmann Equation with Non-Ideal Equation of State. Phys.Rev.,2012, D85:065012.
[146]Weinberg S. Gravitation and cosmology:principles and applications of the general theory of relativity. J. Wiley, New York,,1972. Eq. (2.10.8).
[147]Boris J P, Book D L. Flux-Corrected Transport. I. SHASTA, A Fluid Transport Algorithm That Works. J.Comput.Phys.,1973,11:38-69.
[148]Zalesak S T. Fully Multidimensional Flux-Corrected Transport Algorithms for Fluids J.Comput.Phys.,1979,31:335-362.
[149]Rischke D H, Bernard S, Maruhn J A. Relativistic hydrodynamics for heavy ion collisions.1. General aspects and expansion into vacuum. Nucl.Phys.,1995, A595:346-382.
[150]Frisch U, Hasslacher B, Pomeau Y. A LATTICE GAS AUTOMATA FOR THE NAVIER-STOKES EQUATION. Phys.Rev.Lett.,1986,56:1505-1508.
[151]Wolfram S. Cellular automaton fluid 1:Basic theory. J. Stat.,1986, Phys.45:471.
[152]Qian Y, d'Humieres D, Lallemand P. Lattice BGK Models for Navier-Stokes Equation. Euro-physics Letters,1992,17(6):479-484.
[153]McNamara G R, Zanetti G. Use of the Boltzmann Equation to Simulate Lattice-Gas Automata. Phys. Rev. Lett.,1988,61:2332-2335.
[154]Bhatnager P, Gross E, Krook M. A Model for Collision Process in Gases. Physics Review,1954, 94(3):511-525.
[155]H Chen S C, Matthaeus W H. Recovery of Navier-Stokes equations using a lattice-gas Boltzmann method. Phys. Rev.,1991, A 45:R5339.
[156]He X, Luo L S. Theory of lattice Boltzmann method:From the Boltzmann equation to the lattice Boltzmann equation,. Physical Review E,1997,56:6811-6817.
[157]Zhaoli Guo T S Z. Lattice Boltzmann model for incompressible flows through porous media. PHYSICAL REVIEW E,2002,66:036304.
[158]Benzi R, Succi S, Vergassola M. The lattice Boltzmann equation:theory and applications. Physics Reports,1992,222(3):145-197.
[159]He X, Luo L S. Theory of the lattice Boltzmann method:From the Boltzmann equation to the lattice Boltzmann equation. Phys. Rev. E,1997,56:6811-6817.
[160]Y Qian D d, Lallemand P. Lattice BGK Models for Navier-Stokes Equation. Europhys. Lett., 1992,17:479.
[161]Kataja M, Ruuskanen P. Nonzero chemical potential and the shape of the p(T) distribution of hadrons in heavy ion collisions. Phys.Lett.,1990, B243:181-184.
[162]Sollfrank J, Huovinen P, Kataja M, et al. Hydrodynamical description of 200-A/GeV/c S+Au collisions:Hadron and electromagnetic spectra. Phys.Rev.,1997, C55:392-410.
[163]Schenke B, Jeon S, Gale C. (3+1)D hydrodynamic simulation of relativistic heavy-ion collisions. Phys.Rev.,2010, C82.014903.
[164]N simplex. http://en.wikipedia.org/wiki/Simplex.
[165]Hirano T, Nara Y. Eccentricity fluctuation effects on elliptic flow in relativistic heavy ion collisions. Phys.Rev.,2009, C79:064904.
[166]Zhang B, Ko C, Li B A, et al. A multiphase transport model for nuclear collisions at RHIC. Phys.Rev.,2000, C61:067901.
[167]Chatterjee R, Holopainen H, Renk T, et al. Enhancement of thermal photon production in event-by-event hydrodynamics. Phys.Rev.,2011, C83:054908.
[168]Back B, Baker M, Barton D, et al. The Significance of the fragmentation region in ultrarelativistic heavy ion collisions. Phys.Rev.Lett.,2003,91:052303.
[169]Abelev B, et al. Systematic Measurements of Identified Particle Spectra in pp,d+Au and Au+Au Collisions from STAR. Phys.Rev.,2009, C79:034909.
[170]Adler S, et al. Identified charged particle spectra and yields in Au+Au collisions at S(NN)**1/2 = 200-GeV. Phys.Rev.,2004, C69:034909.
[171]Abelev B, et al. Identified baryon and meson distributions at large transverse momenta from Au+Au collisions at s(NN)**(1/2)= 200-GeV. Phys.Rev.Lett.,2006,97:152301.
[172]Kolb P F, Heinz U W. Hydrodynamic description of ultrarelativistic heavy ion collisions.2003..
[173]Song H, Bass S A, Heinz U. Elliptic flow in 200 A GeV Au+Au collisions and 2.76 A TeV Pb+Pb collisions:insights from viscous hydrodynamics+hadron cascade hybrid model. Phys.Rev.,2011, C83:054912.
[174]Adare A, et al. Measurements of Higher-Order Flow Harmonics in Au+Au Collisions at s**1/2= 200 GeV. Phys.Rev.Lett.,2011,107:252301.
[175]Wang X N. Jet quenching and azimuthal anisotropy of large p(T) spectra in noncentral high-energy heavy ion collisions. Phys.Rev.,2001, C63:054902.
[176]Gyulassy M, Vitev I, Wang X. High p(T) azimuthal asymmetry in noncentral A+A at RHIC. Phys.Rev.Lett.,2001,86:2537-2540.
[177]Bass S A, Gale C, Majumder A, et al. Systematic Comparison of Jet Energy-Loss Schemes in a realistic hydrodynamic medium. Phys.Rev.,2009, C79:024901.
[178]Song H, Bass S A, Heinz U, et al. Hadron spectra and elliptic flow for 200 A GeV Au+Au collisions from viscous hydrodynamics coupled to a Boltzmann cascade. Phys.Rev.,2011, C83:054910.
[179]Aamodt K, et al. Centrality dependence of the charged-particle multiplicity density at mid-rapidity in Pb-Pb collisions at sqrt(sNN)= 2.76 TeV. Phys.Rev.Lett.,2011,106:032301.
[180]Aamodt K, et al. Suppression of Charged Particle Production at Large Transverse Momentum in Central Pb-Pb Collisions at s**1/2= 2.76 TeV. Phys.Lett.,2011, B696:30-39.
[181]Snellings R. Anisotropic flow at the LHC measured with the ALICE detector. J.Phys.G,2011, G38:124013.
[182]Pang L g, Wang Q, Wang X N, et al. Mini-jet thermalization and diffusion of transverse momentum correlation in high-energy heavy-ion collisions. Phys.Rev.,2010, C81:031903.
[183]Braun-Munzinger P, Stachel J, Wetterich C. Chemical freezeout and the QCD phase transition temperature. Phys.Lett.,2004, B596:61-69.
[184]Andronic A, Braun-Munzinger P, Redlich K, et al. The thermal model on the verge of the ultimate test:particle production in Pb-Pb collisions at the LHC. J.Phys.G,2011, G38:124081.
[185]Different versions of parameterized EoS can be found at https://wiki.bnl.gov/TECHQM/index.php/ QCD_Equation_of_State..
[186]Floris M. Identified particles in pp and Pb-Pb collisions at LHC energies with the ALICE detector. J.Phys.G,2011, G38:124025.
[187]Back B, et al. Charged particle multiplicity near mid-rapidity in central Au+Au collisions at SO/2)= 56-A/GeV and 130-A/GeV. Phys.Rev.Lett.,2000,85:3100-3104.
[188]Adler C, et al. Multiplicity distribution and spectra of negatively charged hadrons in Au+Au collisions at s(NN)**(1/2)= 130-GeV. Phys.Rev.Lett.,2001,87:112303.
[189]Hwa R C, Zhu L. Effects of Minijets on Hadronic Spectra and Azimuthal Harmonics in Au-Au Collisions at 200 GeV. Phys.Rev.,2012, C86:024901.
[190]Kajantie K, Landshoff P, Lindfors J. Minijet Production in High-Energy Nucleus-Nucleus Colli-sions. Phys.Rev.Lett.,1987,59:2527.
[191]Eskola K, Kajantie K, Lindfors J. Quark and Gluon Production in High-Energy Nucleus-Nucleus Collisions. Nucl.Phys.,1989, B323:37.
[192]Wang X N, Gyulassy M. Gluon shadowing and jet quenching in A+A collisions at s**(1/2)= 200-GeV. Phys.Rev.Lett.,1992,68:1480-1483.
[193]Eskola K, Muller B, Wang X N. Screening of initial parton production in ultrarelativistic heavy ion collisions. Phys.Lett.,1996, B374:20-24.
[194]Heinz U W. Thermalization at RHIC. AIP Conf.Proc.,2005,739:163-180.
[195]Wang X N. Resolving mini-jets in the minimum biased events of hadronic interactions. Phys.Rev.. 1992, D46:1900-1902.
[196]Wang X N. Studying mini-jets via the P(T) dependence of the two particle correlation in Azimuthal angle Phi. Phys.Rev.,1993, D47:2754-2760.
[197]Stephanov M A, Rajagopal K, Shuryak E V. Event-by-event fluctuations in heavy ion collisions and the QCD critical point. Phys.Rev.,1999, D60:114028.
[198]Jeon S, Koch V. Charged particle ratio fluctuation as a signal for QGP. Phys.Rev.Lett.,2000, 85:2076-2079.
[199]Stephanov M A. Thermal fluctuations in the interacting pion gas. Phys.Rev.,2002, D65:096008.
[200]Aziz M A, Gavin S. Causal diffusion and the survival of charge fluctuations in nuclear collisions. Phys.Rev.,2004, C70:034905.
[201]Gavin S, Abdel-Aziz M. Measuring Shear Viscosity Using Transverse Momentum Correlations in Relativistic Nuclear Collisions. Phys.Rev.Lett.,2006,97:162302.
[202]Wang M, Li L, Liu L, et al. An explorer for the shear viscosity in the formed matter at the RHIC. J.Phys.G,2009, G36:064070.
[203]Kharzeev D, Levin E, McLerran L. Jet azimuthal correlations and parton saturation in the color glass condensate. Nucl.Phys.,2005, A748:627-640.
[204]Adler S, et al. Systematic studies of the centrality and s(NN)**(1/2) dependence of the d E(T)/ d eta and d (N(ch)/d eta in heavy ion collisions at mid-rapidity. Phys.Rev.,2005, C71:034908.
[205]Adams J, et al. Distributions of charged hadrons associated with high transverse momentum par-ticles in pp and Au+Au collisions at s(NN)**(1/2)= 200-GeV. Phys.Rev.Lett.,2005,95:152301.
[206]Collaboration T A. Measurement of elliptic flow and higher-order flow coefficients with the ATLAS detector in sNN**1/2=2.76 TeV Pb+Pb collisions.2011..
[207]Aguiar C, Hama Y, Kodama T, et al. Event-by-event fluctuations in hydrodynamical description of heavy ion collisions. Nucl.Phys.,2002, A698:639-642.
[208]Baier R, Dokshitzer Y L, Mueller A H, et al. Radiative energy loss and p(T) broadening of high-energy partons in nuclei. Nucl.Phys.,1997, B484:265-282.
[209]Baym G. RHIC:From dreams to beams in two decades. Nucl.Phys.,2002, A698:XXIII-XXXII.
[210]Drescher H, Hladik M, Ostapchenko S, et al. Parton based Gribov-Regge theory. Phys.Rept., 2001,350:93-289.
[211]Dumitru A, Gelis F, McLerran L, et al. Glasma flux tubes and the near side ridge phenomenon at RHIC. Nucl.Phys.,2008, A810:91-108.
[212]G Aad e a. Measurement of the azimuthal anisotropy for charged particle production in sqrt(sNN) =2.76 TeV lead-lead collisions with the ATLAS detector. arXiv:1203.3087 [hep-ex]..
[213]Gardim F G, Grassi F, Hama Y, et al. Directed flow at mid-rapidity in event-by-event hydrody-namics. Phys.Rev.,2011, C83:064901.
[214]Gyulassy M, Vitev I, Wang X N, et al. Jet quenching and radiative energy loss in dense nuclear matter.2003..
[215]He M, Fries R J, Rapp R. Scaling of Elliptic Flow, Recombination and Sequential Freeze-Out of Hadrons in Heavy-Ion Collisions. Phys.Rev.,2010, C82:034907.
[216]Hirano T, Nara Y. Dynamical modeling of high energy heavy ion collisions.2012..
[217]Kajantie K, Karimaki V. VOLUME OF LONGITUDINAL PHASE SPACE.1971..
[218]McLerran L D, Venugopalan R. Computing quark and gluon distribution functions for very large nuclei. Phys.Rev.,1994, D49:2233-2241.
[219]Ohlson A. Jets and Jet-like correlations in STAR.2012..
[220]Paiva S, Hama Y, Kodama T. Fluctuation effects in initial conditions for hydrodynamics. Phys.Rev.,1997, C55:1455-1462.
[221]Romatschke P, Venugopalan R. The Unstable Glasma. Phys.Rev.,2006, D74:045011.
[222]Zakharov B. Can we see from jet quenching that quark-gluon plasma becomes more perturbative at the LHC than at the RHIC? J.Phys.,2011, G38:124161.
[223]Wang Y L. Generalized canonical Ward identities. Int.J.Theor.Phys.,2009,48:1422-1430.
[224]Fukushima K. Views of the Chiral Magnetic Effect.2012..
[225]Pal S, Bleicher M. Medium information from anisotropic flow and jet quenching in relativistic heavy ion collisions.2012..
[226]Harnad J, Orlov A Y. Fermionic approach to the evaluation of integrals of rational symmetric functions. Theor.Math.Phys.,2009,158:17-39.
[227]Policastro G, Son D, Starinets A. The Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma. Phys.Rev.Lett.,2001,87:081601.
[228]Adams J, et al. Transverse-momentum p(t) correlations on (eta, phi) from mean-p(t) fluctuations in Au-Au collisions at s(NN)**1/2= 200-GeV. J.Phys.,2006, G32:L37-L48.
[229]Adcox K, et al. Measurement of the mid-rapidity transverse energy distribution from s(NN)**(1/2) = 130-GeV Au+Au collisions at RHIC. Phys.Rev.Lett.,2001,87:052301.
[2]GellMann M. Symmetries of baryons and mesons. Phys.Rev.,1962,125:1067-1084.
[3]Ne'eman Y. Derivation of strong interactions from a gauge invariance. Nucl.Phys.,1961, 26:222-229.
[4]Barnes V, Connolly P, Crennell D, et al. Observation of a Hyperon with Strangeness-3. Phys.Rev.Lett.,1964,12:204-206.
[5]D P H. Phys. Rev,1973, Lett.3:1346-1349.
[6]Gross D, Wilczek F. Ultraviolet Behavior of Nonabelian Gauge Theories. Phys.Rev.Lett.,1973, 30:1343-1346.
[7]Bethke S. alphas at Zinnowitz 2004. Nucl.Phys.Proc.Suppl,2004,135:345-352.
[8]Bjorken J. Asymptotic Sum Rules at Infinite Momentum. Phys.Rev.,1969,179:1547-1553.
[9]Chekanov S, et al. A ZEUS next-to-leading-order QCD analysis of data on deep inelastic scattering. Phys.Rev.,2003, D67:012007.
[10]Breidenbach M, Friedman J I, Kendall H W, et al. Observed Behavior of Highly Inelastic electron-Proton Scattering. Phys.Rev.Lett.,1969,23:935-939.
[11]Lee T, Wick G. Vacuum Stability and Vacuum Excitation in a Spin 0 Field Theory. Phys.Rev, 1974, D9:2291.
[12]HOOFT G. Renormalizable Lagrangians for massive Yang-Mills fields. Nucl. Phys.,1971, B35:167-188..
[13]Maldacena J M. The Large N limit of superconformal field theories and supergravity. Adv.Theor.Math.Phys.,1998,2:231-252.
[14]Gubser S, Klebanov I R, Polyakov A M. Gauge theory correlators from noncritical string theory. Phys.Lett.,1998, B428:105-114.
[15]Witten E. Anti-de Sitter space and holography. Adv.Theor.Math.Phys.,1998,2:253-291.
[16]Pisarski R D. Scattering Amplitudes in Hot Gauge Theories. Phys.Rev.Lett.,1989,63:1129.
[17]Weinberg S. Phenomenological Lagrangians. Physica,1979, A96:327.
[18]Nambu Y, Jona-Lasinio G. Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity.1. Phys.Rev.,1961,122:345-358.
[19]Nambu Y, Jona-Lasinio G. DYNAMICAL MODEL OF ELEMENTARY PARTICLES BASED ON AN ANALOGY WITH SUPERCONDUCTIVITY. II. Phys.Rev.,1961,124:246-254.
[20]Wilson K G. Nonlagrangian models of current algebra. Phys.Rev.,1969,179:1499-1512.
[21]Collins J C, Soper D E, Sterman G F. Factorization for Short Distance Hadron-Hadron Scattering. Nucl.Phys.,1985, B261:104.
[22]Mueller A H. Perturbative QCD at High-Energies. Phys.Rept.,1981,73:237.
[23]Collins J C, Soper D E. Back-To-Back Jets in QCD. Nucl.Phys.,1981, B193:381.
[24]Collins J C, Frankfurt L, Strikman M. Diffractive hard scattering with a coherent pomeron. Phys.Lett.,1993, B307:161-168.
[25]Collins J C, Heppelmann S F, Ladinsky G A. Measuring transversity densities in singly polarized hadron hadron and lepton-hadron collisions. Nucl.Phys.,1994, B420:565-582.
[26]Sterman G F, Weinberg S. Jets from Quantum Chromodynamics. Phys.Rev.Lett.,1977,39:1436.
[27]Basham C, Brown L, Ellis S, et al. Energy Correlations in electron-Positron Annihilation in Quan-tum Chromodynamics:Asymptotically Free Perturbation Theory. Phys.Rev.,1979, D19:2018.
[28]Adcox K, et al. Suppression of hadrons with large transverse momentum in central Au+Au collisions at(?)=130-GeV. Phys.Rev.Lett.,2002,88:022301.
[29]Adler C, et al. Disappearance of back-to-back high pT hadron correlations in central Au+Au collisions at sNN**1/2= 200-GeV. Phys.Rev.Lett.,2003,90:082302.
[30]Adams J, et al. Evidence from d+Au measurements for final state suppression of high p(T) hadrons in Au+Au collisions at RHIC. Phys.Rev.Lett.,2003,91:072304.
[31]Nagamiya S, Gyulassy M. High-energy nuclear collisions. Adv.Nucl.Phys.,1984,13:201-315.
[32]Ritter H, Gutbrod H, Kampert K, et al. Collective flow measured with the plastic ball.1989..
[33]PKienlr. The SIS/ESR Project of GSI,. GSI-report,1985, GST R5-:16.
[34]Harris J W, Muller B. The Search for the quark-gluon plasma. Ann.Rev.Nucl.Part.Sci.,1996, 46:71-107.
[35]Arsene I, et al. Quark gluon plasma and color glass condensate at RHIC? The Perspective from the BRAHMS experiment. Nucl.Phys.,2005, A757:1-27.
[36]Back B, Baker M, Ballintijn M, et al. The PHOBOS perspective on discoveries at RHIC. Nucl.Phys.,2005, A757:28-101.
[37]Adams J, et al. Experimental and theoretical challenges in the search for the quark gluon plasma: The STAR Collaboration's critical assessment of the evidence from RHIC collisions. Nucl.Phys., 2005, A757:102-183.
[38]Adcox K, et al. Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC:Experimental evaluation by the PHENIX collaboration. Nucl.Phys.,2005, A757:184-283.
[39]Armesto e, Borghini e, Jeon e, et al. Heavy Ion Collisions at the LHC-Last Call for Predictions. J.Phys.G,2008, G35:054001.
[40]Gyulassy M. The QGP discovered at RHIC.2004.159-182.
[41]Aoki Y, Endrodi G, Fodor Z, et al. The Order of the quantum chromodynamics transition predicted by the standard model of particle physics. Nature,2006,443:675-678.
[42]Aoki Y, Fodor Z, Katz S, et al. The QCD transition temperature:Results with physical masses in the continuum limit. Phys.Lett.,2006, B643:46-54.
[43]Davidson S, Descotes-Genon S. Minimal Flavour Violation for Leptoquarks. JHEP,2010,1011:073.
[44]Abelev B, et al. Identified particle production, azimuthal anisotropy, and interferometry mea-surements in Au+Au collisions at s(NN)**(1/2)= 9.2-GeV. Phys.Rev.,2010, C81:024911.
[45]Gyulassy M, McLerran L. New forms of QCD matter discovered at RHIC. Nucl.Phys.,2005, A750:30-63.
[46]Karsch F. Lattice QCD at high temperature and density. Lect.Notes Phys.,2002,583:209-249.
[47]Armesto N. Nuclear shadowing. J.Phys.G,2006, G32:R367-R394.
[48]Kharzeev D, Levin E, McLerran L. Parton saturation and N(part) scaling of semihard processes in QCD. Phys.Lett.,2003, B561:93-101.
[49]Adams J, et al. Transverse momentum and collision energy dependence of high p(T) hadron suppression in Au+Au collisions at ultrarelativistic energies. Phys.Rev.Lett.,2003,91:172302.
[50]Kolb P, Huovinen P, Heinz U W, et al. Elliptic flow at SPS and RHIC:From kinetic transport to hydrodynamics. Phys.Lett.,2001, B500:232-240.
[51]Adare A, et al. Scaling properties of azimuthal anisotropy in Au+Au and Cu+Cu collisions at s(NN)= 200-GeV. Phys.Rev.Lett.,2007,98:162301.
[52]Teaney D, Lauret J, Shuryak E V. Flow at the SPS and RHIC as a quark gluon plasma signature. Phys.Rev.Lett.,2001,86:4783-4786.
[53]Huovinen P, Kolb P, Heinz U W, et al. Radial and elliptic flow at RHIC:Further predictions. Phys.Lett.,2001, B503:58-64.
[54]Hirano T, Tsuda K. Collective flow and two pion correlations from a relativistic hydrodynamic model with early chemical freezeout. Phys.Rev.,2002, C66:054905.
[55]Tannenbaum M. Recent results in relativistic heavy ion collisions:From'a new state of matter' to'the perfect fluid'. Rept.Prog.Phys.,2006,69:2005-2060.
[56]Romatschke P, Romatschke U. Viscosity Information from Relativistic Nuclear Collisions:How Perfect is the Fluid Observed at RHIC? Phys.Rev.Lett.,2007,99:172301.
[57]Song H, Heinz U W. Causal viscous hydrodynamics in 2+1 dimensions for relativistic heavy-ion collisions. Phys.Rev.,2008, C77:064901.
[58]Shuryak E V, Zahed I. Rethinking the properties of the quark gluon plasma at T approximately T(c). Phys.Rev.,2004, C70:021901.
[59]Ipp A, Kajantie K, Rebhan A, et al. Unified description of deconfined QCD equation of state. J.Phys.G,2007, G34:S631-S634.
[60]Schenke B, Jeon S, Gale C. Elliptic and triangular flow in event-by-event (3+1)D viscous hydro-dynamics. Phys.Rev.Lett.,2011,106:042301.
[61]Huovinen P, Petreczky P. QCD Equation of State and Hadron Resonance Gas. Nucl.Phys.,2010, A837:26-53.
[62]Huovinen P, Petreczky P. Equation of state at finite baryon density based on lattice QCD. J.Phys.G,2011, G38:124103.
[63]Schenke B, Tribedy P, Venugopalan R. Fluctuating Glasma initial conditions and flow in heavy ion collisions. Phys.Rev.Lett.,2012,108:252301.
[64]Baier R, Mueller A H, Schiff D, et al. Does parton saturation at high density explain hadron multiplicities at RHIC? Phys.Lett.,2002, B539:46-52.
[65]Molnar D, Gyulassy M. Saturation of elliptic flow and the transport opacity of the gluon plasma at RHIC. Nucl.Phys.,2002, A697:495-520.
[66]Mrowczynski S. Streame instabilities of the quark-gluon plasma. Phys.Lett.,1988, B214:587.
[67]Romatschke P, Strickland M. Collective modes of an anisotropic quark gluon plasma. Phys.Rev., 2003, D68:036004.
[68]Arnold P B, Lenaghan J. The Abelianization of QCD plasma instabilities. Phys.Rev.,2004, D70:114007.
[69]Xu Z, Greiner C. Thermalization of gluons in ultrarelativistic heavy ion collisions by including three-body interactions in a parton cascade. Phys.Rev.,2005, C71:064901.
[70]Alver B, Roland G. Collision geometry fluctuations and triangular flow in heavy-ion collisions. Phys.Rev.,2010, C81:054905.
[71]Adler S, et al. Dense-Medium Modifications to Jet-Induced Hadron Pair Distributions in Au+Au Collisions at s(NN)**(1/2)= 200-GeV. Phys.Rev.Lett.,2006,97:052301.
[72]Adare A, et al. Dihadron azimuthal correlations in Au+Au collisions at s(NN)**(1/2)= 200-GeV. Phys.Rev.,2008, C78:014901.
[73]Abelev B, et al. Indications of Conical Emission of Charged Hadrons at RHIC. Phys.Rev.Lett., 2009,102:052302.
[74]Agakishiev H, et al. Measurements of Dihadron Correlations Relative to the Event Plane in Au+Au Collisions at s**1/2= 200 GeV.2010..
[75]Alver B, et al. High transverse momentum triggered correlations over a large pseudorapidity acceptance in Au+Au collisions at s(NN)**1/2= 200 GeV. Phys.Rev.Lett.,2010,104:062301.
[76]Aamodt K, et al. Higher harmonic anisotropic flow measurements of charged particles in Pb-Pb collisions at s**1/2= 2.76 TeV. Phys.Rev.Lett.,2011,107:032301.
[77]Aad G, et al. Measurement of the azimuthal anisotropy for charged particle production in sqrt(sNN)= 2.76 TeV lead-lead collisions with the ATLAS detector. Phys.Rev.,2012, C86:014907.
[78]Romatschke P, Venugopalan R. A Weibel instability in the melting color glass condensate. Eur.Phys.J.,2006, A29:71-75.
[79]Ackermann K, et al. Elliptic flow in Au+Au collisions at (S(NN))**(1/2)= 130 GeV. Phys.Rev.Lett.,2001,86:402-407.
[80]Adams J, et al. Azimuthal anisotropy in Au+Au collisions at s(NN)**(1/2)= 200-GeV. Phys.Rev., 2005, C72:014904.
[81]Adler S, et al. Elliptic flow of identified hadrons in Au+Au collisions at s(NN)**(1/2)= 200-GeV. Phys.Rev.Lett.,2003,91:182301.
[82]Afanasiev S, et al. Systematic Studies of Elliptic Flow Measurements in Au+Au Collisions at s**(1/2)= 200-GeV. Phys.Rev.,2009, C80:024909.
[83]Back B, et al. Centrality and pseudorapidity dependence of elliptic flow for charged hadrons in Au+Au collisions at s(NN)**(1/2)= 200-GeV. Phys.Rev.,2005, C72:051901.
[84]Aamodt K, et al. Elliptic flow of charged particles in Pb-Pb collisions at 2.76 TeV. Phys.Rev.Lett., 2010,105:252302.
[85]Jia J. Measurement of elliptic and higher order flow from ATLAS experiment at the LHC. J. Phys.,2011, G 38:124012.
[86]Ollitrault J Y. Anisotropy as a signature of transverse collective flow. Phys.Rev.,1992, D46:229-245.
[87]Voloshin S, Zhang Y. Flow study in relativistic nuclear collisions by Fourier expansion of Azimuthal particle distributions. Z.Phys.,1996, C70:665-672.
[88]Kolb P F, Sollfrank J, Heinz U W. Anisotropic transverse flow and the quark hadron phase transition. Phys.Rev.,2000, C62:054909.
[89]Heinz U W, Kolb P F. Early thermalization at RHIC. Nucl.Phys.,2002, A702:269-280.
[90]Jacobs P, Wang X N. Matter in extremis:Ultrarelativistic nuclear collisions at RHIC. Prog.Part.Nucl.Phys.,2005,54:443-534.
[91]Muller B, Nagle J L. Results from the relativistic heavy ion collider. Ann.Rev.Nucl.Part.Sci., 2006,56:93-135.
[92]Shuryak E. Physics of Strongly coupled Quark-Gluon Plasma. Prog.Part.Nucl.Phys.,2009, 62:48-101.
[93]Heinz U W. The Strongly coupled quark-gluon plasma created at RHIC. J.Phys.A,2009, A42:214003.
[94]Teaney D. The Effects of viscosity on spectra, elliptic flow, and HBT radii. Phys.Rev.,2003, C68:034913.
[95]Dusling K, Teaney D. Simulating elliptic flow with viscous hydrodynamics. Phys.Rev.,2008, C77:034905.
[96]Song H, Bass S A, Heinz U, et al.200 A GeV Au+Au collisions serve a nearly perfect quark-gluon liquid. Phys.Rev.Lett.,2011,106:192301.
[97]Hirano T, Heinz U W, Kharzeev D, et al. Hadronic dissipative effects on elliptic flow in ultrarel-ativistic heavy-ion collisions. Phys.Lett.,2006, B636:299-304.
[98]Steinheimer J, Bleicher M, Petersen H, et al. (3+1)-dimensional hydrodynamic expansion with a critical point from realistic initial conditions. Phys.Rev.,2008, C77:034901.
[99]Werner K, Karpenko I, Pierog T, et al. Event-by-Event Simulation of the Three-Dimensional Hy-drodynamic Evolution from Flux Tube Initial Conditions in Ultrarelativistic Heavy Ion Collisions. Phys.Rev.,2010, C82:044904.
[100]Andrade R P G, Grassi F, Hama Y, et al. Temporal evolution of tubular initial conditions and their influence on two-particle correlations in relativistic nuclear collisions. Phys.Lett.,2012, B712:226-230.
[101]Petersen H, Qin G Y, Bass S A, et al. Triangular flow in event-by-event ideal hydrodynamics in Au+Au collisions at (sNN)**1/2= 200 A GeV. Phys.Rev.,2010, C82:041901.
[102]Holopainen H, Niemi H, Eskola K J. Event-by-event hydrodynamics and elliptic flow from fluctu-ating initial state. Phys.Rev.,2011, C83:034901.
[103]Albacete J L, Dumitru A, Nara Y. CGC initial conditions at RHIC and LHC. J.Phys.Conf.Ser., 2011,316:012011.
[104]Schenke B, Jeon S, Gale C. Higher flow harmonics from (3+1)D event-by-event viscous hydrody-namics. Phys.Rev.,2012, C85:024901.
[105]Qiu Z, Heinz U W. Event-by-event shape and flow fluctuations of relativistic heavy-ion collision fireballs. Phys.Rev.,2011, C84:024911.
[106]Qiu Z, Shen C, Heinz U. Hydrodynamic elliptic and triangular flow in Pb-Pb collisions at sqrt(s)=2.76ATeV. Phys.Lett.,2012, B707:151-155.
[107]Gardim F G, Grassi F, Luzum M, et al. Anisotropic flow in event-by-event ideal hydrodynamic simulations of s**1/2=200 GeV Au+Au collisions.2012..
[108]Ma G L, Wang X N. Jets, Mach cone, hot spots, ridges, harmonic flow, dihadron and gamma-hadron correlation in high-energy heavy-ion collisions. Phys.Rev.Lett.,2011,106:162301.
[109]Adams J, et al. Minijet deformation and charge-independent angular correlations on momentum subspace (eta, phi) in Au-Au collisions at s(NN)**(1/2)= 130-GeV. Phys.Rev.,2006, C73:064907.
[110]Putschke J. Intra-jet correlations of high-p(t) hadrons from STAR. J.Phys.G,2007, G34:S679-684.
[111]Abelev B, et al. Long range rapidity correlations and jet production in high energy nuclear collisions. Phys.Rev.,2009, C80:064912.
[112]Takahashi J, Tavares B, Qian W, et al. Topology studies of hydrodynamics using two particle correlation analysis. Phys.Rev.Lett.,2009,103:242301.
[113]Werner K, Karpenko I, Mikhailov K, et al. Ridges and Soft Jet Components in Untriggered Di-hadron Correlations in Pb+Pb Collisions at 2.76 TeV.2011..
[114]Xu J, Ko C M. Triangular flow in heavy ion collisions in a multiphase transport model. Phys.Rev., 2011, C84:014903.
[115]Chaudhuri A. Influence of shear viscosity on the correlation between the triangular flow and initial spatial triangularity. Phys.Lett.,2012, B713:91-94.
[116]Miller M L, Reygers K, Sanders S J, et al. Glauber modeling in high energy nuclear collisions. Ann.Rev.Nucl.Part.Sci.,2007,57:205-243.
[117]Drescher H J, Dumitru A, Hayashigaki A, et al. The Eccentricity in heavy-ion collisions from color glass condensate initial conditions. Phys.Rev.,2006, C74:044905.
[118]Drescher H J, Nara Y. Effects of fluctuations on the initial eccentricity from the Color Glass Condensate in heavy ion collisions. Phys.Rev.,2007, C75:034905.
[119]Kharzeev D, Levin E, Nardi M. QCD saturation and deuteron nucleus collisions. Nucl.Phys., 2004, A730:448-459.
[120]Kharzeev D, Levin E, Nardi M. Color glass condensate at the LHC:Hadron multiplicities in pp, pA and AA collisions. Nucl.Phys.,2005, A747:609-629.
[121]Wang X N, Gyulassy M. HIJING:A Monte Carlo model for multiple jet production in p p, p A and A A collisions. Phys.Rev.,1991, D44:3501-3516.
[122]Gyulassy M, Wang X N. HIJING 1.0:A Monte Carlo program for parton and particle production in high-energy hadronic and nuclear collisions. Comput.Phys.Commun.,1994,83:307.
[123]Deng W t, Wang X N. Multiple Parton Scattering in Nuclei:Modified DGLAP Evolution for Fragmentation Functions. Phys.Rev.,2010, C81:024902.
[124]Pratt S, Schindel D. Is HBT really puzzling? AIP Conf.Proc.,2006,828:430-435.
[125]Florchinger S, Wiedemann U A. Fluctuations around Bjorken Flow and the onset of turbulent phenomena. JHEP,2011,1111:100.
[126]Kapusta J, Muller B, Stephanov M. Relativistic Theory of Hydrodynamic Fluctuations with Applications to Heavy Ion Collisions. Phys.Rev.,2012, C85:054906.
[127]Luzum M, Romatschke P. Conformal Relativistic Viscous Hydrodynamics:Applications to RHIC results at s(NN)**(1/2)-200-GeV. Phys.Rev.,2008, C78:034915.
[128]Esumi S. Collective Flow Measurements from the PHENIX Experiment. J.Phys.G,2011, G38:124010.
[129]Geiger K, Muller B. Dynamics of parton cascades in highly relativistic nuclear collisions. Nucl.Phys.,1992, B369:600-654.
[130]Chen J W, Deng J, Dong H, et al. Shear and Bulk Viscosities of a Gluon Plasma in Perturbative QCD:Comparison of Different Treatments for the gg<->ggg Process.2011.
[131]Pang L, Wang Q, Wang X N. Effects of initial flow velocity fluctuation in event-by-event (3+l)D hydrodynamics. Phys.Rev.,2012, C86:024911.
[132]Petersen H, Steinheimer J, Burau G, et al. A Fully Integrated Transport Approach to Heavy Ion Reactions with an Intermediate Hydrodynamic Stage. Phys.Rev.,2008, C78:044901.
[133]Drescher H, Hladik M, Ostapchenko S, et al. A Unified treatment of high-energy interactions. J.Phys.G,1999, G25:L91-L96.
[134]Drescher H, Ostapchenko S, Pierog T, et al. Initial condition for QGP evolution from NEXUS. Phys.Rev.,2002, C65:054902.
[135]Karsch F, Laermann E. Thermodynamics and in medium hadron properties from lattice QCD. 2003..
[136]Cooper F, Frye G. Comment on the Single Particle Distribution in the Hydrodynamic and Sta-tistical Thermodynamic Models of Multiparticle Production. Phys.Rev.,1974, D10:186.
[137]Hirano T. Is early thermalization achieved only near mid-rapidity at RHIC? Phys.Rev.,2002, C65:011901.
[138]Huovinen P, Petersen H. Particlization in hybrid models.2012..
[139]Heinz U W, Shen C, Song H. The viscosity of quark-gluon plasma at RHIC and the LHC. AIP Conf.Proc.,2012,1441:766-770.
[140]Demir N, Bass S A. Shear-Viscosity to Entropy-Density Ratio of a Relativistic Hadron Gas. Phys.Rev.Lett.,2009,102:172302.
[141]Bozek P. Flow and interferometry in 3+1 dimensional viscous hydrodynamics. Phys.Rev.,2012, C85:034901.
[142]Mendoza M, Boghosian B, Herrmann H, et al. Fast Lattice Boltzmann Solver for Relativistic Hydrodynamics. Phys.Rev.Lett.,2010,105:014502.
[143]Romatschke P. New Developments in Relativistic Viscous Hydrodynamics. Int.J.Mod.Phys.,2010, E19:1-53.
[144]Romatschke P, Mendoza M, Succi S. A fully relativistic lattice Boltzmann algorithm. Phys.Rev., 2011, C84:034903.
[145]Romatschke P. Relativistic (Lattice) Boltzmann Equation with Non-Ideal Equation of State. Phys.Rev.,2012, D85:065012.
[146]Weinberg S. Gravitation and cosmology:principles and applications of the general theory of relativity. J. Wiley, New York,,1972. Eq. (2.10.8).
[147]Boris J P, Book D L. Flux-Corrected Transport. I. SHASTA, A Fluid Transport Algorithm That Works. J.Comput.Phys.,1973,11:38-69.
[148]Zalesak S T. Fully Multidimensional Flux-Corrected Transport Algorithms for Fluids J.Comput.Phys.,1979,31:335-362.
[149]Rischke D H, Bernard S, Maruhn J A. Relativistic hydrodynamics for heavy ion collisions.1. General aspects and expansion into vacuum. Nucl.Phys.,1995, A595:346-382.
[150]Frisch U, Hasslacher B, Pomeau Y. A LATTICE GAS AUTOMATA FOR THE NAVIER-STOKES EQUATION. Phys.Rev.Lett.,1986,56:1505-1508.
[151]Wolfram S. Cellular automaton fluid 1:Basic theory. J. Stat.,1986, Phys.45:471.
[152]Qian Y, d'Humieres D, Lallemand P. Lattice BGK Models for Navier-Stokes Equation. Euro-physics Letters,1992,17(6):479-484.
[153]McNamara G R, Zanetti G. Use of the Boltzmann Equation to Simulate Lattice-Gas Automata. Phys. Rev. Lett.,1988,61:2332-2335.
[154]Bhatnager P, Gross E, Krook M. A Model for Collision Process in Gases. Physics Review,1954, 94(3):511-525.
[155]H Chen S C, Matthaeus W H. Recovery of Navier-Stokes equations using a lattice-gas Boltzmann method. Phys. Rev.,1991, A 45:R5339.
[156]He X, Luo L S. Theory of lattice Boltzmann method:From the Boltzmann equation to the lattice Boltzmann equation,. Physical Review E,1997,56:6811-6817.
[157]Zhaoli Guo T S Z. Lattice Boltzmann model for incompressible flows through porous media. PHYSICAL REVIEW E,2002,66:036304.
[158]Benzi R, Succi S, Vergassola M. The lattice Boltzmann equation:theory and applications. Physics Reports,1992,222(3):145-197.
[159]He X, Luo L S. Theory of the lattice Boltzmann method:From the Boltzmann equation to the lattice Boltzmann equation. Phys. Rev. E,1997,56:6811-6817.
[160]Y Qian D d, Lallemand P. Lattice BGK Models for Navier-Stokes Equation. Europhys. Lett., 1992,17:479.
[161]Kataja M, Ruuskanen P. Nonzero chemical potential and the shape of the p(T) distribution of hadrons in heavy ion collisions. Phys.Lett.,1990, B243:181-184.
[162]Sollfrank J, Huovinen P, Kataja M, et al. Hydrodynamical description of 200-A/GeV/c S+Au collisions:Hadron and electromagnetic spectra. Phys.Rev.,1997, C55:392-410.
[163]Schenke B, Jeon S, Gale C. (3+1)D hydrodynamic simulation of relativistic heavy-ion collisions. Phys.Rev.,2010, C82.014903.
[164]N simplex. http://en.wikipedia.org/wiki/Simplex.
[165]Hirano T, Nara Y. Eccentricity fluctuation effects on elliptic flow in relativistic heavy ion collisions. Phys.Rev.,2009, C79:064904.
[166]Zhang B, Ko C, Li B A, et al. A multiphase transport model for nuclear collisions at RHIC. Phys.Rev.,2000, C61:067901.
[167]Chatterjee R, Holopainen H, Renk T, et al. Enhancement of thermal photon production in event-by-event hydrodynamics. Phys.Rev.,2011, C83:054908.
[168]Back B, Baker M, Barton D, et al. The Significance of the fragmentation region in ultrarelativistic heavy ion collisions. Phys.Rev.Lett.,2003,91:052303.
[169]Abelev B, et al. Systematic Measurements of Identified Particle Spectra in pp,d+Au and Au+Au Collisions from STAR. Phys.Rev.,2009, C79:034909.
[170]Adler S, et al. Identified charged particle spectra and yields in Au+Au collisions at S(NN)**1/2 = 200-GeV. Phys.Rev.,2004, C69:034909.
[171]Abelev B, et al. Identified baryon and meson distributions at large transverse momenta from Au+Au collisions at s(NN)**(1/2)= 200-GeV. Phys.Rev.Lett.,2006,97:152301.
[172]Kolb P F, Heinz U W. Hydrodynamic description of ultrarelativistic heavy ion collisions.2003..
[173]Song H, Bass S A, Heinz U. Elliptic flow in 200 A GeV Au+Au collisions and 2.76 A TeV Pb+Pb collisions:insights from viscous hydrodynamics+hadron cascade hybrid model. Phys.Rev.,2011, C83:054912.
[174]Adare A, et al. Measurements of Higher-Order Flow Harmonics in Au+Au Collisions at s**1/2= 200 GeV. Phys.Rev.Lett.,2011,107:252301.
[175]Wang X N. Jet quenching and azimuthal anisotropy of large p(T) spectra in noncentral high-energy heavy ion collisions. Phys.Rev.,2001, C63:054902.
[176]Gyulassy M, Vitev I, Wang X. High p(T) azimuthal asymmetry in noncentral A+A at RHIC. Phys.Rev.Lett.,2001,86:2537-2540.
[177]Bass S A, Gale C, Majumder A, et al. Systematic Comparison of Jet Energy-Loss Schemes in a realistic hydrodynamic medium. Phys.Rev.,2009, C79:024901.
[178]Song H, Bass S A, Heinz U, et al. Hadron spectra and elliptic flow for 200 A GeV Au+Au collisions from viscous hydrodynamics coupled to a Boltzmann cascade. Phys.Rev.,2011, C83:054910.
[179]Aamodt K, et al. Centrality dependence of the charged-particle multiplicity density at mid-rapidity in Pb-Pb collisions at sqrt(sNN)= 2.76 TeV. Phys.Rev.Lett.,2011,106:032301.
[180]Aamodt K, et al. Suppression of Charged Particle Production at Large Transverse Momentum in Central Pb-Pb Collisions at s**1/2= 2.76 TeV. Phys.Lett.,2011, B696:30-39.
[181]Snellings R. Anisotropic flow at the LHC measured with the ALICE detector. J.Phys.G,2011, G38:124013.
[182]Pang L g, Wang Q, Wang X N, et al. Mini-jet thermalization and diffusion of transverse momentum correlation in high-energy heavy-ion collisions. Phys.Rev.,2010, C81:031903.
[183]Braun-Munzinger P, Stachel J, Wetterich C. Chemical freezeout and the QCD phase transition temperature. Phys.Lett.,2004, B596:61-69.
[184]Andronic A, Braun-Munzinger P, Redlich K, et al. The thermal model on the verge of the ultimate test:particle production in Pb-Pb collisions at the LHC. J.Phys.G,2011, G38:124081.
[185]Different versions of parameterized EoS can be found at https://wiki.bnl.gov/TECHQM/index.php/ QCD_Equation_of_State..
[186]Floris M. Identified particles in pp and Pb-Pb collisions at LHC energies with the ALICE detector. J.Phys.G,2011, G38:124025.
[187]Back B, et al. Charged particle multiplicity near mid-rapidity in central Au+Au collisions at SO/2)= 56-A/GeV and 130-A/GeV. Phys.Rev.Lett.,2000,85:3100-3104.
[188]Adler C, et al. Multiplicity distribution and spectra of negatively charged hadrons in Au+Au collisions at s(NN)**(1/2)= 130-GeV. Phys.Rev.Lett.,2001,87:112303.
[189]Hwa R C, Zhu L. Effects of Minijets on Hadronic Spectra and Azimuthal Harmonics in Au-Au Collisions at 200 GeV. Phys.Rev.,2012, C86:024901.
[190]Kajantie K, Landshoff P, Lindfors J. Minijet Production in High-Energy Nucleus-Nucleus Colli-sions. Phys.Rev.Lett.,1987,59:2527.
[191]Eskola K, Kajantie K, Lindfors J. Quark and Gluon Production in High-Energy Nucleus-Nucleus Collisions. Nucl.Phys.,1989, B323:37.
[192]Wang X N, Gyulassy M. Gluon shadowing and jet quenching in A+A collisions at s**(1/2)= 200-GeV. Phys.Rev.Lett.,1992,68:1480-1483.
[193]Eskola K, Muller B, Wang X N. Screening of initial parton production in ultrarelativistic heavy ion collisions. Phys.Lett.,1996, B374:20-24.
[194]Heinz U W. Thermalization at RHIC. AIP Conf.Proc.,2005,739:163-180.
[195]Wang X N. Resolving mini-jets in the minimum biased events of hadronic interactions. Phys.Rev.. 1992, D46:1900-1902.
[196]Wang X N. Studying mini-jets via the P(T) dependence of the two particle correlation in Azimuthal angle Phi. Phys.Rev.,1993, D47:2754-2760.
[197]Stephanov M A, Rajagopal K, Shuryak E V. Event-by-event fluctuations in heavy ion collisions and the QCD critical point. Phys.Rev.,1999, D60:114028.
[198]Jeon S, Koch V. Charged particle ratio fluctuation as a signal for QGP. Phys.Rev.Lett.,2000, 85:2076-2079.
[199]Stephanov M A. Thermal fluctuations in the interacting pion gas. Phys.Rev.,2002, D65:096008.
[200]Aziz M A, Gavin S. Causal diffusion and the survival of charge fluctuations in nuclear collisions. Phys.Rev.,2004, C70:034905.
[201]Gavin S, Abdel-Aziz M. Measuring Shear Viscosity Using Transverse Momentum Correlations in Relativistic Nuclear Collisions. Phys.Rev.Lett.,2006,97:162302.
[202]Wang M, Li L, Liu L, et al. An explorer for the shear viscosity in the formed matter at the RHIC. J.Phys.G,2009, G36:064070.
[203]Kharzeev D, Levin E, McLerran L. Jet azimuthal correlations and parton saturation in the color glass condensate. Nucl.Phys.,2005, A748:627-640.
[204]Adler S, et al. Systematic studies of the centrality and s(NN)**(1/2) dependence of the d E(T)/ d eta and d (N(ch)/d eta in heavy ion collisions at mid-rapidity. Phys.Rev.,2005, C71:034908.
[205]Adams J, et al. Distributions of charged hadrons associated with high transverse momentum par-ticles in pp and Au+Au collisions at s(NN)**(1/2)= 200-GeV. Phys.Rev.Lett.,2005,95:152301.
[206]Collaboration T A. Measurement of elliptic flow and higher-order flow coefficients with the ATLAS detector in sNN**1/2=2.76 TeV Pb+Pb collisions.2011..
[207]Aguiar C, Hama Y, Kodama T, et al. Event-by-event fluctuations in hydrodynamical description of heavy ion collisions. Nucl.Phys.,2002, A698:639-642.
[208]Baier R, Dokshitzer Y L, Mueller A H, et al. Radiative energy loss and p(T) broadening of high-energy partons in nuclei. Nucl.Phys.,1997, B484:265-282.
[209]Baym G. RHIC:From dreams to beams in two decades. Nucl.Phys.,2002, A698:XXIII-XXXII.
[210]Drescher H, Hladik M, Ostapchenko S, et al. Parton based Gribov-Regge theory. Phys.Rept., 2001,350:93-289.
[211]Dumitru A, Gelis F, McLerran L, et al. Glasma flux tubes and the near side ridge phenomenon at RHIC. Nucl.Phys.,2008, A810:91-108.
[212]G Aad e a. Measurement of the azimuthal anisotropy for charged particle production in sqrt(sNN) =2.76 TeV lead-lead collisions with the ATLAS detector. arXiv:1203.3087 [hep-ex]..
[213]Gardim F G, Grassi F, Hama Y, et al. Directed flow at mid-rapidity in event-by-event hydrody-namics. Phys.Rev.,2011, C83:064901.
[214]Gyulassy M, Vitev I, Wang X N, et al. Jet quenching and radiative energy loss in dense nuclear matter.2003..
[215]He M, Fries R J, Rapp R. Scaling of Elliptic Flow, Recombination and Sequential Freeze-Out of Hadrons in Heavy-Ion Collisions. Phys.Rev.,2010, C82:034907.
[216]Hirano T, Nara Y. Dynamical modeling of high energy heavy ion collisions.2012..
[217]Kajantie K, Karimaki V. VOLUME OF LONGITUDINAL PHASE SPACE.1971..
[218]McLerran L D, Venugopalan R. Computing quark and gluon distribution functions for very large nuclei. Phys.Rev.,1994, D49:2233-2241.
[219]Ohlson A. Jets and Jet-like correlations in STAR.2012..
[220]Paiva S, Hama Y, Kodama T. Fluctuation effects in initial conditions for hydrodynamics. Phys.Rev.,1997, C55:1455-1462.
[221]Romatschke P, Venugopalan R. The Unstable Glasma. Phys.Rev.,2006, D74:045011.
[222]Zakharov B. Can we see from jet quenching that quark-gluon plasma becomes more perturbative at the LHC than at the RHIC? J.Phys.,2011, G38:124161.
[223]Wang Y L. Generalized canonical Ward identities. Int.J.Theor.Phys.,2009,48:1422-1430.
[224]Fukushima K. Views of the Chiral Magnetic Effect.2012..
[225]Pal S, Bleicher M. Medium information from anisotropic flow and jet quenching in relativistic heavy ion collisions.2012..
[226]Harnad J, Orlov A Y. Fermionic approach to the evaluation of integrals of rational symmetric functions. Theor.Math.Phys.,2009,158:17-39.
[227]Policastro G, Son D, Starinets A. The Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma. Phys.Rev.Lett.,2001,87:081601.
[228]Adams J, et al. Transverse-momentum p(t) correlations on (eta, phi) from mean-p(t) fluctuations in Au-Au collisions at s(NN)**1/2= 200-GeV. J.Phys.,2006, G32:L37-L48.
[229]Adcox K, et al. Measurement of the mid-rapidity transverse energy distribution from s(NN)**(1/2) = 130-GeV Au+Au collisions at RHIC. Phys.Rev.Lett.,2001,87:052301.