Abstract In Grossu et al., (2019) we proposed a Chaos Many-Body Engine (CMBE) quark toy-model for the Compressed Baryonic Matter (CBM) energies. We started from the following assumptions: (1) the system can be decomposed into a set of two or three-body quark “elementary systems”, i.e. “white” color charged, mesonic or baryonic systems; (2) the bi-particle force is limited to the domain of each elementary system; (3) the physical solution conforms to the minimum potential energy requirement. In the present work we used graph theory for identifying those sets (clusters) of elementary systems close enough to form a bound system (through the exchange of same color charged quarks). In this approach, the cluster production could be understood as an effect of the chaotic behavior of the system. As a direct application, we estimated the pentaquark production probability obtained in p + p collisions, at a center-of-mass energy between 10 and 100 GeV New version program summary Program Title: Chaos Many-Body Engine (CMBE) CPC Library link to program files: http://dx.doi.org/10.17632/rh5txj3n4g.2 Licensing provisions: GPLv2 Programming language: C# 7.3. External routines: BigRational structure (Microsoft). Journal reference of previous version: Computer Physics Communications 239C (2019) 149-152 Does the new version supersede the previous version?: Yes. Nature of problem: Estimate the Pentaquark production in nuclear relativistic collisions. Solution method: Clustering algorithm for identifying all five-body quark white systems. Reasons for the new version: Added the Pentaquark identification new feature. Summary of revisions: • Migration from .Net Framework 4.0 to .Net Framework 4.7.1 • In [1] we implemented a quark confinement algorithm for decomposing the system into a set of two or three-body quark “elementary systems”, i.e. “white” color charged, mesonic or respectively, baryonic systems, in agreement with the minimum potential energy requirement. In this work we added a new O(n3) algorithm (QcdQuarkBagPentaQuarkAlgorithm class), developed in agreement with the SOLID principles, for the identification of those sets (clusters) of elementary systems close enough to form a bound system (through the exchange of same color charged quarks). Taking this into account the system was associated with an undirected graph G [2,3], whose nodes are the elementary systems. Two nodes are connected if the distance between their geometrical centers is lower than the sum of their radii. Thus, each cluster could be associated to a maximal connected subgraph of G. • Unit tests (QcdQuarkBagPentaQuarkAlgorithmTests class) for checking the new algorithm. • In [1] we proposed a quark toy-model for proton–proton collisions at CBM energies [4]. The model was extended for estimating the pentaquark [5] production probability, as seen in Fig. 1 . In this approach, the pentaquark production could be understood as a direct effect of the chaotic behavior of the system [6,7]. Thus, for each center-of-mass energy ( s ∈ 10 , 100 GeV) we simulated 2,000 events by choosing Simulations\Quark Collision from the menu and storing the pentaquark multiplicity at t=300 Fm/c in the quark.pentaquark.log.csv file, generated into the simulation output folder. The collision parameter was given random values in the [0.2, 1.1] Fm range. References I.V. Grossu, C. Besliu, Al. Jipa, D. Felea, E. Stan, T. Esanu, Implementation of quark confinement and retarded interactions algorithms for Chaos Many-Body Engine, Computer Physics Communications 239C (2019) pp. 149-152, DOI: https://doi.org/10.1016/j.cpc.2019.01.023 Alan Gibbons, Algorithmic Graph Theory, Cambridge University Press, 1985. I.V. Grossu, C. Besliu, Al. Jipa, C.C. Bordeianu, D. Felea, E. Stan, T. Esanu, Code C# for chaos analysis of relativistic many-body systems, Computer Physics Communications 181 (2010) 1464–1470, https://doi.org/10.1016/j.cpc.2010.04.015 A. Abuhoza et al, The CBM Collaboration, Nuclear Physics A, Volumes 904--905 , 2 May 2013, Pages 1059c-1062c A. Abdivaliev, C. Besliu et al., Yad.Fiz.29, v.6, 1979. St. Grosu, Quelques effets des fluctuations de la barriere de potentiel a la surface des conducteurs, Studii si cercetari de fizica, 1, XI, 1960 D. Felea, C.C. Bordeianu, I.V. Grossu, C. Besliu, Al. Jipa, A.-A. Radu and E. Stan, Intermittency route to chaos for the nuclear Billiard, EPL, 93 (2011) 42001, DOI: 10 . 1209 ∕ 0295 − 5075 ∕ 93 ∕ 42001

中文翻译：

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用于估计 CBM 能量下质子-质子碰撞中五夸克产生的混沌多体引擎模块

摘要 在 Grossu 等人 (2019) 中，我们提出了一种用于压缩重子物质 (CBM) 能量的混沌多体引擎 (CMBE) 夸克玩具模型。我们从以下假设开始： (1) 该系统可以分解为一组二体或三体夸克“基本系统”，即“白色”带电、介子或重子系统；(2)双粒子力限于每个基本系统的域；(3)物理解符合最小势能要求。在目前的工作中，我们使用图论来识别那些足够接近以形成束缚系统（通过交换相同颜色的带电夸克）的基本系统的集合（簇）。在这种方法中，集群生产可以理解为系统混沌行为的影响。作为直接应用，我们估计了在 p + p 碰撞中获得的五夸克产生概率，质心能量介于 10 到 100 GeV 新版本程序摘要程序标题：混沌多体引擎 (CMBE) CPC 库程序文件链接：http: //dx.doi.org/10.17632/rh5txj3n4g.2 许可条款：GPLv2 编程语言：C# 7.3。外部例程：BigRational 结构（微软）。上一版本期刊参考：Computer Physics Communications 239C (2019) 149-152 新版本是否取代上一版本？：是的。问题的性质：估计核相对论碰撞中的五夸克产物。求解方法：识别所有五体夸克白系统的聚类算法。新版本原因：增加了五夸克识别新功能。修订摘要： • 从 .Net Framework 4 迁移。0 到 .Net Framework 4.7.1 • 在 [1] 中，我们实现了一种夸克限制算法，用于将系统分解为一组二体或三体夸克“基本系统”，即“白色”带电、介子或重子系统，符合最低势能要求。在这项工作中，我们添加了一个新的 O(n3) 算法（QcdQuarkBagPentaQuarkAlgorithm 类），该算法与 SOLID 原则一致，用于识别那些足够接近以形成绑定系统的基本系统的集合（簇）（通过交换相同的带颜色的夸克）。考虑到这一点，系统与无向图 G [2,3] 相关联，其节点是基本系统。如果两个节点的几何中心之间的距离小于它们的半径之和，则两个节点是连接的。因此，每个集群都可以与 G 的最大连通子图相关联。 • 单元测试（QcdQuarkBagPentaQuarkAlgorithmTests 类）用于检查新算法。• 在[1] 中，我们提出了一个用于CBM 能量下质子-质子碰撞的夸克玩具模型[4]。该模型被扩展用于估计五夸克 [5] 生产概率，如图 1 所示。在这种方法中，五夸克的产生可以理解为系统混沌行为的直接影响 [6,7]。因此，对于每个质心能量（ s ∈ 10 , 100 GeV），我们通过从菜单中选择 Simulations\Quark Collision 并将五夸克多重性存储在 quark.pentaquark.log 中 t=300 Fm/c 来模拟 2,000 个事件.csv 文件，生成到仿真输出文件夹中。碰撞参数的随机值在 [0.2, 1.1] Fm 范围内。参考文献 IV Grossu, C. 贝斯柳，阿尔。Jipa, D. Felea, E. Stan, T. Esanu，混沌多体引擎的夸克约束和延迟相互作用算法的实现，计算机物理通信 239C (2019) pp. 149-152，DOI：https://doi。 org/10.1016/j.cpc.2019.01.023 Alan Gibbons，算法图论，剑桥大学出版社，1985 年。IV Grossu，C. Besliu，Al。Jipa、CC Bordeianu、D. Felea、E. Stan、T. Esanu，用于相对论多体系统混沌分析的代码 C#，计算机物理通信 181 (2010) 1464–1470，https://doi.org/10.1016/ j.cpc.2010.04.015 A. Abuhoza 等人，The CBM Collaboration，Nuclear Physics A，第 904--905 卷，2013 年 5 月 2 日，第 1059c-1062c 页 A. Abdivaliev、C. Besliu 等人，Yad.Fiz。 29, v.6, 1979. St. Grosu, Quelques effets des pulses de la barriere de potentiel a la Surface des Conducteurs, Studii si cercetari de fizica, 1, XI, 1960 D. Felea, CC Bordeianu, IV Grossu, C. Besliu, Al。吉帕，A.-A。Radu 和 E. Stan，核台球混乱的间歇性路线，EPL，93 (2011) 42001，DOI：10。1209 ∕ 0295 − 5075 ∕ 93 ∕ 42001