Chaos Many-Body Engine v03: A new version of code C# for chaos analysis of relativistic many-body systems with reactions

Abstract In this paper we present a new version of the Chaos Many-Body Engine C# application (Grossu et al. 2012  [1] ). In order to benefit from the latest technological advantages, we migrated the application from .Net Framework 2.0 to .Net Framework 4.0. New tools were implemented also. Trying to estimate the particle interactions dependence on initial conditions, we considered a new distance, which takes into account only the structural differences between two systems. We used this distance for implementing the “Structural Lyapunov” function. We propose also a new precision test based on temporal reversed simulations. New version program summary Program title: Chaos Many-Body Engine v03 Catalogue identifier: AEGH_v3_0 Program summary URL : http://cpc.cs.qub.ac.uk/summaries/AEGH_v3_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 214429 No. of bytes in distributed program, including test data, etc.: 9512380 Distribution format: tar.gz Programming language: Visual C# .Net 2010 Computer: PC Operating system:  .Net Framework 4.0 running on MS Windows RAM: 128 MB Classification: 24.60.Lz, 05.45.a Catalogue identifier of previous version: AEGH_v2_0 Journal reference of previous version: Computer Physics Communications 183 (2012) 1055–1059 Does the new version supersede the previous version?: Yes Nature of problem: Chaos analysis of three-dimensional, relativistic many-body systems with reactions. Solution method: Second order Runge–Kutta algorithm. Implementation of temporal reversed simulation precision test, and “Structural Lyapunov” function. Reasons for new version: 1. In order to benefit from the advantages involved in the latest technologies (e.g. LINQ Queries  [2] ), Chaos Many-Body Engine was migrated from .Net Framework 2.0 to .Net Framework 4.0. 2. In addition to existing energy conservation assessment  [3] , we propose also a reverse simulation precision test. Thus, for a regular simulation, we considered the corresponding reversed process: initial time equals the end time of regular simulation, and temporal resolution d t 0 . One can compare the initial state of the regular system, and the final state of the reversed one ( t = 0 ) using, for example, the phase-space distance. 3. Trying to measure particle interactions dependence on initial conditions, we considered the following distance, which takes into account only the structure differences between two many-body systems with reactions: (1) d s = ∑ i = 1 n ( N i 1 − N i 2 ) 2 where N i 1 represents the number of particles of type “ i ” from the first system, and N i 2 is the corresponding number for the second system. We sum over all particle types. Inspired by the Lyapunov Exponent method  [4] , we implemented the evolution in time of the “Structural Lyapunov” function, for two identical systems with slightly different initial conditions: (2) L s ( t ) = ln d s ( t ) d s ( 0 ) . Summary of revisions: 1. Migration from .Net Framework 2.0 to .Net Framework 4.0 2. Implementation of new chaos analysis tools: a. Reverse simulation precision test b. “Structural Lyapunov” function. Additional comments: 1. In  [1] we applied the Chaos Many-Body Engine to some nuclear relativistic collisions at 4.5 A GeV/c (SKM 200 collaboration  [5] , [6] ). We considered also some first tests on He+He head-on collisions at 1 A TeV/c (choose the Simulation ∖ Collision menu, and set the appropriate parameters Fig. 1 ). However, in this case, more complex reaction schemas should be considered. Further investigation on higher energies is currently in progress. Download full-size image Fig. 1 . He+He central, head-on collision at 1 A TeV/c (example of use). Restrictions: The reverse simulation precision test does not apply for: systems with reactions, parallel simulations, and Monte Carlo simulations. Running time: quadratic complexity.