Code C# for chaos analysis of relativistic many-body systems with reactions

Abstract

In this work we present a reaction module for “Chaos Many-Body Engine” (Grossu et al., 2010 [1]). Following our goal of creating a customizable, object oriented code library, the list of all possible reactions, including the corresponding properties (particle types, probability, cross section, particle lifetime, etc.), could be supplied as parameter, using a specific XML input file. Inspired by the Poincaré section, we propose also the “Clusterization Map”, as a new intuitive analysis method of many-body systems. For exemplification, we implemented a numerical toy-model for nuclear relativistic collisions at 4.5 A GeV/c (the SKM200 Collaboration). An encouraging agreement with experimental data was obtained for momentum, energy, rapidity, and angular π− distributions. Program summaryProgram title: Chaos Many-Body Engine v02Catalogue identifier: AEGH_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGH_v2_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 184 628No. of bytes in distributed program, including test data, etc.: 7 905 425Distribution format: tar.gzProgramming language: Visual C#.NET 2005Computer: PCOperating system: Net Framework 2.0 running on MS WindowsHas the code been vectorized or parallelized?: Each many-body system is simulated on a separate execution thread. One processor used for each many-body system.RAM: 128 MegabytesClassification: 6.2, 6.5Catalogue identifier of previous version: AEGH_v1_0Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 1464External routines: Net Framework 2.0 LibraryDoes the new version supersede the previous version?: YesNature of problem: Chaos analysis of three-dimensional, relativistic many-body systems with reactions.Solution method: Second order Runge–Kutta algorithm for simulating relativistic many-body systems with reactions. Object oriented solution, easy to reuse, extend and customize, in any development environment which accepts .Net assemblies or COM components. Treatment of two particles reactions and decays. For each particle, calculation of the time measured in the particle reference frame, according to the instantaneous velocity. Possibility to dynamically add particle properties (spin, isospin, etc.), and reactions/decays, using a specific XML input file. Basic support for Monte Carlo simulations. Implementation of: Lyapunov exponent, “fragmentation level”, “average system radius”, “virial coefficient”, “clusterization map”, and energy conservation precision test. As an example of use, we implemented a toy-model for nuclear relativistic collisions at 4.5 A GeV/c.Reasons for new version: Following our goal of applying chaos theory to nuclear relativistic collisions at 4.5 A GeV/c, we developed a reaction module integrated with the Chaos Many-Body Engine.Summary of revisions:1.In the previous version, inheriting the Particle class was the only possibility of implementing more particle properties (spin, isospin, and so on). In the new version, particle properties can be dynamically added using a dictionary object.2.The application was improved in order to calculate the time measured in the own reference frame of each particle.3.We developed a reaction module for treating the following processes:•two particles reactions: a+b→c+d,•decays: a→c+d,•stimulated decays,•more complicated schemas, implemented as various combinations of previous reactions.4.Following our goal of creating a flexible application, the reactions list, including the corresponding properties (cross sections, particles lifetime, etc.), could be supplied as parameter, using a specific XML configuration file.5.The simulation output files were modified for systems with reactions, assuring also the backward compatibility.6.We propose the “Clusterization Map” as a new investigation method of many-body systems.7.The multi-dimensional Lyapunov Exponent was adapted in order to be used for systems with variable structure.8.Basic support for Monte Carlo simulations was also added.Additional comments: Windows forms application for testing the engine. Easy copy/paste based deployment method.Running time: Quadratic complexity.