| New perspectives for many disciplines have been provided by the theories of complex networks.After nearly two decades of development,remarkable crosscutting research results have been made in many fields,which reveals the inherent laws of complex systems in the real world and deepens the understanding of propagation,evolution,synchronization,control,recommendation and other issues.Reaction system is a major object in complex network research,concerning about how the macroscopic structure of the system is mapped,where the reaction path is located,and what functions a specific reaction corresponds to.The structure lays foundation for the system and also determines many of the functions of the system.As one of the basic reaction type,nuclear reaction is the key to the formation of the material world and also an important source of energy,which plays a vital role to explore the origin and evolution of the universe regarding to nuclear astrophysics research,involving heated topics such as the reaction rate,nuclide stability and nuclear synthesis processes.Classical nuclear physics focuses on a single reaction or local process,lacking discussion of the whole system,hence complex networks analysis is a very beneficial attempt.However,as reactions often have many conditions under various categories,a single-layered network mapping method would have difficulties in describing the complete structure thus key information will be lost.The multilayer network eliminates the deficiency by further distinguishing the interaction between individuals in the system,improving the inspection “resolution” of the structure.Presently,there are few studies on the multilayer reaction network,including the nuclear reaction.Therefore,starting with basic elements of nuclear reaction,from microcosmic to macroscopic,from the reduction theory to the holistic theory,this paper intensively studies the structural characteristics of the nuclear reaction system,and the work is conducted mainly from the following aspects:1.The understanding and application are pushed forward of reaction rate,reaction cross-section and reaction process.The theories and the reactions in nuclear astrophysics and nuclear energy are discussed.The differences of reaction rate,cross section and reaction process are compared.Neutron filters in the equipment for nuclear physics experiment and neutron diffusion model of the molten salt reactor in nuclear energy are taken as examples respectively.In addition,the nuclear reaction network method in nuclear physics calculates the evolution of a part in the system with various nuclear parameters as important inputs.These classical nuclear reaction studies are dominated by reductionism,focusing on single or local reactions,which corresponds to simple topologies such as star,ring,and chain.The association of nuclear reactions with graph theory shows the importance of studying the nuclear reaction system in the network fashion.2.An improved reaction network mapping method is proposed,and the nuclear reaction system is analyzed from a macro and statistical point of view.Traditional network mapping methods are susceptible to be interfered by “currency particles” or lose important topological information.In this paper,we propose a hybrid network mapping method of reactant-product and multilayer network in the analysis of REACLIB,mapping the nuclides into nodes and reactions into edges which are labeled according to the different particles needed to generate nuclides.There are four types of edges: neutrons,protons,? particles and others.The edge weight corresponds to the reaction rate.The acquired multilayer network is composed of three regular layers(n,p,h)and a relatively more complicated layer(r),showing different structure from those of the real world systems.The metrics defined by the traditional single layer network may not have reasonable physical meaning,and the hybrid network mapping method effectively preserves the key information of the system.It is also found that edge weight evolution along with temperature change helps a relatively regular network to produce complex phenomena.3.The correlation between physical properties and structural characteristics are further found in the nuclear reaction system.From the complex multilayer network point of view,the degree of difference and node overlapping coefficient are defined for the stable nuclide.The stability is about the equilibrium structure in the outbound and inbound of the reaction.Ther-layer contains rich structure information,corresponding to the decomposition and transformation of a nuclide itself.Under lower environment temperature,the node strength and the half-life of unstable nuclide follows a reciprocal relationship.Based on these correlations,some predicted half-life values are given for unidentified nuclides.In addition,considering the correlation between the neutron capture process and r-layer,the path of the r-process is also given based on the degree difference condition.4.The potential topology of the stable island is given,the structure of which is predicted based on the evolution pattern of motifs in the nuclear reaction network.The problems encountered in stable island prediction and the phenomenon of motifs in complex systems is discussed.The regular structure of n,p and h layers are further described with the help of the correlation between motif spatial characteristics and the physical properties,that is,a single kind of motif repeats throughout the layer but decays near magic number 82 and border area.There are several kinds of motifs in the r-layer,but they all belong to the same class.Stable and adjacent non-stable nuclides often differ by the direction of one edge only.Hypotheses of super heavy region are proposed based on motif,combined with stable nuclide network conditions,and the topological prediction of stable nuclides possibly existing in the island of stability is given.The theory of multilayer network as a holistic method displays advantages in the analysis of nuclear reaction system,which is a supplement to classical theories of nuclear physics,and also enriches the research of complex network on reaction systems,promoting the conclusion of a general law.In this study,the macro structure of nuclear reaction system is discussed,discovering the relationship between nuclear data and network structure,thus physical prediction is given to provide new ideas for the exploration of nuclear astrophysical problems. |
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