Two-Scale Scenario Of Rigidity Percolation Of Sticky Particles

The process of amorphous solid packing driven by density increase in an athermal particle system is called Jamming transition,which is a typical amorphous liquid-solid transition.Over the past two decades,significant progress has been made in understand-ing the nature of the Jamming transition by studying the packing of frictionless particles with pure repulsion.Recently,attractive granular systems have also attracted more and more attention,because there are significant differences in some properties between these attractive systems and pure repulsive systems.Through a series of recent work,we have a deeper understanding of the attracting particle system.However,there are still important unresolved questions about the nature of Jamming transitions in attrac-tive particle systems.Previous studies have shown that the Jamming transition of attracting particles has the characteristics of rigidity percolation,but belongs to a new universal class.In this thesis,we foucus on the rigidity percolation of stick particles.We show that it con-tains more surprise to impact and refresh our conventional understanding of percolation.Then we do a comprehensive exploration of sticky particles under quasi-static shear.At the beginning of this thesis,the basic knowledge and theory of continuous phase transition are introduced.Then,the research background and the latest progress of Jam-ming,and percolation are introduced.The algorithms and models used in the computer simulation process are explained.Especially for the FIRE optimization algorithm and pebble game algorithm,which are widely used in this work,we describe the specific process of algorithm implementation in detail.In the study of the rigidity percolation of siticky particles,the distribution of rigid cluster size exhibits discontinuous.Further studies show that the appearance of"dis-continuity" does not imply that the transition is discontinuous.It actually reflects the coexistence of two distinct length scales,and both lengths diverge in the thermodynamic limit.Our proposed two-scale scenario shows that the Jamming transition is a continu-ous phase transition as long as the attraction exists,no matter how weak it is.Based on this image,we introduce a new scaling exponent introduced by two-scale scenario,and then construct a generalized hyperscaling relation.In the study of quasi-static shear of sticky particles,Through a large number of simulation calculations and careful,in-depth analysis,we found that in the density range below the Jamming transition,the connectivity percolation and the rigidity percolation will be formed one after another under the condition of the quasi-static shear.The criti-cal exponent of phase transition and the two-scale phenomenon under quasi-static shear are discussed in detail.Then we observe the evolution of the mechanical and structural parameters in the quasi-static shear process.A structural characterization correspond to phase separation,gelation and shear jammed was found.Finally,the two-dimensional phase diagrams of the strain γ and density Φ of the weakly attractive granular system under quasi-static shear are drawn by synthesizing the obtained information.The rela-tionship between percolation and each phase was established.Finally,we summarize the research contents of this paper,and the future research directions are prospected.