The paper deals with factorial experimental design models decoding.For the ease of calculation of the experimental mathematical models,it is convenient first to code the independent variables.When selecting independen...The paper deals with factorial experimental design models decoding.For the ease of calculation of the experimental mathematical models,it is convenient first to code the independent variables.When selecting independent variables,it is necessary to take into account the range covered by each.A wide range of choices of different variables is presented in this paper.After calculating the regression model,its variables must be returned to their original values for the model to be easy recognized and represented.In the paper,the procedures of simple first order models,with interactions and with second order models,are presented,which could be a very complicated process.Models without and with the mutual influence of independent variables differ.The encoding and decoding procedure on a model with two independent first-order parameters is presented in details.Also,the procedure of model decoding is presented in the experimental surface roughness parameters models’determination,in the face milling machining process,using the first and second order model central compositional experimental design.The simple calculation procedure is recommended in the case study.Also,a large number of examples using mathematical models obtained on the basis of the presented methodology are presented throughout the paper.展开更多
Hydrodynamic models fail to describe the near-equalυ_(3)/υ_(2)ratio observed in ultra-central heavy-ion collisions,despite their success in other centrality classes.This failure can not be resolved by adjusting the ...Hydrodynamic models fail to describe the near-equalυ_(3)/υ_(2)ratio observed in ultra-central heavy-ion collisions,despite their success in other centrality classes.This failure can not be resolved by adjusting the shear viscous coefficient,as shear viscosity suppresses higher-order anisotropic flows more strongly,leading to an underestimation ofυ_(3)whenυ_(2)matches experimental data.To address this issue,we explore two initial-state modifications to resolve this puzzle:(1)impose a minimum distance between nucleons to simulate the homogenization effect arising from short-range nucleon–nucleon repulsion;and(2)introduce sub-nucleonic structures,specifically“hot spots”within protons,to provide a more refined description of initial-state fluctuations.Using TRENTo initial conditions and 3+1D viscous hydrodynamic model CLVisc,both approaches significantly lower geometric eccentricity,reduce required viscosity,and narrow theυ_(2)-υ_(3)gap in ultra-central collisions.Our results implicate initial-state nuclear and sub-nucleon structures as critical factors in addressing this puzzle.Resolving it would advance nuclear structure studies and improve precision in extracting quark–gluon plasma(QGP)transport coefficients(e.g.,shear viscosity),bridging microscopic nuclear features to macroscopic QGP properties.展开更多
文摘The paper deals with factorial experimental design models decoding.For the ease of calculation of the experimental mathematical models,it is convenient first to code the independent variables.When selecting independent variables,it is necessary to take into account the range covered by each.A wide range of choices of different variables is presented in this paper.After calculating the regression model,its variables must be returned to their original values for the model to be easy recognized and represented.In the paper,the procedures of simple first order models,with interactions and with second order models,are presented,which could be a very complicated process.Models without and with the mutual influence of independent variables differ.The encoding and decoding procedure on a model with two independent first-order parameters is presented in details.Also,the procedure of model decoding is presented in the experimental surface roughness parameters models’determination,in the face milling machining process,using the first and second order model central compositional experimental design.The simple calculation procedure is recommended in the case study.Also,a large number of examples using mathematical models obtained on the basis of the presented methodology are presented throughout the paper.
基金supported by the National Natural Science Foundation of China(Grant Nos.12075098,12535010,12435009,and 1193507)the Guang-dong MPBAR(Grant No.2020B0301030008)。
文摘Hydrodynamic models fail to describe the near-equalυ_(3)/υ_(2)ratio observed in ultra-central heavy-ion collisions,despite their success in other centrality classes.This failure can not be resolved by adjusting the shear viscous coefficient,as shear viscosity suppresses higher-order anisotropic flows more strongly,leading to an underestimation ofυ_(3)whenυ_(2)matches experimental data.To address this issue,we explore two initial-state modifications to resolve this puzzle:(1)impose a minimum distance between nucleons to simulate the homogenization effect arising from short-range nucleon–nucleon repulsion;and(2)introduce sub-nucleonic structures,specifically“hot spots”within protons,to provide a more refined description of initial-state fluctuations.Using TRENTo initial conditions and 3+1D viscous hydrodynamic model CLVisc,both approaches significantly lower geometric eccentricity,reduce required viscosity,and narrow theυ_(2)-υ_(3)gap in ultra-central collisions.Our results implicate initial-state nuclear and sub-nucleon structures as critical factors in addressing this puzzle.Resolving it would advance nuclear structure studies and improve precision in extracting quark–gluon plasma(QGP)transport coefficients(e.g.,shear viscosity),bridging microscopic nuclear features to macroscopic QGP properties.
