Based on the uniaxial compression creep experiments conducted on bauxite sandstone obtained from Sanmenxia,typical creep experiment curves were obtained.From the characteristics of strain component of creep curves,the...Based on the uniaxial compression creep experiments conducted on bauxite sandstone obtained from Sanmenxia,typical creep experiment curves were obtained.From the characteristics of strain component of creep curves,the creep strain is composed of instantaneous elastic strain,ε（me）,instantaneous plastic strain,ε（mp）,viscoelastic strain,ε（ce）,and viscoplastic strain,ε（cp）.Based on the characteristics of instantaneous plastic strain,a new element of instantaneous plastic rheology was introduced,instantaneous plastic modulus was defined,and the modified Burgers model was established.Then identification of direct screening method in this model was completed.According to the mechanical properties of rheological elements,one- and three-dimensional creep equations in different stress levels were obtained.One-dimensional model parameters were identified by the method of least squares,and in the process of computation,Gauss-Newton iteration method was applied.Finally,by fitting the experimental curves,the correctness of direct method model was verified,then the examination of posterior exclusive method of the model was accomplished.The results showed that in the improved Burgers models,the rheological characteristics of sandstone are embodied properly,microscopic analysis of creep curves is also achieved,and the correctness of comprehensive identification method of rheological model is verified.展开更多
We introduce a general multi-defender Stackelberg security game where multiple independent defenders jointly protect a same set of targets from being attacked by a common attacker.In the game,Strong Stackelberg Equili...We introduce a general multi-defender Stackelberg security game where multiple independent defenders jointly protect a same set of targets from being attacked by a common attacker.In the game,Strong Stackelberg Equilibrium is fundamentally problematic,because the notion of‘break-ing ties in defender’s favour’is no longer well defined,as we must specify which defender will receive the favour.To address this issue,we define a new equilibrium concept under a newly defined tie-breaking rule.We characterise Logit Stackelberg Multi-Defender Equilibrium,corre-sponding to a logit tie-breaking rule,as well as an equivalent Nash Equilibrium among defenders,and exhibit algorithms for computing the equilibrium solutions.We find that Logit Stackelberg Multi-Defender Equilibrium and its’equivalent Nash Equilibrium may not exist,which motivates us to find an approximate equilibrium.We design a revised exclusion algorithm to find the approximateε-Nash Equilibrium in which no defender gains more thanεby deviating.展开更多
基金Projects (51174228,51274249) supported by the National Natural Science Foundation of China
文摘Based on the uniaxial compression creep experiments conducted on bauxite sandstone obtained from Sanmenxia,typical creep experiment curves were obtained.From the characteristics of strain component of creep curves,the creep strain is composed of instantaneous elastic strain,ε（me）,instantaneous plastic strain,ε（mp）,viscoelastic strain,ε（ce）,and viscoplastic strain,ε（cp）.Based on the characteristics of instantaneous plastic strain,a new element of instantaneous plastic rheology was introduced,instantaneous plastic modulus was defined,and the modified Burgers model was established.Then identification of direct screening method in this model was completed.According to the mechanical properties of rheological elements,one- and three-dimensional creep equations in different stress levels were obtained.One-dimensional model parameters were identified by the method of least squares,and in the process of computation,Gauss-Newton iteration method was applied.Finally,by fitting the experimental curves,the correctness of direct method model was verified,then the examination of posterior exclusive method of the model was accomplished.The results showed that in the improved Burgers models,the rheological characteristics of sandstone are embodied properly,microscopic analysis of creep curves is also achieved,and the correctness of comprehensive identification method of rheological model is verified.
基金supported by the National Natural Science Foun-dation of China[grant numbers 61572095,61877007]Department of Science and Technology of Shanxi Province[grant numbers 20210302124303,202203021222251].
文摘We introduce a general multi-defender Stackelberg security game where multiple independent defenders jointly protect a same set of targets from being attacked by a common attacker.In the game,Strong Stackelberg Equilibrium is fundamentally problematic,because the notion of‘break-ing ties in defender’s favour’is no longer well defined,as we must specify which defender will receive the favour.To address this issue,we define a new equilibrium concept under a newly defined tie-breaking rule.We characterise Logit Stackelberg Multi-Defender Equilibrium,corre-sponding to a logit tie-breaking rule,as well as an equivalent Nash Equilibrium among defenders,and exhibit algorithms for computing the equilibrium solutions.We find that Logit Stackelberg Multi-Defender Equilibrium and its’equivalent Nash Equilibrium may not exist,which motivates us to find an approximate equilibrium.We design a revised exclusion algorithm to find the approximateε-Nash Equilibrium in which no defender gains more thanεby deviating.
