Based on the molecular theory of non-linear viscoelasticity with constrained entanglements in polymer melts, the material functions in simple shear flow were formulated, the theoretical relations between. eta((gamma) ...Based on the molecular theory of non-linear viscoelasticity with constrained entanglements in polymer melts, the material functions in simple shear flow were formulated, the theoretical relations between. eta((gamma) over dot), psi (10)((gamma) over dot) and shear rate ((gamma) over dot), and topologically constrained dimension number n ' and a were derived. Linear viscoelastic parameters (eta (0) and G(N)(0)) and topologically constrained dimension number (n ' a and <(<upsilon>)over bar>) as a function of the primary molecular weight (M-n), molecular weight between entanglements (M-C) and the entanglement sites sequence distribution in polymer chain were determined. A new method for determination of viscoelastic parameters (eta (0), psi (10), G(N)(0) and J(e)(0)), topologically constrained dimension number (n ', a and v) and molecular weight (M-n, M-c and M-e) from the shear flow measurements was proposed. It was used to determine those parameters and structures of HDPE, making a good agreement between these values and those obtained by other methods. The agreement affords a quantitative verification for the molecular theory of nonlinear viscoelasticity with constrained entanglement in polymer melts.展开更多
Recurrent neural networks (RNNs) have been heavily used in applications relying on sequence data such as time series and natural languages. As a matter of fact, their behaviors lack rigorous quality assurance due to t...Recurrent neural networks (RNNs) have been heavily used in applications relying on sequence data such as time series and natural languages. As a matter of fact, their behaviors lack rigorous quality assurance due to the black-box nature of deep learning. It is an urgent and challenging task to formally reason about the behaviors of RNNs. To this end, we first present an extension of linear-time temporal logic to reason about properties with respect to RNNs, such as local robustness, reachability, and some temporal properties. Based on the proposed logic, we formalize the verification obligation as a Hoare-like triple, from both qualitative and quantitative perspectives. The former concerns whether all the outputs resulting from the inputs fulfilling the pre-condition satisfy the post-condition, whereas the latter is to compute the probability that the post-condition is satisfied on the premise that the inputs fulfill the pre-condition. To tackle these problems, we develop a systematic verification framework, mainly based on polyhedron propagation, dimension-preserving abstraction, and the Monte Carlo sampling. We also implement our algorithm with a prototype tool and conduct experiments to demonstrate its feasibility and efficiency.展开更多
The natural formation and development of urban agglomerations is a process in which core cities continue to unite their neighboring cities to enhance sustainability for their own sustainable development.The upgrade me...The natural formation and development of urban agglomerations is a process in which core cities continue to unite their neighboring cities to enhance sustainability for their own sustainable development.The upgrade mechanism of sustainable development urban agglomeration is a nonlinear composite upgrade curve that is a function of time,increasing with the number of cities.In this paper,the sustainable upgrade function curve,upgrade rate,and upgrade speed of urban agglomerations were solved using a geometrical derivation,and the index system for measuring the upgrade capability of sustainable development of urban agglomerations was established.The dynamic change in economic sustainable upgrade capability,social sustainable upgrade capability,environmental sustainable upgrade capability,and comprehensive sustainable upgrade capability of a Beijing-Tianjin-Hebei urban agglomeration from 2000 to 2015 was measured by technique for order preference by similarity to an ideal solution and a grey correlation method,and a comprehensive,intercity unite strength model and a unite threshold calculation method for urban agglomerations were established.The research shows that the economic sustainable upgrade capability,social sustainable upgrade capability,environmental sustainable upgrade capability,and comprehensive sustainable upgrade capability of the Beijing-Tianjin-Hebei urban agglomeration all show a wave-like rising trend.The average annual upgrade speeds during 2000-2015 are,respectively,2.4%.1.67%,1.1%,and 1.74%,with the intercity comprehensive unite strength of urban agglomerations maintaining a general increase;but there is a limit to the joint threshold.From 2000 to 2015,as the core city of the Beijing-Tianjin-Hebei urban agglomeration,Beijing,to enhance its sustainable upgrade capability,jointly developed with Tianjin,Langfang,and Baoding before 2000,Tangshan in 2002,Cangzhou in 2009,Zhangjiakou and Shijiazhuang in 2012,and Chengde in 2014.By 2015,the comprehensive unite strength between Beijing and four cities(Handan,Qinhuangdao,Hengshui,and Xingtai) was still lower than the unite threshold of 6.14.These four cities are relatively far from Beijing,and offer no substantial contribution to the sustainable upgrade capability of Beijing.Through multiple fittings of the upgrade curve using the long-term sequence index of the comprehensive sustainable upgrade capability of Beijing(the core city of the Beijing-Tianjin-Hebei urban agglomeration) from 2000 to 2015,it was found that the simulated curve of the comprehensive sustainable upgrade function of the agglomeration was very similar to the curve of the comprehensive sustainable upgrade capability,which indicates that the simulation results are satisfactory.The future comprehensive sustainable upgrade capability of the agglomeration can be analyzed and predicted by the comprehensive sustainable upgrade function model.This study provides quantitative decision-supporting evidence for promoting the coordinated development of the Beijing-TianjinHebei urban agglomeration and provides theoretical guidance and algorithms for determining the number of cities joined with the sustainable development of national urban agglomerations.展开更多
基金The authors gratefully a.cknowledge financial supportfrom th6 Natiol-al Natural Science Foundatiol- of CI-h-a. The number of
文摘Based on the molecular theory of non-linear viscoelasticity with constrained entanglements in polymer melts, the material functions in simple shear flow were formulated, the theoretical relations between. eta((gamma) over dot), psi (10)((gamma) over dot) and shear rate ((gamma) over dot), and topologically constrained dimension number n ' and a were derived. Linear viscoelastic parameters (eta (0) and G(N)(0)) and topologically constrained dimension number (n ' a and <(<upsilon>)over bar>) as a function of the primary molecular weight (M-n), molecular weight between entanglements (M-C) and the entanglement sites sequence distribution in polymer chain were determined. A new method for determination of viscoelastic parameters (eta (0), psi (10), G(N)(0) and J(e)(0)), topologically constrained dimension number (n ', a and v) and molecular weight (M-n, M-c and M-e) from the shear flow measurements was proposed. It was used to determine those parameters and structures of HDPE, making a good agreement between these values and those obtained by other methods. The agreement affords a quantitative verification for the molecular theory of nonlinear viscoelasticity with constrained entanglement in polymer melts.
基金supported by the National Natural Science Foundation of China under Grant Nos.61872371,62032024,and U19A2062the Open Fund from the State Key Laboratory of High Performance Computing of China(HPCL)under Grant No.202001-07.
文摘Recurrent neural networks (RNNs) have been heavily used in applications relying on sequence data such as time series and natural languages. As a matter of fact, their behaviors lack rigorous quality assurance due to the black-box nature of deep learning. It is an urgent and challenging task to formally reason about the behaviors of RNNs. To this end, we first present an extension of linear-time temporal logic to reason about properties with respect to RNNs, such as local robustness, reachability, and some temporal properties. Based on the proposed logic, we formalize the verification obligation as a Hoare-like triple, from both qualitative and quantitative perspectives. The former concerns whether all the outputs resulting from the inputs fulfilling the pre-condition satisfy the post-condition, whereas the latter is to compute the probability that the post-condition is satisfied on the premise that the inputs fulfill the pre-condition. To tackle these problems, we develop a systematic verification framework, mainly based on polyhedron propagation, dimension-preserving abstraction, and the Monte Carlo sampling. We also implement our algorithm with a prototype tool and conduct experiments to demonstrate its feasibility and efficiency.
基金supported by the Major Program of National Natural Science Foundation of China(Grant Nos.41590840&41590842)
文摘The natural formation and development of urban agglomerations is a process in which core cities continue to unite their neighboring cities to enhance sustainability for their own sustainable development.The upgrade mechanism of sustainable development urban agglomeration is a nonlinear composite upgrade curve that is a function of time,increasing with the number of cities.In this paper,the sustainable upgrade function curve,upgrade rate,and upgrade speed of urban agglomerations were solved using a geometrical derivation,and the index system for measuring the upgrade capability of sustainable development of urban agglomerations was established.The dynamic change in economic sustainable upgrade capability,social sustainable upgrade capability,environmental sustainable upgrade capability,and comprehensive sustainable upgrade capability of a Beijing-Tianjin-Hebei urban agglomeration from 2000 to 2015 was measured by technique for order preference by similarity to an ideal solution and a grey correlation method,and a comprehensive,intercity unite strength model and a unite threshold calculation method for urban agglomerations were established.The research shows that the economic sustainable upgrade capability,social sustainable upgrade capability,environmental sustainable upgrade capability,and comprehensive sustainable upgrade capability of the Beijing-Tianjin-Hebei urban agglomeration all show a wave-like rising trend.The average annual upgrade speeds during 2000-2015 are,respectively,2.4%.1.67%,1.1%,and 1.74%,with the intercity comprehensive unite strength of urban agglomerations maintaining a general increase;but there is a limit to the joint threshold.From 2000 to 2015,as the core city of the Beijing-Tianjin-Hebei urban agglomeration,Beijing,to enhance its sustainable upgrade capability,jointly developed with Tianjin,Langfang,and Baoding before 2000,Tangshan in 2002,Cangzhou in 2009,Zhangjiakou and Shijiazhuang in 2012,and Chengde in 2014.By 2015,the comprehensive unite strength between Beijing and four cities(Handan,Qinhuangdao,Hengshui,and Xingtai) was still lower than the unite threshold of 6.14.These four cities are relatively far from Beijing,and offer no substantial contribution to the sustainable upgrade capability of Beijing.Through multiple fittings of the upgrade curve using the long-term sequence index of the comprehensive sustainable upgrade capability of Beijing(the core city of the Beijing-Tianjin-Hebei urban agglomeration) from 2000 to 2015,it was found that the simulated curve of the comprehensive sustainable upgrade function of the agglomeration was very similar to the curve of the comprehensive sustainable upgrade capability,which indicates that the simulation results are satisfactory.The future comprehensive sustainable upgrade capability of the agglomeration can be analyzed and predicted by the comprehensive sustainable upgrade function model.This study provides quantitative decision-supporting evidence for promoting the coordinated development of the Beijing-TianjinHebei urban agglomeration and provides theoretical guidance and algorithms for determining the number of cities joined with the sustainable development of national urban agglomerations.
