This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of norm...This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.展开更多
Detonation performance is crucial for evaluating the power of high explosives(HEs),and the equation of state(EOS)that accurately describes the high-temperature,high-pressure,and high-temperature,medium-pressure states...Detonation performance is crucial for evaluating the power of high explosives(HEs),and the equation of state(EOS)that accurately describes the high-temperature,high-pressure,and high-temperature,medium-pressure states of detonation products is key to assessing the damage efficiency of these energetic materials.This article examines the limitations of the VLW EOS in representing the thermodynamic states of explosive detonation gas products under high-temperature and medium-to high-pressure conditions.A new gas EOS for detonation products,called VHL(Virial-Han-Long),is proposed.The accuracy of VHL in describing gas states under high-temperature and medium-to high-pressure conditions is verified,and its performance in evaluating explosive detonation and working capabilities is explored.The results demonstrate that VHL exhibits high precision in calculating detonation performance.Subsequently,the detonation performance of three new HEs(ICM-101,ONC,and TNAZ)was calculated and compared to traditional HEs(TATB,CL-20,and HMX).The results indicate that ONC has superior detonation performance compared to the other explosives,while ICM-101 shows a detonation velocity similar to CL-20 but with slightly lower detonation pressure.The detonation characteristics of TNAZ are comparable to those of the standard HE HMX.From the perspective of products,considering the comprehensive work performance(mechanical work and detonation heat),both ONC and ICM-101demonstrate relatively superior performance.展开更多
Adopting the classical theory of hydrocodes,the constitutive relations of concretes are separated into an equation of state(EoS)which describes the volumetric behavior of concrete material and a strength model which d...Adopting the classical theory of hydrocodes,the constitutive relations of concretes are separated into an equation of state(EoS)which describes the volumetric behavior of concrete material and a strength model which depicts the shear properties of concrete.The experiments on the EoS of concrete is always challenging due to the technical difficulties and equipment limitations,especially for the specimen size effect on the EoS.Although some researchers investigate the shock properties of concretes by fly-plate impact tests,the specimens used in their tests are usually in one size.In this paper,the fly-plate impact tests on concrete specimens with different sizes are performed to investigate the size effect on the shock properties of concrete materials.The mechanical background of the size effect on the shock properties are revealed,which is related to the lateral rarefaction effect and the deviatoric stress produced in the specimen.According to the tests results,the modified EoS considering the size effect on the shock properties of concrete are proposed,which the bulk modulus of concrete is unpredicted by up to 20% if size effects are not accounted for.展开更多
The fluid variational theory and effective one-component model have been used to calculate the Hugoniot equation of state （EOS） of fluid He, D2, and He+D2 mixtures with different He:D2 compositions under high pressu...The fluid variational theory and effective one-component model have been used to calculate the Hugoniot equation of state （EOS） of fluid He, D2, and He+D2 mixtures with different He:D2 compositions under high pressures and temperatures. An examination of the confidence of above computation is performed by comparing experiment and calculation, in which the similar calculation procedure used for He+D2 is adopted, of He and D2 each, since no experimental data are available to conduct this kind of comparison. Good agreement in both comparisons is found. This fact may be looked as if an indirect positive verification of calculation procedure used here at least in the pressure and temperature domain covered by the experimental data of He and D2 used for comparison, numerically nearly up to 35 GPa and 105K.展开更多
The relationship between the technique by state- dependent Riccati equations （SDRE） and Hamilton-Jacobi-lsaacs （HJI） equations for nonlinear H∞ control design is investigated. By establishing the Lyapunov matrix ...The relationship between the technique by state- dependent Riccati equations （SDRE） and Hamilton-Jacobi-lsaacs （HJI） equations for nonlinear H∞ control design is investigated. By establishing the Lyapunov matrix equations for partial derivates of the solution of the SDREs and introducing symmetry measure for some related matrices, a method is proposed for examining whether the SDRE method admits a global optimal control equiva- lent to that solved by the HJI equation method. Two examples with simulation are given to illustrate the method is effective.展开更多
Thermodynamic calculation is the theoretical basis for the study of initiation and detonation,as well as the prerequisite for forecasting the detonation performance of unknown explosives.Based on the VLWR(Virial-Wu)th...Thermodynamic calculation is the theoretical basis for the study of initiation and detonation,as well as the prerequisite for forecasting the detonation performance of unknown explosives.Based on the VLWR(Virial-Wu)thermodynamic code,this paper introduced the universal solid equation of state(EOS)VINET.In order to truly reflect the compressibility of nanocarbon under the extremely high-temperature and high-pressure environment in detonation,an SVM(support vector machine)was utilized to optimize the input parameters of carbon.The detonation performance of several explosives with different densities was calculated by the optimized universal EOS,and the results show that the thermodynamic code coupled with the universal solid EOS VINET can predict the detonation performance parameters of explosives well.To investigate the application of the thermodynamic code with the improved VINET EOS in the working capacity of explosives,the interrelationship between pressure P-particle velocity u and pressure P-volume V were computed for the detonation products of TNT and HMX-based PBX(HMX:binder:insensitive agent=95:4.3:0.7)in the CJ isentropic state.A universal curve proposed by Cooper was used to compared the computed isentropic state,where the ratio of pressure to CJ state were plotted against the ratio of velocity to CJ state.The parameters of the JWL(Jones-Wilkins-Lee)EOS for detonation products were obtained by fitting the P-V curve.The cylinder tests of TNT and HMX-based PBX were numerically simulated using the LS-DYNA,it is verified that,within a certain range,the improved algorithm has superiority in describing the working capacity of explosives.展开更多
Based on the structural characteristics of the double-differenced normal equation, a new method was proposed to resolve the ambiguity float solution through a selection of parameter weights to construct an appropriate...Based on the structural characteristics of the double-differenced normal equation, a new method was proposed to resolve the ambiguity float solution through a selection of parameter weights to construct an appropriate regularized matrix, and a singular decomposition method was used to generate regularization parameters. Numerical test results suggest that the regularized ambiguity float solution is more stable and reliable than the least-squares float solution. The mean square error matrix of the new method possesses a lower correlation than the variancecovariance matrix of the least-squares estimation. The size of the ambiguity search space is reduced and the search efficiency is improved. The success rate of the integer ambiguity searching process is improved significantly when the ambiguity resolution by using constraint equation method is used to determine the correct ambiguity integervector. The ambiguity resolution by using constraint equation method requires an initial input of the ambiguity float solution candidates which are obtained from the LAMBDA method in the new method. In addition, the observation time required to fix reliable integer ambiguities can he significantly reduced.展开更多
风电大规模并网导致系统惯量严重降低,恶化了系统的频率稳定性。针对上述问题,该文结合非线性预测理论以及扩张状态观测理论(extended state observer,ESO)提出双馈风机参与电网频率调节的短期频率支撑方法。首先,建立与系统频率偏差和...风电大规模并网导致系统惯量严重降低,恶化了系统的频率稳定性。针对上述问题,该文结合非线性预测理论以及扩张状态观测理论(extended state observer,ESO)提出双馈风机参与电网频率调节的短期频率支撑方法。首先,建立与系统频率偏差和风机转速相关的目标状态方程,并计算不同控制目标量对应的预测阶;其次,根据非线性预测理论计算预测矩阵,对未来时刻状态跟踪误差进行预测,并求得非线性控制律;最后,引入扩张状态观测器对非线性控制律中的复杂李导数运算进行观测,减轻控制律所需的计算负担。通过MATLAB/SIMULINK搭建含风电系统进行仿真验证,结果表明,所提方法有效地改善了电网的频率响应,并且无需单独设计转速恢复环节,能够实现风机转速的自恢复。展开更多
基金Supported by National Natural Science Foundation of China(11671403,11671236)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.
基金supported by the National Natural Science Foundation of China(Gant Nos.11372291 and 11902298)。
文摘Detonation performance is crucial for evaluating the power of high explosives(HEs),and the equation of state(EOS)that accurately describes the high-temperature,high-pressure,and high-temperature,medium-pressure states of detonation products is key to assessing the damage efficiency of these energetic materials.This article examines the limitations of the VLW EOS in representing the thermodynamic states of explosive detonation gas products under high-temperature and medium-to high-pressure conditions.A new gas EOS for detonation products,called VHL(Virial-Han-Long),is proposed.The accuracy of VHL in describing gas states under high-temperature and medium-to high-pressure conditions is verified,and its performance in evaluating explosive detonation and working capabilities is explored.The results demonstrate that VHL exhibits high precision in calculating detonation performance.Subsequently,the detonation performance of three new HEs(ICM-101,ONC,and TNAZ)was calculated and compared to traditional HEs(TATB,CL-20,and HMX).The results indicate that ONC has superior detonation performance compared to the other explosives,while ICM-101 shows a detonation velocity similar to CL-20 but with slightly lower detonation pressure.The detonation characteristics of TNAZ are comparable to those of the standard HE HMX.From the perspective of products,considering the comprehensive work performance(mechanical work and detonation heat),both ONC and ICM-101demonstrate relatively superior performance.
基金supported by the National Natural Science Foundation of China[Grant Nos.51938011 and 51908405]Australian Research Council。
文摘Adopting the classical theory of hydrocodes,the constitutive relations of concretes are separated into an equation of state(EoS)which describes the volumetric behavior of concrete material and a strength model which depicts the shear properties of concrete.The experiments on the EoS of concrete is always challenging due to the technical difficulties and equipment limitations,especially for the specimen size effect on the EoS.Although some researchers investigate the shock properties of concretes by fly-plate impact tests,the specimens used in their tests are usually in one size.In this paper,the fly-plate impact tests on concrete specimens with different sizes are performed to investigate the size effect on the shock properties of concrete materials.The mechanical background of the size effect on the shock properties are revealed,which is related to the lateral rarefaction effect and the deviatoric stress produced in the specimen.According to the tests results,the modified EoS considering the size effect on the shock properties of concrete are proposed,which the bulk modulus of concrete is unpredicted by up to 20% if size effects are not accounted for.
文摘The fluid variational theory and effective one-component model have been used to calculate the Hugoniot equation of state （EOS） of fluid He, D2, and He+D2 mixtures with different He:D2 compositions under high pressures and temperatures. An examination of the confidence of above computation is performed by comparing experiment and calculation, in which the similar calculation procedure used for He+D2 is adopted, of He and D2 each, since no experimental data are available to conduct this kind of comparison. Good agreement in both comparisons is found. This fact may be looked as if an indirect positive verification of calculation procedure used here at least in the pressure and temperature domain covered by the experimental data of He and D2 used for comparison, numerically nearly up to 35 GPa and 105K.
基金supported by the National Natural Science Foundation of China(60874114)
文摘The relationship between the technique by state- dependent Riccati equations （SDRE） and Hamilton-Jacobi-lsaacs （HJI） equations for nonlinear H∞ control design is investigated. By establishing the Lyapunov matrix equations for partial derivates of the solution of the SDREs and introducing symmetry measure for some related matrices, a method is proposed for examining whether the SDRE method admits a global optimal control equiva- lent to that solved by the HJI equation method. Two examples with simulation are given to illustrate the method is effective.
基金the financial support from the National Natural Science Foundation of China(No.11902298)the National Key Research and Development Program of China(No.2017YFC0804701)。
文摘Thermodynamic calculation is the theoretical basis for the study of initiation and detonation,as well as the prerequisite for forecasting the detonation performance of unknown explosives.Based on the VLWR(Virial-Wu)thermodynamic code,this paper introduced the universal solid equation of state(EOS)VINET.In order to truly reflect the compressibility of nanocarbon under the extremely high-temperature and high-pressure environment in detonation,an SVM(support vector machine)was utilized to optimize the input parameters of carbon.The detonation performance of several explosives with different densities was calculated by the optimized universal EOS,and the results show that the thermodynamic code coupled with the universal solid EOS VINET can predict the detonation performance parameters of explosives well.To investigate the application of the thermodynamic code with the improved VINET EOS in the working capacity of explosives,the interrelationship between pressure P-particle velocity u and pressure P-volume V were computed for the detonation products of TNT and HMX-based PBX(HMX:binder:insensitive agent=95:4.3:0.7)in the CJ isentropic state.A universal curve proposed by Cooper was used to compared the computed isentropic state,where the ratio of pressure to CJ state were plotted against the ratio of velocity to CJ state.The parameters of the JWL(Jones-Wilkins-Lee)EOS for detonation products were obtained by fitting the P-V curve.The cylinder tests of TNT and HMX-based PBX were numerically simulated using the LS-DYNA,it is verified that,within a certain range,the improved algorithm has superiority in describing the working capacity of explosives.
文摘Based on the structural characteristics of the double-differenced normal equation, a new method was proposed to resolve the ambiguity float solution through a selection of parameter weights to construct an appropriate regularized matrix, and a singular decomposition method was used to generate regularization parameters. Numerical test results suggest that the regularized ambiguity float solution is more stable and reliable than the least-squares float solution. The mean square error matrix of the new method possesses a lower correlation than the variancecovariance matrix of the least-squares estimation. The size of the ambiguity search space is reduced and the search efficiency is improved. The success rate of the integer ambiguity searching process is improved significantly when the ambiguity resolution by using constraint equation method is used to determine the correct ambiguity integervector. The ambiguity resolution by using constraint equation method requires an initial input of the ambiguity float solution candidates which are obtained from the LAMBDA method in the new method. In addition, the observation time required to fix reliable integer ambiguities can he significantly reduced.
文摘风电大规模并网导致系统惯量严重降低,恶化了系统的频率稳定性。针对上述问题,该文结合非线性预测理论以及扩张状态观测理论(extended state observer,ESO)提出双馈风机参与电网频率调节的短期频率支撑方法。首先,建立与系统频率偏差和风机转速相关的目标状态方程,并计算不同控制目标量对应的预测阶;其次,根据非线性预测理论计算预测矩阵,对未来时刻状态跟踪误差进行预测,并求得非线性控制律;最后,引入扩张状态观测器对非线性控制律中的复杂李导数运算进行观测,减轻控制律所需的计算负担。通过MATLAB/SIMULINK搭建含风电系统进行仿真验证,结果表明,所提方法有效地改善了电网的频率响应,并且无需单独设计转速恢复环节,能够实现风机转速的自恢复。
