The nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation is analytically investigated by using the formally variable separation approach. New analytical solutions for the governing e...The nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation is analytically investigated by using the formally variable separation approach. New analytical solutions for the governing equation of this system have been obtained for dust acoustic waves in a dust plasma for the first time. We derive exact analytical expressions for the general case of the nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation.展开更多
The everyday fluctuations of temperature and humidity lead to fluctuation of stress on the stones constituting many constructions and produce in long term some kinds of fatigue damage. This paper investigates the comb...The everyday fluctuations of temperature and humidity lead to fluctuation of stress on the stones constituting many constructions and produce in long term some kinds of fatigue damage. This paper investigates the combined role of stone properties variability and environmental conditions on the generation and the amplification of stress variation and fatigue. Thus, the randomness and spatial variability 0fthe mechanical, thermal and hydraulic properties are taken into account in a finite elements model of typical stone wall masonry of Chambord Castle. The quantification of the impact of this spatial variability on the variability of generated stress is performed.展开更多
A bounding surface model incorporating a unified nonlinear strength criterion is proposed.The proposed bounding surface model contains 9 model parameters,which can be determined from the conventional triaxial tests.Th...A bounding surface model incorporating a unified nonlinear strength criterion is proposed.The proposed bounding surface model contains 9 model parameters,which can be determined from the conventional triaxial tests.The bounding surface model can reproduce such behaviours as the strain hardening,the post-peak strain softening,and the volumetric strain contraction and expansion.Based on the comparisons between the predictions and the test results,the proposed strength criterion and model can well reproduce the experimental results of the strength and stress-strain behaviours of rockfill material in three-dimensional stress space.The strength behaviour of rockfill material is summarized as:(a) the failure stress ratio decreases with the initial confining pressure on the meridian plane;(b) the failure deviatoric stress decreases with the Lode angle from 0o to 60o on the deviatoric plane.The stress ratio decreases with increasing one of such factors as the initial void ratio,the intermediate principal stress ratio and the minor principal stress at the same strain when the other factors are given.展开更多
Soil spatial variability is difficult to evaluate due to insufficient test data.An alternative option is estimation by indirect methods such as inverse analysis.In this paper,two examples are presented to demonstrate ...Soil spatial variability is difficult to evaluate due to insufficient test data.An alternative option is estimation by indirect methods such as inverse analysis.In this paper,two examples are presented to demonstrate the capability and accuracy of the probabilistic estimation method to characterize soil spatial variability with displacement responses.The first example is a soil slope subject to a surcharge load,in which the spatially varied field of the elastic modulus is estimated with displacements.The results show that estimations based on horizontal displacements were more accurate than those based on vertical displacements.The accuracy of the estimated field was substantially reduced by increasing variance of elastic modulus.However,the estimation was generally acceptable as the error was not more than 10%,even for the high variance case(COV^l.5).The accuracy of estimation was also affected by the type of covariance function and the correlation length.When the correlation length decreased,the accuracy of estimation was reduced.The second example is a validation of laboratory model tests where a horizontal load was applied on a layered ground.The estimated thicknesses of soil layers were close to those in the real situation,which demonstrates the capacity of the estimation method.展开更多
The microscopic approach is developed for obtaining of the free energy of a superconductor based on direct calculation of the vacuum amplitude.The free energy functional of the spatially inhomogeneous superconductor i...The microscopic approach is developed for obtaining of the free energy of a superconductor based on direct calculation of the vacuum amplitude.The free energy functional of the spatially inhomogeneous superconductor in a magnetic field is obtained with help of the developed approach.The obtained functional is generalization of GinzburgLandau functionals for any temperature,for arbitrary spatial variations of the order parameter and for the nonlocality of a magnetic response and the order parameter.Moreover,the nonlocality of the magnetic response is the consequence of order parameter's nonlocality.The extremals of this functional are considered in the explicit form in the low-and high-temperature limit at the condition of slowness of spatial variations of the order parameter.展开更多
We give estimates of the remainder terms for several conformally-invariant Sobolev-type inequalities on the Heisenberg group. By considering the variations of associated functionals, we give a stability for two dual i...We give estimates of the remainder terms for several conformally-invariant Sobolev-type inequalities on the Heisenberg group. By considering the variations of associated functionals, we give a stability for two dual inequalities: The fractional Sobolev(FS) and Hardy-Littlewood-Sobolev(HLS) inequalities, in terms of distance to the submanifold of extremizers. Then we compare their remainder terms to improve the inequalities in another way. We also compare, in the limit case, the remainder terms of Beckner-Onofri(BO) inequality and its dual logarithmic Hardy-Littlewood-Sobolev(Log-HLS) inequality. Besides, we also list without proof some results for other groups of Iwasawa-type. Our results generalize earlier works on Euclidean spaces of Chen et al.(2013) and Dolbeault and Jankowiak(2014) onto some groups of Heisenberg-type. We worked for "almost"all fractions especially for comparing results, and the stability of HLS is also absolutely new, even for Euclidean case.展开更多
The theoretical model of spatial noise passing through a spatial filter is established in high power laser system under the small signal approximation. The transmission characteristic for a noise signal passing throug...The theoretical model of spatial noise passing through a spatial filter is established in high power laser system under the small signal approximation. The transmission characteristic for a noise signal passing through spatial filters with different magnifications is analyzed by numerical simulation, according to the actual structure of the high power laser system. The results show that the spatial modulation period of low-frequency noise getting through the pinhole will be proportional to the magnification of the spatial filter. When the magnification is less than 1, the safe low-frequency noise will be extruded into the high-frequency region, which is the fast increasing part, and finally develops into the most dangerous part which can damage the optical devices. The conclusion of this research improves the relay imaging theory of a spatial filter and provides an important theoretical basis for a general design of high power laser systems.展开更多
文摘The nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation is analytically investigated by using the formally variable separation approach. New analytical solutions for the governing equation of this system have been obtained for dust acoustic waves in a dust plasma for the first time. We derive exact analytical expressions for the general case of the nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation.
文摘The everyday fluctuations of temperature and humidity lead to fluctuation of stress on the stones constituting many constructions and produce in long term some kinds of fatigue damage. This paper investigates the combined role of stone properties variability and environmental conditions on the generation and the amplification of stress variation and fatigue. Thus, the randomness and spatial variability 0fthe mechanical, thermal and hydraulic properties are taken into account in a finite elements model of typical stone wall masonry of Chambord Castle. The quantification of the impact of this spatial variability on the variability of generated stress is performed.
基金supported by the National Natural Science Foundation of China for Distinguished Young Scholar (Grant No. 50825901)the Public Service Sector R&D Project of Ministry of Water Resource of China(Grant No. 200801014)+1 种基金the Fundamental Research Funds for the Central Universities (Grant No. 2011B14514)Jiangsu Civil Engineering Graduate Center for Innovation and Academic Communication Foundation
文摘A bounding surface model incorporating a unified nonlinear strength criterion is proposed.The proposed bounding surface model contains 9 model parameters,which can be determined from the conventional triaxial tests.The bounding surface model can reproduce such behaviours as the strain hardening,the post-peak strain softening,and the volumetric strain contraction and expansion.Based on the comparisons between the predictions and the test results,the proposed strength criterion and model can well reproduce the experimental results of the strength and stress-strain behaviours of rockfill material in three-dimensional stress space.The strength behaviour of rockfill material is summarized as:(a) the failure stress ratio decreases with the initial confining pressure on the meridian plane;(b) the failure deviatoric stress decreases with the Lode angle from 0o to 60o on the deviatoric plane.The stress ratio decreases with increasing one of such factors as the initial void ratio,the intermediate principal stress ratio and the minor principal stress at the same strain when the other factors are given.
基金the National Natural Science Foundation of China(Nos.51979158,51639008,51679135,and 51422905)the Program of Shanghai Academic Research Leader(No.19XD1421900),China。
文摘Soil spatial variability is difficult to evaluate due to insufficient test data.An alternative option is estimation by indirect methods such as inverse analysis.In this paper,two examples are presented to demonstrate the capability and accuracy of the probabilistic estimation method to characterize soil spatial variability with displacement responses.The first example is a soil slope subject to a surcharge load,in which the spatially varied field of the elastic modulus is estimated with displacements.The results show that estimations based on horizontal displacements were more accurate than those based on vertical displacements.The accuracy of the estimated field was substantially reduced by increasing variance of elastic modulus.However,the estimation was generally acceptable as the error was not more than 10%,even for the high variance case(COV^l.5).The accuracy of estimation was also affected by the type of covariance function and the correlation length.When the correlation length decreased,the accuracy of estimation was reduced.The second example is a validation of laboratory model tests where a horizontal load was applied on a layered ground.The estimated thicknesses of soil layers were close to those in the real situation,which demonstrates the capacity of the estimation method.
文摘The microscopic approach is developed for obtaining of the free energy of a superconductor based on direct calculation of the vacuum amplitude.The free energy functional of the spatially inhomogeneous superconductor in a magnetic field is obtained with help of the developed approach.The obtained functional is generalization of GinzburgLandau functionals for any temperature,for arbitrary spatial variations of the order parameter and for the nonlocality of a magnetic response and the order parameter.Moreover,the nonlocality of the magnetic response is the consequence of order parameter's nonlocality.The extremals of this functional are considered in the explicit form in the low-and high-temperature limit at the condition of slowness of spatial variations of the order parameter.
基金supported by National Natural Science Foundation of China(Grant No.11371036)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.2012000110059)China Scholarship Council(Grant No.201306010009)
文摘We give estimates of the remainder terms for several conformally-invariant Sobolev-type inequalities on the Heisenberg group. By considering the variations of associated functionals, we give a stability for two dual inequalities: The fractional Sobolev(FS) and Hardy-Littlewood-Sobolev(HLS) inequalities, in terms of distance to the submanifold of extremizers. Then we compare their remainder terms to improve the inequalities in another way. We also compare, in the limit case, the remainder terms of Beckner-Onofri(BO) inequality and its dual logarithmic Hardy-Littlewood-Sobolev(Log-HLS) inequality. Besides, we also list without proof some results for other groups of Iwasawa-type. Our results generalize earlier works on Euclidean spaces of Chen et al.(2013) and Dolbeault and Jankowiak(2014) onto some groups of Heisenberg-type. We worked for "almost"all fractions especially for comparing results, and the stability of HLS is also absolutely new, even for Euclidean case.
文摘The theoretical model of spatial noise passing through a spatial filter is established in high power laser system under the small signal approximation. The transmission characteristic for a noise signal passing through spatial filters with different magnifications is analyzed by numerical simulation, according to the actual structure of the high power laser system. The results show that the spatial modulation period of low-frequency noise getting through the pinhole will be proportional to the magnification of the spatial filter. When the magnification is less than 1, the safe low-frequency noise will be extruded into the high-frequency region, which is the fast increasing part, and finally develops into the most dangerous part which can damage the optical devices. The conclusion of this research improves the relay imaging theory of a spatial filter and provides an important theoretical basis for a general design of high power laser systems.