In the present paper,we consider the nonlocal Kirchhoff problem-(ε^2a+εb∫|■u|^2)Δu+u=Q(x)u^p,u>0 in R^3,,where a,b>0,1<p<5 andε>0 is a parameter.Under some assumptions on Q(x),we show the existenc...In the present paper,we consider the nonlocal Kirchhoff problem-(ε^2a+εb∫|■u|^2)Δu+u=Q(x)u^p,u>0 in R^3,,where a,b>0,1<p<5 andε>0 is a parameter.Under some assumptions on Q(x),we show the existence and local uniqueness of positive multi-peak solutions by LyapunovSchmidt reduction method and the local Pohozaev identity method,respectly.展开更多
A new method for quantitative phase analysis is proposed by using X-ray diffraction multi-peak match intensity ratio. This method can obtain the multi-peak match intensity ratio among each phase in the mixture sample ...A new method for quantitative phase analysis is proposed by using X-ray diffraction multi-peak match intensity ratio. This method can obtain the multi-peak match intensity ratio among each phase in the mixture sample by using all diffraction peak data in the mixture sample X-ray diffraction spectrum and combining the relative intensity distribution data of each phase standard peak in JCPDS card to carry on the least square method regression analysis. It is benefit to improve the precision of quantitative phase analysis that the given single line ratio which is usually adopted is taken the place of the multi-peak match intensity ratio and is used in X-ray diffraction quantitative phase analysis of the mixture sample. By analyzing four-group mixture sample, adopting multi-peak match intensity ratio and X-ray diffraction quantitative phase analysis principle of combining the adiabatic and matrix flushing method, it is tested that the experimental results are identical with theory.展开更多
Absorption and refraction of the inner transition F2 ←→F3 of the closed four level N-type atom have been investigated under a weak field. The outer transitions F1←→F3 and F2←→F4 are resonantly interacted with dr...Absorption and refraction of the inner transition F2 ←→F3 of the closed four level N-type atom have been investigated under a weak field. The outer transitions F1←→F3 and F2←→F4 are resonantly interacted with drive field with frequency ωc and Rabi frequency Ωc, and saturation field with ωs and Ωs, respectively. For the suitable Rabi frequencies Ωc and Ωs, we obtain the Mellow absorption spectrum of probe field. The reason is that the drive field excites the atom to the upper level F3 and simultaneously the saturation field takes the atom out of the lower level F2, leading to the stimulated emission. Meanwhile, due to the dynamic energy splitting induced by the drive and saturation fields, the two- and four-peaked absorption spectra are observed. At the zero off-resonance detuning of probe field, we also find the transfer of dispersion from negative to positive with an increment of Ωs. Finally, the refractive index enhancement is predicted for a wide spectral region.展开更多
The optical frequency comb has been widely used in precision measurement. In this study, a multi-peak fitting approach is first proposed to fit the two-photon transition spectrum which overlaps with the neighboring tr...The optical frequency comb has been widely used in precision measurement. In this study, a multi-peak fitting approach is first proposed to fit the two-photon transition spectrum which overlaps with the neighboring transition in Rb-87. The multi-peak fitting approach is used to eliminate the frequency shift affected by the neighboring transition. With locking the carrier envelope offset frequency at 1/4 repetition frequency, the transition frequency is measured to be 770569132739.9 +/- 5.8 kHz, which agrees well with the previous result recommended by Comite International des Poids et Mesures.展开更多
In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate cri...In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.展开更多
A gas-kinetic numerical method for directly solving the mesoscopic velocity distribution function equation is presented and applied to the study of three-dimensional complex flows and micro-channel flows covering vari...A gas-kinetic numerical method for directly solving the mesoscopic velocity distribution function equation is presented and applied to the study of three-dimensional complex flows and micro-channel flows covering various flow regimes. The unified velocity distribution function equation describing gas transport phenomena from rarefied transition to continuum flow regimes can be presented on the basis of the kinetic Boltzmann-Shakhov model equation. The gas-kinetic finite-difference schemes for the velocity distribution function are constructed by developing a discrete velocity ordinate method of gas kinetic theory and an unsteady time-splitting technique from computational fluid dynamics. Gas-kinetic boundary conditions and numerical modeling can be established by directly manipulating on the mesoscopic velocity distribution function. A new Gauss-type discrete velocity numerical integra- tion method can be developed and adopted to attack complex flows with different Mach numbers. HPF paral- lel strategy suitable for the gas-kinetic numerical method is investigated and adopted to solve three-dimensional complex problems. High Mach number flows around three-dimensional bodies are computed preliminarilywith massive scale parallel. It is noteworthy and of practical importance that the HPF parallel algorithm for solving three-dimensional complex problems can be effectively developed to cover various flow regimes. On the other hand, the gas-kinetic numerical method is extended and used to study micro-channel gas flows including the classical Couette flow, the Poiseuillechannel flow and pressure-driven gas flows in twodimensional short micro-channels. The numerical experience shows that the gas-kinetic algorithm may be a powerful tool in the numerical simulation of microscale gas flows occuring in the Micro-Electro-Mechanical System （MEMS）.展开更多
基金supported by Natural Science Foundation of China(11771166)Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT 17R46financially supported by funding for basic research business in Central Universities(innovative funding projects)(2018CXZZ090)。
文摘In the present paper,we consider the nonlocal Kirchhoff problem-(ε^2a+εb∫|■u|^2)Δu+u=Q(x)u^p,u>0 in R^3,,where a,b>0,1<p<5 andε>0 is a parameter.Under some assumptions on Q(x),we show the existence and local uniqueness of positive multi-peak solutions by LyapunovSchmidt reduction method and the local Pohozaev identity method,respectly.
文摘A new method for quantitative phase analysis is proposed by using X-ray diffraction multi-peak match intensity ratio. This method can obtain the multi-peak match intensity ratio among each phase in the mixture sample by using all diffraction peak data in the mixture sample X-ray diffraction spectrum and combining the relative intensity distribution data of each phase standard peak in JCPDS card to carry on the least square method regression analysis. It is benefit to improve the precision of quantitative phase analysis that the given single line ratio which is usually adopted is taken the place of the multi-peak match intensity ratio and is used in X-ray diffraction quantitative phase analysis of the mixture sample. By analyzing four-group mixture sample, adopting multi-peak match intensity ratio and X-ray diffraction quantitative phase analysis principle of combining the adiabatic and matrix flushing method, it is tested that the experimental results are identical with theory.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10334010 10304001, 10521002, 10434020, 10328407 and 90501007）. We are grateful to Professor Zhang J X for her helpful discussions.
文摘Absorption and refraction of the inner transition F2 ←→F3 of the closed four level N-type atom have been investigated under a weak field. The outer transitions F1←→F3 and F2←→F4 are resonantly interacted with drive field with frequency ωc and Rabi frequency Ωc, and saturation field with ωs and Ωs, respectively. For the suitable Rabi frequencies Ωc and Ωs, we obtain the Mellow absorption spectrum of probe field. The reason is that the drive field excites the atom to the upper level F3 and simultaneously the saturation field takes the atom out of the lower level F2, leading to the stimulated emission. Meanwhile, due to the dynamic energy splitting induced by the drive and saturation fields, the two- and four-peaked absorption spectra are observed. At the zero off-resonance detuning of probe field, we also find the transfer of dispersion from negative to positive with an increment of Ωs. Finally, the refractive index enhancement is predicted for a wide spectral region.
基金Supported by the National Natural Science Foundation of China under Grant Nos 91336103,10934010 and 61078026
文摘The optical frequency comb has been widely used in precision measurement. In this study, a multi-peak fitting approach is first proposed to fit the two-photon transition spectrum which overlaps with the neighboring transition in Rb-87. The multi-peak fitting approach is used to eliminate the frequency shift affected by the neighboring transition. With locking the carrier envelope offset frequency at 1/4 repetition frequency, the transition frequency is measured to be 770569132739.9 +/- 5.8 kHz, which agrees well with the previous result recommended by Comite International des Poids et Mesures.
基金supported by the Natural Science Foundation of China(11771166,12071169)the Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT17R46。
文摘In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.
基金the National Natural Science Foundation of China(90205009 and 10321002)the National Parallel Computing Center in Beijing.
文摘A gas-kinetic numerical method for directly solving the mesoscopic velocity distribution function equation is presented and applied to the study of three-dimensional complex flows and micro-channel flows covering various flow regimes. The unified velocity distribution function equation describing gas transport phenomena from rarefied transition to continuum flow regimes can be presented on the basis of the kinetic Boltzmann-Shakhov model equation. The gas-kinetic finite-difference schemes for the velocity distribution function are constructed by developing a discrete velocity ordinate method of gas kinetic theory and an unsteady time-splitting technique from computational fluid dynamics. Gas-kinetic boundary conditions and numerical modeling can be established by directly manipulating on the mesoscopic velocity distribution function. A new Gauss-type discrete velocity numerical integra- tion method can be developed and adopted to attack complex flows with different Mach numbers. HPF paral- lel strategy suitable for the gas-kinetic numerical method is investigated and adopted to solve three-dimensional complex problems. High Mach number flows around three-dimensional bodies are computed preliminarilywith massive scale parallel. It is noteworthy and of practical importance that the HPF parallel algorithm for solving three-dimensional complex problems can be effectively developed to cover various flow regimes. On the other hand, the gas-kinetic numerical method is extended and used to study micro-channel gas flows including the classical Couette flow, the Poiseuillechannel flow and pressure-driven gas flows in twodimensional short micro-channels. The numerical experience shows that the gas-kinetic algorithm may be a powerful tool in the numerical simulation of microscale gas flows occuring in the Micro-Electro-Mechanical System （MEMS）.
