-In this paper, an analytical solution in the outer region of finite water depth is derived for the second-order diffraction potential, which gives a clear physical meaning of the wave transmission and reflection char...-In this paper, an analytical solution in the outer region of finite water depth is derived for the second-order diffraction potential, which gives a clear physical meaning of the wave transmission and reflection characteristics in the far field. A numerical method-simple Green's function technique-for calculating the second-order diffraction potential in the inner region is also described. Numerical results are provided for the second-order wave forces on a semi-submerged cylinder. It is found that the contribution of second-order diffraction potential to second-order wave forces is important. The effect of water depth and submerged depth on the wave force is also discussed.展开更多
Beam splitting is one of the main approaches to achieving x-ray ghost imaging, and the intensity correlation between diffraction beam and transmission beam will directly affect the imaging quality. In this paper, we i...Beam splitting is one of the main approaches to achieving x-ray ghost imaging, and the intensity correlation between diffraction beam and transmission beam will directly affect the imaging quality. In this paper, we investigate the intensity correlation between the split x-ray beams by Laue diffraction of stress-free crystal. The analysis based on the dynamical theory of x-ray diffraction indicates that the spatial resolution of diffraction image and transmission image are reduced due to the position shift of the exit beam. In the experimental setup, a stress-free crystal with a thickness of hundredmicrometers-level is used for beam splitting. The crystal is in a non-dispersive configuration equipped with a double-crystal monochromator to ensure that the dimension of the diffraction beam and transmission beam are consistent. A correlation coefficient of 0.92 is achieved experimentally and the high signal-to-noise ratio of the x-ray ghost imaging is anticipated.Results of this paper demonstrate that the developed beam splitter of Laue crystal has the potential in the efficient data acquisition of x-ray ghost imaging.展开更多
Formulas of diffraction field of lossy wedges with less than 180?wedge angle are derived on the basis of the Fresnel-Kirchhoff wave theory and their numerical results are compared with those of the heuristic lossy wed...Formulas of diffraction field of lossy wedges with less than 180?wedge angle are derived on the basis of the Fresnel-Kirchhoff wave theory and their numerical results are compared with those of the heuristic lossy wedge diffraction coefficient given by Luebbers (1984), showing good agreement between the two types of numerical results which have different bases in theory. The agreement shows that the lossy wedge diffraction coefficient as an extension of UTD is quite reasonable.展开更多
This paper proposes second-order consensus protocols with time-delays and gives the measure of the robustness of the protocols to the time-delay existing in the network of agents with second-order dynamics. By employi...This paper proposes second-order consensus protocols with time-delays and gives the measure of the robustness of the protocols to the time-delay existing in the network of agents with second-order dynamics. By employing a frequency domain method, it is proven that the information states and their time derivatives of all the agents in the network achieve consensus asymptotically, respectively, for appropriate communication timedelay if the topology of weighted network is connected. Particularly, a tight upper bound on the communication time-delay that can be tolerated in the dynamic network is found. The consensus protocols are distributed in the sense that each agent only needs information from its neighboring agents, which reduces the complexity of connections between neighboring agents significantly. Numerical simulation results are provided to demonstrate the effectiveness and the sharpness of the theoretical results for second-order consensus in networks in the presence of communication time-delays.展开更多
The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the po...The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the possibility of sudden price variations （jumps） resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.展开更多
A complete semi-analytical solution is obtained for second-order diffraction of plane bichromatic waves by a fixed truncated circular column.The fluid domain is divided into interior and exterior regions.In the exteri...A complete semi-analytical solution is obtained for second-order diffraction of plane bichromatic waves by a fixed truncated circular column.The fluid domain is divided into interior and exterior regions.In the exterior region,the second-order velocity potential is expressed in terms of‘locked-wave’and‘free-wave’ components,both are solved using Fourier and eigenfunction expansions.The re- sulting‘locked wave’potential is expressed by one-dimensional Green's integrals with oscillating integrands.In order to increase computational efficiency,the far-field part of the integrals are carried out analytically.Solutions in both regions are matched on the interface by the potential and its normal derivative continuity conditions.Based on the present approach,the sum-and difference-frequency potentials are efficiently evaluated and are used to generate the quadratic transfer functions which correlates the incident wave spectrum with second-order forcing spectrum on the column.The sum-frequency QTFs for a TLP column are present,which are compared for some frequency pairs with those from a fully numerical procedure.Satisfactory agreement has been obtained.QTF spectra for a case study TLP column,generated using the semi-analytical solution are presented.Also given are the results for nonlinear wave field around the column.展开更多
The second-order temporal interference of two independent single-mode continuous-wave lasers is discussed by em- ploying two-photon interference in Feynman＇s path integral theory. It is concluded that whether the sec...The second-order temporal interference of two independent single-mode continuous-wave lasers is discussed by em- ploying two-photon interference in Feynman＇s path integral theory. It is concluded that whether the second-order temporal interference pattern can or cannot be retrieved via two-photon coincidence counting rate is dependent on the resolution time of the detection system and the frequency difference between these two lasers. Two identical and tunable single-mode continuous-wave diode lasers are employed to verify the predictions. These studies are helpful to understand the physics of two-photon interference with photons of different spectra.展开更多
Based on a full vector-diffraction theory, a detailed theoretical study is carried out, aiming at providing a clear insight into the effects of different focusing and off-axis parabola parameters on far-field vector-d...Based on a full vector-diffraction theory, a detailed theoretical study is carried out, aiming at providing a clear insight into the effects of different focusing and off-axis parabola parameters on far-field vector-diffraction properties of an offaxis parabolic mirror in the presence of misalignments of the incoming beam. The physical origin of these effects is also explored. The results show that the far-field intensity profile is altered by the distortion-, coma-, and astigmatism-like aberrations, which are caused by oblique incidence rather than inherent aberrations for the off-axis configuration. The radius of 90% encircled energy also increases but does not change monotonically with incident beam size increasing, or rather,it first decreases and then increases. The focal shift strongly depends on the effective focal length and oblique incidence angle, but it is almost independent of the beam size, which affects the focusing spot patterns. The intensity distribution produces a higher astigmatic image with off-axis angle increasing. Coma-like aberration starts to become dominant with beam size increasing and results in larger curved propagation trajectory. The incident polarization also affects the intensity distribution. The variation in the Strehl ratio with oblique incidence angle strongly depends on the misalignment direction and beam size as well. In addition, we find that the difference in locus between the catacaustic and the diffraction focus in the meridian is small. But the locus of the sagittal foci is obviously different from the locus of the meridian foci and the catacaustic focus. Moreover, the peak intensity of the sagittal focus is maximum, and the ratio of the peak intensity to that in the meridian plane is approximately 1.5. Understanding these effects is valuable for assessing a practical focused intensity and describing the motion of charged particles under a strong electric field in ultraintense laser–matter interaction.展开更多
Based on a modified coupled wave theory of Kogelnik, we have studied the diffraction of an ultrashort pulsed beam with an arbitrary polarization state from a volume holographic grating in photorefractive LiNbO3 crysta...Based on a modified coupled wave theory of Kogelnik, we have studied the diffraction of an ultrashort pulsed beam with an arbitrary polarization state from a volume holographic grating in photorefractive LiNbO3 crystals. The results indicate that the diffracted intensity distributions in the spectral and temporal domains and the diffraction efficiency of the grating are both changed by the polarization state and spectral bandwidth of the input pulsed beam. A method is given of choosing the grating parameters and input conditions to obtain a large variation range of the spectral bandwidth of the diffracted pulsed beam with an appropriate diffraction efficiency. Our study presents a possibility of using a volume holographic grating recorded in anisotropic materials to shape a broadband ultrashort pulsed beam by modulating its polarization state.展开更多
The purpose of this paper is to study the oscillation of second-order half-linear neutral differential equations with advanced argument of the form(r(t)((y(t)+p(t)y(τ(t)))')^(α))'+q(t)yα(σ(t))=0,t≥t_(0),w...The purpose of this paper is to study the oscillation of second-order half-linear neutral differential equations with advanced argument of the form(r(t)((y(t)+p(t)y(τ(t)))')^(α))'+q(t)yα(σ(t))=0,t≥t_(0),when∫^(∞)r^(−1/α)(s)ds<∞.We obtain sufficient conditions for the oscillation of the studied equations by the inequality principle and the Riccati transformation.An example is provided to illustrate the results.展开更多
位于谐振区的雷达目标可由极点特征进行识别,但极点特征的物理意义及其对应的谐振机理并不明确。针对该问题,本文利用一致性几何绕射理论(uniform geometrical theory of diffraction,UTD),研究了曲面绕射的谐振机理,并提出了一种用于...位于谐振区的雷达目标可由极点特征进行识别,但极点特征的物理意义及其对应的谐振机理并不明确。针对该问题,本文利用一致性几何绕射理论(uniform geometrical theory of diffraction,UTD),研究了曲面绕射的谐振机理,并提出了一种用于谐振区含曲面目标识别的极点正向推算方法。首先,用投影递推寻迹算法在目标表面获取爬行波的闭合路径及几何参数;然后,基于UTD给出曲面绕射场表达式,推导出用于预测极点的谐振方程;最后,通过对理想导体球及椭球进行极点预测,与频域仿真提取的极点进行对比,综合误差在5%以内,验证了建模方法的准确性。展开更多
In this paper,we study the existence and multiplicity of homoclinic solutions for a class of second-order Hamiltonian system:u″(t)−L(t)u(t)+▽V(t,u)=0,where L(t)and V(t,u)are not periodic in t.First,we introduce the ...In this paper,we study the existence and multiplicity of homoclinic solutions for a class of second-order Hamiltonian system:u″(t)−L(t)u(t)+▽V(t,u)=0,where L(t)and V(t,u)are not periodic in t.First,we introduce the definition of index and establish the corresponding index theory.Then,by using the index theory and critical point theory,we prove our main results under the asymptotic quadratic conditions of the potential function.展开更多
文摘-In this paper, an analytical solution in the outer region of finite water depth is derived for the second-order diffraction potential, which gives a clear physical meaning of the wave transmission and reflection characteristics in the far field. A numerical method-simple Green's function technique-for calculating the second-order diffraction potential in the inner region is also described. Numerical results are provided for the second-order wave forces on a semi-submerged cylinder. It is found that the contribution of second-order diffraction potential to second-order wave forces is important. The effect of water depth and submerged depth on the wave force is also discussed.
基金Project supported by the National Key Research and Development Program of China (Grant Nos.2022YFF0709103,2022YFA1603601,2021YFF0601203,and 2021YFA1600703)the National Natural Science Foundation of China (Grant No.81430087)the Shanghai Pilot Program for Basic Research-Chinese Academy of Sciences,Shanghai Branch (Grant No.JCYJ-SHFY-2021-010)。
文摘Beam splitting is one of the main approaches to achieving x-ray ghost imaging, and the intensity correlation between diffraction beam and transmission beam will directly affect the imaging quality. In this paper, we investigate the intensity correlation between the split x-ray beams by Laue diffraction of stress-free crystal. The analysis based on the dynamical theory of x-ray diffraction indicates that the spatial resolution of diffraction image and transmission image are reduced due to the position shift of the exit beam. In the experimental setup, a stress-free crystal with a thickness of hundredmicrometers-level is used for beam splitting. The crystal is in a non-dispersive configuration equipped with a double-crystal monochromator to ensure that the dimension of the diffraction beam and transmission beam are consistent. A correlation coefficient of 0.92 is achieved experimentally and the high signal-to-noise ratio of the x-ray ghost imaging is anticipated.Results of this paper demonstrate that the developed beam splitter of Laue crystal has the potential in the efficient data acquisition of x-ray ghost imaging.
文摘Formulas of diffraction field of lossy wedges with less than 180?wedge angle are derived on the basis of the Fresnel-Kirchhoff wave theory and their numerical results are compared with those of the heuristic lossy wedge diffraction coefficient given by Luebbers (1984), showing good agreement between the two types of numerical results which have different bases in theory. The agreement shows that the lossy wedge diffraction coefficient as an extension of UTD is quite reasonable.
基金supported by the National Natural Science Foundation of China (6057408860274014)
文摘This paper proposes second-order consensus protocols with time-delays and gives the measure of the robustness of the protocols to the time-delay existing in the network of agents with second-order dynamics. By employing a frequency domain method, it is proven that the information states and their time derivatives of all the agents in the network achieve consensus asymptotically, respectively, for appropriate communication timedelay if the topology of weighted network is connected. Particularly, a tight upper bound on the communication time-delay that can be tolerated in the dynamic network is found. The consensus protocols are distributed in the sense that each agent only needs information from its neighboring agents, which reduces the complexity of connections between neighboring agents significantly. Numerical simulation results are provided to demonstrate the effectiveness and the sharpness of the theoretical results for second-order consensus in networks in the presence of communication time-delays.
基金supported by the National Board for Higher Mathematics,Mumbai,India under Grant No.2/48(5)/2013/NBHM(R.P.)/RD-II/688 dt 16.01.2014
文摘The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the possibility of sudden price variations （jumps） resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.
文摘A complete semi-analytical solution is obtained for second-order diffraction of plane bichromatic waves by a fixed truncated circular column.The fluid domain is divided into interior and exterior regions.In the exterior region,the second-order velocity potential is expressed in terms of‘locked-wave’and‘free-wave’ components,both are solved using Fourier and eigenfunction expansions.The re- sulting‘locked wave’potential is expressed by one-dimensional Green's integrals with oscillating integrands.In order to increase computational efficiency,the far-field part of the integrals are carried out analytically.Solutions in both regions are matched on the interface by the potential and its normal derivative continuity conditions.Based on the present approach,the sum-and difference-frequency potentials are efficiently evaluated and are used to generate the quadratic transfer functions which correlates the incident wave spectrum with second-order forcing spectrum on the column.The sum-frequency QTFs for a TLP column are present,which are compared for some frequency pairs with those from a fully numerical procedure.Satisfactory agreement has been obtained.QTF spectra for a case study TLP column,generated using the semi-analytical solution are presented.Also given are the results for nonlinear wave field around the column.
基金Project supported by the National Natural Science Foundation of China(Grant No.11404255)the Doctor Foundation of Education Ministry of China(Grant No.20130201120013)
文摘The second-order temporal interference of two independent single-mode continuous-wave lasers is discussed by em- ploying two-photon interference in Feynman＇s path integral theory. It is concluded that whether the second-order temporal interference pattern can or cannot be retrieved via two-photon coincidence counting rate is dependent on the resolution time of the detection system and the frequency difference between these two lasers. Two identical and tunable single-mode continuous-wave diode lasers are employed to verify the predictions. These studies are helpful to understand the physics of two-photon interference with photons of different spectra.
基金Project supported by the Science Foundation for Youth Scholars of Minjiang University,China(Grant No.Mj9n201602)the National Science and Technology Major Project of the Ministry of Science and Technology of China。
文摘Based on a full vector-diffraction theory, a detailed theoretical study is carried out, aiming at providing a clear insight into the effects of different focusing and off-axis parabola parameters on far-field vector-diffraction properties of an offaxis parabolic mirror in the presence of misalignments of the incoming beam. The physical origin of these effects is also explored. The results show that the far-field intensity profile is altered by the distortion-, coma-, and astigmatism-like aberrations, which are caused by oblique incidence rather than inherent aberrations for the off-axis configuration. The radius of 90% encircled energy also increases but does not change monotonically with incident beam size increasing, or rather,it first decreases and then increases. The focal shift strongly depends on the effective focal length and oblique incidence angle, but it is almost independent of the beam size, which affects the focusing spot patterns. The intensity distribution produces a higher astigmatic image with off-axis angle increasing. Coma-like aberration starts to become dominant with beam size increasing and results in larger curved propagation trajectory. The incident polarization also affects the intensity distribution. The variation in the Strehl ratio with oblique incidence angle strongly depends on the misalignment direction and beam size as well. In addition, we find that the difference in locus between the catacaustic and the diffraction focus in the meridian is small. But the locus of the sagittal foci is obviously different from the locus of the meridian foci and the catacaustic focus. Moreover, the peak intensity of the sagittal focus is maximum, and the ratio of the peak intensity to that in the meridian plane is approximately 1.5. Understanding these effects is valuable for assessing a practical focused intensity and describing the motion of charged particles under a strong electric field in ultraintense laser–matter interaction.
基金Project supported by the State Key Development Program for Basic Research of China （Grant No 2002CCA03500）, and the National Natural Science Foundation of China （Grant No 60177016）.
文摘Based on a modified coupled wave theory of Kogelnik, we have studied the diffraction of an ultrashort pulsed beam with an arbitrary polarization state from a volume holographic grating in photorefractive LiNbO3 crystals. The results indicate that the diffracted intensity distributions in the spectral and temporal domains and the diffraction efficiency of the grating are both changed by the polarization state and spectral bandwidth of the input pulsed beam. A method is given of choosing the grating parameters and input conditions to obtain a large variation range of the spectral bandwidth of the diffracted pulsed beam with an appropriate diffraction efficiency. Our study presents a possibility of using a volume holographic grating recorded in anisotropic materials to shape a broadband ultrashort pulsed beam by modulating its polarization state.
基金This research is supported by the Shandong Provincial Natural Science Foundation of China(ZR2017MA043).
文摘The purpose of this paper is to study the oscillation of second-order half-linear neutral differential equations with advanced argument of the form(r(t)((y(t)+p(t)y(τ(t)))')^(α))'+q(t)yα(σ(t))=0,t≥t_(0),when∫^(∞)r^(−1/α)(s)ds<∞.We obtain sufficient conditions for the oscillation of the studied equations by the inequality principle and the Riccati transformation.An example is provided to illustrate the results.
文摘位于谐振区的雷达目标可由极点特征进行识别,但极点特征的物理意义及其对应的谐振机理并不明确。针对该问题,本文利用一致性几何绕射理论(uniform geometrical theory of diffraction,UTD),研究了曲面绕射的谐振机理,并提出了一种用于谐振区含曲面目标识别的极点正向推算方法。首先,用投影递推寻迹算法在目标表面获取爬行波的闭合路径及几何参数;然后,基于UTD给出曲面绕射场表达式,推导出用于预测极点的谐振方程;最后,通过对理想导体球及椭球进行极点预测,与频域仿真提取的极点进行对比,综合误差在5%以内,验证了建模方法的准确性。
基金Supported by the Fundamental Research Funds for the Central Universities(Grant No.2019XKQYMS91)。
文摘In this paper,we study the existence and multiplicity of homoclinic solutions for a class of second-order Hamiltonian system:u″(t)−L(t)u(t)+▽V(t,u)=0,where L(t)and V(t,u)are not periodic in t.First,we introduce the definition of index and establish the corresponding index theory.Then,by using the index theory and critical point theory,we prove our main results under the asymptotic quadratic conditions of the potential function.
