-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
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 employin...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
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
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
Head-up displays(HUDs)are emerging as key components of intelligent vehicles,requiring wide-depth,large-area,and high-efficiency dynamic imaging,which remains difficult to realize with traditional refractive optics.Co...Head-up displays(HUDs)are emerging as key components of intelligent vehicles,requiring wide-depth,large-area,and high-efficiency dynamic imaging,which remains difficult to realize with traditional refractive optics.Computer-generated holography(CGH)with diffraction optics offers a promising solution to these technical demands.However,CGH optimization based on the fast Fourier transform(FFT)faces limitations such as zero-padding redundancy,coupled sampling intervals,and incompatible near-and farfield propagation models.Here,we report a holography-based multiplane HUD using a matrix multiplication(MM)-assisted diffraction algorithm that restructures the Fresnel integral into two sequential matrix operations,thus eliminating zero-padding and enabling fully decoupled sampling between object and image planes.Compared with FFT-based angular spectrum methods,the MM approach significantly improves computational speed and memory efficiency for hologram design,which is validated by demonstrating dual-plane holography with a size ratio exceeding 100:1 and unified reconstruction across Fresnel and Fraunhofer regimes within a single computation.A prototype HUD system is demonstrated successfully to exhibit multiple-plane holographic virtual images that can be mixed with real-world objects at three independent planes.The technique might be one of the potential candidates for next-generation intelligent vehicle displays.展开更多
Kinetic viscosity of particles in the kinetic theory of granular flow(KTGF)was derived from the turbulence viscosity of the gas phase based on the kinetic theory of gas,with the effects of the dense phase of granular ...Kinetic viscosity of particles in the kinetic theory of granular flow(KTGF)was derived from the turbulence viscosity of the gas phase based on the kinetic theory of gas,with the effects of the dense phase of granular materials.KTGF is prominent in predicting the dense particle flow,being the primary numerical method for the gas-particle flow in fluidization,predominantly in the large-scale simulations as a Eulerian method.Recent studies presented that the second-order moment(SOM)of KTGF is superior to the classic KTGF in the particle-flow prediction.The difference between classic KTGF and SOM KTGF exists in the numerical model of the kinetic stresses of particles,which is calculated by the pseudo kinetic viscosity of particles in classic KTGF and by the SOM of the fluctuating velocity of particles by using the partial differential equations in SOM-KTGF.In this study,the gas-particle flow was simulated using SOM-KTGF and the stress tensors of particles predicted by the two methods were compared.It was demonstrated that the normal components of the kinetic stress tensor predicted by the two methods were close in value.However,the kinetic shear-stress was over-predicted by the classic KTGF in the dilute phase of particles in the gas-particle flow of fluidization,when the volume fraction of particles was less than 0.01.Therefore,SOM-KTGF is superior to the classic KTGF,particularly when the particle flow is dominated by the interstitial gas phase,as the particle-laden flow occurs in the lower volume fraction of particles in the dense regime,and further in the dilute and median regimes,when the volume fraction of particles less than 0.01.This superiority is caused by the high-fidelity prediction of the kinetic shear stress in SOM-KTGF rather than the prediction by classic KTGF.In addition,SOM-KTGF extended the application of KTGF from dense flows of particles in fluidization to median-dilute flows of particles in pneumatic conveying,when the volume fraction is less than 0.001.展开更多
Understanding the physical features of the diffracted sound field on the surface of an axisymmetric body is important for predicting the self-noise of a sonar mounted on an underwater platform. The diffracted sound fi...Understanding the physical features of the diffracted sound field on the surface of an axisymmetric body is important for predicting the self-noise of a sonar mounted on an underwater platform. The diffracted sound field from the transition region of an axisymmetric body was calculated by the geometrical theory of diffraction. The diffraction ray between the source point and the receiving point on the surface of an axisymmetric body was calculated by using the dynamic programming method. Based on the diffracted sound field, a simulation scheme for the noise correlation of the conformal array was presented. It was shown that the normalized pressure of the diffracted sound field from the transition region reduced with the increases of the frequency and the curvature of the ray. The flow noises of two models were compared and a rather optimum fore-body geometric shape was given. Furthermore, it was shown that the correlation of the flow noise in the low frequencies was stronger than that in the high frequencies. And the flow noise received by the acoustic array on the curved surface had a stronger correlation than that on the head plane at the designed center frequency, which is important for sonar system design.展开更多
A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different ...A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different complex nonsmooth/discontinuous interfaces, we develop an R(x)-orthonormal theory, where R(x) is an integrable flexural rigidity function. The R(x)-orthonormal bases in the linear space of boundary functions are constructed, of which the second-order derivatives of the boundary functions are asked to be orthonormal with respect to the weight function R(x). When the vibration modes of the symmetric composite beam are expressed in terms of the R(x)-orthonormal bases we can derive an eigenvalue problem endowed with a special structure of the coefficient matrix A :=[aij ],aij= 0 if i + j is odd. Based on the special structure we can prove two new theorems, which indicate that the characteristic equation of A can be decomposed into the product of the characteristic equations of two sub-matrices with dimensions half lower. Hence, we can sequentially solve the natural frequencies in closed-form owing to the specialty of A. We use this powerful new theory to analyze the free vibration performance and the vibration modes of symmetric composite beams with three different interfaces.展开更多
Nonlinear wave loads can induce low-frequency and high-frequency resonance motions of a moored platform in deep water. For the analysis of the nonlinear response of an offshore platform under the action of irregular w...Nonlinear wave loads can induce low-frequency and high-frequency resonance motions of a moored platform in deep water. For the analysis of the nonlinear response of an offshore platform under the action of irregular waves, the most widely used method in practice is the Cummins method, in which the second-order exciting forces in the time domain are computed by a two-term Volterra series model based on incident waves, first-order body motion response, and quadratic transfer functions(QTFs). QTFs are bichromatic waves acting on a body and are computed in the frequency domain in advance. For moving bodies, QTFs are related to the first-order body response, which is to be determined in the simulation process of body motion response but is unknown in the computation procedure of QTFs. In solving this problem, Teng and Cong(2017) proposed a method to divide the QTFs into different components,which are unrelated to the body response. With the application of the new QTF components, a modified Cummins method can be developed for the simulation of the nonlinear response of a moored floating platform. This paper presents a review of the theory.展开更多
In the present paper,two-and three-dimensional velocity potentials generated by pulsating pressure distributions of infinite extent on the free surface of infinite-depth waters are strictly derived based on special ca...In the present paper,two-and three-dimensional velocity potentials generated by pulsating pressure distributions of infinite extent on the free surface of infinite-depth waters are strictly derived based on special cases of concentrated pulsating pressure.The far-field asymptotic behaviour of the potentials and the radiation conditions to be satisfied by them are discussed. It is proved in a general sense that the potentials should be composed of a forced wave component,a free wave component and a local disturbance component.The radiation condition of the forced wave component should correspond to the far-field asymptotic behaviour of the pressure distribution,Hence,the formulation of radiation conditions for the second-order diffraction potentials has theoretically become clear,The radiation conditions for two-and three-dimensional problems are explicitly given in the paper.展开更多
Since the first discovery and description of materials,whose structures are not periodic,enormous efforts have been made in studying these aperiodic structures.With these efforts including the development of superspac...Since the first discovery and description of materials,whose structures are not periodic,enormous efforts have been made in studying these aperiodic structures.With these efforts including the development of superspace group theory and structure solution algorithms,numerous incommensurately modulated structures which represent the vast majority of known aperiodic structures have been determined with single crystal X-ray diffraction data.However,the determination of modulated structures remains very difficult for polycrystalline materials.Powder X-ray diffraction and electron microscopy techniques yield remarkable information for polycrystalline materials.By combining these two methods,modulated structures of polycrystalline materials that impede solution by conventional methods can be determined.The power of these methods is illustrated with the examples of the determination of modulated structures of polycrystalline materials.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.
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.
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.
基金supported by the National Key Research and Development Program of China(Grant No.2022YFB3607300)the National Natural Science Foundation of China(Grant Nos.62322512,62225506,and 12134013)+7 种基金the Fundamental Research Funds for the Central Universities(Grant Nos.WK2030000108 and WK2030000090)the CAS Project for Young Scientists in Basic Research(Grant No.YSBR-049)supported by the National Natural Science Foundation of China(Grant Nos.12174260 and 12574326)the Shanghai Rising-Star Program(Grant No.21QA1406400)the Shanghai Science and Technology Development Fund(Grant Nos.21ZR1443500 and 21ZR1443600)the support from the China Postdoctoral Science Foundation(Grant No.2023M743364)support from the Center for Micro and Nanoscale Research and Fabrication,University of Science and Technology of Chinasupported by the UPOLabs,which provided the experimental and technical support。
文摘Head-up displays(HUDs)are emerging as key components of intelligent vehicles,requiring wide-depth,large-area,and high-efficiency dynamic imaging,which remains difficult to realize with traditional refractive optics.Computer-generated holography(CGH)with diffraction optics offers a promising solution to these technical demands.However,CGH optimization based on the fast Fourier transform(FFT)faces limitations such as zero-padding redundancy,coupled sampling intervals,and incompatible near-and farfield propagation models.Here,we report a holography-based multiplane HUD using a matrix multiplication(MM)-assisted diffraction algorithm that restructures the Fresnel integral into two sequential matrix operations,thus eliminating zero-padding and enabling fully decoupled sampling between object and image planes.Compared with FFT-based angular spectrum methods,the MM approach significantly improves computational speed and memory efficiency for hologram design,which is validated by demonstrating dual-plane holography with a size ratio exceeding 100:1 and unified reconstruction across Fresnel and Fraunhofer regimes within a single computation.A prototype HUD system is demonstrated successfully to exhibit multiple-plane holographic virtual images that can be mixed with real-world objects at three independent planes.The technique might be one of the potential candidates for next-generation intelligent vehicle displays.
基金funded by Ministry of Education of China,under the grant of Excellent Doctoral Student(2010).
文摘Kinetic viscosity of particles in the kinetic theory of granular flow(KTGF)was derived from the turbulence viscosity of the gas phase based on the kinetic theory of gas,with the effects of the dense phase of granular materials.KTGF is prominent in predicting the dense particle flow,being the primary numerical method for the gas-particle flow in fluidization,predominantly in the large-scale simulations as a Eulerian method.Recent studies presented that the second-order moment(SOM)of KTGF is superior to the classic KTGF in the particle-flow prediction.The difference between classic KTGF and SOM KTGF exists in the numerical model of the kinetic stresses of particles,which is calculated by the pseudo kinetic viscosity of particles in classic KTGF and by the SOM of the fluctuating velocity of particles by using the partial differential equations in SOM-KTGF.In this study,the gas-particle flow was simulated using SOM-KTGF and the stress tensors of particles predicted by the two methods were compared.It was demonstrated that the normal components of the kinetic stress tensor predicted by the two methods were close in value.However,the kinetic shear-stress was over-predicted by the classic KTGF in the dilute phase of particles in the gas-particle flow of fluidization,when the volume fraction of particles was less than 0.01.Therefore,SOM-KTGF is superior to the classic KTGF,particularly when the particle flow is dominated by the interstitial gas phase,as the particle-laden flow occurs in the lower volume fraction of particles in the dense regime,and further in the dilute and median regimes,when the volume fraction of particles less than 0.01.This superiority is caused by the high-fidelity prediction of the kinetic shear stress in SOM-KTGF rather than the prediction by classic KTGF.In addition,SOM-KTGF extended the application of KTGF from dense flows of particles in fluidization to median-dilute flows of particles in pneumatic conveying,when the volume fraction is less than 0.001.
基金Project supported by the National Natural Science Foundational of China (Grant No.10774119)the Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No.NCET-08-0455)+2 种基金the Natural Science Foundation of Shaanxi Province of China (Grant No.SJ08F07)the Foundation of National Laboratory of Acoustics of Chinathe Foundation for Fundamental Research of Northwestern Polytechnical University of China (Grant No.2007004)
文摘Understanding the physical features of the diffracted sound field on the surface of an axisymmetric body is important for predicting the self-noise of a sonar mounted on an underwater platform. The diffracted sound field from the transition region of an axisymmetric body was calculated by the geometrical theory of diffraction. The diffraction ray between the source point and the receiving point on the surface of an axisymmetric body was calculated by using the dynamic programming method. Based on the diffracted sound field, a simulation scheme for the noise correlation of the conformal array was presented. It was shown that the normalized pressure of the diffracted sound field from the transition region reduced with the increases of the frequency and the curvature of the ray. The flow noises of two models were compared and a rather optimum fore-body geometric shape was given. Furthermore, it was shown that the correlation of the flow noise in the low frequencies was stronger than that in the high frequencies. And the flow noise received by the acoustic array on the curved surface had a stronger correlation than that on the head plane at the designed center frequency, which is important for sonar system design.
文摘A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different complex nonsmooth/discontinuous interfaces, we develop an R(x)-orthonormal theory, where R(x) is an integrable flexural rigidity function. The R(x)-orthonormal bases in the linear space of boundary functions are constructed, of which the second-order derivatives of the boundary functions are asked to be orthonormal with respect to the weight function R(x). When the vibration modes of the symmetric composite beam are expressed in terms of the R(x)-orthonormal bases we can derive an eigenvalue problem endowed with a special structure of the coefficient matrix A :=[aij ],aij= 0 if i + j is odd. Based on the special structure we can prove two new theorems, which indicate that the characteristic equation of A can be decomposed into the product of the characteristic equations of two sub-matrices with dimensions half lower. Hence, we can sequentially solve the natural frequencies in closed-form owing to the specialty of A. We use this powerful new theory to analyze the free vibration performance and the vibration modes of symmetric composite beams with three different interfaces.
基金the National Key R&D Program of China (Grant No.2016YFE0200100)the National Natural Science Foundation of China (Grant Nos.51490672 and 51479026).
文摘Nonlinear wave loads can induce low-frequency and high-frequency resonance motions of a moored platform in deep water. For the analysis of the nonlinear response of an offshore platform under the action of irregular waves, the most widely used method in practice is the Cummins method, in which the second-order exciting forces in the time domain are computed by a two-term Volterra series model based on incident waves, first-order body motion response, and quadratic transfer functions(QTFs). QTFs are bichromatic waves acting on a body and are computed in the frequency domain in advance. For moving bodies, QTFs are related to the first-order body response, which is to be determined in the simulation process of body motion response but is unknown in the computation procedure of QTFs. In solving this problem, Teng and Cong(2017) proposed a method to divide the QTFs into different components,which are unrelated to the body response. With the application of the new QTF components, a modified Cummins method can be developed for the simulation of the nonlinear response of a moored floating platform. This paper presents a review of the theory.
基金The present study is supported by the grant from the Natural Science Foundation of China.
文摘In the present paper,two-and three-dimensional velocity potentials generated by pulsating pressure distributions of infinite extent on the free surface of infinite-depth waters are strictly derived based on special cases of concentrated pulsating pressure.The far-field asymptotic behaviour of the potentials and the radiation conditions to be satisfied by them are discussed. It is proved in a general sense that the potentials should be composed of a forced wave component,a free wave component and a local disturbance component.The radiation condition of the forced wave component should correspond to the far-field asymptotic behaviour of the pressure distribution,Hence,the formulation of radiation conditions for the second-order diffraction potentials has theoretically become clear,The radiation conditions for two-and three-dimensional problems are explicitly given in the paper.
基金supported by the Natural Science Foundation of China(21321001 and 21527803)the National Basic Research Program of China(2013CB8933402).
文摘Since the first discovery and description of materials,whose structures are not periodic,enormous efforts have been made in studying these aperiodic structures.With these efforts including the development of superspace group theory and structure solution algorithms,numerous incommensurately modulated structures which represent the vast majority of known aperiodic structures have been determined with single crystal X-ray diffraction data.However,the determination of modulated structures remains very difficult for polycrystalline materials.Powder X-ray diffraction and electron microscopy techniques yield remarkable information for polycrystalline materials.By combining these two methods,modulated structures of polycrystalline materials that impede solution by conventional methods can be determined.The power of these methods is illustrated with the examples of the determination of modulated structures of polycrystalline materials.
