As one of the fitting methods, the polynomial approximation is effective to process sophisticated problem. In this paper, we employ this approach to handle the scattering of scalar field around the Schwarzschild-de Si...As one of the fitting methods, the polynomial approximation is effective to process sophisticated problem. In this paper, we employ this approach to handle the scattering of scalar field around the Schwarzschild-de Sitter blackhole. The complicated relationship between tortoise coordinate and radial coordinate is replaced by the approximate polynomial. The Schroedinger-like equation, the real boundary conditions and the polynomial approximation construct a full Sturm Liouville type problem. Then this boundary value problem can be solved numerically for two limiting cases： the first one is the Nariai black-hole whose horizons are close to each other, the second one is the black-hole with the horizons widely separated. Compared with previous results （Brevik and Tian）, the field near the event horizon and cosmological horizon can have a better description.展开更多
This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation techn...This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation technique introduced by Tadmor-Tang,an optimal pointwise convergence rate is derived for the vanishing viscosity approximations to the initial-boundary value problem for scalar convex conservation laws,whose weak entropy solution is piecewise C 2 -smooth with interaction of elementary waves and the ...展开更多
This paper presents an economic lot-sizing problem with perishable inventory and general economies of scale cost functions. For the case with backlogging allowed, a mathematical model is formulated, and several proper...This paper presents an economic lot-sizing problem with perishable inventory and general economies of scale cost functions. For the case with backlogging allowed, a mathematical model is formulated, and several properties of the optimal solutions are explored. With the help of these optimality properties, a polynomial time approximation algorithm is developed by a new method. The new method adopts a shift technique to obtain a feasible solution of subproblem and takes the optimal solution of the subproblem as an approximation solution of our problem. The worst case performance for the approximation algorithm is proven to be （4√2 ＋ 5）/7. Finally, an instance illustrates that the bound is tight.展开更多
A new tight frame called as monoscale orthonormal ridgelet frame （MORF） is proposed. The localization principle and the orthonormal ridgelet constructed by Donoho are applied to construct the MORF, which are used to...A new tight frame called as monoscale orthonormal ridgelet frame （MORF） is proposed. The localization principle and the orthonormal ridgelet constructed by Donoho are applied to construct the MORF, which are used to evaluate the order of nonlinear approximation for image with edge. Because the new tight frame not only has directionality but also bears orthonormality. It overcomes redundancy of Candes＇s monoscale ridgelets and provides many excellent properties in practical application. Theoretical analysis and experiments demonstrate that the new frame has remarkable potential for image compression, image reconstruction, and image denoising with the simple refinement for MORF.展开更多
Until now, most researches into the rogue-wave-structure interaction have relied on experimental measurement and numerical simulation. Owing to the complexity of the physical mechanism of rogue waves, theoretical stud...Until now, most researches into the rogue-wave-structure interaction have relied on experimental measurement and numerical simulation. Owing to the complexity of the physical mechanism of rogue waves, theoretical study on the wave-structure issue still makes little progress. In this paper, the rogue wave flow around a vertical cylinder is analytically studied within the scope of the potential theory. The rogue wave is modeled by the Gauss envelope, which is one particular case of the well-known focusing theory. The formulae of the wave-induced horizontal force and bending moment are proposed. For the convenience of engineering application, the derived formulae are simplified appropriately, and verified against numerical results. In addition, the influence of wave parameters, such as the energy focusing degree and the wave focusing position, is thoroughly investigated.展开更多
A numerical triangulation and transformation into the time domain of a Kirchhoff approximation(KA)method is proposed for the modeling of bistatic scattering from an underwater non-penetrable target.The time domain sol...A numerical triangulation and transformation into the time domain of a Kirchhoff approximation(KA)method is proposed for the modeling of bistatic scattering from an underwater non-penetrable target.The time domain solution in this approximation can be split up into two parts:the solution of reflected field,contributing around the specular direction,and the solution of shadow radiation,contributing around the forward direction.An average solution in the time domain satisfying the reciprocity principle is presented.The solution is expressed in terms of non-singular functions.The proposed method is validated against a normal mode method for bistatic scattering from a rigid sphere.Moreover,the reflected and shadow highlights on the surface of the sphere are shown to verify the integration surface of the reflected field and shadow radiation.It is also tested against a finite element method and an experiment involving a scaled Benchmark Target Strength Simulation Submarine model.The time-angle bistatic spectra for the model are evaluated by the direct and transformed average solutions of KA,and the former accelerates its speed of calculation.The results are good,and show that this method can be used to predict the bistatic scattered field of a non-penetrable target.展开更多
Electromagnetic wave scattering from multilayers consisting of two two-layer Caussian rough surfaces with lossless media is investigated in the Kirchhoff approximation （KA）, with consideration of the shadowing effec...Electromagnetic wave scattering from multilayers consisting of two two-layer Caussian rough surfaces with lossless media is investigated in the Kirchhoff approximation （KA）, with consideration of the shadowing effects. The tapered incident wave is introduced into the classic KA, and the bistatic scattering coefficient is redetermined. The advantage of this method is that it is faster in computation than the exact numerical methods. The numerical results show that the bistatic scattering coefficient calculated in the KA is in good agreement with that obtained by using the method of moment （MOM） over a most angular range, which indicates the validity of the KA proposed in our paper. Finally, the effects of the relative permittivity, the root-mean-square （RMS） height, the correlative length, and the average height between the two interfaces on the bistatic scattering coefficient are discussed in detail.展开更多
We investigate the dynamics of resonant Raman scattering in the course of the frequency de- tuning. The dephasing in the time domain makes the scattering fast when the photon energy is tuned from the absorption resona...We investigate the dynamics of resonant Raman scattering in the course of the frequency de- tuning. The dephasing in the time domain makes the scattering fast when the photon energy is tuned from the absorption resonance. This makes frequency detuning to act as a camera shutter with a regulated scattering duration and provides a practical tool of controlling the scattering time in ordinary stationary measurements. The theory is applied to resonant Raman spectra of a couple of few-mode model systems and to trans-1,3,5-hexatriene and guanine-cytosine （G-C） Watson-Crick base pairs （DNA） molecules. Besides some particular physical effects, the regime of fast scattering leads to a simplification of the spectrum as well as to the scattering theory itself. Strong overtones appear in the Raman spectra when the photon frequency is tuned in the resonant region, while in the mode of fast scattering, the overtones are gradually quenched when the photon frequency is tuned more than one vibra- tional quantum below the first absorption resonance. The detuning from the resonant region thus leads to a strong purification of the Raman spectrum from the contamination by higher overtones and soft modes and purifies the spectrum also in terms of avoidance of dissociation and interfering fluorescence decay of the resonant state. This makes frequency detuning a very useful practical tool in the analysis of the resonant Raman spectra of complex systems and considerably improves the prospects for using the Raman effect for detection of foreign substances at ultra-low concentrations.展开更多
A sixteen moment approximation based on a bi-Maxwellian that contains the stress tensor and the heat flow vector is applied to describe the ion velocity distribution which influences the incoherent scatter spectra. A ...A sixteen moment approximation based on a bi-Maxwellian that contains the stress tensor and the heat flow vector is applied to describe the ion velocity distribution which influences the incoherent scatter spectra. A discussion is made about the effects on the incoherent scatter spectra caused by different values of the normalized perpendicular drift velocity D, aspect angle Φ between the magnetic field and the line-of-sight direction, and the ratio α of the ion-neutral collision to ion cyclotron frequency. Numerical results show that the shifting and asymmetry of incoherent scatter spectra appear parallel to E × B and E as the normalized perpendicular drift velocity D increases due to the ion drift velocity, the stress tensor and the heat flow vector respectively. However, the spectrum is always typically double-humped Maxwellian parallel to B. The ion velocity distribution is more distorted from the Maxwellian as the aspect angle Φ increases from 0° to 90°, and consequently the incoherent scatter spectra is no longer typically double-humped Maxwellian. Asαincreases, the ion velocity distribution becomes Maxwellian and the incoherent scatter spectra become typically double-humped Maxwellian even with a large value of the normalized perpendicular drift velocity D. It is reasonable to use the sixteen-moment approximation to describe the non-Maxwellian plasma characterized by the large temperature anisotropy.展开更多
In this paper, we use the metric coefficients and the equation of motion obtained in the second post- Newtonian approximation of scalar-tensor theory to derive the second-order light propagation equation and the light...In this paper, we use the metric coefficients and the equation of motion obtained in the second post- Newtonian approximation of scalar-tensor theory to derive the second-order light propagation equation and the light deflection angle and compare it with previous works. These results are useful for precision astrometry missions like ASTROD, GALA, Darwin and SIM which aim at astrometry with micro-arcsecond and nano-aresecond accuracies, and need for the second post-Newtonian framework and ephemeris for observations to determine the stellar and spacecraft positions.展开更多
Using an improved approximate formula to the centrifugal term, we present arbitrary l-state scattering solutions of the hyperbolic potential. The approximate analytical formula of scattering phase shifts and normalize...Using an improved approximate formula to the centrifugal term, we present arbitrary l-state scattering solutions of the hyperbolic potential. The approximate analytical formula of scattering phase shifts and normalized wavefunctions are presented. All data calculated by the above approximate analytical formula are compared with those obtained by using the numerical integration method in the scattering state cases. We find that this improved approximate formula is better than previous one since the calculated results are in good agreement with those exact ones.展开更多
The relationship between the order of approximation by neural network based on scattered threshold value nodes and the neurons involved in a single hidden layer is investigated. The results obtained show that the degr...The relationship between the order of approximation by neural network based on scattered threshold value nodes and the neurons involved in a single hidden layer is investigated. The results obtained show that the degree of approximation by the periodic neural network with one hidden layer and scattered threshold value nodes is increased with the increase of the number of neurons hid in hidden layer and the smoothness of excitation function.展开更多
Backscattered fields from one-dimensional time-varying Gerstners sea surface are calculated utilising the secondorder small slope approximation. It is well known that spectral properties of the backscattered echoes re...Backscattered fields from one-dimensional time-varying Gerstners sea surface are calculated utilising the secondorder small slope approximation. It is well known that spectral properties of the backscattered echoes relate to the velocity of the small elementary scatterers on sea surface profiles. Therefore, modeling Doppler spectra from the ocean requires an accurate description of the sea surface motion. The profile of nonlinear Gerstners sea surface shows verticalskewness of sea waves, it is sharper at the crest and flatter at the trough than linear waves, and its maximum slope position is closer to the crest than to the trough. Furthermore, the horizontal component of the small elementary scatterers orbit velocity on the sea surface, which yields noticeable influence on Doppler spectra, can be obtained conveniently by Gerstners sea surface model. In this study the characteristics of Doppler spectra of backscattered fields from time-varying Gerstners sea surface are investigated and the dependences of the Doppler frequency and the Doppler bandwidth on the parameters, such as the wind speed, the radar frequency, the incident angle, etc. are discussed. It is shown that the Doppler bandwidth of microwave scattered fields from Gerstners sea surface is considerably broadened. For the case of high frequency backscattered fields, the values of the higher-order spectrum peaks are larger than those obtained by linear sea surface.展开更多
The first-order small slope approximation is applied to model the scattering strength from a rough surface in underwater acoustics to account for seafloor for high frequencies from 10 kHz to hundreds of kilohertz. Emp...The first-order small slope approximation is applied to model the scattering strength from a rough surface in underwater acoustics to account for seafloor for high frequencies from 10 kHz to hundreds of kilohertz. Emphasis is placed on simulating the response from two-dimensional anisotropic rough surfaces. Several rough surfaces are described based on structure functions such as the particular sandy ripples shape. The scattering strength is predicted by the small slope approximation and is first compared to a well known bistatic method, interpolating the Kirchhoff approximation and the small perturbations model, assuming that the rough interface is isotropic. Results obtained from the two different models are similar and show a higher level in the specular direction than in the other directions. For an isotropic surface, changing the propagation plane gives similar results. Then, SSA, which lets us adapt the structure function of the roughness straight away, is tested trough several anisotropic surfaces. In a longitudinal direction of ripples, the scattering strength is mostly in the specular direction, whereas in the transversal direction of ripples, the scattering strength prediction shows high values for different angular directions. Thus the scattering strength is spread in a very different way strictly related to the particular features of the ripples. Combine our results, indicates the importance of taking into account the anisotropy of a surface in a scattering prediction process, taking into account the positions of the emitter and of the receiver which are naturally significant when predicting scattering strength.展开更多
A bipartition model for ion transport in solids has been presented.Unlike the earlier bipartition model,a single-scattering approximation has been adopted and angular correlation of energy transfer has been partly tak...A bipartition model for ion transport in solids has been presented.Unlike the earlier bipartition model,a single-scattering approximation has been adopted and angular correlation of energy transfer has been partly taken into account.By the present bipartition model,the reflection coefficients and energy spectrum of reflected ions have been calculated.The results show that the present bipartition model gives better descriptions of reflection although it is simpler in calculation than the earlier bipartition model.展开更多
The isoscalar giant dipole resonance(ISGDR)in nuclei is studied in the framework of a fully self-consistent relativistic continuum random phase approximation(RCRPA).In this method the contribution of the continuum spe...The isoscalar giant dipole resonance(ISGDR)in nuclei is studied in the framework of a fully self-consistent relativistic continuum random phase approximation(RCRPA).In this method the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single particle Green's function technique.We employ different type interactions(NL1,NL3,NL3^(*),NL4,TM1,NLSH and PK1)corresponding to incompressibilities in the range 200–360 MeV.The results are discussed in comparison with the existing experimental data.It is found that the termη=5/3<r^(2)>can remove spurious components from the admixture of the center of mass state perfectly.The ISGDR distribution has two components,the lower-energy component and the higher-energy component.There is a large amount of very sharp peaks in the lower-energy region in RCRPA calculations.Only the higher-energy component is sensitive to the value of nuclear incompressibility employed in the calculations;the position of the lower-energy component is completely independent of the nuclear incompressibility Knm.展开更多
The eikonal approximation(EA)is widely used in various high-energy scattering problems.In this work we generalize this approximation from the scattering problems with time-independent Hamiltonian to the ones with peri...The eikonal approximation(EA)is widely used in various high-energy scattering problems.In this work we generalize this approximation from the scattering problems with time-independent Hamiltonian to the ones with periodical Hamiltonians,i.e.,the Floquet scattering problems.We further illustrate the applicability of our generalized EA via the scattering problem with respect to a shaking spherical square-well potential,by comparing the results given by this approximation and the exact ones.The generalized EA we developed is helpful for the research of manipulation of high-energy scattering processes with external field,e.g.the manipulation of atom,molecule or nuclear collisions or reactions via strong laser fields.展开更多
The generalized Born approximation is an approximation method that represents the scattering term by the error between the exact Green's function and the approximate Green's function,mainly for the gradient sc...The generalized Born approximation is an approximation method that represents the scattering term by the error between the exact Green's function and the approximate Green's function,mainly for the gradient scattering problem.However,so far,the research on the generalized Born approximation has only stayed in theory,and its implementation techniques are rarely reported.In order to fill this gap,the basic theory of generalized Born approximation is reviewed,and the implementation method of generalized Born approximation is discussed in this paper.In particular,the problem of calculating boundary effect elimination is discussed in detail.Finally,through model trial calculation,the calculation of gradient scattering,by comparing Born approximation and finite difference method,shows that using the generalized Born approximation to calculate gradient scattering achieves higher computational accuracy.展开更多
基金supported by the National Basic Research Program of China (Grant No 2003CB716300)National Natural Science Foundation of China (Grant No 10573003)
文摘As one of the fitting methods, the polynomial approximation is effective to process sophisticated problem. In this paper, we employ this approach to handle the scattering of scalar field around the Schwarzschild-de Sitter blackhole. The complicated relationship between tortoise coordinate and radial coordinate is replaced by the approximate polynomial. The Schroedinger-like equation, the real boundary conditions and the polynomial approximation construct a full Sturm Liouville type problem. Then this boundary value problem can be solved numerically for two limiting cases： the first one is the Nariai black-hole whose horizons are close to each other, the second one is the black-hole with the horizons widely separated. Compared with previous results （Brevik and Tian）, the field near the event horizon and cosmological horizon can have a better description.
基金supported by the NSF China#10571075NSF-Guangdong China#04010473+1 种基金The research of the second author was supported by Jinan University Foundation#51204033the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State education Ministry#2005-383
文摘This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation technique introduced by Tadmor-Tang,an optimal pointwise convergence rate is derived for the vanishing viscosity approximations to the initial-boundary value problem for scalar convex conservation laws,whose weak entropy solution is piecewise C 2 -smooth with interaction of elementary waves and the ...
基金supported by National Natural Science Foundation of China (No. 10671108 and 70971076)Found for the Doctoral Program of Higher Education of Ministry of Education of China (No. 20070446001)+1 种基金Innovation Planning Project of Shandong Province (No. SDYY06034)Foundation of Qufu Normal University (No. XJZ200849)
文摘This paper presents an economic lot-sizing problem with perishable inventory and general economies of scale cost functions. For the case with backlogging allowed, a mathematical model is formulated, and several properties of the optimal solutions are explored. With the help of these optimality properties, a polynomial time approximation algorithm is developed by a new method. The new method adopts a shift technique to obtain a feasible solution of subproblem and takes the optimal solution of the subproblem as an approximation solution of our problem. The worst case performance for the approximation algorithm is proven to be （4√2 ＋ 5）/7. Finally, an instance illustrates that the bound is tight.
基金This project was supported by the National Nature Science Foundation of China (60473119)
文摘A new tight frame called as monoscale orthonormal ridgelet frame （MORF） is proposed. The localization principle and the orthonormal ridgelet constructed by Donoho are applied to construct the MORF, which are used to evaluate the order of nonlinear approximation for image with edge. Because the new tight frame not only has directionality but also bears orthonormality. It overcomes redundancy of Candes＇s monoscale ridgelets and provides many excellent properties in practical application. Theoretical analysis and experiments demonstrate that the new frame has remarkable potential for image compression, image reconstruction, and image denoising with the simple refinement for MORF.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51579146,51490674,and51609101)the Shanghai Rising-Star Program(Grant No.16QA1402300)
文摘Until now, most researches into the rogue-wave-structure interaction have relied on experimental measurement and numerical simulation. Owing to the complexity of the physical mechanism of rogue waves, theoretical study on the wave-structure issue still makes little progress. In this paper, the rogue wave flow around a vertical cylinder is analytically studied within the scope of the potential theory. The rogue wave is modeled by the Gauss envelope, which is one particular case of the well-known focusing theory. The formulae of the wave-induced horizontal force and bending moment are proposed. For the convenience of engineering application, the derived formulae are simplified appropriately, and verified against numerical results. In addition, the influence of wave parameters, such as the energy focusing degree and the wave focusing position, is thoroughly investigated.
基金the Oceanic Interdisciplinary Program of Shanghai Jiao Tong University(project number SL2021PT108)。
文摘A numerical triangulation and transformation into the time domain of a Kirchhoff approximation(KA)method is proposed for the modeling of bistatic scattering from an underwater non-penetrable target.The time domain solution in this approximation can be split up into two parts:the solution of reflected field,contributing around the specular direction,and the solution of shadow radiation,contributing around the forward direction.An average solution in the time domain satisfying the reciprocity principle is presented.The solution is expressed in terms of non-singular functions.The proposed method is validated against a normal mode method for bistatic scattering from a rigid sphere.Moreover,the reflected and shadow highlights on the surface of the sphere are shown to verify the integration surface of the reflected field and shadow radiation.It is also tested against a finite element method and an experiment involving a scaled Benchmark Target Strength Simulation Submarine model.The time-angle bistatic spectra for the model are evaluated by the direct and transformed average solutions of KA,and the former accelerates its speed of calculation.The results are good,and show that this method can be used to predict the bistatic scattered field of a non-penetrable target.
基金supported by the National Natural Science Foundation of China (Grant No 60571058)the Specialized Research Fund for the Doctoral Program of Higher Education,China (Grant No 20070701010)
文摘Electromagnetic wave scattering from multilayers consisting of two two-layer Caussian rough surfaces with lossless media is investigated in the Kirchhoff approximation （KA）, with consideration of the shadowing effects. The tapered incident wave is introduced into the classic KA, and the bistatic scattering coefficient is redetermined. The advantage of this method is that it is faster in computation than the exact numerical methods. The numerical results show that the bistatic scattering coefficient calculated in the KA is in good agreement with that obtained by using the method of moment （MOM） over a most angular range, which indicates the validity of the KA proposed in our paper. Finally, the effects of the relative permittivity, the root-mean-square （RMS） height, the correlative length, and the average height between the two interfaces on the bistatic scattering coefficient are discussed in detail.
文摘We investigate the dynamics of resonant Raman scattering in the course of the frequency de- tuning. The dephasing in the time domain makes the scattering fast when the photon energy is tuned from the absorption resonance. This makes frequency detuning to act as a camera shutter with a regulated scattering duration and provides a practical tool of controlling the scattering time in ordinary stationary measurements. The theory is applied to resonant Raman spectra of a couple of few-mode model systems and to trans-1,3,5-hexatriene and guanine-cytosine （G-C） Watson-Crick base pairs （DNA） molecules. Besides some particular physical effects, the regime of fast scattering leads to a simplification of the spectrum as well as to the scattering theory itself. Strong overtones appear in the Raman spectra when the photon frequency is tuned in the resonant region, while in the mode of fast scattering, the overtones are gradually quenched when the photon frequency is tuned more than one vibra- tional quantum below the first absorption resonance. The detuning from the resonant region thus leads to a strong purification of the Raman spectrum from the contamination by higher overtones and soft modes and purifies the spectrum also in terms of avoidance of dissociation and interfering fluorescence decay of the resonant state. This makes frequency detuning a very useful practical tool in the analysis of the resonant Raman spectra of complex systems and considerably improves the prospects for using the Raman effect for detection of foreign substances at ultra-low concentrations.
基金supported by the Foundation of National Key Laboratory of Electromagnetic EnvironmentNational Natural Science Foundation of China (No. 40310223)
文摘A sixteen moment approximation based on a bi-Maxwellian that contains the stress tensor and the heat flow vector is applied to describe the ion velocity distribution which influences the incoherent scatter spectra. A discussion is made about the effects on the incoherent scatter spectra caused by different values of the normalized perpendicular drift velocity D, aspect angle Φ between the magnetic field and the line-of-sight direction, and the ratio α of the ion-neutral collision to ion cyclotron frequency. Numerical results show that the shifting and asymmetry of incoherent scatter spectra appear parallel to E × B and E as the normalized perpendicular drift velocity D increases due to the ion drift velocity, the stress tensor and the heat flow vector respectively. However, the spectrum is always typically double-humped Maxwellian parallel to B. The ion velocity distribution is more distorted from the Maxwellian as the aspect angle Φ increases from 0° to 90°, and consequently the incoherent scatter spectra is no longer typically double-humped Maxwellian. Asαincreases, the ion velocity distribution becomes Maxwellian and the incoherent scatter spectra become typically double-humped Maxwellian even with a large value of the normalized perpendicular drift velocity D. It is reasonable to use the sixteen-moment approximation to describe the non-Maxwellian plasma characterized by the large temperature anisotropy.
基金Supported by the National Natural Science Foundation of China under Grant No. 10875171
文摘In this paper, we use the metric coefficients and the equation of motion obtained in the second post- Newtonian approximation of scalar-tensor theory to derive the second-order light propagation equation and the light deflection angle and compare it with previous works. These results are useful for precision astrometry missions like ASTROD, GALA, Darwin and SIM which aim at astrometry with micro-arcsecond and nano-aresecond accuracies, and need for the second post-Newtonian framework and ephemeris for observations to determine the stellar and spacecraft positions.
基金Supported by the National Natural Science Foundation of China under Grant No.11275165the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province,China under Grant No.11KJD430007Jiangsu Overseas Research and Training Program for University Prominent Young and Middle-aged Teachers and Presidents
文摘Using an improved approximate formula to the centrifugal term, we present arbitrary l-state scattering solutions of the hyperbolic potential. The approximate analytical formula of scattering phase shifts and normalized wavefunctions are presented. All data calculated by the above approximate analytical formula are compared with those obtained by using the numerical integration method in the scattering state cases. We find that this improved approximate formula is better than previous one since the calculated results are in good agreement with those exact ones.
文摘The relationship between the order of approximation by neural network based on scattered threshold value nodes and the neurons involved in a single hidden layer is investigated. The results obtained show that the degree of approximation by the periodic neural network with one hidden layer and scattered threshold value nodes is increased with the increase of the number of neurons hid in hidden layer and the smoothness of excitation function.
基金Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 40906088)the National Natural Science Foundation of China (Grant No. 60971067)Specialised Research Fund for the Doctoral Program of Higher Education (Grant No. 200804231021)
文摘Backscattered fields from one-dimensional time-varying Gerstners sea surface are calculated utilising the secondorder small slope approximation. It is well known that spectral properties of the backscattered echoes relate to the velocity of the small elementary scatterers on sea surface profiles. Therefore, modeling Doppler spectra from the ocean requires an accurate description of the sea surface motion. The profile of nonlinear Gerstners sea surface shows verticalskewness of sea waves, it is sharper at the crest and flatter at the trough than linear waves, and its maximum slope position is closer to the crest than to the trough. Furthermore, the horizontal component of the small elementary scatterers orbit velocity on the sea surface, which yields noticeable influence on Doppler spectra, can be obtained conveniently by Gerstners sea surface model. In this study the characteristics of Doppler spectra of backscattered fields from time-varying Gerstners sea surface are investigated and the dependences of the Doppler frequency and the Doppler bandwidth on the parameters, such as the wind speed, the radar frequency, the incident angle, etc. are discussed. It is shown that the Doppler bandwidth of microwave scattered fields from Gerstners sea surface is considerably broadened. For the case of high frequency backscattered fields, the values of the higher-order spectrum peaks are larger than those obtained by linear sea surface.
文摘The first-order small slope approximation is applied to model the scattering strength from a rough surface in underwater acoustics to account for seafloor for high frequencies from 10 kHz to hundreds of kilohertz. Emphasis is placed on simulating the response from two-dimensional anisotropic rough surfaces. Several rough surfaces are described based on structure functions such as the particular sandy ripples shape. The scattering strength is predicted by the small slope approximation and is first compared to a well known bistatic method, interpolating the Kirchhoff approximation and the small perturbations model, assuming that the rough interface is isotropic. Results obtained from the two different models are similar and show a higher level in the specular direction than in the other directions. For an isotropic surface, changing the propagation plane gives similar results. Then, SSA, which lets us adapt the structure function of the roughness straight away, is tested trough several anisotropic surfaces. In a longitudinal direction of ripples, the scattering strength is mostly in the specular direction, whereas in the transversal direction of ripples, the scattering strength prediction shows high values for different angular directions. Thus the scattering strength is spread in a very different way strictly related to the particular features of the ripples. Combine our results, indicates the importance of taking into account the anisotropy of a surface in a scattering prediction process, taking into account the positions of the emitter and of the receiver which are naturally significant when predicting scattering strength.
基金Supported by the Youth Scientific and Technology Foundation of Sichuan Province.
文摘A bipartition model for ion transport in solids has been presented.Unlike the earlier bipartition model,a single-scattering approximation has been adopted and angular correlation of energy transfer has been partly taken into account.By the present bipartition model,the reflection coefficients and energy spectrum of reflected ions have been calculated.The results show that the present bipartition model gives better descriptions of reflection although it is simpler in calculation than the earlier bipartition model.
基金the National Natural Science Foundation of China under Grant Nos 11175216 and 11275018the National Basic Research Program of China under Grant No 2013CB834404the Science Planning Project of the Communication University of China under Grant No XNL1207.
文摘The isoscalar giant dipole resonance(ISGDR)in nuclei is studied in the framework of a fully self-consistent relativistic continuum random phase approximation(RCRPA).In this method the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single particle Green's function technique.We employ different type interactions(NL1,NL3,NL3^(*),NL4,TM1,NLSH and PK1)corresponding to incompressibilities in the range 200–360 MeV.The results are discussed in comparison with the existing experimental data.It is found that the termη=5/3<r^(2)>can remove spurious components from the admixture of the center of mass state perfectly.The ISGDR distribution has two components,the lower-energy component and the higher-energy component.There is a large amount of very sharp peaks in the lower-energy region in RCRPA calculations.Only the higher-energy component is sensitive to the value of nuclear incompressibility employed in the calculations;the position of the lower-energy component is completely independent of the nuclear incompressibility Knm.
基金supported by the National Key Research and Development Program of China (Grant No.2022YFA1405300)the Innovation Program for Quantum Science and Technology (Grant No.2023ZD0300700)。
文摘The eikonal approximation(EA)is widely used in various high-energy scattering problems.In this work we generalize this approximation from the scattering problems with time-independent Hamiltonian to the ones with periodical Hamiltonians,i.e.,the Floquet scattering problems.We further illustrate the applicability of our generalized EA via the scattering problem with respect to a shaking spherical square-well potential,by comparing the results given by this approximation and the exact ones.The generalized EA we developed is helpful for the research of manipulation of high-energy scattering processes with external field,e.g.the manipulation of atom,molecule or nuclear collisions or reactions via strong laser fields.
基金Supported by Project of the National Natural Science Foundation of China(No.41974135)
文摘The generalized Born approximation is an approximation method that represents the scattering term by the error between the exact Green's function and the approximate Green's function,mainly for the gradient scattering problem.However,so far,the research on the generalized Born approximation has only stayed in theory,and its implementation techniques are rarely reported.In order to fill this gap,the basic theory of generalized Born approximation is reviewed,and the implementation method of generalized Born approximation is discussed in this paper.In particular,the problem of calculating boundary effect elimination is discussed in detail.Finally,through model trial calculation,the calculation of gradient scattering,by comparing Born approximation and finite difference method,shows that using the generalized Born approximation to calculate gradient scattering achieves higher computational accuracy.
