The waveform of the explosion shock wave under free-field air explosion is an extremely complex problem.It is generally considered that the waveform consists of overpressure peak,positive pressure zone and negative pr...The waveform of the explosion shock wave under free-field air explosion is an extremely complex problem.It is generally considered that the waveform consists of overpressure peak,positive pressure zone and negative pressure zone.Most of current practice usually considers only the positive pressure.Many empirical relations are available to predict overpressure peak,the positive pressure action time and pressure decay law.However,there are few models that can predict the whole waveform.The whole process of explosion shock wave overpressure,which was expressed as the product of the three factor functions of peak,attenuation and oscillation,was proposed in the present work.According to the principle of explosion similarity,the scaled parameters were introduced and the empirical formula was absorbed to form a mathematical model of shock wave overpressure.Parametric numerical simulations of free-field air explosions were conducted.By experimental verification of the AUTODYN numerical method and comparing the analytical and simulated curves,the model is proved to be accurate to calculate the shock wave overpressure under free-field air explosion.In addition,through the model the shock wave overpressure at different time and distance can be displayed in three dimensions.The model makes the time needed for theoretical calculation much less than that for numerical simulation.展开更多
The motion of a bubble near the free surface is solved by the boundary element method based on the linear wave equation, and the influence of fluid compressibility on bubble dynamics is analyzed. Based on the solution...The motion of a bubble near the free surface is solved by the boundary element method based on the linear wave equation, and the influence of fluid compressibility on bubble dynamics is analyzed. Based on the solution of the bubble motion, the far-field radiation noise induced by the bubble is calculated using Kirchhoff moving boundary integral equation, and the influence of free surface on far-field noise is researched. As the results, the oscillation amplitude of the bubble is weakened in compressible fluid compared with that in incompressible fluid, and the free surface amplifies the effect of fluid compressibility. When the distance between the bubble and an observer is much larger than that between the bubble and free surface, the sharp wave trough of the sound pressure at the observer occurs. With the increment of the distance between the bubble and free surface, the time of the wave trough appearing is delayed and the value of the wave trough increase. When the distance between the observer and the bubble is reduced, the sharp wave trough at the observer disappears.展开更多
The effect of magnetic field on the plane vibrations for an elastodynamic orthotropic sphere is studied. Equations of elastodynamic problems of the orthotropic hollow sphere in terms of displacement are solved. The nu...The effect of magnetic field on the plane vibrations for an elastodynamic orthotropic sphere is studied. Equations of elastodynamic problems of the orthotropic hollow sphere in terms of displacement are solved. The numerical results of the frequency equations in the presence of magnetic field are discussed and shown graphically. Compar-isons are made with the result in the presence and absence of magnetic field in the case of orthotropic sphere. The results show that the effect of magnetic field is very pronounced.展开更多
After reviewing the studies on the lateral artificial boundaries in dynamic soil-structure interactions,the free field boundary was theoretically analyzed in asymmetric-and symmetric-matrix forms.First,the lumped mass...After reviewing the studies on the lateral artificial boundaries in dynamic soil-structure interactions,the free field boundary was theoretically analyzed in asymmetric-and symmetric-matrix forms.First,the lumped mass system was combined with viscous or viscoelastic elements to obtain a lumped mass-free field boundary.Second,typical examples were implemented using the finite element software ABAQUS.The incident shear wave was taken to be perpendicular to the bottom to verify the effectiveness of the lumped mass-free field under various sites:underground structures,uniform sites,and layered sites.Finally,the accuracy of the lumped mass-free field boundary was compared with those of the viscoelastic and roller boundaries on different calculation scales,soil damping ratios,structure sizes,and ground motion characteristics.Subsequently,the engineering design values for different damping ratios are given.The results show that the precision of the lumped mass-free field boundary was reasonable,and the operation was simple within the same engineering application.展开更多
Cherenkov free electron laser(CFEL) is simulated numerically by using the single particle method to optimize the electron beam. The electron beam is assumed to be moving near the surface of a flat dielectric slab alon...Cherenkov free electron laser(CFEL) is simulated numerically by using the single particle method to optimize the electron beam. The electron beam is assumed to be moving near the surface of a flat dielectric slab along a growing radiation. The set of coupled nonlinear differential equations of motion is solved to study the electron dynamics. For three sets of parameters, in high power CFEL, it is found that an axial magnetic field is always necessary to keep the electron beam in the interaction region and its optimal strength is reported for each case. At the injection point, the electron beam’s distance above the dielectric surface is kept at a minimum value so that the electrons neither hit the dielectric nor move away from it to the weaker radiation fields and out of the interaction region. The optimal electron beam radius and current are thereby calculated. This analysis is in agreement with two previous numerical studies for a cylindrical waveguide but is at odds with analytical treatments of a flat dielectric that does not use an axial magnetic field. This is backed by an interesting physical reasoning.展开更多
In the semi-free acoustic field, the actual acoustic pressure at any point is composed of two parts: The direct acoustic pressure and the reflected acoustic pressure. The general acoustic holographic theories and alg...In the semi-free acoustic field, the actual acoustic pressure at any point is composed of two parts: The direct acoustic pressure and the reflected acoustic pressure. The general acoustic holographic theories and algorithms request that there is only the direct acoustic pressure contained in the pressure at any point on the hologram surface, consequently, they cannot be used to reconstruct acoustic source and predict acoustic field directly. To take the reflected pressure into consideration, near-field acoustic holography for semi-free acoustic field based on wave superposition approach is proposed to realize the holographic reconstruction and prediction of the semi-free acoustic field, and the wave superposition approach is adopted as a holographic transform algorithm. The proposed theory and algorithm are realized and verified with a numerical example, and the drawbacks of the general theories and algorithms in the holographic reconstruction and prediction of the semi-free acoustic field are also demonstrated by this numerical example.展开更多
Basic equations are derived for kinematical force-free fields of a magnetic arch in a perfect conducting fluid, and the stationary and unsteady similarity solutions are discussed in this paper.
Through theoretical analysis,we show how aligning pulse durations affect the degree and the time-rate slope of nitrogen field-free alignment at a fixed pulse intensity.It is found that both the degree and the slope fi...Through theoretical analysis,we show how aligning pulse durations affect the degree and the time-rate slope of nitrogen field-free alignment at a fixed pulse intensity.It is found that both the degree and the slope first increase,then saturate,and finally decrease with the increasing pump duration.The optimal durations for the maximum degree and the maximum slope of the alignment are found to be different.Additionally,they are found to mainly depend on the molecular rotational period,and are affected by the temperature and the aligning pump intensities.The mechanism of molecular alignment is also discussed.展开更多
Based on Thomas-Fermi model, the interior potential boundary condition with the effect of electric field was defined, the calculation method of free energy for atom cluster under electric field was established. The ch...Based on Thomas-Fermi model, the interior potential boundary condition with the effect of electric field was defined, the calculation method of free energy for atom cluster under electric field was established. The change of free energy of Al-Cu-Li alloy under the effect of electric field was calculated quantitatively. It is shown that: near the zero electric field and the side of positive electric field, the free energy of Cu4LiAl7 compound at aging temperature 460 K is higher than that of free energy at solid solution temperature 725 K, but once the negative electric field increases to certain degree there will be opposite result. Under the effect of electric field, at 725 K the free energy of Cu4LiAl7 is higher than that of Al-1.0%Li-4.0%Cu, and at 460 K the free energy of compound is lower than that of solid solution. When the copper content in the Al-Li-Cu solid solution is below 5%, under the effect of electric field the free energy of solid solution increases gradually with the increasing of copper content, but the increasing amplitude reduces with the increasing of copper content. The free energy of binary solid solution increases with the addition of lithium, and with the increasing of electric field intensity the free energy margin of two kinds of solid solution becomes bigger.展开更多
This paper studies the molecular rotational excitation and field-free spatial alignment in a nonresonant intense laser field numerically and analytically by using the time-dependent SchrSdinger equation. The broad rot...This paper studies the molecular rotational excitation and field-free spatial alignment in a nonresonant intense laser field numerically and analytically by using the time-dependent SchrSdinger equation. The broad rotational wave packets excited by the femtosecond pulse are defined in conjugate angle space, and their coefficients are obtained by solving a set of coupled linear equations. Both single molecule orientation angles and an ensemble of O2 and CO molecule angular distributions are calculated in detail. The numerical results show that, for single molecule highest occupied molecular orbital (HOMO) symmetry σ tends to have a molecular orientation along the laser polarization direction and the permanent dipole moment diminishes the mean of the orientation angles; for an ensemble of molecules, angular distributions provide more complex and additional information at times where there are no revivals in the single molecule plot. In particular, at the revival peak instant, with the increase of temperature of the molecular ensemble, the anisotropic angular distributions with respect to the laser polarization direction of the πg orbital gradually transform to the symmetrical distributions regarding the laser polarization vector and for two HOMO configurations angular distributions of all directions are confined within a smaller angle when the temperature of the molecular ensemble is higher.展开更多
A method of measuring in-situ magnetic field gradient is proposed in this paper. The magnetic shield is widely used in the atomic magnetometer. However, there is magnetic field gradient in the magnetic shield, which w...A method of measuring in-situ magnetic field gradient is proposed in this paper. The magnetic shield is widely used in the atomic magnetometer. However, there is magnetic field gradient in the magnetic shield, which would lead to additional gradient broadening. It is impossible to use an ex-situ magnetometer to measure magnetic field gradient in the region of a cell, whose length of side is several centimeters. The method demonstrated in this paper can realize the in-situ measurement of the magnetic field gradient inside the cell, which is significant for the spin relaxation study. The magnetic field gradients along the longitudinal axis of the magnetic shield are measured by a spin-exchange relaxation-free (SERF) magnetometer by adding a magnetic field modulation in the probe beam's direction. The transmissivity of the cell for the probe beam is always inhomogeneous along the pump beam direction, and the method proposed in this paper is independent of the intensity of the probe beam, which means that the method is independent of the cell's transmissivity. This feature makes the method more practical experimentally. Moreover, the AC-Stark shift can seriously degrade and affect the precision of the magnetic field gradient measurement. The AC-Stark shift is suppressed by locking the pump beam to the resonance of potassium's D1 line. Furthermore, the residual magnetic fields are measured with σ+- and σ--polarized pump beams, which can further suppress the effect of the AC-Stark shift. The method of measuring in-situ magnetic field gradient has achieved a magnetic field gradient precision of better than 30 pT/mm.展开更多
Any electronic eigenstate of the paramagnetic ion open-shell is characterized by the three independent multipole asphericities for and 6 related to the second moments of the relevant crystal-field splittings by , wher...Any electronic eigenstate of the paramagnetic ion open-shell is characterized by the three independent multipole asphericities for and 6 related to the second moments of the relevant crystal-field splittings by , where . The Ak as the reduced matrix elements can serve as a reliable measure of the state capability for the splitting produced by the k-rank component of the crystal-field Hamiltonian. These multipolar characteristics allow one to verify any fitted crystal-field parameter set by comparing the calculated second moments and the experimental ones of the relevant crystal-field splittings. We present the multipole characteristics Ak for the extensive set of eigenstates from the lower parts of energy spectra of the tripositive 4 f N ions applying in the calculations the improved eigenfunctions of the free lanthanide ions obtained based on the M. Reid f-shell programs. Such amended asphericities are compared with those achieved for the simplified Russell-Saunders states. Next, they are classified with respect to the absolute or relative weight of Ak in the multipole structure of the considered states. For the majority of the analyzed states (about 80%) the Ak variation is of order of only a few percent. Some essential changes are found primarily for several states of Tm3+, Er3+, Nd3+, and Pr3+ ions. The detailed mechanisms of such Ak changes are unveiled. Particularly, certain noteworthy cancelations as well as enhancements of their magnitudes are explained.展开更多
The introduction of a new concept of space-energy duality serves to extend the applicability of the Einstein field equation in the context of a 4-index framework. The utilization of the Weyl tensor enables the derivat...The introduction of a new concept of space-energy duality serves to extend the applicability of the Einstein field equation in the context of a 4-index framework. The utilization of the Weyl tensor enables the derivation of Einstein’s equations in the 4-index format. Additionally, a two-index field equation is presented, comprising a conventional Einstein field equation and a trace-free Einstein equation. Notably, the cosmological constant is associated with a novel concept that facilitates the encoding of space and energy information, thereby enabling the recognition of mutual interactions between space and energy in the presence of gravitational forces, as dictated by Einstein’s field equations (EFE) and Trace-Free Einstein Equation (TFE).展开更多
基金partially sponsored by Foundation of PLA Rocket Force
文摘The waveform of the explosion shock wave under free-field air explosion is an extremely complex problem.It is generally considered that the waveform consists of overpressure peak,positive pressure zone and negative pressure zone.Most of current practice usually considers only the positive pressure.Many empirical relations are available to predict overpressure peak,the positive pressure action time and pressure decay law.However,there are few models that can predict the whole waveform.The whole process of explosion shock wave overpressure,which was expressed as the product of the three factor functions of peak,attenuation and oscillation,was proposed in the present work.According to the principle of explosion similarity,the scaled parameters were introduced and the empirical formula was absorbed to form a mathematical model of shock wave overpressure.Parametric numerical simulations of free-field air explosions were conducted.By experimental verification of the AUTODYN numerical method and comparing the analytical and simulated curves,the model is proved to be accurate to calculate the shock wave overpressure under free-field air explosion.In addition,through the model the shock wave overpressure at different time and distance can be displayed in three dimensions.The model makes the time needed for theoretical calculation much less than that for numerical simulation.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51679044 and 51479041)
文摘The motion of a bubble near the free surface is solved by the boundary element method based on the linear wave equation, and the influence of fluid compressibility on bubble dynamics is analyzed. Based on the solution of the bubble motion, the far-field radiation noise induced by the bubble is calculated using Kirchhoff moving boundary integral equation, and the influence of free surface on far-field noise is researched. As the results, the oscillation amplitude of the bubble is weakened in compressible fluid compared with that in incompressible fluid, and the free surface amplifies the effect of fluid compressibility. When the distance between the bubble and an observer is much larger than that between the bubble and free surface, the sharp wave trough of the sound pressure at the observer occurs. With the increment of the distance between the bubble and free surface, the time of the wave trough appearing is delayed and the value of the wave trough increase. When the distance between the observer and the bubble is reduced, the sharp wave trough at the observer disappears.
文摘The effect of magnetic field on the plane vibrations for an elastodynamic orthotropic sphere is studied. Equations of elastodynamic problems of the orthotropic hollow sphere in terms of displacement are solved. The numerical results of the frequency equations in the presence of magnetic field are discussed and shown graphically. Compar-isons are made with the result in the presence and absence of magnetic field in the case of orthotropic sphere. The results show that the effect of magnetic field is very pronounced.
基金Natural Science Foundation of Henan Province under Grant No.222300420415。
文摘After reviewing the studies on the lateral artificial boundaries in dynamic soil-structure interactions,the free field boundary was theoretically analyzed in asymmetric-and symmetric-matrix forms.First,the lumped mass system was combined with viscous or viscoelastic elements to obtain a lumped mass-free field boundary.Second,typical examples were implemented using the finite element software ABAQUS.The incident shear wave was taken to be perpendicular to the bottom to verify the effectiveness of the lumped mass-free field under various sites:underground structures,uniform sites,and layered sites.Finally,the accuracy of the lumped mass-free field boundary was compared with those of the viscoelastic and roller boundaries on different calculation scales,soil damping ratios,structure sizes,and ground motion characteristics.Subsequently,the engineering design values for different damping ratios are given.The results show that the precision of the lumped mass-free field boundary was reasonable,and the operation was simple within the same engineering application.
文摘Cherenkov free electron laser(CFEL) is simulated numerically by using the single particle method to optimize the electron beam. The electron beam is assumed to be moving near the surface of a flat dielectric slab along a growing radiation. The set of coupled nonlinear differential equations of motion is solved to study the electron dynamics. For three sets of parameters, in high power CFEL, it is found that an axial magnetic field is always necessary to keep the electron beam in the interaction region and its optimal strength is reported for each case. At the injection point, the electron beam’s distance above the dielectric surface is kept at a minimum value so that the electrons neither hit the dielectric nor move away from it to the weaker radiation fields and out of the interaction region. The optimal electron beam radius and current are thereby calculated. This analysis is in agreement with two previous numerical studies for a cylindrical waveguide but is at odds with analytical treatments of a flat dielectric that does not use an axial magnetic field. This is backed by an interesting physical reasoning.
基金This project is supported by National Natural Science Foundation of China (No.10504006, No.50575063).
文摘In the semi-free acoustic field, the actual acoustic pressure at any point is composed of two parts: The direct acoustic pressure and the reflected acoustic pressure. The general acoustic holographic theories and algorithms request that there is only the direct acoustic pressure contained in the pressure at any point on the hologram surface, consequently, they cannot be used to reconstruct acoustic source and predict acoustic field directly. To take the reflected pressure into consideration, near-field acoustic holography for semi-free acoustic field based on wave superposition approach is proposed to realize the holographic reconstruction and prediction of the semi-free acoustic field, and the wave superposition approach is adopted as a holographic transform algorithm. The proposed theory and algorithm are realized and verified with a numerical example, and the drawbacks of the general theories and algorithms in the holographic reconstruction and prediction of the semi-free acoustic field are also demonstrated by this numerical example.
文摘Basic equations are derived for kinematical force-free fields of a magnetic arch in a perfect conducting fluid, and the stationary and unsteady similarity solutions are discussed in this paper.
基金Project supported by the National Natural Science Foundation of China (Grants Nos. 10634020,11074014 and 10821062)
文摘Through theoretical analysis,we show how aligning pulse durations affect the degree and the time-rate slope of nitrogen field-free alignment at a fixed pulse intensity.It is found that both the degree and the slope first increase,then saturate,and finally decrease with the increasing pump duration.The optimal durations for the maximum degree and the maximum slope of the alignment are found to be different.Additionally,they are found to mainly depend on the molecular rotational period,and are affected by the temperature and the aligning pump intensities.The mechanism of molecular alignment is also discussed.
基金Project(50671084) supported by the National Natural Science Foundation of ChinaProject(2003E103) supported by Natural Science Foundation of Shaanxi Province, China
文摘Based on Thomas-Fermi model, the interior potential boundary condition with the effect of electric field was defined, the calculation method of free energy for atom cluster under electric field was established. The change of free energy of Al-Cu-Li alloy under the effect of electric field was calculated quantitatively. It is shown that: near the zero electric field and the side of positive electric field, the free energy of Cu4LiAl7 compound at aging temperature 460 K is higher than that of free energy at solid solution temperature 725 K, but once the negative electric field increases to certain degree there will be opposite result. Under the effect of electric field, at 725 K the free energy of Cu4LiAl7 is higher than that of Al-1.0%Li-4.0%Cu, and at 460 K the free energy of compound is lower than that of solid solution. When the copper content in the Al-Li-Cu solid solution is below 5%, under the effect of electric field the free energy of solid solution increases gradually with the increasing of copper content, but the increasing amplitude reduces with the increasing of copper content. The free energy of binary solid solution increases with the addition of lithium, and with the increasing of electric field intensity the free energy margin of two kinds of solid solution becomes bigger.
基金supported by the Program of Excellent Team in Harbin Institute of Technologythe Program for New Century Excellent Talents in University (NCET)National Natural Science Foundation of China (Grant Nos 10774033,60878018 and 10674036)
文摘This paper studies the molecular rotational excitation and field-free spatial alignment in a nonresonant intense laser field numerically and analytically by using the time-dependent SchrSdinger equation. The broad rotational wave packets excited by the femtosecond pulse are defined in conjugate angle space, and their coefficients are obtained by solving a set of coupled linear equations. Both single molecule orientation angles and an ensemble of O2 and CO molecule angular distributions are calculated in detail. The numerical results show that, for single molecule highest occupied molecular orbital (HOMO) symmetry σ tends to have a molecular orientation along the laser polarization direction and the permanent dipole moment diminishes the mean of the orientation angles; for an ensemble of molecules, angular distributions provide more complex and additional information at times where there are no revivals in the single molecule plot. In particular, at the revival peak instant, with the increase of temperature of the molecular ensemble, the anisotropic angular distributions with respect to the laser polarization direction of the πg orbital gradually transform to the symmetrical distributions regarding the laser polarization vector and for two HOMO configurations angular distributions of all directions are confined within a smaller angle when the temperature of the molecular ensemble is higher.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61227902,61374210,and 61121003)
文摘A method of measuring in-situ magnetic field gradient is proposed in this paper. The magnetic shield is widely used in the atomic magnetometer. However, there is magnetic field gradient in the magnetic shield, which would lead to additional gradient broadening. It is impossible to use an ex-situ magnetometer to measure magnetic field gradient in the region of a cell, whose length of side is several centimeters. The method demonstrated in this paper can realize the in-situ measurement of the magnetic field gradient inside the cell, which is significant for the spin relaxation study. The magnetic field gradients along the longitudinal axis of the magnetic shield are measured by a spin-exchange relaxation-free (SERF) magnetometer by adding a magnetic field modulation in the probe beam's direction. The transmissivity of the cell for the probe beam is always inhomogeneous along the pump beam direction, and the method proposed in this paper is independent of the intensity of the probe beam, which means that the method is independent of the cell's transmissivity. This feature makes the method more practical experimentally. Moreover, the AC-Stark shift can seriously degrade and affect the precision of the magnetic field gradient measurement. The AC-Stark shift is suppressed by locking the pump beam to the resonance of potassium's D1 line. Furthermore, the residual magnetic fields are measured with σ+- and σ--polarized pump beams, which can further suppress the effect of the AC-Stark shift. The method of measuring in-situ magnetic field gradient has achieved a magnetic field gradient precision of better than 30 pT/mm.
文摘Any electronic eigenstate of the paramagnetic ion open-shell is characterized by the three independent multipole asphericities for and 6 related to the second moments of the relevant crystal-field splittings by , where . The Ak as the reduced matrix elements can serve as a reliable measure of the state capability for the splitting produced by the k-rank component of the crystal-field Hamiltonian. These multipolar characteristics allow one to verify any fitted crystal-field parameter set by comparing the calculated second moments and the experimental ones of the relevant crystal-field splittings. We present the multipole characteristics Ak for the extensive set of eigenstates from the lower parts of energy spectra of the tripositive 4 f N ions applying in the calculations the improved eigenfunctions of the free lanthanide ions obtained based on the M. Reid f-shell programs. Such amended asphericities are compared with those achieved for the simplified Russell-Saunders states. Next, they are classified with respect to the absolute or relative weight of Ak in the multipole structure of the considered states. For the majority of the analyzed states (about 80%) the Ak variation is of order of only a few percent. Some essential changes are found primarily for several states of Tm3+, Er3+, Nd3+, and Pr3+ ions. The detailed mechanisms of such Ak changes are unveiled. Particularly, certain noteworthy cancelations as well as enhancements of their magnitudes are explained.
文摘The introduction of a new concept of space-energy duality serves to extend the applicability of the Einstein field equation in the context of a 4-index framework. The utilization of the Weyl tensor enables the derivation of Einstein’s equations in the 4-index format. Additionally, a two-index field equation is presented, comprising a conventional Einstein field equation and a trace-free Einstein equation. Notably, the cosmological constant is associated with a novel concept that facilitates the encoding of space and energy information, thereby enabling the recognition of mutual interactions between space and energy in the presence of gravitational forces, as dictated by Einstein’s field equations (EFE) and Trace-Free Einstein Equation (TFE).