Vol. 66, No. 13 (2017)
2017-07-05
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS
2017, 66 (13): 134201.
doi: 10.7498/aps.66.134201
Abstract +
The polarization state is one of the most important basic properties of the electromagnetic wave. Researchers have made great efforts to manipulate it. Control of the polarization state of an electromagnetic wave is a promising promotion for figuring out many practical engineering problems in infrared remote sensing, optical communication and infrared target recognition. In this paper, we propose a wide-band and high-efficient linear-polarization converter on the basis of the metamaterial, which is comprised of silicon nanorod array and subwavelength metal grating that can realize a 90 polarization converter of linearly polarized light and is composed of silicon nanorod array cascade subwavelength metal grating:on one side of design located is the cuboid silicon nanorod array, on the other side of the design the subwavelength metallic grating on the silicon substrate, and the angle between silicon nanorod array and subwavelength metal grating is 45. Because of the deference in geometrical dimension between the long axis and the short axis of the nanorod, results of the equivalent refractive index of the long axis direction and the short axis direction are different, and the anisotropic birefrigent effect is formed. Based on the Jones matrix, the feasibility of polarization converter is described. The polarization converter efficiency and polarization state of the structure are simulated and analyzed by the finite-difference time-domain method. And the variation characteristics of polarization converter transmittance are simulated under several nanorod with different heights and widths. In order to improve the contrast ratio and the transmission, the effective medium theory is used to design the metal grating for improving the transmission. According to the theory of optical thin film, we design the subwavelength metal grating with suitable duty cycle as the anti-reflection coating. The simulation results show that the structure can realize 90 rotation of linearly polarized light, the polarization converter efficiency is greater than 60% in a spectral range of 3.4-4.5 m and the contrast ratio is greater than 104 in a spectral range of 3-5 m. This structure can effectively realize the 90 polarization conversion in the spectral range of medium wave infrared and has the advantages of high conversion efficiency and high contrast ratio. In addition, the range of spectral of polarization conversion can be changed by adjusting the height and width of the nanorod. It can be applied to optical transmission control of optical network and optical information system, because of its excellent optical performance with the advantages of high polarization conversion efficiency and wide band in the mid-infrared waveband and low preparation difficulty.
2017, 66 (13): 134202.
doi: 10.7498/aps.66.134202
Abstract +
Ptychographic iterative engine (PIE) method can provide high-resolution amplitude and phase distributions in short-wavelength imaging,such as electron beam and X-ray imaging.Traditional PIE relies on the sub field of view (sub-FoV) scanning,and the coincidence between these adjacent sub-FoVs is required in order to ensure the high accuracy in sample information retrieval.However,in the applications of electron beam imaging,attachments or contaminants on the sample surface will be dragged with the probe light during the sub-FoV scanning due to the adsorption of charges,and the inevitable attachment and contaminant shifting will change the probe light,therefore generating inconsistent probe light,and reducing the imaging resolution and accuracy,since the deteriorated probe light destroys the PIE scanning demands.In order to maintain the high resolution and accuracy in the electron beam imaging,the attachment and contaminant shifting during the sub-FoV scanning should be avoided.Here,a shearing interference based PIE using Mllenstedt biprism is proposed in this paper.Mllenstedt biprism is widely used in the electron beam imaging,and by applying the voltage to the wire,the generated electrical field can control the deflection of the electron beam,working similarly to a biprism modulating the wavefront passing through it.In the proposed approach,setting the Mllenstedt biprism after the sample,and changing the voltage on the Mllenstedt biprism,the beam deflection angle proportional to the added voltage can generate a series of interferograms with different fringe densities.Because the traditional sub-FoV scanning is replaced by wide-field scanning by changing the voltage on the Mllenstedt biprism,the proposed method can maintain the stable probe light,avoiding the inevitable attachment and contaminant shifting,and both the amplitude and phase can be retrieved from these interferograms by using a modified PIE algorithm.In order to verify the proposed PIE method,besides the theoretical analysis,numerical calculations are provided.The biprism phase distribution is adopted to simulate the electron beam deflection caused by the Mllenstedt biprism.Additionally,by changing the voltage on the wire,different biprism phase distributions are generated to produce various interferograms.By the modified PIE method,accurate amplitude and phase distribution within error less than 0.2% can be obtained through using less than 50 iterations,indicating a rapid convergence rate.Moreover,the errors in the imaging system, such as phase deviation,position shifting,and rotation are also quantitatively analyzed.Numerical computation proves that the direction of the biprism can be precisely determined according to the frequency distribution of the fringe,and the accurate sample information can still be retrieved even with a deviation of 30% in phase deviation and 30 m in position shifting,proving the deviations of the direction and position of the Mllenstedt biprism,as well as the phase distribution can be corrected automatically in the iterative process.Finally,the modified PIE relying on the lensfree configuration can reach the resolution of the diffraction limit in imaging similar to those PIE approaches.The proposed technique can overcome difficulties of current PIE in using electron beam,thus promoting the development and application of PIE in electron microscopy.
2017, 66 (13): 134203.
doi: 10.7498/aps.66.134203
Abstract +
Recently,multi-wavelength pulsed lasers have become a research hotspot due to their versatile applications,such as precision spectroscopy,microwave/terahertz photonics,optical signal processing,and wavelength division multiplexed optical fiber communication systems.As a promising candidate,passively mode-locked fiber laser has the advantages of ultrashort pulse,ultrahigh peak power,compact structure and low-cost.In the existing multi-wavelength passively mode-locked fiber lasers,multi-wavelength mode-locked operation is achieved by adjusting the intracavity modulators to a proper state after laser has worked.It is inconvenient for practical use,so,its application scope is restricted.In this paper,a new method to achieve dual-wavelength mode-locked operation in an erbium-doped fiber laser is proposed. For an erbium-doped fiber,the peaks of both absorption and emission spectra overlap in the 1530 nm-region.So the emission light in the 1530 nm-region will be re-absorbed by the erbium-doped fiber with low pump power or long gain fiber.Utilizing the emission re-absorption effect,the gain spectrum can be modified by different lengths of gain fiber. In the experiment,an all-fiber ring cavity is adopted and a transmission-type semiconductor saturable absorber is used as a modelocker.The cavity consists of ～3.2-m-long single mode fiber and an erbium-doped fiber.Gain fibers with different lengths are used in the cavity to reveal the dependence of emission re-absorption on both gain spectrum and mode-locked output spectrum.According to the experimental results,there are two humps in the amplified spontaneous emission spectrum located in the 1530 nm-region and 1560 nm-region,respectively.With the gain fiber length increasing, gain spectrum in the 1530 nm-region is suppressed,and gain intensity in the 1560 nm-region gradually surpasses that in the 1530 nm-region.Based on the experimental results,self-starting dual-wavelength mode-locked operation is achieved with a 31-cm-long gain fiber.The two spectral peaks with close intensity are located at 1532.4 nm and 1552.3 nm, respectively.The maximum output power is 4.8 mW at a repetition rate of 58.01 MHz and a signal-to-noise ratio of 58.2 dB.This self-starting dual-wavelength mode-locked erbium-doped fiber laser is convenient for practical use and can meet the requirements for many potential applications.
2017, 66 (13): 134204.
doi: 10.7498/aps.66.134204
Abstract +
The analytic function for the amplified spontaneous emission spectrum of InP/InGaAsP multi-quantum wells is studied by spectrum fitting. Three fitting functions, Lorentz, Gaussian and Sech line shape functions are chosen, and the analytical expressions for the above three functions are obtained with Levenberg-Marquardt algorithm, respectively. The center wavelength of Lorentz line shape function spectrum fitting is 1548.707 nm with 66.23 nm of full-width half maximum (FWHM), -0.00036484 mW power compensation, 0.98294 of R-square and 4.7674310-6 of residual sum of squares; the center wavelength of Gaussian line shape function spectrum fitting is 1548.651 nm with 61.42 nm of FWHM, 0.00212 mW power compensation, 0.99191 of R-square and 2.2650510-6 of residual sum of squares; the center wavelength of Sech line shape function spectrum fitting is 1548.787 nm with 36.99 nm of FWHM, 0.00222 mW power compensation, 0.98128 of R-square and 5.2433110-6 of residual sum of squares. It can be seen that Gaussian line shape function spectrum fitting has the highest R-square and smallest residual sum of squares, and the residual squares of data are symmetrically distributed among 0.0001. Gaussian line shape function spectrum fitting has higher fitting degree. It is demonstrated that InP/InGaAsP multi-quantum wells is a kind of active layer quantum well structure semiconductor material, whose amplified spontaneous emission spectrum line shape belongs to inhomogeneous broadening due to the effect of lattice defects, the corresponding line shape function is Gaussian line shape function, and the amplified spontaneous emission spectrum line shape function can be used for designing the optical passive devices.
2017, 66 (13): 134302.
doi: 10.7498/aps.66.134302
Abstract +
Based on the Longuet-Higgins wave model theory, a modified phase modulation method of simulating freak waves is improved in this paper. The method can generate freak waves at assigned time and place, and their waveforms can not only maintain the frequency spectrum structure of the target spectrum and also satisfy the wave series statistics to a great extent. Then, the electromagnetic backscattering model of freak and background wave is established by the finite difference time domain method and the two-scale method. After averaging relative deviation and analyzing the error of the root mean square deviation within the measurement uncertainties, considering the computational efficiency, we use the two-scale model method to calculate the electromagnetic scattering coefficient of freak wave. Numerical results show that the normalized radar cross section (NRCS) of freak wave is much smaller than that of background wave. On the other hand, we analyze the electromagnetic scattering properties of freak waves under the different polarization modes, incident angles and incident frequencies. We find that in the condition of grazing incidence, the backscatter coefficient of freak wave increases with the increase of the incident frequency, but the increase amplitude is reduced, which meets the rough surface scattering theory. When the incident frequency is fixed and the incident〉is small, the backscatter coefficient calculation results of freak wave are similar under the condition of different polarizations VV's and HH's, but the backscatter coefficient of freak wave decreases obviously with the increase of incident angle, which is caused by the radar electromagnetic wave that is parallel to the sea surface and contacts it gradually. In addition, we find that the backscatter coefficient calculation result of freak waves under the VV polarization is much higher than under HH polarization from the two groups of experimental figures. According to the result of datum analysis, a conclusion is drawn that we can determine where the freak wave is when the NRCS difference of synthetic aperture radar (SAR) image is smaller than -11.8 dB. In the practical engineering application, the characteristic parameters are difficult to observe, while the difference in electromagnetic scattering coefficient between freak wave and background wave can be calculated from the SAR image of sea surface. This conclusion provides a reference standard for predicting the freak waves in engineering application, through which we can calculate the characteristic parameters of freak wave, determine its position, and study the electromagnetic scattering characteristics under the different polarization modes, incident angles and incident frequencies in future researches.
2017, 66 (13): 134301.
doi: 10.7498/aps.66.134301
Abstract +
A multi-stage model of nonlinear interaction between micro-crack and ultrasound based on equivalent elastic modulus is presented in this paper. In this model, the interface characteristics of micro-cracks at a micro-level and the relative motion at a macro-level are unified into an elastic modulus of the mesoscopic element. The equivalent elastic modulus is used to characterize the stress-strain of the damage region. Then piecewise function is used to describe the nonlinear interaction between ultrasound and micro-crack. Finally, the wave equation is solved by the finite element simulation. In this manner, the nonlinear interaction law between ultrasound and micro-crack is obtained, and the validity of the model is verified. The simulation results also show that compared with bilinear stiffness model and contact surface model, the multi-stage model can well reflect the distortion of the waveform in one period of ultrasonic wave passing through the micro-crack. In addition, the influences of the crack angle, the crack length and the input amplitude on the second harmonics generation and the third harmonics generation are analyzed. In the end, the comparison and analysis of the experimental test and simulation calculations based on the proposed multi-stage model show that the proposed multi-stage model and the experimental test can well reflect the second harmonic signal produced by the nonlinear interaction of micro-crack and ultrasound, and the second harmonic amplitudes of the experimental test are basically the same as the simulation calculations based on the proposed multi-stage model. Thus, the effectiveness of the proposed multi-stage model is verified. The model provides a new simulation method to quantitatively detect the micro-crack by ultrasonic nonlinear effect.
Research and application of plasma recoil pressure physical model for pulsed laser ablation material
2017, 66 (13): 134205.
doi: 10.7498/aps.66.134205
Abstract +
In this paper, the physical properties of plasma in the isothermal expansion process when material is ablated by pulsed laser is analyzed. It is shown that the recoil pressure distribution of the plasma near the material surface indicates an exponential decrease as the distance from the material surface increases and the recoil pressure distribution exhibits the characteristics of a Poisson distribution in the X direction; the recoil pressure distribution is in accordance with Maxwell's velocity distribution law in the Y direction; the recoil pressure distribution conforms to a Gaussian distribution in the Z direction. A three-dimensional plasma recoil pressure equation and the plasma kinetic equation for laser-ablation materials are studied. These equations only require parameters to relate to plasma temperature, laser parameters and material properties, thus having a certain diversity.
The equations are used for numerically analyzing the pulsed laser ablation of a bronze-bonded diamond grinding wheel. The numerical analysis shows that in the X and Y direction the plasma expansion dimension shows linear growth. After the pulse is ended, the plasma expansion dimension values reach their maxima. The plasma expansion velocity shows nonlinear growth. After the pulse is ended, the expansion velocity first increases and then decreases along the X direction and Y direction. Based on the analyses of the plasma expansion dimension and the plasma expansion velocity, the maximum plasma recoil pressure appears at a location approximately 0.05 mm away from the surface of the grinding wheel after approximately 25 ns. Through calculating the Saha equation, the degree of ionization is 0.0012 at 7506 K, and the maximum plasma recoil pressure value is approximately 870 Pa.
The experiments on the pulsed laser ablation of a bronze-bonded diamond grinding wheel under the corresponding conditions are conducted. A high-speed camera is used to observe splash phenomenon in the laser ablation process. A grating spectrometer is used to measure the plasma emission spectrum. According to the Boltzmann plot method, the electron temperature value is calculated to be 7506 K; according to the Stark broadening method, the electron density values range from 7.6451015 to 1.16081016 cm-3 and the recoil pressure values from 792 to 1203 Pa. The experiments show that the recoil pressure during the pulsed laser ablation of bronze-bonded diamond grinding wheel process can be ignored, and the correctness and feasibility of the plasma recoil pressure equation are also verified, which has heuristic significance for optimizing the laser ablation process.
2017, 66 (13): 134206.
doi: 10.7498/aps.66.134206
Abstract +
The positioning accuracy of the footprint of a satellite laser altimeter is primarily dependent on the accuracy of its laser pointing, e.g., a 30 arcsec pointing bias will induce 87 m horizontal error and 1.5 m vertical error when the altitude is 600 km and the laser incident angle is 1. In order to achieve the three-dimensional high-precision observation on the Earth surface, on-orbit calibration is needed to remove the systematic pointing bias mainly arising from the thermal effect. The current methods of on-orbit calibration and verification for laser altimeters are the attitude maneuvering and the footprint detection, respectively. However, the attitude maneuvering is not applicable to the existing satellite platform of China, which uses the large platform with a three-axis attitude stabilization system. The current footprint detection method can only achieve on-orbit verification task, i.e., the horizontal and vertical errors can be evaluated by analyzing the captured laser footprints but the systematic pointing bias cannot be estimated and removed. An improved design scenario of energy detector that is used for capturing laser footprint is given in this paper. The quantification level of the captured laser energy is equal to 8, which is bigger than that of the energy detector designed for geoscience laser altimeter systems corresponding to level 2. Benefiting from the new design scenario, fewer detectors are needed to achieve the same precision when calculating the centroid geolocations of captured footprints. A new systematic misalignment estimation model in the laser direction cosines is deduced, and it is used to estimate the systematic bias by using the detected footprints based on the Gauss-Markoff criterion. With the new detectors and bias estimation model, the footprint detection method now can achieve on-orbit calibration, as well as on-orbit verification. According to the presented calculation model, simulation experiments are operated to analyse three effects that may influence the performance of the footprint detection on-orbit calibration, i.e., the laser incident angle on the detector array, the surface roughness of the site where detectors lay out, and the grid density of the detector array. The simulation results indicate that, when the horizontal positioning accuracy of the captured footprint centroid demands better than 1.8 m which corresponds to 0.6 arcsec laser pointing accuracy when the altitude of the satellite is 600 km, the grid distance of the detector array can be 20 m, the laser incident angle on the detector array should be larger than 3, and the surface roughness of the calibration site should be less than 0.1 m. The designed detectors and calibration method will be used to capture laser footprints and remove the systematic bias for the laser altimeter on China GF-7 satellite, which is one of the upcoming high-resolution satellites for Earth observation.
2017, 66 (13): 134207.
doi: 10.7498/aps.66.134207
Abstract +
Intense few-cycle pulses are widely used in transient light synthesis,high harmonic generation (HHG) and especially in isolated attosecond pulse generation.To obtain intense few-cycle pulses,the intense supercontinuum is needed.The traditional way to generate intense supercontinuum is using rare gas filled hollow-core fibers.Since the input energy of hollow-core fiber system is limited to a level of tens of mJ,it is necessary to find new ways to achieve energy scaling.In this paper we demonstrate the efficient generation of supercontinuum by solid thin plates,compression and its application in HHG.
The Ti:sapphire laser used in the present experiment emits 0.8 mJ in energy with a duration of 30 fs at 1 kHz.After passing through a 3:1 telescope,the beam has a diameter changed from 12 mm to 4 mm.Then the laser is focused by an f=2000 mm lens into a 600 m-diameter spot.After propagating through 7 fused silica plates placed at Brewster's angle (55.5) with a thickness of 0.1 mm,the 0.7 mJ octave spanning supercontinuum is achieved,corresponding to an efficiency of 87.5%.The first three plates are placed at 31,11,2.5 mm in front of the beam waist,and the last four plates are placed at 2,7,12,17 mm behind the beam waist respectively.With a pair of wedges and 4 pairs of chirped mirrors,the 0.68 mJ supercontinuum is compressed to a duration of 6.3 fs,which is measured by TG-FROG.
The 0.5 mJ,6.3 fs pulse is used to perform high-harmonic generation experiment.The beam diameter is 150 m when focused by an f=400 mm lens,with a laser intensity of 8.11014 W/cm2.The 1 mm Ne gas jet is used to perform HHG experiment with a back pressure of 300 mbar.To block the near-infrared light,a 150 m Zirconium foil is placed behind the gas jet.Then the XUV spectrum is detected by a spectrometer,which consists of a flat field grating and a CCD camera.For driving pulses of few-cycle regime without dispersion,the cutoff spectrum of HHG is continuous.But when the pulse is stretched by positive or negative dispersion,the cutoff spectrum turns discrete.The HHG result is that the cutoff region is continuous when the wedge is in a certain place.Then by increasing or reducing the insertion of the wedge,the cutoff spectrum becomes discrete.Our result is consistent with HHG generated by few-cycle pulses.
In conclusion,we demonstrate high-harmonic generation based on supercontinuum generated by solid thin plates. The 0.7 mJ supercontinuum is achieved when 0.8 mJ pulses are injected to 7 thin fused silica plates.The supercontinuum is compressed to 0.68 mJ,6.3 fs.The 0.5 mJ,6.3 fs pulse is used to perform HHG experiments.The HHG result was consistent with few-cycle driving pulses.Our research indicates that solid state supercontinuum has great potential applications in HHG and isolated attosecond pulse generation.
2017, 66 (13): 134208.
doi: 10.7498/aps.66.134208
Abstract +
When infrared (IR) is over 12 m, conventional chalcogenide (ChG) fibers are confused by the multiphonon absorption of Se, and novel glass materials for far-IR have become one of hot research points in recent years. Here, a novel ChG glass and fiber for far-IR without containing Se/As is well investigated. The glasses GeTe-AgI are purified by distillation and synthesized by melt-quenching method. The thermal properties and the infrared transmissions are reported. The step-index fiber, fabricated via a novel extrusion method, exhibits excellent transmission at 8-15 m: 24 dB/m in a range of 8-15 m and 15.6 dB/m at 10.6 m. The influences of oxygen contaminant and the purity of AgI on the glass transmission and fiber attenuation are discussed. Structural and physical properties of GeTe-AgI glass system are studied with differential scanning calorimetry and ellipsometer instrument. Optical spectra of GeTe-AgI glass system are obtained by spectrophotometer and infrared spectrometer. Main purification process with oxygen-getters (magnesium) is disclosed. The fiber attenuation is measured by the cut-back method with a Fourier transform infrared spectrometer. The lowest loss of this fiber can be reduced to 15.6 dB/m at 10.6 m. The results show that these glasses are well transparent in a wide IR window from 1.7 to 25 m, and these glass fibers can transmit light up to 15 m, thus the GeTe-AgI glass system is one of good candidates for far-IR. The fiber attenuation can be reduced effectively by the reasonable purification and novel extruded-processing. These environment friendly fibers are suited for far-IR applications, such as greenhouse gas sensing and the power delivery of CO2 laser.
2017, 66 (13): 134701.
doi: 10.7498/aps.66.134701
Abstract +
The immiscible displacement process in micro-channel, which widely existes in daily life and industrial production, is an important research subject. This subject is a typical contact line problem involving complicated fluid-fluid interactions and fluid-solid interactions which have attracted the interest of many scholars. Although the immiscible displacement in micro-channels has been studied by some researches, the problem is still not fully understood because the mechanism of the immiscible displacement is very complex. In order to further explain the physical mechanism of immiscible displacement process in micro-channels, detailed numerical simulations are carried out in a complex micro-channel containing a semicircular cavity and a semicircular by bulge using an improved pseudo-potential lattice Boltzmann method (LBM). This model overcomes the drawback of the dependence of the fluid properties on the grid size, which exists in the original pseudo-potential LBM. Initially, the cavity is filled with the liquid and the rest of the area is filled with its vapour. The semicircular bulge represents the roughness of the micro-channel. The approach is first validated by the Laplace law. The results show that the numerical results are in good agreement with the theoretical predictions. Then the model is employed to study the immiscible displacement process in the micro-channel. The effects of the surface wettability, the surface roughness, the viscosity ratio between the liquid phase and the gas phase, and the distance between the semicircular cavity and the semicircular bulge are studied. The simulation results show that the influence of the surface wettability on the displacement process is a decisive factor compared with other factors. With the increase of the contact angle, the displacement efficiency increases and the displacement time decreases. When the contact〉is larger than a certain value, all of the liquid can be displaced from the cavity. At that time, the displacement efficiency is equal to 1. The above results are consistent with the theoretical prediction that with the increase of the contact angle, the liquid is easily driven out of the cavity because the adhesion force of the liquid in the cavity decreases. On the other hand, the influence of the surface roughness on the displacement process is more complex. The displacement efficiency increases with the radius of the semicircle bulge increasing in a certain range. When the radius is larger than a certain value, the liquid cannot be ejected from the cavity due to the velocity around the cavity is too small. Furthermore, the liquid cannot be displaced from the cavity at a small viscosity ratio. As the viscosity ratio increases, the displacement efficiency increases and the displacement time decreases. As for the distance between the semicircular bulge and the semicircular cavity, it promotes the displacement process at an early stage. When the distance exceeds a certain value, it has little effect on the displacement process.
CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES
2017, 66 (13): 136103.
doi: 10.7498/aps.66.136103
Abstract +
Mg-Al alloys are the most widely used Mg-based industrial alloys, but their composition rules behind the apparent industrial specifications are largely unknown, which hinders the development of new alloys. As is well known, industrial alloys often undergo the process of a high-temperature solution treatment, and the final structures originate from the single-phase solid solution parent state. Since solid solutions are characterized by short-range chemical orders, necessarily the optimum alloy composition should be related to the presence of a certain short-range chemical structure unit. In the present paper, by introducing our cluster-resonance model for short-range-order structure description of solid solutions, a chemical structure unit of Mg-Al binary solid solution is established,[Al-Mg12]Mg1, which represents the characteristic short-range-order structure, with the bracketed part being the nearest-neighbor cluster centered by Al and shelled by 12Mg and with one glue atom Mg located between the clusters. Because of the existence of other alloying elements besides Al, a general formula[(Al, A)1-Mg12]-(Mg, B) is then proposed, where A represents the elements showing a negative mixing enthalpy with Mg, while B showing a positive one. This formula is used to explain the multi-component Mg-Al industrial alloys. Based on this chemical formula, typical Mg-Al industrial alloy specifications in ASTM handbook are well explained. For instance, cast AZ63A alloy is formulated as[Al0.78Zn0.16-Mg12]Mg1.04Mn0.02, cast AZ81A as[Al0.97Zn0.03-Mg12]Mg0.98Mn0.02, and wrought AZ80A as[Al1.02n0.03-Mg12]Mg0.94Mn0.01. The deviations from the ideal chemical structure unit in different Mg-Al alloys are well correlated to their corresponding alloy performances. Those alloys, where the numbers of center atoms are close to ones in their cluster formulas, exhibit excellent comprehensive mechanical performances in both strength and plasticity. While the alloy with less than one center atom only shows good plastic performance with a relatively poor strength, and the one with more than one center atom shows just the reverse tendency. Among cast Mg-Al alloys, AZ81A, whose cluster formula completely matches the stable chemical structure unit, exhibits the optimized combination of strength (275 MPa) and plasticity (elongation 15%). Among wrought Mg-Al alloys, AZ61A and AZ80A, whose cluster formulas show minor deviations of -0.11 and 0.05 in the center site from the ideal chemical structure unit, also have good comprehensive mechanical properties, respectively with the strengths of 310 MPa and 380 MPa, and the elongations of 16% and 7%. Based on the results in the present paper, the simple composition rule behind the complex industrial alloy specifications as unveiled here, can be a powerful approach to the development of Mg-Al alloys.
2017, 66 (13): 136401.
doi: 10.7498/aps.66.136401
Abstract +
In the electromagnetic levitation experiment, the liquid flow in the undercooled liquid alloy remarkably affects the relevant thermodynamic property measurement and solidification microstructure. Therefore, it is of great importance to understand the fluid convection inside the undercooled melt. Theoretical calculation and electromagnetic levitation experiment have been used to investigate the internal velocity distribution and rapid solidification mechanism of Fe50Cu50 alloy. Based on axisymmetric electromagnetic levitation model, the distribution patterns of magnetic flux density and inducted current for levitated Fe50Cu50 alloy are calculated together with the mean Lorenz force. The Navier-Stokes equations are further taken into account in order to clarify the internal fluid flow. The results of the theoretical calculation reveal that the fluid velocity within levitated melt is strongly dependent on three factors, i.e., current density, current frequency and melt undercooling. As one of these factors increases, the maximum fluid velocity decreases while the average fluid velocity increases. Meanwhile, the area with fluid velocity larger than 100 mm·-1 is significantly extended. Furthermore, the fluid flow within levitated melt displays an annular tubular distribution characteristic. The Fe50Cu50 alloy melt is undercooled and solidified under electromagnetic levitation condition. In this undercooling regime △ T50Cu50 alloy melt has suppressed phase separation substantially. Once the undercooling attains a value of 150 K, metastable phase separation leads to the formation of layered pattern structure consisting of floating Fe-rich zone and sinking Cu-rich zone. A core-shell macrosegregation morphology with the Cu-rich zone distributed in the center and outside of the sample and Fe-rich zone in the middle occurs if the undercooling increases to 204 K. With the enhancement of undercooling after phase separation, the grain size of α -Fe dendrites in Cu-rich zone presents a decreasing trend. In contrast to the phase separated morphology of Fe50Cu50 alloy under the glass fluxing condition, the phase separated morphologies show obviously different characteristics. In such a case, the forced convection induced by electromagnetic stirring results in the formation of wavy interface between Fe-rich and Cu-rich zones, the distorted morphology of the Cu-rich spheres distributed in the Fe-rich zone, and the increased appearance probabilities of Cu-rich spheres at the upper part of electromagnetically levitated sample. Experimental observations demonstrate that the distribution pattern of Cu-rich spheres in Fe-rich zone is influenced by the tubular fluid flow inside the melt.
2017, 66 (13): 136801.
doi: 10.7498/aps.66.136801
Abstract +
As a kind of nano-material, graphyne nanoribbon has some physical properties and its properties should be studied for its better usage. In the process of preparing graphyne nanoribbons, it is possible that vacancy defects exist in the lattice structure, which will affect the physical properties of the graphyne nanoribbons. The flotation of graphyne is closer to the actual situation in engineering than the complete graphyne nanoribbons, and the diversity of vacancy defects can lead to various thermal conductivities, so it is very important to simulate the effects of various vacancy defects on thermal conductivity. In order to better predicte and control heat transfer characteristics of graphyne nanoribbons, this paper focuses on the effects of vacancy defects on the heat transfer characteristics of graphyne nanoribbons. According to the different cutting directions of graphyne nanoribbons, two different types of graphyne nanoribbons are obtained, i.e., armchair type and zigzag type. We compare the effects of vacancy defects on the thermal conductivity of two different chiral graphynes nanoribbons to improve the persuasiveness of the conclusion. In this paper, non-equilibrium molecular dynamics method is adopted, by applying periodic boundary conditions in the length direction of the nanoribbons, the interaction between the carbon-carbon atoms is described based on a potential function of adaptive intermolecular reactive empirical bond order (AIREBO). At 300 K, the effects of single vacancy defect in the acetylene chain, single vacancy defect in the benzene ring or double vacancy defects in the acetylene chain on the thermal conductivities of single-layer graphyne nanoribbons are simulated. Fourier's law is used to calculate the thermal conductivities of graphyne nanoribbons. The simulation results show that for the thermal conductivity of graphyne nanoribbons in a-few-dozen nanometer range:1) as a result of the phonon scattering and enhanced phonon Umklapp process, the graphyne nanoribbons with vacancy defects will cause the thermal conductivity to decrease and becomes lower than that of the complete graphyne nanoribbons; 2) due to the difference in phonon density-of-states matching degree, the vacancy defect in the benzene ring of graphyne nanoribbons has a greater effect on the thermal conductivity than that of vacancy defect in the acetylene chain of graphyne nanoribbons, the vacancy defects have a strong influence on the thermal conductivity of in the acetylene chain of graphyne nanoribbons; 3) because of the influence of size effect, the thermal conductivity of graphyne nanoribbon increases with length increasing. In this paper, the research of the thermal conductivity of graphyne nanoribbon provides the reference for controlling their thermal conductivity on a certain scale.
2017, 66 (13): 136101.
doi: 10.7498/aps.66.136101
Abstract +
Structure evolution under dynamic compression condition (high temperature, high pressure and high strain rate) is one of the most important problems in engineering and applied physics, which is vital for understanding the kinetic mechanism of shock-induced phase transition. In this work, an in-situ dynamic X-ray diffraction (DXRD) diagnostic method is established to probe the lattice response driven by shock waves. The geometry is suitable for the study of laser-shocked crystals. In order to eliminate the measurement error arising from the difference in experimental setup, the static and dynamic lattice diffraction signals are measured simultaneously in one shot by using a nanosecond burst of X-ray emitted from a laser-produced plasma. Experimental details in our investigation are as follows. 1) The laser driven shock wave transit time △ tShock and the shock pressure in sample are accurately determined from the shock-wave profile measurement by dual laser heterodyne velocimetry. 2) A laser pump-and-probe technique for adjusting the time-delay of DXRD diagnosis during △ tShock, with a series of repeated shock loadings is then employed to generate and measure the dynamic structure evolution. Using this method, the dynamic lattice response of[111] single-crystal iron is studied on Shenguang-Ⅱ facility. Single-shot diffraction patterns from both unshocked and shocked crystal are successfully obtained. An elastic-plastic transition process –elastic wave followed by a plastic wave– is observed in shocked[111] single-crystal iron on a lattice scale. The lattice compressibility values of the elastic wave and plastic wave are in agreement with those derived from the wave profiles. It is found that the Hugoniot elastic limit is measured to be about 6 GPa under nanosecond-pulsed laser shock compression. Such a high yield strength is consistent with recent laser ramp compression experimental results in polycrystalline Fe[Smith et al. 2011 J. Appl. Phys. 110 123515], suggesting that the peak pressure of elastic wave is dependent on the loading rate and the thickness of sample. Based on the analysis of diffraction patterns, the BCC phase is determined to be stable till 23.9 GPa, the highest pressure explored in this work, which might indicate that the phase transition strongly couples with the crystal orientation and loading rate. Some possible physical mechanisms remain to be further studied:whether the transition time hysteresis occurs or the metastable FCC phase exists in shocked[111] single crystal Fe, or the phase transition onset pressure increases under high strain-rate compression. Our DXRD results provide a primary experimental reference for the follow-up study on the phase kinetics.
EDITOR'S SUGGESTION
2017, 66 (13): 136102.
doi: 10.7498/aps.66.136102
Abstract +
Exploring the atom-scale details such as morphology of coexisting phase during phase transitions is very important for understanding their microscopic mechanism.While most theories,such as the classic nucleation theory,usually over-simplify the character of the critical nucleus,like the shape,structure,and most current experiment techniques are hardly to capture the instantaneous microscopic details,the atomistic molecular dynamics (MD) or Monte Carlo (MC) simulation provides a promise to detect the intermediate process of phase transitions.However,the standard canonicalensemble MD/MC simulation technique can not sufficiently sample the instantaneous (unstable in thermodynamics) coexistent phase.Therefore,the MC in the general canonical ensemble,such as general isothermal-volume ensemble (gNVT),combined with the enhanced sampling techniques,such as the replica exchange (RE) method,was presented to stabilize then to sufficiently sample the atomic conformations of the phase coexistence.Due to the limit of the RE, the RE-MC simulation on gNVT is usually applied in smaller systems.In this paper,we first extend the gNVT-based MC simulation to the MD in the generalized isothermal-isobaric ensemble (gNPT) and very simply implement it in the standard atomic MD soft packages without modifying the code,so that we can use these packages in MD simulation of realistic systems.Then we simulate the vapour-liquid phase transition of all-atomic water model.At least at not very low pressures,we find that the individual gNPT simulation is already enough to reach equilibrium in any region of the phase transition,not only in the normal liquid and vapour regions,but in the super-saturation regions,and even in the vapour-liquid coexistent regions.The obtained energy-temperature curve in the cooling gNPT well matches with that in the heating procedure without any hysteresis.It indicates that it is not necessary to use the RE technique in the gNPT,and the intermediate states during phase transitions in larger systems can be effectively simulated by a series of independent individual gNPT-MD simulations in the standard soft packages.We also propose a method to accurately determine the interface between the two phases in the coexistence,then provide a quantitative measurement about the interface tension and the morphology of the coexistent phase in the larger all-atomic water at various temperatures and pressures.The results show that the liquid droplet (or vapour bubble) at the low pressure is close to a sphere due to the larger interface tension,as expectation of the classic nucleation theory of the first-order phase phase transition,but becomes more and more irregular as the decrease of the interfacial tension as increasing the pressure to approach to the critical pressure,where the phase transition is the second order one.
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES
2017, 66 (13): 137802.
doi: 10.7498/aps.66.137802
Abstract +
The surface polarization energy that arises from the difference in dielectric coefficient between the quantum dot (QD) and the background medium is investigated by the equivalent image charge method. A general expression for the bandgap of QD depending on the dielectric coefficient of background medium is presented by solving the exciton Schrödinger equation with the perturbation method. As examples, the sizedependent bandgaps, bandgap shifts, absorption-peak wavelengths and absorption-peakwavelength shifts of PbSe, PbS and CdSe QDs doped in different background media are determined in detail. There is evidence to show that the effects of surface polarization on the bandgap and the first absorption-peak wavelength of QD are considerable. The bandgap decreases with the increase of dielectric coefficient of background medium, which causes the absorption-peak wavelength to be red shifted. The effect of surface polarization on the bandgap depends substantially on the sign and value of image charge. When the dielectric coefficient of QD is greater than that of background medium, the absorption-peak wavelength comes to blue shift due to surface polarization of QD. On the contrary, the absorption-peak wavelength comes to redshift. The absorption-peak wavelength shifts of QDs doped in different background media will reach a maximum in a certain diameter depending on the kind of QD.
2017, 66 (13): 137501.
doi: 10.7498/aps.66.137501
Abstract +
Control of magnetic properties by an applied electric field has significant potential applications in the field of novel magnetic information devices,with some advantages such as low dissipation and small sizes.Till now,many scientific and technical problems in this field have been widely investigated theoretically and experimentally.However,a lacuna still exists in the papers concerning the investigations performed by micromagnetic simulation which is a powerful tool for revealing magnetic behaviors in a complicated magnetic system.Based on the basic principle for electric-field manipulation of magnetic properties,we study the electric-field control of magnetic properties of a square-shaped singlecrystal Fe3O4 thin film formed on a single-crystal PZN-PT piezoelectric substrate by the micromagnetic simulation method via object oriented micro-magnetic frame (OOMMF),a software for micromagnetic simulation.The magnetic hysteresis loops are collected for the Fe3O4/PZN-PT composite system under magnetic fields applied in the[100]and[010]crystallographic directions of Fe3O4 and an electric field applied along the[001]axis of the PZN-PT substrate. The applied electric field acts as an stress anisotropy energy.The result of our simulation is similar to the reported result of an experimental investigation for the same system and is consistent with that of our theoretical analysis based on a thermodynamic route.The results reveal that the film exhibits typical soft-magnetic behavior without applying an electric field.When an electric field is applied to the PZN-PT substrate,the coercivity and squareness ratio of Fe3O4 is greatly affected.Under an external magnetic field along the[100]axis of Fe3O4,the applying of a positive electric field clearly enhances the coercivity and squareness ratio.On the other hand,when an external magnetic field is applied along the[010]direction of Fe3O4,the coercivity and squareness ratio is increased by applying a negative electric field.In both cases,the coercivity and squareness ratio reaches 1 when the absolute value of E is 0.6 MV/m or larger.This high coercivity and squareness ratio is vital to magnetic information memory.These results are attributed to the competition between an electric-field-induced uni-axial stress anisotropy energy and the intrinsic in-plane four-fold magnetocrystalline anisotropy energy of a Fe3O4 thin film.When the absolute value of E is sufficiently large (1 MV/m), the electric-field-induced stress anisotropic energy significantly overweighs the intrinsic magnetocrystalline anisotropy energy,and the Fe3O4 thin film exhibits an approximate uniaxial magnetic anisotropy energy.Under the electric fields of 1-MV/m and -1-MV/m,the effective easy axis is along the[100]and[010]direction of the Fe3O4 thin film,respectively. Additionally,we also find that applying a 1-MV/m (-1-MV/m) electric-field can cause the frequency for ferromagnetic resonance to increase (reduce) almost 1 GHz,offering the possibility of developing a microwave device with tunable frequency.
2017, 66 (13): 137101.
doi: 10.7498/aps.66.137101
Abstract +
The origin of the p-type conductivity in N-doped ZnO has been a controversial issue for years, since isolated N substituted for O site (NO) was found to have high ionization energy. A recent experiment demonstrates that the p-type conductivity is attributed to the VZn-NO-H shallow acceptor complex. However, besides the complex, there are many other defects in ZnO, such as twin grain boundaries. They are commonly two-dimensional defects, and inevitably affect the p-type conductivity of the complex. By applying first principle calculations, we present the electronic structures and p-type conductivity of ZnO ∑7 (1230) twin grain boundaries containing VZn-NO-H complexes. Four types of ∑7 twin grain boundaries are investigated, and the VZn-NO-H complex is found to have a tendency to appearing in the stress raisers of the twin grain boundaries. The lowest formation energy under Zn-rich condition is only 0.52 eV for the complex in GB7a, a type of ∑7 twin grain boundary with anion-anion bonds, while the value is 3.25 eV for the complex in bulk ZnO. For the ionization energy, the complex in GB7a is more easily ionized, and has a value of 0.38 eV, compared with 0.67 eV in bulk ZnO. The result of density of states shows that the electron transition is dominated by the empty defect levels in forbidden band, which are occupied by O 2p and N 2p orbital. Further analysis indicates that the special structure of GB7a shortens the distances between NO and its neighbor O atoms, and the shortest N–O bond is only 2.38 Å, which also means a strong orbital hybridization between O and N. As a result, the energy level splitting is enhanced, and the empty energy level in the forbidden band is shifted down to valence band maximum. So, GB7a can favor the ionization in VZn-NO-H complex. Although GB7a is a special case of the twin grain boundaries, the result also gives us a new idea to understand the origin of p-type conductivity in N-doped ZnO.
2017, 66 (13): 137801.
doi: 10.7498/aps.66.137801
Abstract +
Transition metal dichalcogenides (TMDs) have received widespread attention because of their excellent performances in the field of optoelectronic, nanoelectronic device and photocatalytic exploration. The structures of TMDs can be expressed by the MX2, M=Mo, W; X=S, Se, Te, etc. As a typical TMD, MoSe2 has a graphene-like two-dimensional periodic structure with perfect physical, photoelcrtonic and catalytic properties. Currently, there are various methods to prepare the nanolevel MoSe2, such as the mechanical exfoliation, physical vapor deposition (PVD), hydrothermal method, chemical vapor deposition (CVD), etc, and most studies focused on regular triangular morphologies of the surfaces of different substrates. The new morphology, such as the hexangular star bilayer, has not been systematically investigated. In this study, the hexangular star MoSe2 nanosheets are successfully synthesized by using a simple CVD method in an atmosphere of mixed H2/Ar with a flow rate ratio of 1:4. Molybdenum trioxide(MoO3) and selenium (Se) powders are chosen to be the Mo and Se source, respectively. Moreover, the structure of the obtained MoSe2 nanosheet is characterized by Raman, SEM, EDS, XRD and TEM. The results of Raman spectrum and SEM indicate that the hexangular star MoSe2 possesses a bilayer structure. The TEM characterization reveals that the MoSe2 is a single crystal with a hexagonal lattice structure and good quality. The heating time at high temperature has a remarkable influence on the MoSe2 bilayer growth process. The growth process of the hexangular star MoSe2 bilayer is inferred to experience a three-step process. First, Mo and Se sources are gasified into gaseous molecules and then the Mo molecules are selenized into the MoSe2 crystal nucleus under high temperature. Next, these crystal nucleus are in a triangular epitaxial growth under the action of carrier gas. As heating time increases, the space steric effect leads to different interlayer separations between the two MoSe2 layers in various stacking configurations, eventually forming a hexangular star bilayer. The PL result shows that the spectra split into two main emission peaks, i.e., the direct and indirect bandgaps of the hexangular star structure appearing at 1.53 eV (810.2 nm) and 1.78 eV (696.9 nm), respectively. It might be due to the spin-orbit coupling interaction between the double MoSe2 molecules. The wide spectral range of the MoSe2 bilayer indicates that it has a potencial application in the photoelectric detectors.
INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY
2017, 66 (13): 138201.
doi: 10.7498/aps.66.138201
Abstract +
Most Na+ channels open transiently upon depolarization of cardiac cell membrane and then are quickly inactivated. However, some Na+ channels remain active, which generate the late sodium current during the action potential plateau. So far, late sodium current has been regarded as a relevant contributor to arrhythmias and its inhibition can suppress re-entrant and multifocal ventricular fibrillation so that its inhibition may become a novel therapeutic strategy to treat cardiac arrhythmias in the future. Therefore, how to inhibit late sodium current has received special attention. Since both the late sodium current and defibrillation shocks can lead to the increase of action potential duration, the late sodium current can be used to terminate ventricular fibrillation. However, the suppression of spiral wave and spatiotemporal chaos in cardiac tissues via late sodium current has been neglected. In this paper, we use the model of human heart to study the suppression of spiral wave and spatiotemporal chaos in two-dimensional cardiac tissue by generating late sodium current. We suggest that such a control strategy to induce late sodium current. The slow inactivation gate of sodium channel is clamped to 0.7 while the threshold voltage of corresponding fast inactivation gate is real-timely modulated. We first reduce the threshold voltage from 71.55 mV to 50.55 mV within the time interval T1, and then increase it from 50.55 mV to 71.55 mV within the time interval T2. When the threshold voltage returns to 71.55 mV, the changes of the relevant inactivation gates of sodium channel go back to normal dynamic state. Numerical simulation results show that when the control parameters are properly chosen, the control-induced late sodium current can effectively suppress spiral wave and spatiotemporal chaos even if there are some cardiac cells with spontaneous late sodium current. The advantage of the control scheme is that the control-induced late sodium current is small. The control duration is short because the spiral wave and spatiotemporal chaos disappear mainly due to the conduction obstacle. In a few cases, the spatiotemporal chaos disappears through the transition from spiral wave to target wave. We hope that these results may provide a new strategy to treat heart disease.
2017, 66 (13): 138101.
doi: 10.7498/aps.66.138101
Abstract +
Ni-Fe-Ti ternary alloys, as a type of structural and magnetic material, have received more attention in the industrial fields in recent decades. For the purpose of providing necessary experimental data and theoretical basis for industrial appliance of these alloys, the researches of rapid solidification mechanism and relevant application performances of Ni45Fe40Ti15 ternary alloy are carried out in this paper. Rapid solidification of undercooled Ni45Fe40Ti15 ternary alloy is realized in a 3 m drop tube under the condition of containerless and microgravity state. In an experiment, the sample with a mass of 2 g is placed in a φ16 mm×150 mm quartz tube with a 0.3-mm-diameter nozzle at its bottom. The quartz tube is then installed in the induction coil on the top of the drop tube. The tube body is evacuated to a pressure of 2×10-5 Pa and backfilled with the mixture gas of Ar and He gases to about 1×105 Pa. After that the sample is melted by induction heating and superheated to about 200 K above its liquidus temperature. Under such a condition, the melt is ejected through the nozzle by a flow of Ar gas and dispersed into fine liquid droplets. These liquid droplets solidify rapidly during free fall, and the droplets with the diameters ranging from 160 to 1050 μm are achieved. As droplet diameter decreases, both cooling rate and undercooling of the alloy droplet increase exponentially, i.e., from 1.10×103 to 3.87×104 K·-1 and from 42 to 210 K (0.14TL) respectively. The microstructure consists of γ -(Fe, Ni) solid solution and interdendritic Fe2Ti intermetallic compound. As undercooling increases, the coarse γ -(Fe, Ni) dendrites become refined, the secondary dendrite arm spacing linearly decreases. Compared with the result in the glass fluxing experiment, the dendrites are much refined by drop tube processing due to the higher cooling rate obtained. The amounts of solute Ni and Ti content in the γ -(Fe, Ni) phase enlarge evidently with the increase of undercooling, suggesting the occurrence of solute trapping. The magnetic properties of thealloy droplets sre also analyzed. When droplet diameter decreases from 1100 to 300 μm, the saturation magnetization increases from 22.47 to 41.82 Am2·kg-1, the coercive force decreases from 3.33 to 0.80 KAm-1, and the squareness ratio decreases approximately by four times. This indicates that the soft magnetic properties of the alloy are improved remarkably by drop tube processing. Furthermore, the mechanism for substantial effect of undercooling on magnetic parameter such as coercive force needs to be further investigated.
EDITOR'S SUGGESTION
2017, 66 (13): 138501.
doi: 10.7498/aps.66.138501
Abstract +
Graphene (GN), a monolayer two-dimensional (2D) system closely arranged into a benzene ring structure by C atoms, has so far aroused considerable research interest due to its novel electronic, magnetic, mechanical and thermal properties. But 2D GN is a semimetal with zero band gap, and the lowest conduction band touches the highest valence band at Fermi level, leading to the inability to achieve the off effect in the electronic device. Therefore, many researchers are searching the solutions. A simple and feasible method is to convert 2D GN into quasi-one-dimensional (1D) graphene nanoribbons, quantum-dot arrays (QDAs) and zero-dimensional (0D) quantum-dot by tailoring it along a specific single crystallographic direction. The QDAs, due to their structural diversity, have great potential applications in future nano-integrated circuit. In this work, first-principles method based on density functional theory is used to study the magneto-electronic and magnetic transport properties of four 1D quantum-dot arrays (1D QDAs) consisting of triangular graphene nanoflakes with different linking modes. The calculated binding energy suggests that these structures are very stable, and the arrays that are linked by the bottom-side are more stable than that only by the vertex. In particular, it is found that the electronic and magnetic features are not only related to the different magnetic states, but also depend on linking modes. For example, in the non-magnetism state, different QDAs can be a metal or a narrowed band-gap semiconductor. In the ferromagnetic state, different QDAs can be half-metal materials or bipolar magnetic semiconductors with different gaps, and have greatly different magnetic moments from 1.985 to 7.994B/unit cell, reaching a difference almost as large as four times. While in the antiferromagnetic state, all QDAs are semiconductors but with different gaps. These results imply that the linking modes play a crucial role in effectively tuning the electronic and magnetic features for nanostructures. The calculated atom-projected density of states indicates that the highest valence band and the lowest conduction band are determined by the edge C atoms. The half-metallic and bipolar magnetic semiconducting behaviors presented by 1D QDA are extremely important for developing magnetic devices, which is not found in the intrinsic graphene nanoribbons. And, we also investigate the magnetic device properties based on one kind of QDA, and the single or dual spin-filtering effect with the perfect (100%) spin polarization and a rectification ratio of about 104 can be predicted. Particularly, a giant magnetoresistance over 109% is found unambiguously, which is two orders of magnitude higher than the value predicted based on the zigzag graphene nanoribbons and five orders of magnitude higher than previously reported experimental values for the MgO tunnel junction. Our results thus provide strong evidence for the effectiveness of QDAs on the magneto-electronic properties.
GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS
2017, 66 (13): 139101.
doi: 10.7498/aps.66.139101
Abstract +
The global navigation satellite system (GNSS) signal modulation type plays a crucial role in determining the performances of positioning, navigation and timing (PNT) services. Currently, the binary offset carrier (BOC) modulation signal and binary coded symbol (BCS) modulation signal are both bipolar signals, which greatly restrict the room of improving the GNSS signal performance. Therefore, multi-level coded symbol (MCS) modulation has received great attention in the field of GNSS signal design. The MCS modulation is the most extensive step-coded symbol modulation mode, where BOC modulation and BCS modulation are its special cases. Since the waveform symbol of the MCS modulation signal can be arbitrarily valued, the optimal GNSS signal can be designed. However, like the BOC modulation signal, the MCS modulation signal also has the problem of ambiguous tracking, and then results in a large pseudo range measurement error, which is unacceptable for the new generation GNSS with high accuracy. In recent years, the unambiguous tracking of GNSS signals has become a hot research subject in the navigation signal processing domain and many methods are presented, and those methods can be divided into three categories:BPSK-like method, bump jump (BJ) method, and side-peak cancellation (SC) method. However, these methods are designed for BOC signal, and they are not suitable for MCS signal.
Therefore, in this paper we propose a general unambiguous tracking algorithm based on the pseudo correlation function (PCF), which is suitable for MCS modulated signals. Firstly, the unitary expression of MCS modulated signal based on waveform value vector is given, then the unitary formula of cross-correlation function for MCS signal is derived and the definition of PCF is given. Then the constraint condition which should be satisfied to realize unambiguous tracking is analyzed in depth, and the universal constructing method of two reference signals and the relationship between each other are derived according to this constraint condition, which brings great convenience for solving the specific MCS signal. The code tracking loop model of GNSS receiver based on the proposed method is illustrated. It is observed that the proposed method can receive different MCS signals under the same receiver loop framework, and can simplify the design of the receiver while eliminating the tracking ambiguous problem. Finally, as a special case of MCS signal, the applications of the proposed method in four kinds of BOC signals are discussed respectively, and then the waveform value vector of the reference signal and the unitary expression of code discriminator are derived. Simulation results show that the proposed method can effectively solve the ambiguous tracking problem of MCS signal, which has good performance and broad application prospect.
2017, 66 (13): 139102.
doi: 10.7498/aps.66.139102
Abstract +
Horizontal disk, sphere, and spherical crown are a very important type of scatter in geophysics research. In the marine environment, a disk-like scatter can be used to describe several resistive targets, e.g., basaltic sills and stratigraphic hydrocarbon reservoirs while spherical crown can be used to approximately depict the topography of interface for basement rock. This type of scatter has characteristics of axisymmetrical distribution of the conductivity. If some approaches can be established to efficiently simulate the marine controlled source electromagnetic (MCSEM) response to this scatter, it will be meaningful to investigate the nature of MCSEM responses in complex formation and to build appropriate method of processing and explaining MCSEM data. In this paper, the resistive scatters are approximated by one or several horizontal concentric disks with different radii and thickness values, based on the axially symmetrical spatial distribution of conductivity. Then, a combination of these concentric disks with air, sea water and surrounding beds will construct a horizontally stratified inhomogeneous formation with common axis-center, whose spatial distribution of conductivity is layered in the vertical direction and axisymmetric in the horizontal direction. Based on the approximations mentioned above, the computation of MCSEM response excited by horizontal electrical dipole (HED) located at the z-axis is entirely transformed into two axially symmetrical problems for the Fourier harmonic components of the electromagnetic (EM) fields. The differential operators about the horizontal magnetic components and transformation of horizontal electrical components and other EM components from horizontal magnetic components are derived. Then, the numerical mode matching approach is extended to the simulation of the EM field and three-dimensional (3D) MCSEM responses excited by the HED in the formation. The procedure for solving the EM field is presented. The semi-analytic solution of EM field in the whole space is obtained to efficiently and numerically model MCSEM response in the complex formation. Finally, the efficiency and accuracy of the present method are demonstrated numerically. The characteristics of 3D MCSEM responses in three different cases are further investigated.
2017, 66 (13): 139601.
doi: 10.7498/aps.66.139601
Abstract +
Forbush decrease (FD) event is one of the most important short-term modulations of galactic cosmic rays (GCRs) caused by intense solar activities such as interplanetary coronal mass ejection (ICME). The modulation mechanisms of GCRs by the disturbed interplanetary magnetic fields (IMF) of ICME and the accompanying forward interplanetary shock (IP) are not clear yet.
In this work, we present a one-dimensional dynamic model of the GCR barrier driven by ICME. In our model, the time dependent radial diffusion coefficient rr of GCRs is depressed to be (r)rr (0 (r) 1) as they run into the disturbed IMF. The scale factor (r) is inversely proportional to the local solar wind speed away from the Sun. Within the disturbed area at any time, (r) increases exponentially from the local minimum (rsh)) at the IP front to 1 at the end of the ICME tail. In addition, (rsh)) switches gradually from its global minimum m at the bursting of the CME to 1 as the shock moving toward the outer boundary of the heliosphere. The geometrical and dynamic parameters of the ICME and IP are derived from the observations of GOES and ACE satellites.
Based on the stochastic transport theory, the one-dimensional backward stochastic differential equation (SDE) method is adopted to simulate the transport of GCRs modulated by single halo ICME. The evolution of the neutron flux at the ground is calculated according to the recently reported proton-neutron yield function. As an example, the FD event on 15 May 2005, caused by the CME event bursting on 13 May 2005, is studied and simulated. The results show that the calculated neutron flux evolution, including not only the main and recovery phases, but also the pre-enhancement before the arriving of the CME at the Earth, is consistent with the observation of Oulu neutron monitor.
According to the trajectories of GCRs, it can be found that, the per-enhancement of the neutron flux is a result of the scattering by the forward IP passing 1 AU. Before the IP reaches the switch cutoff Rc, GCRs are evidently confined in the sheath between the IP and CME. After that, the GCRs will stay for longer time in the magnetic cloud of the ICME as a result of the damping of IP strength.
The parameterzed one-dimensional GCRs modulation model and the SDE method, as have been confirmed by the neutron monitor observation on the Earth, can be used further to calculate and predict the GCRs fluxes of other places, such as the Mars, in the heliosphere.
GENERAL
2017, 66 (13): 130302.
doi: 10.7498/aps.66.130302
Abstract +
Study on propagation of cylindrical electromagnetic waves in various inhomogeneous and nonlinear media is of fundamental importance, which can be described by the cylindrical nonlinear Maxwell's equations. In recent years, finding exact solutions for these equations has emerged as a popular research topic. The exact solutions play an irreplaceable role in understanding and predicting physical phenomena, and developing numerical calculation methods, and so on. However, due to the extreme complexity of nonlinear partial differential equations, exact solutions of the cylindrical Maxwell's equations were only able to be obtained in a nonlinear and nondispersive medium whose dielectric function is an exponential function in previous researches. Actually, there is no general method at present which can exactly solve arbitrary cylindrical nonlinear Maxwell's equations. Therefore, finding physically admissible solutions meeting certain particular condition for the cylindrical nonlinear Maxwell's equations might be feasible.
In this paper, we discuss the traveling wave solutions which are very important in electromagnetic theory, especially in solitary wave theory. To our knowledge, research on obtaining traveling wave solutions of the cylindrical nonlinear Maxwell's equations is still lacking. The main conclusions in this paper are listed as follows.
Firstly, we introduce the cylindrical nonlinear Maxwell's equations mentioned in some previous publications, which can describe cylindrical electromagnetic waves propagation in inhomogeneous nonlinear and nondispersive media. In this paper, we focus on the nondispersive media with arbitrary nonlinearity and power-law inhomogeneity.
Secondly, we point out that the electric field component E of the model has no plane traveling wave solutions E=g(r-kt), after theoretical analysis and study. Then generalized traveling wave solutions in form of E=g(lnr-kt) for the electric field component are obtained by finding correct variable substitution and solving second-order nonlinear ordinary differential equation.Finally, we provide two examples to show the physical meanings of our generalized traveling wave solutions. We find that the transmitting speeds of vibrations vary with different points of the electric field. Actually, the transmitting speed of the vibration of a certain point closer to the cylinder center is lower. As a result, we observed a physical phenomenon similar to that of self-steepening.
Our work can be used to analyze the electromagnetic properties of ferroelectric materials and new materials. Theoretically, it can also provide an approach to studying the cylindrical nonlinear Maxwell's equations.
2017, 66 (13): 130303.
doi: 10.7498/aps.66.130303
Abstract +
We investigate one-dimensional discrete-time quantum walk on the line where the links between neighboring sites are randomly broken. Two link-broken ways, static percolation and dynamical percolation, are considered. The former means that the broken links are fixed in position space at each time step, while the latter is that broken links are varied with time step. Our attention focuses on the effects of these disorders on two physical quantities, the probability distribution and the entanglement between the coin degree of freedom and position degree of freedom. Choosing Hadamard coin operator and assuming the walker to start from the position eigenstate|0〉and attach itself to a coherent coin state 1/√2 (|↑〉+ i|↓〉), we give the statistical average results after making numerical calculations many times. The choices of coin operator and initial state, resulting in a symmetric probability distribution about origin in the ideal case, is helpful in comparing with different cases in different disorder strengths. It is shown that the probability distribution of static percolation quantum walk can change from a coherent behavior at short time to Anderson localization at longer time, while the dynamical percolation quantum walk can change to a classical diffusive behavior. With the decrease of the percolation probability, these transitions become faster. The entanglement for ideal case without disorder reaches a constant value after a short time evolution. The static percolation makes the entanglement less than that of ideal case and fluctuate irregularly around a certain value. The situation is very different for the dynamical percolation:the entanglement increases smoothly with the time step and can exceed the constant value in the ideal case at some time. Both of entanglements for two types of percolations decrease with reducing percolation probability. As a striking characteristic, the entanglement in dynamical case can tend to maximum regardless of percolation probability in long time limit, while the static case cannot. In the model for our study, the randomized unitary operations, induced by the static and dynamical percolations, can lead to some noticeable effects on the transport and entanglement of discrete time quantum walk. The results about the interplay between disorder and entanglement not only assist quantum information processing, but also give more options to further explore and understand disorder physical processes in nature.
2017, 66 (13): 130304.
doi: 10.7498/aps.66.130304
Abstract +
Recently, a quantum secure direct communication (QSDC) protocol based on the mixture of Bell state particles and single photons[Acta Phys. Sin. 65 230301(2016)] was put forward. In this QSDC protocol, the single photons and the Bell states were both used as information carriers. To be specific, each Bell state as well as single photon was encoded by three bits of classical information. After the sender told the receiver how to measure the particles, the receiver could read out the secret message sent by the sender. Speciously, the information transmission efficiency of this protocol was high. Unfortunately, there exists the information leakage problem in this protocol. When the sender announces that the receiver uses the Z-basis to measure a single photon, everyone knows that the sent secret message is 000 or 001, that is, the first two bits are leaked out; when the sender announces that the receiver uses the X-basis to measure a single photon, everyone knows that the sent secret message is 010 or 011, that is, the first two bits are leaked out too; when the sender announces that the receiver uses the Bell-basis to measure a pair of particles from a Bell state, everyone knows that the sent secret message is 100, 101, 110 or 111, that is, the first bit is leaked out. In a word, two of the three bits of classical information encoded in a single photon, and one of the three bits of classical information encoded in a Bell state are leaked out. Therefore, this scheme is not secure. On the basis of keeping the original idea and changing the contents of the protocol as less as possible, we put forward an improved message encoding rule to solve the information leakage problem, that is, the single photon is only encoded by one bit of classical information, and the Bell state is only encoded by two bits of classical information. In fact, this makes the information capacity of the improved protocol achieves the Helovo bound. So it has high coding capacity. We hope researchers pay more attention to the information leakage problem in quantum secure communication protocols, and thus design truly secure ones.
EDITOR'S SUGGESTION
2017, 66 (13): 130305.
doi: 10.7498/aps.66.130305
Abstract +
Compared with the scalar Bose-Einstein condensate, the spinor Bose-Einstein condensate, in which internal degrees of freedom are essentially free, has aroused the great interest in the study of topological excitations. In particular, the spinor Bose-Einstein condensate with rotation provides a new opportunity for studying novel quantum states including a coreless vortex and vortex lattice. To date, in the presence of rotation, a great many of studies on the topological excitations have focused on the Bose-Einstein condensate system with the uniform Zeeman field or without external magnetic field. However, the ground state structure of a rotating Bose-Einstein condensate in the presence of in-plane gradient-magnetic-field remains an open question. In this work, by using the imaginary-time propagation method, we study the ground state structure of a rotating Bose-Einstein condensate with in-plane quadrupole field. We first examine the effect of in-plane quadrupole field on trapped spinor Bose-Einstein condensate. The numerical results show that Mermin-Ho vortex can be induced only by the cooperation between quadrupole field and rotation. When magnetic field gradient is increased, the vortices around Mermin-Ho vortex display the symmetrical arrangement. For an even larger magnetic field gradient strength, the system only presents the Mermin-Ho vortex because the in-plane quadrupole field can prevent the vortices around Mermin-Ho vortex from occurring. Next, we examine the effect of the rotation on trapped spinor Bose-Einstein condensate. A phase transition from a polar-core vortex to a Mermin-Ho vortex is found through applying a rotational potential, which is caused by the cooperation between the in-plane quadrupole field and the rotation. We further study the combined effects of spin exchange interaction and density-density interaction. The results confirm that in the presence of the quadrupole field both spin exchange interaction and density-density interaction, acting as controllable parameters, can control the number of the vortices around Mermin-Ho vortex. The corresponding number of the vortices shows step behavior with increasing the ratio between spin exchange interaction and density-density interaction, which behaves as hexagon, pentagon, square and triangle. It is found that two types of topology structures, i.e., the hyperbolic meron and half-skyrmion, can occur in the present system. These vortex structures can be realized via time-of-flight absorption imaging technique. Our results not only provide an opportunity to investigate the exotic vortex structures and the corresponding phase transitions in a controlled platform, but also lay the foundation for the study of topological defect subjected to gauge field and dipolar interaction in future.
2017, 66 (13): 130501.
doi: 10.7498/aps.66.130501
Abstract +
As is well known,copper is such an unbelievable element that it can affect the phase transition behaviors of binary TiNi alloy when it displaces Ni element up to near upon 25%.The martensitic transition behaviors of TiNi1-xCux alloys appear from high-temperature cubic B2 phase to intermediate B19 structure with orthorhombic system and then finally to low-temperature B19' phase with monoclinic system with x 10% on cooling,so called two-stage martensitic phase transformation.Whereas,it directly transforms into orthorhombic B19 phase withx 20% on cooling,so called one-stage martensitic phase transformation.The orthorhombic B19 phase becomes final low-temperature phase while monoclinic phase will be unstable on cooling.The electronic structures and the formation energies of various point defects, Mulliken bond orders,etc.are studied for TiNi1-xCuxx alloys,however,the phase transition pathway at an atomic level has not been described at all,and further,the difference in transition pathway between TiNi and Ti1Ni1-xCuxx has not been understood so far.In this work,we optimize the crystal structures of TiNi and Ti50Ni25Cu25 alloys with initial geometry from experimental data.In order to choose the proper positions of Cu atom,we calculate the total energy of each doping system and find the most stable configuration.To study the transformation mechanism of TiNi,we calculate the phonon-dispersion spectra of each phase with both frozen-phonon method and linear response method,and then find the atomic vibrations with the imaginary frequency.Finally,with the help of this atomic vibration direction with negative frequency,we find the intermediate structures by the linear interpolation method and calculate their total energies.The phase transformation of TiNi from cubic to orthorhombic phase is driven by the phonon softening at the M point (0.5,0.5,0) of Brillouin zone.For orthorhombic and monoclinic phase,TiNi has real phonon frequencies for all k points and modes.A barrier of 1.6 meV is calculated between orthorhombic and monoclinic phase while no barrier is found between cubic and orthorhombic phase of TiNi,so it is easy to transform from cubic to orthorhombic and then to monoclinic phase.There exists a potential energy barrier of 10.3 meV at least between orthorhombic and monoclinic phase for Ti50Ni25Cu25,which is too high for its transition to overcome the maximum value of potential energy which corresponds to =93.4.The difference in transition pathway between TiNi and Ti50Ni25Cu25 accords well with the experimental measurement,so that the copper concentration with 25% in binary TiNi alloy will offer a new transition path from cubic to orthorhombic phase.
2017, 66 (13): 130601.
doi: 10.7498/aps.66.130601
Abstract +
Ground based airglow imaging interferometer (GBAⅡ) prototype made by our group is used to successfully detect the atmospheric wind velocity and temperature at the altituded of 90-100 km. In order to improve GBAⅡ's velocity accuracy, its calibrations are studied in this paper where covered are the calibration of imaging interference fringe center position, CCD dark noise and flat field, the decay coefficient of GBAⅡ's optical system, the phase step length, GBAⅡ's optical path difference with the angle of incidence, GBAⅡ instrument response and the zero wind speed phase calibration, etc. The theoretical and experimental researches of calibration show the following conclusions. The fringe center coordinates by shooting 30 imaging interference fringes are confirmed on the pixel of CCD (123.3, 121.1) by using the least squares method; by 632.8 nm laser for the CCD flat field calibration, the parameters of CCD's flat field coefficients, dark intensity, dead pixels and the imaging interference fringes before and after flat field are all obtained, respectively; the comparison between GBAⅡ's one edge fringe bright whose incidence angle of 10.24 and the center fringe bright whose incidence angle of 0 shows that the edge fringe phase is stepped by 0.356 fringes relative to the center fringe. After taking the sample of 200 imaging interference fringes, from the sine fit curve of the phase step interval at an incident angle of 10.24, the fitted root mean square (RMS) deviation is obtained to be 90.34% and the step interval of 4.06 nm for one interference fringes is corresponding to the stepped phase of 0.0094up; According to the forward formula, GBAⅡ's system decay coefficient calibration is performed after taking imaging interference fringes by IDL programming, the RMS deviation of fitted curve is 99.98%; GBAⅡ's response is 4.9710-3 counts (Rayleigh)-1 from the 632.8 nm laser experiment; GBAⅡ's zero wind speed calibration phases are obtained to be -9.2442 and -68.6353 for the 532.0 nm and 632.8 nm lasers for the outdoor experiment, respectively. This paper provides a series of calibration methods for GBAⅡ and these methods are all verifies experimentally. These calibration methods can support the upper atmospheric wind field passive measurement.
2017, 66 (13): 130301.
doi: 10.7498/aps.66.130301
Abstract +
At the cosmological scale, there exist many anisotropic anomalies in the low-l multipoles of the CMB angular power spectrum. Especially, the normals to the octopole and quadrupole planes are aligned with the direction of the cosmological dipole at a level inconsistent with Gaussian random. The inconsistency indicates that the anomalies may not be boost effect from the CMB rest frame to the peculiar frame. It hints us that the boost invariance might be violated on a cosmological scale. There are some discrepancies between the astronomical and cosmological observations, and the predictions are solely based on general relativity and the standard model for elementary particle physics. The solutions are the introduction of dark matter and dark energy. However, all the experiments aiming at finding dark matter particles give negative result and it is still a mystery:what the dark energy is comprised of. We suppose that the Lorentz symmetry begins to be violated partly from the scale of galaxy and utilize the very special relativity symmetry group E(2) as an example to illustrate the Lorentz violation effect on the large-scale effective gravity. A local E(2) but Lorentz invariant gauge theory can be constructed based on the equivalence principle and the gauge principle. To realize the E(2) symmetry, the closure requirement of Maurer-Cartan eqnarray on E(2) algebra needs to be satisfied by postulating constraint conditions among the components of the Lorentz connection. The local Lorentz invariant gauge theory with a Hilbert-Einstein action is a theory with torsion in general case. However in the case of scalar matter source, the theory is exactly the theory of general relativity with Levi-Civita connection and zero torsion. In the E(2) gauge theory case, the closure requirement of Maurer-Cartan eqnarray for E(2) algebra postulates 12 constraint eqnarrays among the components of the Lorentz connection and the eqnarrays of motion for connection reduce the number of independent components of connection to 12. The eqnarrays of motion for the tetrad field do not contain only the involved tetrad field components nor these relevant independent components. So the whole number of variables needed to be solved is 12 more than that in general relativity while there are 12 more eqnarrays in the meantime. The torsion or the contortion field of the E(2) gauge theory is non-trivial even in the case of scalar matter source distribution. Decompose the connection into Levi-Civita one and the contortion part and rewrite the eqnarrays for tetrad field in the formalism of general relativity, then there will appear an effective energy-momentum tensor contributed by the contortion distribution, in addition to the ordinary matter source distribution even for the case of scalar matter source. We expect it to contribute at least part of the dark matter effect. We also examine the holding of the first and second Bianchi identities induced by Jacobi identity of the E(2) gauge theory. The approach of our modified gravity is different from other approach of modified gravity in the sense that we construct the modified gravity by modifying the spacetime symmetry on a large scale and the emergence of effective energy-momentum tensor caused by Lorentz violation effect is due to a purely large scale effect.
2017, 66 (13): 130502.
doi: 10.7498/aps.66.130502
Abstract +
The optimal performance of heat engine is an important issue in thermodynamics, but the heat transfer between the working medium and two heat reservoirs induces the irreversibility during the operation of heat engine. Based on two important parameters introduced in this paper(namely, the power gain and the efficiency gain), for heat engine operating in the linear and nonlinear heat transfer processes, the formula for the efficiency at arbitrary power is achieved in terms of a simplified Curzon-Ahlborn heat engine model and the componendo and dividendo rule. The features of heat engine at arbitrary power output are also discussed in detail based on the numerical calculations. It is indicated that the parameter as a function of the power gain P contains two branches:the efficiency shows the monotonous variation on the first branch (the favorable case); the efficiency exhibits the non-monotonous characteristics and has the maximum value on the second branch(the unfavorable case). The working region of the heat engine is reduced as the heat transfer exponent increases, which results from the radiative contribution in the nonlinear heat transfer process. For the first branch, the contour-line plot of versus TL/TH and P clearly demonstrates that has the decreasing trend with increasing TL/TH and|P|; for the second branch, monotonically deceases as TL/TH increases, but shows the non-monotonic behaviors as|P|increases. The efficiency has the maximum value in the region where TL/TH and|P|have the small values, and the working regime of heat engines in the nonlinear heat transfer process is relatively small due to the complexity of the nonlinear heat transfer process. The curves of the efficiency in two heat transfer processes are loop-shaped, when|P| 0 and|P| 1, the curves of ~P in two heat transfer processes are same. But in other regimes, the efficiency of the heat engine with the linear heat transfer process is bigger than in the nonlinear heat transfer process. Furthermore, it is found that a considerably larger efficiency can be obtained when heat engine working close to the maximum power. This implies that there exists the trade-off working point where the heat engine can perform the most effective heat-work conversion. In addition, the curves of the power gain vs. the efficiency gain also display the loop-shaped characteristics, but there is the weak difference on the second branch. Our results are very conducive to understanding the optimal performance of heat engines in different heat transfer processes.
2017, 66 (13): 130201.
doi: 10.7498/aps.66.130201
Abstract +
In this work, an improved parallel SPH method is proposed to accurately solve the three-dimensional (3D) transient heat conduction equation with variable coefficients. The improvements are described as follows. Firstly, the first-order symmetric smoothed particle hydrodynamics (SPH) method is extended to the simulating of the 3D problem based on Taylor expansion. Secondly, the concept of stabilized up-wind technique is introduced into the convection term. Thirdly, the MPI parallel technique based on the neighboring particle mark method is introduced into the above improved SPH method, and named the corrected parallel SPH method for 3D problems (CPSPH-3D). Subsequently, the accuracy, convergence and the computational efficiency of the proposed CPSPH-3D method are tested by simulating the 3D transient heat conduction problems with constant/variable coefficient, and compared with the analytical solution. Meanwhile, the capacity of the proposed CPSPH-3D for solving the 3D heat conduction problems with the Dirichlet and Newmann boundaries is illustrated, in which the change of temperature with time under the complex cylindrical area is also considered. The numerical results show that:1) the proposed CPSPH-3D method has the better stability, higher accuracy and computational efficiency than the conventional SPH method no matter whether the particle distribution is uniform; 2) the calculating time can be well reduced by increasing the number of CPUs when the particle number is refined in the simulations of CPSPH-3D. Finally, the temperature variation in the 3D functionally gradient material is predicted by the corrected parallel SPH method, and compared with the other numerical results. The process of temperature variation in the functionally gradient material can be shown accurately.
