The flow behavior in porous media with threshold pressure gradient(TPG) is more complex than Darcy flow and the equations of motion, and outer boundary and inner boundary with TPG are also different from Darcy flow fo...The flow behavior in porous media with threshold pressure gradient(TPG) is more complex than Darcy flow and the equations of motion, and outer boundary and inner boundary with TPG are also different from Darcy flow for unsteady flow of a producing well in a reservoir. An analytic method to solve this kind of problem is in a need of reestablishment. The classical method of Green's function and Newman product principle in a new way are used to solve the unsteady state flow problems of various shapes of well and reservoir while considering the TPG. Four Green's functions of point, line, band and circle while considering the TPG are achieved. Then, two well models of vertical well and horizontal well are built and simultaneously the function to calculate the moving boundary of each well model is provided. The results show that when considering TPG the pressure field is much different, which has a sudden pressure change, with a moving boundary in it. And the moving boundary of each well model increases with time but slows down rapidly, especially when the TGP is large.展开更多
The Khuri-Jones correction to the partial wave scattering amplitude at threshold is an automorphic function for a dihedron. An expression for the partial wave amplitude is obtained at the pole which the upper half-pla...The Khuri-Jones correction to the partial wave scattering amplitude at threshold is an automorphic function for a dihedron. An expression for the partial wave amplitude is obtained at the pole which the upper half-plane maps on to the interior of semi-infinite strip. The Lehmann ellipse exists below threshold for bound states. As the system goes from below to above threshold, the discrete dihedral (elliptic) group of Type 1 transforms into a Type 3 group, whose loxodromic elements leave the fixed points 0 and ∞ invariant. The transformation of the indifferent fixed points from -1 and +1 to the source-sink fixed points 0 and ∞ is the result of a finite resonance width in the imaginary component of the angular momentum. The change in symmetry of the groups, and consequently their tessellations, can be used to distinguish bound states from resonances.展开更多
Sustainable rural development is predicated on a delicate balance between rural territorial functions and eco-logical constraints.While various functions can catalyze economic growth in rural settings,aligning them wi...Sustainable rural development is predicated on a delicate balance between rural territorial functions and eco-logical constraints.While various functions can catalyze economic growth in rural settings,aligning them with inherent ecological variables is essential.An exhaustive analysis of Beijing’s Pinggu District elucidated specific supply-demand thresholds and evaluated the adaptability of current utilization within these boundaries,culmi-nating in a novel optimization strategy.Notably,while locals place significant emphasis on production functions,the area’s topography and soil characteristics present palpable challenges to achieving these goals.We discov-ered that‘shackle type’predominantly characterize individual rural territorial functions,while‘diversified weak function optimization type’define multifunctional aspects,showcasing varied development paths and uncov-ering potential strategies for sustainable improvement.This study contributes a groundbreaking perspective to sustainable rural development,offering key insights and strategic recommendations for policy formulation.展开更多
In this paper, the optimization of quantizer’s segment threshold is done. The quantizer is designed on the basis of approximative spline functions. Coefficients on which we form approximative spline functions are cal...In this paper, the optimization of quantizer’s segment threshold is done. The quantizer is designed on the basis of approximative spline functions. Coefficients on which we form approximative spline functions are calculated by minimization mean square error (MSE). For coefficients determined in this way, spline functions by which optimal compressor function is approximated are obtained. For the quantizer designed on the basis of approximative spline functions, segment threshold is numerically determined depending on maximal value of the signal to quantization noise ratio (SQNR). Thus, quantizer with optimized segment threshold is achieved. It is shown that by quantizer model designed in this way and proposed in this paper, the SQNR that is very close to SQNR of nonlinear optimal companding quantizer is achieved.展开更多
In the acoustic detection process of buried non-metallic pipelines,the echo signal is often interfered by a large amount of noise,which makes it extremely difficult to effectively extract useful signals.An denoising a...In the acoustic detection process of buried non-metallic pipelines,the echo signal is often interfered by a large amount of noise,which makes it extremely difficult to effectively extract useful signals.An denoising algorithm based on empirical mode decomposition(EMD)and wavelet thresholding was proposed.This method fully considered the nonlinear and non-stationary characteristics of the echo signal,making the denoising effect more significant.Its feasibility and effectiveness were verified through numerical simulation.When the input SNR(SNRin)is between-10 dB and 10 dB,the output SNR(SNRout)of the combined denoising algorithm increases by 12.0%-34.1%compared to the wavelet thresholding method and by 19.60%-56.8%compared to the EMD denoising method.Additionally,the RMSE of the combined denoising algorithm decreases by 18.1%-48.0%compared to the wavelet thresholding method and by 22.1%-48.8%compared to the EMD denoising method.These results indicated that this joint denoising algorithm could not only effectively reduce noise interference,but also significantly improve the positioning accuracy of acoustic detection.The research results could provide technical support for denoising the echo signals of buried non-metallic pipelines,which was conducive to improving the acoustic detection and positioning accuracy of underground non-metallic pipelines.展开更多
In order to solve the problems of local maximum modulus extraction and threshold selection in the edge detection of finite resolution digital images, a new wavelet transform based adaptive dual threshold edge detec...In order to solve the problems of local maximum modulus extraction and threshold selection in the edge detection of finite resolution digital images, a new wavelet transform based adaptive dual threshold edge detection algorithm is proposed. The local maximum modulus is extracted by linear interpolation in wavelet domain. With the analysis on histogram, the image is filtered with an adaptive dual threshold method, which effectively detects the contours of small structures as well as the boundaries of large objects. A wavelet domain's propagation function is used to further select weak edges. Experimental results have shown the self adaptivity of the threshold to images having the same kind of histogram, and the efficiency even in noise tampered images.展开更多
Partial discharge(PD)is an important reason for the insulation failure of the switchgear.In the process of PD detection,PD signal is often annihilated in strong noise.In order to improve the accuracy of PD detection i...Partial discharge(PD)is an important reason for the insulation failure of the switchgear.In the process of PD detection,PD signal is often annihilated in strong noise.In order to improve the accuracy of PD detection in power plant switchgear,a method based on continuous adaptive wavelet threshold switchgear PD signals denoising is proposed in this paper.By constructing a continuous adaptive threshold function and introducing adjustment parameters,the problems of over⁃processing of traditional hard threshold functions and incomplete denoising of soft threshold functions can be improved.The analysis results of simulated signals and measured signals show that the continuous adaptive wavelet threshold denoising method is significantly better than the traditional denoising method for the PD signal.The proposed method in this paper retains the characteristics of the original signal.Compared with the traditional denoising methods,after denoising the simulated signals,the signal⁃to⁃noise ratio(SNR)is increased by more than 30%,and the root⁃mean⁃square error(RMSE)is reduced by more than 30%.After denoising the real signal,the noise suppression ratio(NRR)is increased by more than 40%.The recognition accuracy rate of PD signal has also been improved to a certain extent,which proves that the method has a certain practicability.展开更多
When DR (Digital Radiography) images are filtered, it is necessary to preserve the edges and key details. But the existing methods may inevitably take fine details mistaken for noise to remove. In order to solve the...When DR (Digital Radiography) images are filtered, it is necessary to preserve the edges and key details. But the existing methods may inevitably take fine details mistaken for noise to remove. In order to solve the problem an improved anisotropic diffu- sion filtering model is proposed. Firstly, a novel diffusion function is introduced based on Perona and Malik model, which well overcomes the high rate of convergence. Secondly, the gradient threshold is modified to an adaptive estimation function, so it is bet- ter at adaptive threshold regulations according to the pixels and iteration times. Finally, the edges are extracted from the restored im- ages and the results are evaluated quantificationally. It is shown from the experiments that the proposed method is effective not only in noise reduction but also in details preserved.展开更多
In this paper the influences of the metal-gate and high-k/SiO 2 /Si stacked structure on the metal-oxide-semiconductor field-effect transistor(MOSFET) are investigated.The flat-band voltage is revised by considering...In this paper the influences of the metal-gate and high-k/SiO 2 /Si stacked structure on the metal-oxide-semiconductor field-effect transistor(MOSFET) are investigated.The flat-band voltage is revised by considering the influences of stacked structure and metal-semiconductor work function fluctuation.The two-dimensional Poisson's equation of potential distribution is presented.A threshold voltage analytical model for metal-gate/high-k/SiO 2 /Si stacked MOSFETs is developed by solving these Poisson's equations using the boundary conditions.The model is verified by a two-dimensional device simulator,which provides the basic design guidance for metal-gate/high-k/SiO 2 /Si stacked MOSFETs.展开更多
In this paper, we prove an analogous to a result of Erdös and Rényi and of Kelly and Oxley. We also show that there are several properties of k-balanced matroids for which there exists a threshold function.
Temporal activity patterns in animals emerge from complex interactions between choices made by organisms as responses to biotic interactions and challenges posed by external factors. Temporal activity pattern is an in...Temporal activity patterns in animals emerge from complex interactions between choices made by organisms as responses to biotic interactions and challenges posed by external factors. Temporal activity pattern is an inherently continuous process, even being recorded as a time series. The discreteness of the data set is clearly due to data-acquisition limitations rather than a true underlying discrete nature of the phenomenon itself. Therefore, curves are a natural representation for high-frequency data. Here, we fully model temporal activity data as curves integrating wavelets and functional data analysis, allowing for testing hypotheses based on curves rather than on scalar and vector-valued data. Temporal activity data were obtained experimentally for males and females of a small-bodied marsupial and modelled as wavelets with independent and identically distributed errors and dependent errors. The null hypothesis of no difference in temporal activity pattern between male and female curves was tested with functional analysis of variance (FANOVA). The null hypothesis was rejected by FANOVA and we discussed the differences in temporal activity pattern curves between males and females in terms of ecological and life-history attributes of the reference species. We also performed numerical analysis that shed light on the regularity properties of the wavelet bases used and the thresholding parameters.展开更多
By utilizing the capability of high-speed computing,powerful real-time processing of TMS320F2812 DSP,wavelet thresholding denoising algorithm is realized based on Digital Signal Processors.Based on the multi-resolutio...By utilizing the capability of high-speed computing,powerful real-time processing of TMS320F2812 DSP,wavelet thresholding denoising algorithm is realized based on Digital Signal Processors.Based on the multi-resolution analysis of wavelet transformation,this paper proposes a new thresholding function,to some extent,to overcome the shortcomings of discontinuity in hard-thresholding function and bias in soft-thresholding function.The threshold value can be abtained adaptively according to the characteristics of wavelet coefficients of each layer by adopting adaptive threshold algorithm and then the noise is removed.The simulation results show that the improved thresholding function and the adaptive threshold algorithm have a good effect on denoising and meet the criteria of smoothness and similarity between the original signal and denoising signal.展开更多
A novel flotation froth image segmentation based on threshold level set method is put forward in view of the problem of over-segmentation and under-segmentation which occurs when the existing method segmented the flot...A novel flotation froth image segmentation based on threshold level set method is put forward in view of the problem of over-segmentation and under-segmentation which occurs when the existing method segmented the flotation froth images. Firstly, the proposed method adopts histogram equalization to improve the contrast of the image, and then chooses the upper threshold and lower threshold from grey value of histogram of the image equalization, and complete image segmentation using the level set method. In this paper, the model which integrates edge with region level set model is utilized, and the speed energy term is introduced to segment the target. Experimental results show that the proposed method has better segmentation results and higher segmentation efficiency on the images with under-segmentation and incorrect segmentation, and it is meaningful for ore dressing industrial.展开更多
A numerical investigation of laser wavelength dependence on the threshold intensity of spark ignition in molecular hydrogen over a wide pressure range is presented. A modified electron cascade model (Gamal et al., 199...A numerical investigation of laser wavelength dependence on the threshold intensity of spark ignition in molecular hydrogen over a wide pressure range is presented. A modified electron cascade model (Gamal et al., 1993) is applied under the experimental conditions that carried out by Phuoc (2000) to determine the threshold intensity dependence on gas pressure for spark ignition in hydrogen combustion using two laser wavelengths namely;1064 nm and 532 nm. The model involves the solution of the time dependent Boltzmann equation for the electron energy distribution function (EEDF) and a set of rate equations that describe the change of the formed excited molecules population. The model takes into account most of the physical processes that expected to occur in the interaction region. The results showed good agreement between the calculated thresholds for spark ignition and those measured ones for both wavelengths, where the threshold intensities corresponding to the short wavelength (532 nm) are found to be higher than those calculated for the longer one (1064 nm). This result indicates the depletion of the high density of low energy electrons generated through multi-photon ionization at the short wavelength via electron diffusion and vibrational excitation. The study of the EEDF and its parameters (viz, the temporal evolution of: the electron density, ionization rate electron mean energy, …) revealed the important role played by each physical process to the spark ignition as a function of both laser wavelength and gas pressure. More over the study of the time variation of the EEDF explains the characteristics of the ignited spark at the two wavelengths for the tested pressure values.展开更多
Two new versions of accelerated first-order methods for minimizing convex composite functions are proposed. In this paper, we first present an accelerated first-order method which chooses the step size 1/ Lk to be 1/ ...Two new versions of accelerated first-order methods for minimizing convex composite functions are proposed. In this paper, we first present an accelerated first-order method which chooses the step size 1/ Lk to be 1/ L0 at the beginning of each iteration and preserves the computational simplicity of the fast iterative shrinkage-thresholding algorithm. The first proposed algorithm is a non-monotone algorithm. To avoid this behavior, we present another accelerated monotone first-order method. The proposed two accelerated first-order methods are proved to have a better convergence rate for minimizing convex composite functions. Numerical results demonstrate the efficiency of the proposed two accelerated first-order methods.展开更多
基金Project(51304220) supported by the National Natural Science Foundation of ChinaProject(3144033) supported by the Beijing Natural Science Foundation,ChinaProject(20130007120014) supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China
文摘The flow behavior in porous media with threshold pressure gradient(TPG) is more complex than Darcy flow and the equations of motion, and outer boundary and inner boundary with TPG are also different from Darcy flow for unsteady flow of a producing well in a reservoir. An analytic method to solve this kind of problem is in a need of reestablishment. The classical method of Green's function and Newman product principle in a new way are used to solve the unsteady state flow problems of various shapes of well and reservoir while considering the TPG. Four Green's functions of point, line, band and circle while considering the TPG are achieved. Then, two well models of vertical well and horizontal well are built and simultaneously the function to calculate the moving boundary of each well model is provided. The results show that when considering TPG the pressure field is much different, which has a sudden pressure change, with a moving boundary in it. And the moving boundary of each well model increases with time but slows down rapidly, especially when the TGP is large.
文摘The Khuri-Jones correction to the partial wave scattering amplitude at threshold is an automorphic function for a dihedron. An expression for the partial wave amplitude is obtained at the pole which the upper half-plane maps on to the interior of semi-infinite strip. The Lehmann ellipse exists below threshold for bound states. As the system goes from below to above threshold, the discrete dihedral (elliptic) group of Type 1 transforms into a Type 3 group, whose loxodromic elements leave the fixed points 0 and ∞ invariant. The transformation of the indifferent fixed points from -1 and +1 to the source-sink fixed points 0 and ∞ is the result of a finite resonance width in the imaginary component of the angular momentum. The change in symmetry of the groups, and consequently their tessellations, can be used to distinguish bound states from resonances.
基金funding of the National Natural Science Foundation of China(Grants No.42077434,41771560)the Taishan Scholar Foundation of Shandong Province(Grant No.2023).
文摘Sustainable rural development is predicated on a delicate balance between rural territorial functions and eco-logical constraints.While various functions can catalyze economic growth in rural settings,aligning them with inherent ecological variables is essential.An exhaustive analysis of Beijing’s Pinggu District elucidated specific supply-demand thresholds and evaluated the adaptability of current utilization within these boundaries,culmi-nating in a novel optimization strategy.Notably,while locals place significant emphasis on production functions,the area’s topography and soil characteristics present palpable challenges to achieving these goals.We discov-ered that‘shackle type’predominantly characterize individual rural territorial functions,while‘diversified weak function optimization type’define multifunctional aspects,showcasing varied development paths and uncov-ering potential strategies for sustainable improvement.This study contributes a groundbreaking perspective to sustainable rural development,offering key insights and strategic recommendations for policy formulation.
基金Serbian Ministry of Education and Science through Mathematical Institute of Serbian Academy of Sciences and Arts(Project III44006)Serbian Ministry of Education and Science(Project TR32035)
文摘In this paper, the optimization of quantizer’s segment threshold is done. The quantizer is designed on the basis of approximative spline functions. Coefficients on which we form approximative spline functions are calculated by minimization mean square error (MSE). For coefficients determined in this way, spline functions by which optimal compressor function is approximated are obtained. For the quantizer designed on the basis of approximative spline functions, segment threshold is numerically determined depending on maximal value of the signal to quantization noise ratio (SQNR). Thus, quantizer with optimized segment threshold is achieved. It is shown that by quantizer model designed in this way and proposed in this paper, the SQNR that is very close to SQNR of nonlinear optimal companding quantizer is achieved.
基金supported by Nanchong Southwest Petroleum University Science and Technology Strategic Cooperation Project(Nos.23XNSYSX0022,23XNSYSX0026)Provincial Science and Technology Plan Project(No.2023ZHCG0020)Southwest Petroleum University Natural Science“Sailing Plan”Project(No.2023QHZ003)。
文摘In the acoustic detection process of buried non-metallic pipelines,the echo signal is often interfered by a large amount of noise,which makes it extremely difficult to effectively extract useful signals.An denoising algorithm based on empirical mode decomposition(EMD)and wavelet thresholding was proposed.This method fully considered the nonlinear and non-stationary characteristics of the echo signal,making the denoising effect more significant.Its feasibility and effectiveness were verified through numerical simulation.When the input SNR(SNRin)is between-10 dB and 10 dB,the output SNR(SNRout)of the combined denoising algorithm increases by 12.0%-34.1%compared to the wavelet thresholding method and by 19.60%-56.8%compared to the EMD denoising method.Additionally,the RMSE of the combined denoising algorithm decreases by 18.1%-48.0%compared to the wavelet thresholding method and by 22.1%-48.8%compared to the EMD denoising method.These results indicated that this joint denoising algorithm could not only effectively reduce noise interference,but also significantly improve the positioning accuracy of acoustic detection.The research results could provide technical support for denoising the echo signals of buried non-metallic pipelines,which was conducive to improving the acoustic detection and positioning accuracy of underground non-metallic pipelines.
基金supported by the Tianjin Natural Science Foundation(08JCYBJC02200)the Keygrant Project of Chinese Ministry of Education(309009)the Natural Science Foundation of China(11171164)
文摘In order to solve the problems of local maximum modulus extraction and threshold selection in the edge detection of finite resolution digital images, a new wavelet transform based adaptive dual threshold edge detection algorithm is proposed. The local maximum modulus is extracted by linear interpolation in wavelet domain. With the analysis on histogram, the image is filtered with an adaptive dual threshold method, which effectively detects the contours of small structures as well as the boundaries of large objects. A wavelet domain's propagation function is used to further select weak edges. Experimental results have shown the self adaptivity of the threshold to images having the same kind of histogram, and the efficiency even in noise tampered images.
基金Sponsored by the Liaoning Provincial Department of Education Scientific Research Funding Project(Youth)(Grant No.JDL2020020)the Changzhou City Applied Basic Research Program(Grant No.CJ2020007).
文摘Partial discharge(PD)is an important reason for the insulation failure of the switchgear.In the process of PD detection,PD signal is often annihilated in strong noise.In order to improve the accuracy of PD detection in power plant switchgear,a method based on continuous adaptive wavelet threshold switchgear PD signals denoising is proposed in this paper.By constructing a continuous adaptive threshold function and introducing adjustment parameters,the problems of over⁃processing of traditional hard threshold functions and incomplete denoising of soft threshold functions can be improved.The analysis results of simulated signals and measured signals show that the continuous adaptive wavelet threshold denoising method is significantly better than the traditional denoising method for the PD signal.The proposed method in this paper retains the characteristics of the original signal.Compared with the traditional denoising methods,after denoising the simulated signals,the signal⁃to⁃noise ratio(SNR)is increased by more than 30%,and the root⁃mean⁃square error(RMSE)is reduced by more than 30%.After denoising the real signal,the noise suppression ratio(NRR)is increased by more than 40%.The recognition accuracy rate of PD signal has also been improved to a certain extent,which proves that the method has a certain practicability.
基金Supported by Natural Science Foundation of China(61163047)Natural Science Foundation of Jiangxi Province(20114BAB201036)
文摘When DR (Digital Radiography) images are filtered, it is necessary to preserve the edges and key details. But the existing methods may inevitably take fine details mistaken for noise to remove. In order to solve the problem an improved anisotropic diffu- sion filtering model is proposed. Firstly, a novel diffusion function is introduced based on Perona and Malik model, which well overcomes the high rate of convergence. Secondly, the gradient threshold is modified to an adaptive estimation function, so it is bet- ter at adaptive threshold regulations according to the pixels and iteration times. Finally, the edges are extracted from the restored im- ages and the results are evaluated quantificationally. It is shown from the experiments that the proposed method is effective not only in noise reduction but also in details preserved.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 60936005 and 61076097)the Cultivation Fund of the Key Scientific and Technical Innovation Project,Ministry of Education of China (Grant No. 708083)the Fundamental Research Funds for the Central Universities (Grant No. 20110203110012)
文摘In this paper the influences of the metal-gate and high-k/SiO 2 /Si stacked structure on the metal-oxide-semiconductor field-effect transistor(MOSFET) are investigated.The flat-band voltage is revised by considering the influences of stacked structure and metal-semiconductor work function fluctuation.The two-dimensional Poisson's equation of potential distribution is presented.A threshold voltage analytical model for metal-gate/high-k/SiO 2 /Si stacked MOSFETs is developed by solving these Poisson's equations using the boundary conditions.The model is verified by a two-dimensional device simulator,which provides the basic design guidance for metal-gate/high-k/SiO 2 /Si stacked MOSFETs.
文摘In this paper, we prove an analogous to a result of Erdös and Rényi and of Kelly and Oxley. We also show that there are several properties of k-balanced matroids for which there exists a threshold function.
文摘Temporal activity patterns in animals emerge from complex interactions between choices made by organisms as responses to biotic interactions and challenges posed by external factors. Temporal activity pattern is an inherently continuous process, even being recorded as a time series. The discreteness of the data set is clearly due to data-acquisition limitations rather than a true underlying discrete nature of the phenomenon itself. Therefore, curves are a natural representation for high-frequency data. Here, we fully model temporal activity data as curves integrating wavelets and functional data analysis, allowing for testing hypotheses based on curves rather than on scalar and vector-valued data. Temporal activity data were obtained experimentally for males and females of a small-bodied marsupial and modelled as wavelets with independent and identically distributed errors and dependent errors. The null hypothesis of no difference in temporal activity pattern between male and female curves was tested with functional analysis of variance (FANOVA). The null hypothesis was rejected by FANOVA and we discussed the differences in temporal activity pattern curves between males and females in terms of ecological and life-history attributes of the reference species. We also performed numerical analysis that shed light on the regularity properties of the wavelet bases used and the thresholding parameters.
文摘By utilizing the capability of high-speed computing,powerful real-time processing of TMS320F2812 DSP,wavelet thresholding denoising algorithm is realized based on Digital Signal Processors.Based on the multi-resolution analysis of wavelet transformation,this paper proposes a new thresholding function,to some extent,to overcome the shortcomings of discontinuity in hard-thresholding function and bias in soft-thresholding function.The threshold value can be abtained adaptively according to the characteristics of wavelet coefficients of each layer by adopting adaptive threshold algorithm and then the noise is removed.The simulation results show that the improved thresholding function and the adaptive threshold algorithm have a good effect on denoising and meet the criteria of smoothness and similarity between the original signal and denoising signal.
文摘A novel flotation froth image segmentation based on threshold level set method is put forward in view of the problem of over-segmentation and under-segmentation which occurs when the existing method segmented the flotation froth images. Firstly, the proposed method adopts histogram equalization to improve the contrast of the image, and then chooses the upper threshold and lower threshold from grey value of histogram of the image equalization, and complete image segmentation using the level set method. In this paper, the model which integrates edge with region level set model is utilized, and the speed energy term is introduced to segment the target. Experimental results show that the proposed method has better segmentation results and higher segmentation efficiency on the images with under-segmentation and incorrect segmentation, and it is meaningful for ore dressing industrial.
文摘A numerical investigation of laser wavelength dependence on the threshold intensity of spark ignition in molecular hydrogen over a wide pressure range is presented. A modified electron cascade model (Gamal et al., 1993) is applied under the experimental conditions that carried out by Phuoc (2000) to determine the threshold intensity dependence on gas pressure for spark ignition in hydrogen combustion using two laser wavelengths namely;1064 nm and 532 nm. The model involves the solution of the time dependent Boltzmann equation for the electron energy distribution function (EEDF) and a set of rate equations that describe the change of the formed excited molecules population. The model takes into account most of the physical processes that expected to occur in the interaction region. The results showed good agreement between the calculated thresholds for spark ignition and those measured ones for both wavelengths, where the threshold intensities corresponding to the short wavelength (532 nm) are found to be higher than those calculated for the longer one (1064 nm). This result indicates the depletion of the high density of low energy electrons generated through multi-photon ionization at the short wavelength via electron diffusion and vibrational excitation. The study of the EEDF and its parameters (viz, the temporal evolution of: the electron density, ionization rate electron mean energy, …) revealed the important role played by each physical process to the spark ignition as a function of both laser wavelength and gas pressure. More over the study of the time variation of the EEDF explains the characteristics of the ignited spark at the two wavelengths for the tested pressure values.
基金Sponsored by the National Natural Science Foundation of China(Grant No.11461021)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2017JM1014)
文摘Two new versions of accelerated first-order methods for minimizing convex composite functions are proposed. In this paper, we first present an accelerated first-order method which chooses the step size 1/ Lk to be 1/ L0 at the beginning of each iteration and preserves the computational simplicity of the fast iterative shrinkage-thresholding algorithm. The first proposed algorithm is a non-monotone algorithm. To avoid this behavior, we present another accelerated monotone first-order method. The proposed two accelerated first-order methods are proved to have a better convergence rate for minimizing convex composite functions. Numerical results demonstrate the efficiency of the proposed two accelerated first-order methods.