The analytic continuation serves as a crucial bridge between quantum Monte Carlo calculations in imaginary-time formalism,specifically the Green's functions,and physical measurements(the spectral functions)in real...The analytic continuation serves as a crucial bridge between quantum Monte Carlo calculations in imaginary-time formalism,specifically the Green's functions,and physical measurements(the spectral functions)in real time.Various approaches have been developed to enhance the accuracy of analytic continuation,including the Padéapproximation,the maximum entropy method,and stochastic analytic continuation.In this study,we employ different deep learning techniques to investigate the analytic continuation for the quantum impurity model.A significant challenge in this context is that the sharp Abrikosov-Suhl resonance peak may be either underestimated or overestimated.We fit both the imaginary-time Green's function and the spectral function using Chebyshev polynomials in logarithmic coordinates.We utilize Full-Connected Networks(FCN),Convolutional Neural Networks(CNNs),and Residual Networks(ResNet)to address this issue.Our findings indicate that introducing noise during the training phase significantly improves the accuracy of the learning process.The typical absolute error achieved is less than 10-4.These investigations pave the way for machine learning to optimize the analytic continuation problem in many-body systems,thereby reducing the need for prior expertise in physics.展开更多
Stability is the key to inverse Q-filtering. In this paper we present a stable approach to inverse Q-filtering, based on the theory of wavefield downward continuation. It is implemented in a layered manner, assuming a...Stability is the key to inverse Q-filtering. In this paper we present a stable approach to inverse Q-filtering, based on the theory of wavefield downward continuation. It is implemented in a layered manner, assuming a layered-earth Q model. For each individual constant Q layer, the seismic wavefield recorded at the surface is first extrapolated down to the top of the current layer and a constant Q inverse filter is then applied to the current layer. When extrapolating within the overburden, a stable wavefield continuation algorithm in combination with a stabilization factor is applied. This avoids accumulating inverse Q-filter errors within the overburden. Within the current constant Q layer, we use Gabor spectral analysis on the signals to pick time-variant gain-constrained frequencies and then deduce the corresponding gain-constrained amplitudes to stabilize the inverse Q-filtering algorithm. The algorithm is tested and verified application to field data.展开更多
In order to eliminate the effect of ocean bottom topography on seismic wave field,we transformed curved（x,z）coordinate system grids into rectangular（ξ,η）coordinate system grids and derived a 2-D scalar acoustic ...In order to eliminate the effect of ocean bottom topography on seismic wave field,we transformed curved（x,z）coordinate system grids into rectangular（ξ,η）coordinate system grids and derived a 2-D scalar acoustic wave equation in theξ,ηdomain.The seismic wave field collected at the sea surface was downward continued to the ocean bottom by the inverse finite difference method with the water velocity and then was reversely continued to the ocean surface by the finite difference method using the layer velocity from just below the ocean bottom in the（ξ,η）domain.Simulation calculations and practical application show that this method can not only remove the reflection travel time distortion but also correct the dynamic parameter changes caused by the ocean bottom topography.The inverted velocity after wave field continuation is much more accurate than before continuation and the image section was greatly improved compared to the original wave field.展开更多
This paper presents the flight dynamical behavior of the thrust vectoring aircraft with extended bifurcation and continuation methods. In contrast to the standard bifurcation and continuation methods, the extended met...This paper presents the flight dynamical behavior of the thrust vectoring aircraft with extended bifurcation and continuation methods. In contrast to the standard bifurcation and continuation methods, the extended methods are capable of calculating the continuation curves of the equilibrium points for the particular type of trimming flight. Therefore, these methods can not only give the performance measures of aircraft, but also determine the stability of trimming points. In this paper, the methods are used to verify the effectiveness of the thrust vectoring control law, to define the flight envelope boundary, to analyze the stability and controllability of trimming flight, and to predict the departures of the instable flight. The result shows that the extended methods provide more flight dynamic information and are useful in preliminary design of the thrust vectoring aircraft.展开更多
Based on the preferential continuation method proposed by Pawlowski （1995）, we propose a method and procedure for gravity anomaly separation with the preferential upward continuation operator in the case that the va...Based on the preferential continuation method proposed by Pawlowski （1995）, we propose a method and procedure for gravity anomaly separation with the preferential upward continuation operator in the case that the various sources are uncorrelated with one another and the continuation height is enough large. We also present a method for estimating optimum upward-continuation height, based on analyzing the characteristics of the preferential upward continuation operators of a synthesized gravity anomaly varying with different continuation heights. The method is tested on the raw Bouguer gravity data over an iron deposit. The result shows that the method separates the data into regional anomaly and residual anomaly efficiently and clearly.展开更多
In this article, the unique continuation and persistence properties of solutions of the 2-component Degasperis-Procesi equations are discussed. It is shown that strong solutions of the 2-component Degasperis-Procesi e...In this article, the unique continuation and persistence properties of solutions of the 2-component Degasperis-Procesi equations are discussed. It is shown that strong solutions of the 2-component Degasperis-Procesi equations, initially decaying exponentially together with its spacial derivative, must be identically equal to zero if they also decay exponentially at a later time.展开更多
基金Sponsored by National Natural Science Foundation of China(Grant No.12174101)Fundamental Research Funds for the Central Universities(Grant No.2022MS051).
文摘The analytic continuation serves as a crucial bridge between quantum Monte Carlo calculations in imaginary-time formalism,specifically the Green's functions,and physical measurements(the spectral functions)in real time.Various approaches have been developed to enhance the accuracy of analytic continuation,including the Padéapproximation,the maximum entropy method,and stochastic analytic continuation.In this study,we employ different deep learning techniques to investigate the analytic continuation for the quantum impurity model.A significant challenge in this context is that the sharp Abrikosov-Suhl resonance peak may be either underestimated or overestimated.We fit both the imaginary-time Green's function and the spectral function using Chebyshev polynomials in logarithmic coordinates.We utilize Full-Connected Networks(FCN),Convolutional Neural Networks(CNNs),and Residual Networks(ResNet)to address this issue.Our findings indicate that introducing noise during the training phase significantly improves the accuracy of the learning process.The typical absolute error achieved is less than 10-4.These investigations pave the way for machine learning to optimize the analytic continuation problem in many-body systems,thereby reducing the need for prior expertise in physics.
基金This research is sponsored by the National"973"Project(No.2007CB209603)the"863"Project(No.2006AA06Z108)
文摘Stability is the key to inverse Q-filtering. In this paper we present a stable approach to inverse Q-filtering, based on the theory of wavefield downward continuation. It is implemented in a layered manner, assuming a layered-earth Q model. For each individual constant Q layer, the seismic wavefield recorded at the surface is first extrapolated down to the top of the current layer and a constant Q inverse filter is then applied to the current layer. When extrapolating within the overburden, a stable wavefield continuation algorithm in combination with a stabilization factor is applied. This avoids accumulating inverse Q-filter errors within the overburden. Within the current constant Q layer, we use Gabor spectral analysis on the signals to pick time-variant gain-constrained frequencies and then deduce the corresponding gain-constrained amplitudes to stabilize the inverse Q-filtering algorithm. The algorithm is tested and verified application to field data.
基金sponsored by the National 973 Program of China(Grant No.2009CB219505)International Science&Technology Cooperation Program of China(Grant No.2010DFA21630)
文摘In order to eliminate the effect of ocean bottom topography on seismic wave field,we transformed curved（x,z）coordinate system grids into rectangular（ξ,η）coordinate system grids and derived a 2-D scalar acoustic wave equation in theξ,ηdomain.The seismic wave field collected at the sea surface was downward continued to the ocean bottom by the inverse finite difference method with the water velocity and then was reversely continued to the ocean surface by the finite difference method using the layer velocity from just below the ocean bottom in the（ξ,η）domain.Simulation calculations and practical application show that this method can not only remove the reflection travel time distortion but also correct the dynamic parameter changes caused by the ocean bottom topography.The inverted velocity after wave field continuation is much more accurate than before continuation and the image section was greatly improved compared to the original wave field.
文摘This paper presents the flight dynamical behavior of the thrust vectoring aircraft with extended bifurcation and continuation methods. In contrast to the standard bifurcation and continuation methods, the extended methods are capable of calculating the continuation curves of the equilibrium points for the particular type of trimming flight. Therefore, these methods can not only give the performance measures of aircraft, but also determine the stability of trimming points. In this paper, the methods are used to verify the effectiveness of the thrust vectoring control law, to define the flight envelope boundary, to analyze the stability and controllability of trimming flight, and to predict the departures of the instable flight. The result shows that the extended methods provide more flight dynamic information and are useful in preliminary design of the thrust vectoring aircraft.
基金supported jointly by projects of the 863 Program (Grant Nos.2006AA06Z111,2006AA06A201-3,and 20060109A1002-0201-03)
文摘Based on the preferential continuation method proposed by Pawlowski （1995）, we propose a method and procedure for gravity anomaly separation with the preferential upward continuation operator in the case that the various sources are uncorrelated with one another and the continuation height is enough large. We also present a method for estimating optimum upward-continuation height, based on analyzing the characteristics of the preferential upward continuation operators of a synthesized gravity anomaly varying with different continuation heights. The method is tested on the raw Bouguer gravity data over an iron deposit. The result shows that the method separates the data into regional anomaly and residual anomaly efficiently and clearly.
基金supported by NNSFC(11001219,10925104)the Scientific Research Program Funded by Shaanxi Provincial Education Department(2010JK860)
文摘In this article, the unique continuation and persistence properties of solutions of the 2-component Degasperis-Procesi equations are discussed. It is shown that strong solutions of the 2-component Degasperis-Procesi equations, initially decaying exponentially together with its spacial derivative, must be identically equal to zero if they also decay exponentially at a later time.
