To overcome the difficulty of realizing large-scale quantum Fourier transform(QFT) within existing technology, this paper implements a resource-saving method(named t-bit semiclassical QFT over Z2n), which could realiz...To overcome the difficulty of realizing large-scale quantum Fourier transform(QFT) within existing technology, this paper implements a resource-saving method(named t-bit semiclassical QFT over Z2n), which could realize large-scale QFT using an arbitrary-scale quantum register. By developing a feasible method to realize the control quantum gate Rk, we experimentally realize the 2-bit semiclassical QFT over Z23 on IBM’s quantum cloud computer, which shows the feasibility of the method. Then, we compare the actual performance of 2-bit semiclassical QFT with standard QFT in the experiments.The squared statistical overlap experimental data shows that the fidelity of 2-bit semiclassical QFT is higher than that of standard QFT, which is mainly due to fewer two-qubit gates in the semiclassical QFT. Furthermore, based on the proposed method, N = 15 is successfully factorized by implementing Shor’s algorithm.展开更多
Local Fourier analysis(LFA)is a useful tool in predicting the convergence factors of geometric multigrid methods(GMG).As is well known,on rectangular domains with periodic boundary conditions this analysis gives the e...Local Fourier analysis(LFA)is a useful tool in predicting the convergence factors of geometric multigrid methods(GMG).As is well known,on rectangular domains with periodic boundary conditions this analysis gives the exact convergence factors of such met hods.When other boundary conditions are considered,however,this analysis was judged as been heuristic,with limited capabilities in predicting multigrid convergence rates.In this work,using the Fourier method,we extend these results by proving that such analysis yields the exact convergence factors for a wider class of problems,some of which can not be handled by the traditional rigorous Fourier analysis.展开更多
In the seismic event classification,determining the seismic features of rockfall is significantly important for the automatic classification of seismic events because of the huge amount of raw data recorded by seismic...In the seismic event classification,determining the seismic features of rockfall is significantly important for the automatic classification of seismic events because of the huge amount of raw data recorded by seismic stations in continuous monitoring. At the same time, the rockfall seismic features are still not completely understood.This study concentrates on the rockfall frequency content, amplitude(ground velocity), seismic waveform and duration analysis, of an artificial rockfall test at Torgiovannetto(a former quarry in Central Italy). A total of 90 blocks were released in the test, and their seismic signals and moving trajectories were recorded by four tri-axial seismic stations and four cameras, respectively. In the analysis processing,all the artificial rockfall signal traces were cut separately and the seismic features were extracted individually and automatically. In this study, the relationships between a) frequency content and impacted materials, b) frequency content and the distance between block releasing position and seismic station(source-receiver distance) were discussed. As a result, we found that the frequency content of rockfall focuses on 10-60 Hz and 80-90 Hz within a source-receiver distance of 200 m, and it is well correlated with impacted material and source-receiver distance. To evaluate the difference between earthquake and rockfall, 23 clear earthquake signals recorded in a seven month-long continuous seismic monitoring, carried out with the four seismic stations, were picked out, according to the Italian national earthquakes database(INGV). On these traces we performed the same analysis as in the artificial rockfall traces, and two parameters were defined to separate rockfall events from earthquake noise. The first one, the amplitude ratio, is related to the amplitude variation of rockfall between two stations and is greater than that of earthquakes, because of the higher attenuation occurring for rockfall events, which consists in high frequencies whereas for earthquakes it consists展开更多
The amount of digital data is increasing every day.At every step of our daily lives,we deal with technologies in which our data are stored (e.g.,mobile phones and laptops),and this is one of the main reasons for the d...The amount of digital data is increasing every day.At every step of our daily lives,we deal with technologies in which our data are stored (e.g.,mobile phones and laptops),and this is one of the main reasons for the design of various types of encryption and user identity verification algorithms.These algorithms are meant not only to fulfill the desire of protecting data but also to address the possibility of granting access of specific digital data to selected individuals.This process brings with it the problem of identity verification.This paper discusses the problem of voice verification and presents a voice verification method based on artificial intelligence methods. Numerous tests are performed herein to demonstrate the effectiveness of the presented solution.The research results are shown and discussed in terms of the advantages and disadvantages of the solution.展开更多
The present work is devoted to the development of the extension of FRT (Finite Radon Transform) to the tridimensional case. One simple formulation is proposed and it is shown that it is the exact discretization of the...The present work is devoted to the development of the extension of FRT (Finite Radon Transform) to the tridimensional case. One simple formulation is proposed and it is shown that it is the exact discretization of the continuous Discrete Radon Transform. More precisely this is the case when the sampling is given on a regular grid i.e. the continuous function is filtered by the mean of the box function. Relation of this transform with the Discrete Fourier one is given and is for some help in numerical implementation.展开更多
The dispersive Fourier transform(DFT) technique opens a fascinating pathway to explore ultrafast non-repetitive events and has been employed to study the build-up process of mode-locked lasers. However, the shutting p...The dispersive Fourier transform(DFT) technique opens a fascinating pathway to explore ultrafast non-repetitive events and has been employed to study the build-up process of mode-locked lasers. However, the shutting process for the mode-locked fiber laser seems to be beyond the scope of researchers, and the starting dynamics under nearzero dispersion remains unclear. Here, the complete evolution dynamics(from birth to extinction) of the conventional soliton(CS), stretched pulse(SP), and dissipative soliton(DS) are investigated by using the DFT technique.CS, SP, and DS fiber lasers mode locked by single-walled carbon nanotubes(SWNTs) are implemented via engineering the intracavity dispersion map. The relaxation oscillation can always be observed before the formation of stable pulse operation due to the inherent advantage of SWNT, but it exhibits distinct evolution dynamics in the starting and shutting processes. The shutting processes are dependent on the dispersion condition and turn-off time, which is against common sense. Some critical phenomena are also observed, including transient complex spectrum broadening and frequency-shift interaction of SPs and picosecond pulses. These results will further deepen understanding of the mode-locked fiber laser from a real-time point of view and are helpful for laser design and applications.展开更多
This paper proposes an approach to extract the mode shapes of beam-like structures from the dynamic response of a moving mass. When a mass passes through a beam containing several artificially installed humps, its ver...This paper proposes an approach to extract the mode shapes of beam-like structures from the dynamic response of a moving mass. When a mass passes through a beam containing several artificially installed humps, its vertical acceleration can be recorded. After applying fast Fourier transformation to the dynamic response, one can extract the mode shapes of the beam. The surface roughness was neglected compared to the humps and its adverse effect on the extraction was reduced. The passing mass performs as both “exciter” and “massage receiver”;therefore, this method requires only one single accelerometer, making it more convenient and time saving in practice. Moreover, to estimate the possible error in extracting mode shapes, a wavenumber domain filtering technique is used to reconstruct the general profiles of mode shapes. Experimental validation of this approach in laboratory scale was conducted. The experimental results show that the proposed method performs well in extracting lower order mode shapes. It should also be noted that the passing mass can not have a very high velocity (e.g. 80 mm/s), otherwise the mass may jump and separate from the beam, and the proposed method may fail to identify mode shapes.展开更多
This paper gives several structure-preserving schemes for the Degasperis-Procesi equation which has bi-Hamiltonian structures consisted of both complex and non-local Hamiltonian differential operators. For this sake, ...This paper gives several structure-preserving schemes for the Degasperis-Procesi equation which has bi-Hamiltonian structures consisted of both complex and non-local Hamiltonian differential operators. For this sake, few structure-preserving schemes have been proposed so far. In our work, based on one of the bi-Hamiltonian structures, a symplectic scheme and two new energy-preserving schemes are constructed. The symplecticity comes straightly from the application of the implicit midpoint method on the semi-discrete system which is proved to remain Hamiltonian, while the energy conservation is derived by the combination of the averaged vector field method of second and fourth order, respectively. Some numerical results are presented to show that the three schemes do have the advantages in numerical stability, accuracy in long time computing and ability to preserve the invariants of the DP equation.展开更多
Background: Cotton fiber maturity is an important property that partially determines the processing and performance of cotton. Due to difficulties of obtaining fiber maturity values accurately from every plant of a ge...Background: Cotton fiber maturity is an important property that partially determines the processing and performance of cotton. Due to difficulties of obtaining fiber maturity values accurately from every plant of a genetic population, cotton geneticists often use micronaire (MIC) and/or lint percentage for classifying immature phenotypes from mature fiber phenotypes although they are complex fiber traits. The recent development of an algorithm for determining cotton fiber maturity (MIR) from Fourier transfonn infrared (FT-IR) spectra explores a novel way to measure fiber maturity efficiently and accurately. However, the algorithm has not been tested with a genetic population consisting of a large number of progeny plants. Results: The merits and limits of the MIC- or lint percentage-based phenotyping method were demonstrated by comparing the observed phenotypes with the predicted phenotypes based on their DNA marker genotypes in a genetic population consisting of 708 F2 plants with various fiber maturity. The observed MIC-based fiber phenotypes matched to the predicted phe no types better than the observed lint percentage-based fiber phenotypes. The lint percentage was obtained from each of F2 plants, whereas the MIC values were unable to be obtained from the entire population since certain F2 plants produced insufficient fiber mass for their measurements. To test the feasibility of cotton fiber infrared maturity (MIR) as a viable phenotyping tool for genetic analyses, we measured FT-IR spectra from the second population composed of 80 F2 plants with various fiber maturities, determined MIR values using the algorithms, and compared them with their genotypes in addition to other fiber phenotypes. The results showed that MiR values were successfully obtained from each of the F2 plants, and the observed MIR-based phenotypes fit well to the predicted phenotypes based on their DNA marker genotypes as well as the observed phenotypes based on a combination of MIC and lint percentage. Conclusions: The MIR value obtained 展开更多
The purpose of this paper is to present a quantitative SNR analysis of quadratic frequency modulated(QFM)signals.This analysis is located in the continuous-time local polynomial Fourier transform(LPFT)domain using a G...The purpose of this paper is to present a quantitative SNR analysis of quadratic frequency modulated(QFM)signals.This analysis is located in the continuous-time local polynomial Fourier transform(LPFT)domain using a Gaussian window function based on the definition of 3 dB signal-to-noise ratio(SNR).First,the maximum value of the local polynomial periodogram(LPP),and the 3 dB bandwidth in the LPFT domain for a QFM signal is derived,respectively.Then,based on these results,the 3 dB SNR of a QFM signal with Gaussian window function is given in the LPFT domain with one novel idea highlighted:the relationship among standard SNR,parameters of QFM signals and Gaussian window function is clear,and the potential application is demonstrated in the parameter estimation of a QFM signal using the LPFT.Moreover,the 3 dB SNR in the LPFT domain is compared with that in the linear canonical transform(LCT)domain.The validity of theoretical derivations is confirmed via simulation results.It is shown that,in terms of SNR,QFM signals in the LPFT domain can achieve a significantly better performance than those in the LCT domain.展开更多
It is well-known that reaction–diffusion systems are used to describe the pattern formation models.In this paper,we will investigate the pattern formation generated by the fractional reaction–diffusion systems.We fi...It is well-known that reaction–diffusion systems are used to describe the pattern formation models.In this paper,we will investigate the pattern formation generated by the fractional reaction–diffusion systems.We first explore the mathematical mechanism of the pattern by applying the linear stability analysis for the fractional Gierer–Meinhardt system.Then,an efficient high-precision numerical scheme is used in the numerical simulation.The proposed method is based on an exponential time differencing Runge–Kutta method in temporal direction and a Fourier spectral method in spatial direction.This method has the advantages of high precision,better stability,and less storage.Numerical simulations show that the system control parameters and fractional order exponent have decisive influence on the generation of patterns.Our numerical results verify our theoretical results.展开更多
The scattering and reflection of SH waves by a slope on an elastic wedged space is investigated. A series solution is obtained by using the wave function expansion method. The slope on a wedged space is divided into t...The scattering and reflection of SH waves by a slope on an elastic wedged space is investigated. A series solution is obtained by using the wave function expansion method. The slope on a wedged space is divided into two subregions by an artificial, auxiliary circular arc. The wave fields with unknown complex coefficients within each sub-region are derived. Applying Graf addition theorem, the scattered waves in the sub-regions are expressed in a global coordinate system. Fourier transform is adopted to derive a consistent form of standing waves in the inner region using the orthogonality of the cosine functions. The boundary-valued problem is solved by stress and displacement continuity along the artificial, auxiliary arc to obtain the unknown complex coefficients. Parametric studies are next performed to investigate how the topography from the slope on the wedged space will affect the scattering and diffraction, and hence the amplification and de-amplification of the SH waves. Numerical results show that the surface motions on the slope of the wedged space is influenced greatly by the topography. Amplification of the surface motions near the slope vertex is significant. The corresponding phases along the wedged space surfaces are consistent with the direction that the SH waves are propagating.展开更多
Computation of stereoscopic depth and disparity map extraction are dynamic research topics.A large variety of algorithms has been developed,among which we cite feature matching, moment extraction, and image representa...Computation of stereoscopic depth and disparity map extraction are dynamic research topics.A large variety of algorithms has been developed,among which we cite feature matching, moment extraction, and image representation using descriptors to determine a disparity map. This paper proposes a new method for stereo matching based on Fourier descriptors. The robustness of these descriptors under photometric and geometric transformations provides a better representation of a template or a local region in the image. In our work, we specifically use generalized Fourier descriptors to compute a robust cost function.Then, a box filter is applied for cost aggregation to enforce a smoothness constraint between neighboring pixels. Optimization and disparity calculation are done using dynamic programming, with a cost based on similarity between generalized Fourier descriptors using Euclidean distance. This local cost function is used to optimize correspondences. Our stereo matching algorithm is evaluated using the Middlebury stereo benchmark;our approach has been implemented on parallel high-performance graphics hardware using CUDA to accelerate our algorithm, giving a real-time implementation.展开更多
We establish the well-posedness of the fractional PDE which arises by considering the gradient flow associated with a fractional Gross-Pitaevskii free energy functional and some basic properties of the solution.The eq...We establish the well-posedness of the fractional PDE which arises by considering the gradient flow associated with a fractional Gross-Pitaevskii free energy functional and some basic properties of the solution.The equation reduces to the Allen-Cahn or Cahn-Hilliard equations in the case where the mass tends to zero and an integer order derivative is used in the energy.We study how the presence of a non-zero mass affects the nature of the solutions compared with the Cahn-Hilliard case.In particular,we show that,analogous to the Cahn-Hilliard case,the solutions consist of regions in which the solution is a piecewise constant(whose value depends on the mass and the fractional order)separated by an interface whose width is independent of the mass and the fractional derivative.However,if the average value of the initial data exceeds some threshold(which we determine explic让ly),then the solution will tend to a single constant steady state.展开更多
The classification of spatial characteristics and discharge modes of dielectric barrier discharge(DBD)are gaining increasing attention in industrial applications,especially in the field of surface treatment of materia...The classification of spatial characteristics and discharge modes of dielectric barrier discharge(DBD)are gaining increasing attention in industrial applications,especially in the field of surface treatment of materials.In this work,gray level histogram(GLH)and Fourier energy spectrum based on the digital image processing tech no logy are applied to investigate the spatial structure and discharge mode of mesh-plate DBD.The coefficient of variation(CV)is calculated to describe the uniformity of the discharge.The results show that the discharge mode of mesh-plate DBD changes from periodic discharge to filamentary discharge when the applied voltage increases from 11-15 kV.Moreover,a more regular spatial structure is obtained under lower applied voltages during the discharge process.It is also found that the apertures of mesh electrodes which are below 1 mm have smaller values of CV compared to plate electrodes,indicating more uniform discharge.Finally,polypropylene is treated by mesh-plate DBD for surface modification.The hydrophilicity is significantly improved as the water contact angle decreased by 64°,and the dyeing depth is also enhanced.展开更多
Traditional orthogonal frequency division multiplexing(OFDM)transmitter is implemented by exploiting inverse fast Fourier transform(IFFT),up-sampling,and low pass shaping filter(LPSF)modules,which occupy a large numbe...Traditional orthogonal frequency division multiplexing(OFDM)transmitter is implemented by exploiting inverse fast Fourier transform(IFFT),up-sampling,and low pass shaping filter(LPSF)modules,which occupy a large number of hardware resources and severely lower down the operation speed.To address these limitations,we propose a novel OFDM transmitter architecture,by which the aforementioned modules can be discarded and replaced with some simple switches.In the proposed architecture,direct digital synthesis(DDS)method is employed to generate digital sub-carriers and to transform OFDM data from frequency domain to time domain.Through some sophisticated simplifications,the proposed architecture can avoid using multipliers and remarkably save hardware resources.Finally,comparative experiments are carried out on field programmable gate array(FPGA)platform which demonstrates that our DDS-based architecture saves more than half of the hardware resources and doubles the achievable maximum frequency compared with traditional structure.展开更多
Atmospheric transmission from Dome A, Antarctica, presents new possibilities in the field of terahertz astronomy, where space telescopes have been the only observational tools until now. Using atmospheric transmission...Atmospheric transmission from Dome A, Antarctica, presents new possibilities in the field of terahertz astronomy, where space telescopes have been the only observational tools until now. Using atmospheric transmission measurements from Dome A with a Fourier transform spectrometer, transmission spectra and long-term stabilities have been analyzed at 1.461 THz, 3.393 THz, 5.786 THz and 7.1 THz, which show that important atmospheric windows for terahertz astronomy open for a reasonable length of time in the winter season. With large aperture terahertz telescopes and interferometers at Dome A, high angular resolution terahertz observations are foreseen of atomic fine-structure lines from ionized gas and a water ice feature from protoplanetary disks.展开更多
The randomness of random number generators(RNGs)is important for the reliability of cryptographic systems since the outputs of RNGs are usually utilized to construct cryptographic parameters.Statistical tests are empl...The randomness of random number generators(RNGs)is important for the reliability of cryptographic systems since the outputs of RNGs are usually utilized to construct cryptographic parameters.Statistical tests are employed to evaluate the randomness of the RNG outputs.The discrete Fourier transform(DFT)test is an important test item of the most popular statistical test suite NIST SP800-22.In the standard NIST DFT test and related improved studies,there exist accuracy and efficiency issues.First,the bit sequences generated by known good RNGs have a high probability to be rejected when the sequences are long or the sequence number is large,due to the deviation between the actual distribution of the test statistic values and the assumed normal distribution.Second,the long test time and high memory consumptions of the complex DFT test algorithm also affect its practicability.To solve these problems,we propose a new DFT test method for long sequences(10^6 or more bits).Different from the previous DFT test methods focusing on making the distribution of the test statistic values closer to the normal distribution,we reconstruct the statistic to follow the chi-square distribution.Our experiment result shows that our method has higher reliability in the two-level test,and could effectively reduce the test time and the memory consumptions.When applying our method on randomness test,the test efficiency has been increased to about 4 times for 106-bit sequences and 7 times for 10^7-bit sequences.In conclusion,our method has lower probability of making errors,and is more suitable for practical application scenarios.展开更多
The most important performance of a beating-up mechanism is that the dwelling time of the sley must ensure the completion of the weft insertion. To meet this requirement, a new non-circular combined gear train beating...The most important performance of a beating-up mechanism is that the dwelling time of the sley must ensure the completion of the weft insertion. To meet this requirement, a new non-circular combined gear train beating-up mechanism which is composed of two-stage planetary gear trains is proposed. The first-stage is a Fourier planetary gear train and the second-stage is a non-circular planetary gear train. For designing of this new mechanism, the ideal kinematic equations of the sley are constructed first. Then the kinematic model of the first-stage Fourier planetary gear train is established and the reverse solution for the pitch curves of the second-stage non-circular gears is deduced. With a computer-aided design program, the influences of several important parameters on the pitch curves of the second-stage non-circular gears are analyzed, and a set of preferable structural parameters are obtained. Finally, a test bed of this mechanism is developed and the experimental results show that this new beating-up mechanism can achieve the designed dwelling time, namely it can meet the requirements of beating-up process.展开更多
基金the National Basic Research Program of China(Grant No.2013CB338002)the National Natural Science Foundation of China(Grant No.61502526).
文摘To overcome the difficulty of realizing large-scale quantum Fourier transform(QFT) within existing technology, this paper implements a resource-saving method(named t-bit semiclassical QFT over Z2n), which could realize large-scale QFT using an arbitrary-scale quantum register. By developing a feasible method to realize the control quantum gate Rk, we experimentally realize the 2-bit semiclassical QFT over Z23 on IBM’s quantum cloud computer, which shows the feasibility of the method. Then, we compare the actual performance of 2-bit semiclassical QFT with standard QFT in the experiments.The squared statistical overlap experimental data shows that the fidelity of 2-bit semiclassical QFT is higher than that of standard QFT, which is mainly due to fewer two-qubit gates in the semiclassical QFT. Furthermore, based on the proposed method, N = 15 is successfully factorized by implementing Shor’s algorithm.
基金the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement NO 705402,POROSOSthe Spanish project FEDER/MCYT MTM2016-75139-R+1 种基金the DGA(Grupo de referencia APEDIF,ref.E24_17R)NSF DMS-1522615 and DMS-1720114.
文摘Local Fourier analysis(LFA)is a useful tool in predicting the convergence factors of geometric multigrid methods(GMG).As is well known,on rectangular domains with periodic boundary conditions this analysis gives the exact convergence factors of such met hods.When other boundary conditions are considered,however,this analysis was judged as been heuristic,with limited capabilities in predicting multigrid convergence rates.In this work,using the Fourier method,we extend these results by proving that such analysis yields the exact convergence factors for a wider class of problems,some of which can not be handled by the traditional rigorous Fourier analysis.
基金The Department of Earth Sciences of the University of Florence(Italy)supported this research as part of its program to improve rockslide early warning system(PRIN 2009-Advanced monitoring techniques for the development of early warning procedures on large rockslides-prot.20084FAHR7_001)the financial support provided by China Scholarship Council(CSC)to Liang Feng during his abroad studying in Italy.
文摘In the seismic event classification,determining the seismic features of rockfall is significantly important for the automatic classification of seismic events because of the huge amount of raw data recorded by seismic stations in continuous monitoring. At the same time, the rockfall seismic features are still not completely understood.This study concentrates on the rockfall frequency content, amplitude(ground velocity), seismic waveform and duration analysis, of an artificial rockfall test at Torgiovannetto(a former quarry in Central Italy). A total of 90 blocks were released in the test, and their seismic signals and moving trajectories were recorded by four tri-axial seismic stations and four cameras, respectively. In the analysis processing,all the artificial rockfall signal traces were cut separately and the seismic features were extracted individually and automatically. In this study, the relationships between a) frequency content and impacted materials, b) frequency content and the distance between block releasing position and seismic station(source-receiver distance) were discussed. As a result, we found that the frequency content of rockfall focuses on 10-60 Hz and 80-90 Hz within a source-receiver distance of 200 m, and it is well correlated with impacted material and source-receiver distance. To evaluate the difference between earthquake and rockfall, 23 clear earthquake signals recorded in a seven month-long continuous seismic monitoring, carried out with the four seismic stations, were picked out, according to the Italian national earthquakes database(INGV). On these traces we performed the same analysis as in the artificial rockfall traces, and two parameters were defined to separate rockfall events from earthquake noise. The first one, the amplitude ratio, is related to the amplitude variation of rockfall between two stations and is greater than that of earthquakes, because of the higher attenuation occurring for rockfall events, which consists in high frequencies whereas for earthquakes it consists
基金the Diamond Grant 2016 (No.0080/DIA/2016/45) funded by the Polish Ministry of Science and Higher Education.
文摘The amount of digital data is increasing every day.At every step of our daily lives,we deal with technologies in which our data are stored (e.g.,mobile phones and laptops),and this is one of the main reasons for the design of various types of encryption and user identity verification algorithms.These algorithms are meant not only to fulfill the desire of protecting data but also to address the possibility of granting access of specific digital data to selected individuals.This process brings with it the problem of identity verification.This paper discusses the problem of voice verification and presents a voice verification method based on artificial intelligence methods. Numerous tests are performed herein to demonstrate the effectiveness of the presented solution.The research results are shown and discussed in terms of the advantages and disadvantages of the solution.
文摘The present work is devoted to the development of the extension of FRT (Finite Radon Transform) to the tridimensional case. One simple formulation is proposed and it is shown that it is the exact discretization of the continuous Discrete Radon Transform. More precisely this is the case when the sampling is given on a regular grid i.e. the continuous function is filtered by the mean of the box function. Relation of this transform with the Discrete Fourier one is given and is for some help in numerical implementation.
基金National Natural Science Foundation of China(NSFC)(11774310,61525505,61705193)China Postdoctoral Science Foundation(2017M610367).
文摘The dispersive Fourier transform(DFT) technique opens a fascinating pathway to explore ultrafast non-repetitive events and has been employed to study the build-up process of mode-locked lasers. However, the shutting process for the mode-locked fiber laser seems to be beyond the scope of researchers, and the starting dynamics under nearzero dispersion remains unclear. Here, the complete evolution dynamics(from birth to extinction) of the conventional soliton(CS), stretched pulse(SP), and dissipative soliton(DS) are investigated by using the DFT technique.CS, SP, and DS fiber lasers mode locked by single-walled carbon nanotubes(SWNTs) are implemented via engineering the intracavity dispersion map. The relaxation oscillation can always be observed before the formation of stable pulse operation due to the inherent advantage of SWNT, but it exhibits distinct evolution dynamics in the starting and shutting processes. The shutting processes are dependent on the dispersion condition and turn-off time, which is against common sense. Some critical phenomena are also observed, including transient complex spectrum broadening and frequency-shift interaction of SPs and picosecond pulses. These results will further deepen understanding of the mode-locked fiber laser from a real-time point of view and are helpful for laser design and applications.
文摘This paper proposes an approach to extract the mode shapes of beam-like structures from the dynamic response of a moving mass. When a mass passes through a beam containing several artificially installed humps, its vertical acceleration can be recorded. After applying fast Fourier transformation to the dynamic response, one can extract the mode shapes of the beam. The surface roughness was neglected compared to the humps and its adverse effect on the extraction was reduced. The passing mass performs as both “exciter” and “massage receiver”;therefore, this method requires only one single accelerometer, making it more convenient and time saving in practice. Moreover, to estimate the possible error in extracting mode shapes, a wavenumber domain filtering technique is used to reconstruct the general profiles of mode shapes. Experimental validation of this approach in laboratory scale was conducted. The experimental results show that the proposed method performs well in extracting lower order mode shapes. It should also be noted that the passing mass can not have a very high velocity (e.g. 80 mm/s), otherwise the mass may jump and separate from the beam, and the proposed method may fail to identify mode shapes.
基金the National Natural Science Foundation of China (Grant No. 11771213)the National Key Research and Development Project of China (Grant No. 2016YFC0600310)the Major Projects of Natural Sciences of University in Jiangsu Province of China (Grant No. 15KJA110002).
文摘This paper gives several structure-preserving schemes for the Degasperis-Procesi equation which has bi-Hamiltonian structures consisted of both complex and non-local Hamiltonian differential operators. For this sake, few structure-preserving schemes have been proposed so far. In our work, based on one of the bi-Hamiltonian structures, a symplectic scheme and two new energy-preserving schemes are constructed. The symplecticity comes straightly from the application of the implicit midpoint method on the semi-discrete system which is proved to remain Hamiltonian, while the energy conservation is derived by the combination of the averaged vector field method of second and fourth order, respectively. Some numerical results are presented to show that the three schemes do have the advantages in numerical stability, accuracy in long time computing and ability to preserve the invariants of the DP equation.
文摘Background: Cotton fiber maturity is an important property that partially determines the processing and performance of cotton. Due to difficulties of obtaining fiber maturity values accurately from every plant of a genetic population, cotton geneticists often use micronaire (MIC) and/or lint percentage for classifying immature phenotypes from mature fiber phenotypes although they are complex fiber traits. The recent development of an algorithm for determining cotton fiber maturity (MIR) from Fourier transfonn infrared (FT-IR) spectra explores a novel way to measure fiber maturity efficiently and accurately. However, the algorithm has not been tested with a genetic population consisting of a large number of progeny plants. Results: The merits and limits of the MIC- or lint percentage-based phenotyping method were demonstrated by comparing the observed phenotypes with the predicted phenotypes based on their DNA marker genotypes in a genetic population consisting of 708 F2 plants with various fiber maturity. The observed MIC-based fiber phenotypes matched to the predicted phe no types better than the observed lint percentage-based fiber phenotypes. The lint percentage was obtained from each of F2 plants, whereas the MIC values were unable to be obtained from the entire population since certain F2 plants produced insufficient fiber mass for their measurements. To test the feasibility of cotton fiber infrared maturity (MIR) as a viable phenotyping tool for genetic analyses, we measured FT-IR spectra from the second population composed of 80 F2 plants with various fiber maturities, determined MIR values using the algorithms, and compared them with their genotypes in addition to other fiber phenotypes. The results showed that MiR values were successfully obtained from each of the F2 plants, and the observed MIR-based phenotypes fit well to the predicted phenotypes based on their DNA marker genotypes as well as the observed phenotypes based on a combination of MIC and lint percentage. Conclusions: The MIR value obtained
基金National Natural Science Foundation of China(Grant No.61671063)Foundation for Innovative Research Groups of National Natural Science Foundation of China(Grant No.61421001).
文摘The purpose of this paper is to present a quantitative SNR analysis of quadratic frequency modulated(QFM)signals.This analysis is located in the continuous-time local polynomial Fourier transform(LPFT)domain using a Gaussian window function based on the definition of 3 dB signal-to-noise ratio(SNR).First,the maximum value of the local polynomial periodogram(LPP),and the 3 dB bandwidth in the LPFT domain for a QFM signal is derived,respectively.Then,based on these results,the 3 dB SNR of a QFM signal with Gaussian window function is given in the LPFT domain with one novel idea highlighted:the relationship among standard SNR,parameters of QFM signals and Gaussian window function is clear,and the potential application is demonstrated in the parameter estimation of a QFM signal using the LPFT.Moreover,the 3 dB SNR in the LPFT domain is compared with that in the linear canonical transform(LCT)domain.The validity of theoretical derivations is confirmed via simulation results.It is shown that,in terms of SNR,QFM signals in the LPFT domain can achieve a significantly better performance than those in the LCT domain.
基金the National Natural Science Foundation of China (Grant Nos.61573008 and 61703290)Natural Science Foundation of Liaoning Province,China (Grant No.20180550996).
文摘It is well-known that reaction–diffusion systems are used to describe the pattern formation models.In this paper,we will investigate the pattern formation generated by the fractional reaction–diffusion systems.We first explore the mathematical mechanism of the pattern by applying the linear stability analysis for the fractional Gierer–Meinhardt system.Then,an efficient high-precision numerical scheme is used in the numerical simulation.The proposed method is based on an exponential time differencing Runge–Kutta method in temporal direction and a Fourier spectral method in spatial direction.This method has the advantages of high precision,better stability,and less storage.Numerical simulations show that the system control parameters and fractional order exponent have decisive influence on the generation of patterns.Our numerical results verify our theoretical results.
文摘The scattering and reflection of SH waves by a slope on an elastic wedged space is investigated. A series solution is obtained by using the wave function expansion method. The slope on a wedged space is divided into two subregions by an artificial, auxiliary circular arc. The wave fields with unknown complex coefficients within each sub-region are derived. Applying Graf addition theorem, the scattered waves in the sub-regions are expressed in a global coordinate system. Fourier transform is adopted to derive a consistent form of standing waves in the inner region using the orthogonality of the cosine functions. The boundary-valued problem is solved by stress and displacement continuity along the artificial, auxiliary arc to obtain the unknown complex coefficients. Parametric studies are next performed to investigate how the topography from the slope on the wedged space will affect the scattering and diffraction, and hence the amplification and de-amplification of the SH waves. Numerical results show that the surface motions on the slope of the wedged space is influenced greatly by the topography. Amplification of the surface motions near the slope vertex is significant. The corresponding phases along the wedged space surfaces are consistent with the direction that the SH waves are propagating.
文摘Computation of stereoscopic depth and disparity map extraction are dynamic research topics.A large variety of algorithms has been developed,among which we cite feature matching, moment extraction, and image representation using descriptors to determine a disparity map. This paper proposes a new method for stereo matching based on Fourier descriptors. The robustness of these descriptors under photometric and geometric transformations provides a better representation of a template or a local region in the image. In our work, we specifically use generalized Fourier descriptors to compute a robust cost function.Then, a box filter is applied for cost aggregation to enforce a smoothness constraint between neighboring pixels. Optimization and disparity calculation are done using dynamic programming, with a cost based on similarity between generalized Fourier descriptors using Euclidean distance. This local cost function is used to optimize correspondences. Our stereo matching algorithm is evaluated using the Middlebury stereo benchmark;our approach has been implemented on parallel high-performance graphics hardware using CUDA to accelerate our algorithm, giving a real-time implementation.
基金the MURI/ARO on"Fractional PDEs for Conservation Laws and Beyond:Theory,Numerics and Applications"(W91 INF-15-1-0562).
文摘We establish the well-posedness of the fractional PDE which arises by considering the gradient flow associated with a fractional Gross-Pitaevskii free energy functional and some basic properties of the solution.The equation reduces to the Allen-Cahn or Cahn-Hilliard equations in the case where the mass tends to zero and an integer order derivative is used in the energy.We study how the presence of a non-zero mass affects the nature of the solutions compared with the Cahn-Hilliard case.In particular,we show that,analogous to the Cahn-Hilliard case,the solutions consist of regions in which the solution is a piecewise constant(whose value depends on the mass and the fractional order)separated by an interface whose width is independent of the mass and the fractional derivative.However,if the average value of the initial data exceeds some threshold(which we determine explic让ly),then the solution will tend to a single constant steady state.
基金the Joint Funds of National Natural Science Foundation of China(No.U1462105).
文摘The classification of spatial characteristics and discharge modes of dielectric barrier discharge(DBD)are gaining increasing attention in industrial applications,especially in the field of surface treatment of materials.In this work,gray level histogram(GLH)and Fourier energy spectrum based on the digital image processing tech no logy are applied to investigate the spatial structure and discharge mode of mesh-plate DBD.The coefficient of variation(CV)is calculated to describe the uniformity of the discharge.The results show that the discharge mode of mesh-plate DBD changes from periodic discharge to filamentary discharge when the applied voltage increases from 11-15 kV.Moreover,a more regular spatial structure is obtained under lower applied voltages during the discharge process.It is also found that the apertures of mesh electrodes which are below 1 mm have smaller values of CV compared to plate electrodes,indicating more uniform discharge.Finally,polypropylene is treated by mesh-plate DBD for surface modification.The hydrophilicity is significantly improved as the water contact angle decreased by 64°,and the dyeing depth is also enhanced.
基金Supported by the Educational Science Research Project of Hubei Province(B2014243).
文摘Traditional orthogonal frequency division multiplexing(OFDM)transmitter is implemented by exploiting inverse fast Fourier transform(IFFT),up-sampling,and low pass shaping filter(LPSF)modules,which occupy a large number of hardware resources and severely lower down the operation speed.To address these limitations,we propose a novel OFDM transmitter architecture,by which the aforementioned modules can be discarded and replaced with some simple switches.In the proposed architecture,direct digital synthesis(DDS)method is employed to generate digital sub-carriers and to transform OFDM data from frequency domain to time domain.Through some sophisticated simplifications,the proposed architecture can avoid using multipliers and remarkably save hardware resources.Finally,comparative experiments are carried out on field programmable gate array(FPGA)platform which demonstrates that our DDS-based architecture saves more than half of the hardware resources and doubles the achievable maximum frequency compared with traditional structure.
基金supported by the Polar Research Institute of China and the Chinese Arctic and Antarctic Administrationthe University of New South Wales PLATO teamthe Chinese Academy of Sciences Center for Antarctic Astronomy team.
文摘Atmospheric transmission from Dome A, Antarctica, presents new possibilities in the field of terahertz astronomy, where space telescopes have been the only observational tools until now. Using atmospheric transmission measurements from Dome A with a Fourier transform spectrometer, transmission spectra and long-term stabilities have been analyzed at 1.461 THz, 3.393 THz, 5.786 THz and 7.1 THz, which show that important atmospheric windows for terahertz astronomy open for a reasonable length of time in the winter season. With large aperture terahertz telescopes and interferometers at Dome A, high angular resolution terahertz observations are foreseen of atomic fine-structure lines from ionized gas and a water ice feature from protoplanetary disks.
基金National Key R&D Program of China(Grant No.2018YFB-0904900)National Cryptography Development Fund(Grant Nos.MMJJ20170214,MMJJ20170211).
文摘The randomness of random number generators(RNGs)is important for the reliability of cryptographic systems since the outputs of RNGs are usually utilized to construct cryptographic parameters.Statistical tests are employed to evaluate the randomness of the RNG outputs.The discrete Fourier transform(DFT)test is an important test item of the most popular statistical test suite NIST SP800-22.In the standard NIST DFT test and related improved studies,there exist accuracy and efficiency issues.First,the bit sequences generated by known good RNGs have a high probability to be rejected when the sequences are long or the sequence number is large,due to the deviation between the actual distribution of the test statistic values and the assumed normal distribution.Second,the long test time and high memory consumptions of the complex DFT test algorithm also affect its practicability.To solve these problems,we propose a new DFT test method for long sequences(10^6 or more bits).Different from the previous DFT test methods focusing on making the distribution of the test statistic values closer to the normal distribution,we reconstruct the statistic to follow the chi-square distribution.Our experiment result shows that our method has higher reliability in the two-level test,and could effectively reduce the test time and the memory consumptions.When applying our method on randomness test,the test efficiency has been increased to about 4 times for 106-bit sequences and 7 times for 10^7-bit sequences.In conclusion,our method has lower probability of making errors,and is more suitable for practical application scenarios.
基金National Natural Science Foundation of China(Nos.516754865150523951575496).
文摘The most important performance of a beating-up mechanism is that the dwelling time of the sley must ensure the completion of the weft insertion. To meet this requirement, a new non-circular combined gear train beating-up mechanism which is composed of two-stage planetary gear trains is proposed. The first-stage is a Fourier planetary gear train and the second-stage is a non-circular planetary gear train. For designing of this new mechanism, the ideal kinematic equations of the sley are constructed first. Then the kinematic model of the first-stage Fourier planetary gear train is established and the reverse solution for the pitch curves of the second-stage non-circular gears is deduced. With a computer-aided design program, the influences of several important parameters on the pitch curves of the second-stage non-circular gears are analyzed, and a set of preferable structural parameters are obtained. Finally, a test bed of this mechanism is developed and the experimental results show that this new beating-up mechanism can achieve the designed dwelling time, namely it can meet the requirements of beating-up process.