This paper presents sensitivity analysis of vibration frequencies of flexible manipulators with respect to variations of systems parameters such as rotational inertia of hub,and mass,moment,and side of tip load.Both E...This paper presents sensitivity analysis of vibration frequencies of flexible manipulators with respect to variations of systems parameters such as rotational inertia of hub,and mass,moment,and side of tip load.Both Euler-Bernoulli and Timoshenko dynamical models of flexible manipulators are discussed.By using variational method,sensitivity indices are obtained with explicit expressions for measuring the sensitivity of frequencies.Based on variational formulations,a novel method for deriving the orthogonal relations among vibration modal shape functions of flexible manipulators is introduced.With this method,the orthogonal relations can be derived easily without invoking the tedious process of differentiation and integration by part,as commonly used in their derivation.展开更多
Within the framework of the first-order Born approximation, the triple differential cross sections (TDCSs) for simultaneous ionization and excitation of helium are calculated. The wave function of the ejected electr...Within the framework of the first-order Born approximation, the triple differential cross sections (TDCSs) for simultaneous ionization and excitation of helium are calculated. The wave function of the ejected electron is chosen to be orthogonal or non-orthogonal to the wave function of the bound electron before ionization. It is found that the orthogonality has a strong effect on the TDCS, especially when plane waves and Coulomb waves are used to describe the projectile and the ejected electron.展开更多
This paper introduced a dynamical system (neural networks) algorithm for solving a least squares problem with orthogonality constraints, which has wide applications in computer vision and signal processing. A rigorous...This paper introduced a dynamical system (neural networks) algorithm for solving a least squares problem with orthogonality constraints, which has wide applications in computer vision and signal processing. A rigorous analysis for the convergence and stability of the algorithm was provided. Moreover, a so called zero extension technique was presented to keep the algorithm always convergent to the needed result for any randomly chosen initial data. Numerical experiments illustrate the effectiveness and efficiency of the algorithm.展开更多
Let X be a Minkowski plane, i.e., a real two dimensional normed linear space. We use projections to give a definition of the angle Aq(x, y) between two vectors x and y in X, such that x is Birkhoff orthogonal to y i...Let X be a Minkowski plane, i.e., a real two dimensional normed linear space. We use projections to give a definition of the angle Aq(x, y) between two vectors x and y in X, such that x is Birkhoff orthogonal to y if and only if Aq(x,y)=π/2. Some other properties of this angle are also discussed.展开更多
In this paper, we present various notions and aspects of orthogonality in normed spaces. Characterizations and generalizations of orthogonality are also consid- ered. Results on orthogonality of the range and the kern...In this paper, we present various notions and aspects of orthogonality in normed spaces. Characterizations and generalizations of orthogonality are also consid- ered. Results on orthogonality of the range and the kernel of elementary operators and the operators implementing them also are given.展开更多
In this paper, we reexamine the method of successive approximation presented by Prof. Chien Wei-zangfor solving the problem of large deflection of a circular plate, and find that the method could be regarded as the me...In this paper, we reexamine the method of successive approximation presented by Prof. Chien Wei-zangfor solving the problem of large deflection of a circular plate, and find that the method could be regarded as the method of strained parameters in the singular perturbation theory. In terms of the parameter representing the ratio of the center deflection to the thickness of the plate, we make the asymptotic expansions of the deflection, membrane stress and the parameter of load as in Ref. [1], and then give the orthogonality conditions (i.e. the solvability conditions) for the resulting equations, by which the stiffness characteristics of the plate could be determined. It is pointed out that with the solutions for the small deflection problem of the circular plate and the orthogonality conditions, we can derive the third order approximate relations between the parameter of load and the center deflection and the first-term approximation of membrane stresses at the center and edge of the plate without solving the differential equations. For some special cases (i.e. under uniform load, under compound toad, with different boundary conditiors), we deduce the specific expressions and obtain the results in agreement with the previous ones given by Chien Wei-zang, Yeh kai-yuan and Hwang Chien in Refs. [1 - 4J.展开更多
Abstract. Let {L(Ln^(A,λ)(x)}n≥0 be the sequence of monic Laguerre matrix polynomials defined on [0,∞) byLn^(A,λ)(x)=n!/(-λ)^n ∑nk-0(-λ)^k/k!(n-k)!(A+I)n[(A+I)k]^-1x^k,where A ∈ C^r×...Abstract. Let {L(Ln^(A,λ)(x)}n≥0 be the sequence of monic Laguerre matrix polynomials defined on [0,∞) byLn^(A,λ)(x)=n!/(-λ)^n ∑nk-0(-λ)^k/k!(n-k)!(A+I)n[(A+I)k]^-1x^k,where A ∈ C^r×r. It is known that {Ln^(A,λ)(x)}n≥0 is orthogonal with respect to a matrix moment functional when A satisfies the spectral condition that Re(z) 〉 -1 for every z E or(a). In this note we show that forA such that σ(A) does not contain negative integers, the Laguerre matrix polynomials Ln^(A,λ)(x) are orthogonal with respect to a non-diagonal SobolevLaguerre matrix moment functional, which extends two cases: the above matrix case and the known scalar case.展开更多
An implicit algorithm of Bi-penalty approximation with orthogonality projection for the numerical simulation of Bingham fluid flow problems is proposed in this paper. A Newton fluid flow with two kinds of artificial v...An implicit algorithm of Bi-penalty approximation with orthogonality projection for the numerical simulation of Bingham fluid flow problems is proposed in this paper. A Newton fluid flow with two kinds of artificial viscosity subjected to the inequality constraint is introduced to approximate the Bingham fluid flow. This approach can effectively simulate the Bingham fluid flow with floating rigid cores or fixing rigid cores.展开更多
For square contingency tables with ordered categories, the present paper gives several theorems that the symmetry model holds if and only if the generalized linear diagonals-parameter symmetry model for cell probabili...For square contingency tables with ordered categories, the present paper gives several theorems that the symmetry model holds if and only if the generalized linear diagonals-parameter symmetry model for cell probabilities and for cumulative probabilities and the mean nonequality model of row and column variables hold. It also shows the orthogonality of statistic for testing goodness-of-fit of the symmetry model. An example is given.展开更多
To obtain convergent numerical approximations without using any orthogonalization operations is of great importance in electronic structure calculations.In this paper,we propose and analyze a class of iteration scheme...To obtain convergent numerical approximations without using any orthogonalization operations is of great importance in electronic structure calculations.In this paper,we propose and analyze a class of iteration schemes for the discretized Kohn-Sham Density Functional Theory model,with which the iterative approximations are guaranteed to converge to the Kohn-Sham orbitals without any orthogonalization as long as the initial orbitals are orthogonal and the time step sizes are given properly.In addition,we present a feasible and efficient approach to get suitable time step sizes and report some numerical experiments to validate our theory.展开更多
The thought how dual vectors are constructed in a new orthogonality relationship for theory of elasticity is generalized into orthotropic thin plate bending problems by using the analogy theory between plane elasticit...The thought how dual vectors are constructed in a new orthogonality relationship for theory of elasticity is generalized into orthotropic thin plate bending problems by using the analogy theory between plane elasticity problems and plate bending problems. Dual differential equations are directly obtained by using a mixed variables method. A dual differential matrix to be derived possesses a peculiarity of which principal diagonal sub-matrixes are zero matrixes. Two independently and symmetrically orthogonality sub-relationships are discovered. By using the integral form for elastic bending theory of orthotropic thin plate the orthogonality relationship is demonstrated. By selecting felicitous dual vectors a new orthogonality relationship for theory of elasticity can be generalized into elastic bending theory of orthotropic thin plate. By using the integral form a variational principle which is relative to differential form and a whole function expression are proposed.展开更多
The ability to expand genetic code in living cells has emerged as a powerful method with diverse applications.Here,we design re-placement of the anticodons of E.coli tRNAs that recognize codons for 20 natural amino ac...The ability to expand genetic code in living cells has emerged as a powerful method with diverse applications.Here,we design re-placement of the anticodons of E.coli tRNAs that recognize codons for 20 natural amino acids,with three anti-stop codons,resulting in a total of 60 engineered tRNA constructs.We test these constructs one by one in E.coli,and found that six tRNAsCUA(tyrV,serX,hisR,trpT,glnV and leuX),two tRNAsUCA(trpT and leuX)and one tRNAUUA(tyrV)allowed efficient expression of Red Fluorescence Protein(RFP)with the presence of a corresponding stop codon in frame.Furthermore,we exploit the mutual orthogonality of tRNASer CUA,tRNATrpUCA and tRNATyrUUA with corresponding stop codons and demonstrated that the tRNASer CUA and the tRNATrp UCA can provide dynamic range and low crosstalk.Finally,we show the TAG and TGA can not only be used as an"AND gate"circuit to control the translation of target gene,but also be used to control the translation of a prodeoxyviolacein(PDV)pathway and a reporter in parallel.Overall,this work provides flexible tools for translational control and holds great potential to promote synthetic biology studies.展开更多
Using the fixed point method, we prove the Hyers Ulam stability of an orthogonally quintic functional equation in Banach spaces and in non-Archimedean Banach spaces.
Chlorophyll-a(Chl-a)concentration is a primary indicator for marine environmental monitoring.The spatio-temporal variations of sea surface Chl-a concentration in the Yellow Sea(YS)and the East China Sea(ECS)in 2001-20...Chlorophyll-a(Chl-a)concentration is a primary indicator for marine environmental monitoring.The spatio-temporal variations of sea surface Chl-a concentration in the Yellow Sea(YS)and the East China Sea(ECS)in 2001-2020 were investigated by reconstructing the MODIS Level 3 products with the data interpolation empirical orthogonal function(DINEOF)method.The reconstructed results by interpolating the combined MODIS daily+8-day datasets were found better than those merely by interpolating daily or 8-day data.Chl-a concentration in the YS and the ECS reached its maximum in spring,with blooms occurring,decreased in summer and autumn,and increased in late autumn and early winter.By performing empirical orthogonal function(EOF)decomposition of the reconstructed data fields and correlation analysis with several potential environmental factors,we found that the sea surface temperature(SST)plays a significant role in the seasonal variation of Chl a,especially during spring and summer.The increase of SST in spring and the upper-layer nutrients mixed up during the last winter might favor the occurrence of spring blooms.The high sea surface temperature(SST)throughout the summer would strengthen the vertical stratification and prevent nutrients supply from deep water,resulting in low surface Chl-a concentrations.The sea surface Chl-a concentration in the YS was found decreased significantly from 2012 to 2020,which was possibly related to the Pacific Decadal Oscillation(PDO).展开更多
Based on numerical solutions of the time-dependent Schr ¨odinger equation, we theoretically investigate the photoelectron spectrum of hydrogen atoms ionized by a pair of ultrashort, intense, and orthogonally pola...Based on numerical solutions of the time-dependent Schr ¨odinger equation, we theoretically investigate the photoelectron spectrum of hydrogen atoms ionized by a pair of ultrashort, intense, and orthogonally polarized laser pulses with a relative time delay in a pump–probe configuration. The pump pulse resonantly excites electrons from the 1s and 2p levels,inducing Rabi oscillations. The resulting dynamically enhanced Autler–Townes(AT) splitting is observed in the photoelectron energy spectrum upon interaction with the second probe pulse. In contrast to the previous parallel-polarization scheme, the proposed orthogonal-polarization configuration enables the resolution of dynamically enhanced AT splitting over a considerably wider range of probe photon energies.展开更多
In this paper,the bifurcation properties of the vibro-impact systems with an uncertain parameter under the impulse and harmonic excitations are investigated.Firstly,by means of the orthogonal polynomial approximation(...In this paper,the bifurcation properties of the vibro-impact systems with an uncertain parameter under the impulse and harmonic excitations are investigated.Firstly,by means of the orthogonal polynomial approximation(OPA)method,the nonlinear damping and stiffness are expanded into the linear combination of the state variable.The condition for the appearance of the vibro-impact phenomenon is to be transformed based on the calculation of themean value.Afterwards,the stochastic vibro-impact systemcan be turned into an equivalent high-dimensional deterministic non-smooth system.Two different Poincarésections are chosen to analyze the bifurcation properties and the impact numbers are identified for the periodic response.Consequently,the numerical results verify the effectiveness of the approximation method for analyzing the considered nonlinear system.Furthermore,the bifurcation properties of the system with an uncertain parameter are explored through the high-dimensional deterministic system.It can be found that the excitation frequency can induce period-doubling bifurcation and grazing bifurcation.Increasing the randomintensitymay result in a diffusion-based trajectory and the impact with the constraint plane,which induces the topological behavior of the non-smooth system to change drastically.It is also found that grazing bifurcation appears in advance with increasing of the random intensity.The stronger impulse force can result in the appearance of the diffusion phenomenon.展开更多
To investigate the influence of structural parameters on the performances and internal flow characteristics of partial flow pumps at a low specific speed of 10000 rpm,special attention was paid to the first and second...To investigate the influence of structural parameters on the performances and internal flow characteristics of partial flow pumps at a low specific speed of 10000 rpm,special attention was paid to the first and second stage impeller guide vanes.Moreover,the impeller blade outlet width,impeller inlet diameter,blade inclination angle,and number of blades were considered for orthogonal tests.Accordingly,nine groups of design solutions were formed,and then used as a basis for the execution of numerical simulations(CFD)aimed at obtaining the efficiency values and heads for each design solution group.The influence of impeller geometric parameters on the efficiency and head was explored,and the“weight”of each factor was obtained via a range analysis.Optimal structural parameters were finally chosen on the basis of the numerical simulation results,and the performances of the optimized model were verified accordingly(yet by means of CFD).Evidence is provided that the increase in the efficiency and head of the optimized model was 12.11%and 23.5 m,respectively,compared with those of the original model.展开更多
When the amphibious vehicle navigates in water,the angle of the anti-wave plate and the position of the center of gravity greatly influence the navigation characteristics.In the relevant research on reducing the navig...When the amphibious vehicle navigates in water,the angle of the anti-wave plate and the position of the center of gravity greatly influence the navigation characteristics.In the relevant research on reducing the navigation resistance of amphibious vehicles by adjusting the angle of the anti-wave plate,there is a lack of scientific selection of parameters and reasonable research of simulation results by using mathematical methods,and the influence of the center of gravity position on navigation characteristics is not considered at the same time.To study the influence of the combinations of the angle of the anti-wave plate and the position of the center of gravity on the resistance reduction characteristics,a numerical calculation model of the amphibious unmanned vehicle was established by using the theory of computational fluid dynamics,and the experimental data verified the correctness of the numerical model.Based on this numerical model,the navigation characteristics of the amphibious unmanned vehicle were studied when the center of gravity was located at different positions,and the orthogonal experimental design method was used to optimize the parameters of the angle of the anti-wave plate and the position of the center of gravity.The results show that through the parameter optimization analysis based on the orthogonal experimental method,the combination of the optimal angle of the anti-wave plate and the position of the center of gravity is obtained.And the numerical simulation result of resistance is consistent with the predicted optimal solution.Compared with the maximum navigational resistance,the parameter optimization reduces the navigational resistance of the amphibious unmanned vehicle by 24%.展开更多
文摘This paper presents sensitivity analysis of vibration frequencies of flexible manipulators with respect to variations of systems parameters such as rotational inertia of hub,and mass,moment,and side of tip load.Both Euler-Bernoulli and Timoshenko dynamical models of flexible manipulators are discussed.By using variational method,sensitivity indices are obtained with explicit expressions for measuring the sensitivity of frequencies.Based on variational formulations,a novel method for deriving the orthogonal relations among vibration modal shape functions of flexible manipulators is introduced.With this method,the orthogonal relations can be derived easily without invoking the tedious process of differentiation and integration by part,as commonly used in their derivation.
基金Project supported by the Anhui University Doctoral Research Starting Foundation,China(Grant Nos.02303319 and 33190203)the National Natural Science Foundation of China(Grant No.11274219)
文摘Within the framework of the first-order Born approximation, the triple differential cross sections (TDCSs) for simultaneous ionization and excitation of helium are calculated. The wave function of the ejected electron is chosen to be orthogonal or non-orthogonal to the wave function of the bound electron before ionization. It is found that the orthogonality has a strong effect on the TDCS, especially when plane waves and Coulomb waves are used to describe the projectile and the ejected electron.
基金National Natural Science Foundation of China (No. 1990 10 18)
文摘This paper introduced a dynamical system (neural networks) algorithm for solving a least squares problem with orthogonality constraints, which has wide applications in computer vision and signal processing. A rigorous analysis for the convergence and stability of the algorithm was provided. Moreover, a so called zero extension technique was presented to keep the algorithm always convergent to the needed result for any randomly chosen initial data. Numerical experiments illustrate the effectiveness and efficiency of the algorithm.
文摘Let X be a Minkowski plane, i.e., a real two dimensional normed linear space. We use projections to give a definition of the angle Aq(x, y) between two vectors x and y in X, such that x is Birkhoff orthogonal to y if and only if Aq(x,y)=π/2. Some other properties of this angle are also discussed.
基金National Council for Science and Technology (NCST) of KenyaDAAD-Germany for the financial support
文摘In this paper, we present various notions and aspects of orthogonality in normed spaces. Characterizations and generalizations of orthogonality are also consid- ered. Results on orthogonality of the range and the kernel of elementary operators and the operators implementing them also are given.
基金Project supported by the National Natural Science Foundation of China
文摘In this paper, we reexamine the method of successive approximation presented by Prof. Chien Wei-zangfor solving the problem of large deflection of a circular plate, and find that the method could be regarded as the method of strained parameters in the singular perturbation theory. In terms of the parameter representing the ratio of the center deflection to the thickness of the plate, we make the asymptotic expansions of the deflection, membrane stress and the parameter of load as in Ref. [1], and then give the orthogonality conditions (i.e. the solvability conditions) for the resulting equations, by which the stiffness characteristics of the plate could be determined. It is pointed out that with the solutions for the small deflection problem of the circular plate and the orthogonality conditions, we can derive the third order approximate relations between the parameter of load and the center deflection and the first-term approximation of membrane stresses at the center and edge of the plate without solving the differential equations. For some special cases (i.e. under uniform load, under compound toad, with different boundary conditiors), we deduce the specific expressions and obtain the results in agreement with the previous ones given by Chien Wei-zang, Yeh kai-yuan and Hwang Chien in Refs. [1 - 4J.
基金Supported by the National Natural Science Foundation of China(No.10571122)the Beijing Natural Science Foundation(No.1052006)+1 种基金the Project of Excellent Young Teachersthe Doctoral Programme Foundation of National Education Ministry of China
文摘Abstract. Let {L(Ln^(A,λ)(x)}n≥0 be the sequence of monic Laguerre matrix polynomials defined on [0,∞) byLn^(A,λ)(x)=n!/(-λ)^n ∑nk-0(-λ)^k/k!(n-k)!(A+I)n[(A+I)k]^-1x^k,where A ∈ C^r×r. It is known that {Ln^(A,λ)(x)}n≥0 is orthogonal with respect to a matrix moment functional when A satisfies the spectral condition that Re(z) 〉 -1 for every z E or(a). In this note we show that forA such that σ(A) does not contain negative integers, the Laguerre matrix polynomials Ln^(A,λ)(x) are orthogonal with respect to a non-diagonal SobolevLaguerre matrix moment functional, which extends two cases: the above matrix case and the known scalar case.
文摘An implicit algorithm of Bi-penalty approximation with orthogonality projection for the numerical simulation of Bingham fluid flow problems is proposed in this paper. A Newton fluid flow with two kinds of artificial viscosity subjected to the inequality constraint is introduced to approximate the Bingham fluid flow. This approach can effectively simulate the Bingham fluid flow with floating rigid cores or fixing rigid cores.
文摘For square contingency tables with ordered categories, the present paper gives several theorems that the symmetry model holds if and only if the generalized linear diagonals-parameter symmetry model for cell probabilities and for cumulative probabilities and the mean nonequality model of row and column variables hold. It also shows the orthogonality of statistic for testing goodness-of-fit of the symmetry model. An example is given.
基金This work was supported by the National Key R&D Program of China under grants 2019YFA0709600,2019YFA0709601the National Natural Science Foundation of China under grant 12021001.
文摘To obtain convergent numerical approximations without using any orthogonalization operations is of great importance in electronic structure calculations.In this paper,we propose and analyze a class of iteration schemes for the discretized Kohn-Sham Density Functional Theory model,with which the iterative approximations are guaranteed to converge to the Kohn-Sham orbitals without any orthogonalization as long as the initial orbitals are orthogonal and the time step sizes are given properly.In addition,we present a feasible and efficient approach to get suitable time step sizes and report some numerical experiments to validate our theory.
基金supported by the National Natural Science Foundation of China(Grant No.10272063)the Basic Science Research Foundation of Tsinghua University(JC2002003)+1 种基金the Special Scientific Foundation for Chinese Doctoral Education(20020003044)the Foundation for the Author of National Excellent Doctoral Dissertation of China(200242).
文摘The thought how dual vectors are constructed in a new orthogonality relationship for theory of elasticity is generalized into orthotropic thin plate bending problems by using the analogy theory between plane elasticity problems and plate bending problems. Dual differential equations are directly obtained by using a mixed variables method. A dual differential matrix to be derived possesses a peculiarity of which principal diagonal sub-matrixes are zero matrixes. Two independently and symmetrically orthogonality sub-relationships are discovered. By using the integral form for elastic bending theory of orthotropic thin plate the orthogonality relationship is demonstrated. By selecting felicitous dual vectors a new orthogonality relationship for theory of elasticity can be generalized into elastic bending theory of orthotropic thin plate. By using the integral form a variational principle which is relative to differential form and a whole function expression are proposed.
基金The authors are grateful for the financial support fromthe National Key Research and Development Program of China(No.2018YFA0903700)the National Natural Science Foundation of China(Nos.31800719,21621004)the International(regional)cooperation and exchange projects(No.31861143017)。
文摘The ability to expand genetic code in living cells has emerged as a powerful method with diverse applications.Here,we design re-placement of the anticodons of E.coli tRNAs that recognize codons for 20 natural amino acids,with three anti-stop codons,resulting in a total of 60 engineered tRNA constructs.We test these constructs one by one in E.coli,and found that six tRNAsCUA(tyrV,serX,hisR,trpT,glnV and leuX),two tRNAsUCA(trpT and leuX)and one tRNAUUA(tyrV)allowed efficient expression of Red Fluorescence Protein(RFP)with the presence of a corresponding stop codon in frame.Furthermore,we exploit the mutual orthogonality of tRNASer CUA,tRNATrpUCA and tRNATyrUUA with corresponding stop codons and demonstrated that the tRNASer CUA and the tRNATrp UCA can provide dynamic range and low crosstalk.Finally,we show the TAG and TGA can not only be used as an"AND gate"circuit to control the translation of target gene,but also be used to control the translation of a prodeoxyviolacein(PDV)pathway and a reporter in parallel.Overall,this work provides flexible tools for translational control and holds great potential to promote synthetic biology studies.
基金supported by Basic Science Research Program through National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (Grant No. NRF-2012R1A1A2004299)
文摘Using the fixed point method, we prove the Hyers Ulam stability of an orthogonally quintic functional equation in Banach spaces and in non-Archimedean Banach spaces.
基金Supported by the Fundamental Research Funds for the Central Universities(Nos.202341017,202313024)。
文摘Chlorophyll-a(Chl-a)concentration is a primary indicator for marine environmental monitoring.The spatio-temporal variations of sea surface Chl-a concentration in the Yellow Sea(YS)and the East China Sea(ECS)in 2001-2020 were investigated by reconstructing the MODIS Level 3 products with the data interpolation empirical orthogonal function(DINEOF)method.The reconstructed results by interpolating the combined MODIS daily+8-day datasets were found better than those merely by interpolating daily or 8-day data.Chl-a concentration in the YS and the ECS reached its maximum in spring,with blooms occurring,decreased in summer and autumn,and increased in late autumn and early winter.By performing empirical orthogonal function(EOF)decomposition of the reconstructed data fields and correlation analysis with several potential environmental factors,we found that the sea surface temperature(SST)plays a significant role in the seasonal variation of Chl a,especially during spring and summer.The increase of SST in spring and the upper-layer nutrients mixed up during the last winter might favor the occurrence of spring blooms.The high sea surface temperature(SST)throughout the summer would strengthen the vertical stratification and prevent nutrients supply from deep water,resulting in low surface Chl-a concentrations.The sea surface Chl-a concentration in the YS was found decreased significantly from 2012 to 2020,which was possibly related to the Pacific Decadal Oscillation(PDO).
基金supported by the National Natural Science Foundation of China(Grant Nos.12074265,12234002,and 92250303)the Guangdong Basic and Applied Basic Research Foundation(Grant No.2022A1515010329)。
文摘Based on numerical solutions of the time-dependent Schr ¨odinger equation, we theoretically investigate the photoelectron spectrum of hydrogen atoms ionized by a pair of ultrashort, intense, and orthogonally polarized laser pulses with a relative time delay in a pump–probe configuration. The pump pulse resonantly excites electrons from the 1s and 2p levels,inducing Rabi oscillations. The resulting dynamically enhanced Autler–Townes(AT) splitting is observed in the photoelectron energy spectrum upon interaction with the second probe pulse. In contrast to the previous parallel-polarization scheme, the proposed orthogonal-polarization configuration enables the resolution of dynamically enhanced AT splitting over a considerably wider range of probe photon energies.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.12172266,12272283)the Bilateral Governmental Personnel Exchange Project between China and Slovenia for the Years 2021-2023(Grant No.12)+2 种基金Slovenian Research Agency ARRS in Frame of Bilateral Project(Grant No.P2-0137)the Fundamental Research Funds for the Central Universities(Grant No.QTZX23004)Joint University Education Project between China and East European(Grant No.2021122).
文摘In this paper,the bifurcation properties of the vibro-impact systems with an uncertain parameter under the impulse and harmonic excitations are investigated.Firstly,by means of the orthogonal polynomial approximation(OPA)method,the nonlinear damping and stiffness are expanded into the linear combination of the state variable.The condition for the appearance of the vibro-impact phenomenon is to be transformed based on the calculation of themean value.Afterwards,the stochastic vibro-impact systemcan be turned into an equivalent high-dimensional deterministic non-smooth system.Two different Poincarésections are chosen to analyze the bifurcation properties and the impact numbers are identified for the periodic response.Consequently,the numerical results verify the effectiveness of the approximation method for analyzing the considered nonlinear system.Furthermore,the bifurcation properties of the system with an uncertain parameter are explored through the high-dimensional deterministic system.It can be found that the excitation frequency can induce period-doubling bifurcation and grazing bifurcation.Increasing the randomintensitymay result in a diffusion-based trajectory and the impact with the constraint plane,which induces the topological behavior of the non-smooth system to change drastically.It is also found that grazing bifurcation appears in advance with increasing of the random intensity.The stronger impulse force can result in the appearance of the diffusion phenomenon.
基金National Key R&D Program of China(Grant No.2020YFC1512404).
文摘To investigate the influence of structural parameters on the performances and internal flow characteristics of partial flow pumps at a low specific speed of 10000 rpm,special attention was paid to the first and second stage impeller guide vanes.Moreover,the impeller blade outlet width,impeller inlet diameter,blade inclination angle,and number of blades were considered for orthogonal tests.Accordingly,nine groups of design solutions were formed,and then used as a basis for the execution of numerical simulations(CFD)aimed at obtaining the efficiency values and heads for each design solution group.The influence of impeller geometric parameters on the efficiency and head was explored,and the“weight”of each factor was obtained via a range analysis.Optimal structural parameters were finally chosen on the basis of the numerical simulation results,and the performances of the optimized model were verified accordingly(yet by means of CFD).Evidence is provided that the increase in the efficiency and head of the optimized model was 12.11%and 23.5 m,respectively,compared with those of the original model.
基金supported by the National Natural Science Foundation of China(52174154).
文摘When the amphibious vehicle navigates in water,the angle of the anti-wave plate and the position of the center of gravity greatly influence the navigation characteristics.In the relevant research on reducing the navigation resistance of amphibious vehicles by adjusting the angle of the anti-wave plate,there is a lack of scientific selection of parameters and reasonable research of simulation results by using mathematical methods,and the influence of the center of gravity position on navigation characteristics is not considered at the same time.To study the influence of the combinations of the angle of the anti-wave plate and the position of the center of gravity on the resistance reduction characteristics,a numerical calculation model of the amphibious unmanned vehicle was established by using the theory of computational fluid dynamics,and the experimental data verified the correctness of the numerical model.Based on this numerical model,the navigation characteristics of the amphibious unmanned vehicle were studied when the center of gravity was located at different positions,and the orthogonal experimental design method was used to optimize the parameters of the angle of the anti-wave plate and the position of the center of gravity.The results show that through the parameter optimization analysis based on the orthogonal experimental method,the combination of the optimal angle of the anti-wave plate and the position of the center of gravity is obtained.And the numerical simulation result of resistance is consistent with the predicted optimal solution.Compared with the maximum navigational resistance,the parameter optimization reduces the navigational resistance of the amphibious unmanned vehicle by 24%.