In recent years,the study of higher-order topological states and their material realizations has become a research frontier in topological condensed matter physics.We demonstrate that twisted bilayer graphene with sma...In recent years,the study of higher-order topological states and their material realizations has become a research frontier in topological condensed matter physics.We demonstrate that twisted bilayer graphene with small twist angles behaves as a second-order topological insulator possessing topological corner charges.Using a tight-binding model,we compute the topological band indices and corner states of finite-sized twisted bilayer graphene flakes.It is found that for any small twist angle,whether commensurate or incommensurate,the gaps both below and above the flat bands are associated with nontrivial topological indices.Our results not only extend the concept of second-order band topology to arbitrary small twist angles but also confirm the existence of corner states at acute-angle corners.展开更多
Continuous control protocols are extensively utilized in traditional MASs,in which information needs to be transmitted among agents consecutively,therefore resulting in excessive consumption of limited resources.To de...Continuous control protocols are extensively utilized in traditional MASs,in which information needs to be transmitted among agents consecutively,therefore resulting in excessive consumption of limited resources.To decrease the control cost,based on ISC,several LFC problems are investigated for second-order MASs without and with time delay,respectively.Firstly,an intermittent sampled controller is designed,and a sufficient and necessary condition is derived,under which state errors between the leader and all the followers approach zero asymptotically.Considering that time delay is inevitable,a new protocol is proposed to deal with the time-delay situation.The error system’s stability is analyzed using the Schur stability theorem,and sufficient and necessary conditions for LFC are obtained,which are closely associated with the coupling gain,the system parameters,and the network structure.Furthermore,for the case where the current position and velocity information are not available,a distributed protocol is designed that depends only on the sampled position information.The sufficient and necessary conditions for LFC are also given.The results show that second-order MASs can achieve the LFC if and only if the system parameters satisfy the inequalities proposed in the paper.Finally,the correctness of the obtained results is verified by numerical simulations.展开更多
The vehicle-road coupling dynamics problem is a prominent issue in transportation,drawing significant attention in recent years.These dynamic equations are characterized by high-dimensionality,coupling,and time-varyin...The vehicle-road coupling dynamics problem is a prominent issue in transportation,drawing significant attention in recent years.These dynamic equations are characterized by high-dimensionality,coupling,and time-varying dynamics,making the exact solutions challenging to obtain.As a result,numerical integration methods are typically employed.However,conventional methods often suffer from low computational efficiency.To address this,this paper explores the application of the parameter freezing precise exponential integrator to vehicle-road coupling models.The model accounts for road roughness irregularities,incorporating all terms unrelated to the linear part into the algorithm's inhomogeneous vector.The general construction process of the algorithm is detailed.The validity of numerical results is verified through approximate analytical solutions(AASs),and the advantages of this method over traditional numerical integration methods are demonstrated.Multiple parameter freezing precise exponential integrator schemes are constructed based on the Runge-Kutta framework,with the fourth-order four-stage scheme identified as the optimal one.The study indicates that this method can quickly and accurately capture the dynamic system's vibration response,offering a new,efficient approach for numerical studies of high-dimensional vehicle-road coupling systems.展开更多
In this paper,we investigate the phenomena of electromagnetically induced transparency and the generation of second-order sideband in a Laguerre–Gaussian cavity optorotational system with a Kerr nonlinear medium.Usin...In this paper,we investigate the phenomena of electromagnetically induced transparency and the generation of second-order sideband in a Laguerre–Gaussian cavity optorotational system with a Kerr nonlinear medium.Using the perturbation method,we analyze the first-and second-order sideband generations in the output field from the system under the actions of a strong control field and a weak probe field.Numerical simulations show that the Kerr nonlinearity can lead to the occurrence of the asymmetric line shape in the transmission of the probe field.Comparing with traditional scheme for generating the second-order sideband,our spectral shape of the second-order sideband is amplified and becomes asymmetric,which has potential applications in precision measurement,high-sensitivity devices,and frequency conversion.展开更多
This study develops a high-order computational scheme for analyzing unsteady tangent hyperbolic fluid flow with variable thermal conductivity,thermal radiation,and coupled heat andmass transfer effects.Amodified twost...This study develops a high-order computational scheme for analyzing unsteady tangent hyperbolic fluid flow with variable thermal conductivity,thermal radiation,and coupled heat andmass transfer effects.Amodified twostage Exponential Time Integrator is introduced for temporal discretization,providing second-order accuracy in time.A compact finite difference method is employed for spatial discretization,yielding sixth-order accuracy at most grid points.The proposed framework ensures numerical stability and convergence when solving stiff,nonlinear parabolic systems arising in fluid flow and heat transfer problems.The novelty of the work lies in combining exponential integrator schemes with compact high-order spatial discretization,enabling accurate and efficient simulations of tangent hyperbolic fluids under complex boundary conditions,such as oscillatory plates and varying thermal conductivity.This approach addresses limitations of classical Euler,Runge–Kutta,and spectral methods by significantly reducing numerical errors(up to 45%)and computational cost.Comprehensive parametric studies demonstrate how viscous dissipation,chemical reactions,the Weissenberg number,and the Hartmann number influence flow behaviour,heat transfer,and mass transfer.Notably,heat transfer rates increase by 18.6%with stronger viscous dissipation,while mass transfer rates rise by 21.3%with more intense chemical reactions.The real-world relevance of the study is underscored by its direct applications in polymer processing,heat exchanger design,radiative thermal management in aerospace,and biofluid transport in biomedical systems.The proposed scheme thus provides a robust numerical framework that not only advances the mathematical modelling of non-Newtonian fluid flows but also offers practical insights for engineering systems involving tangent hyperbolic fluids.展开更多
In this work,a consistent and physically accurate implementation of the general framework of unified second-order time accurate integrators via the well-known GSSSS framework in the Discrete Element Method is presente...In this work,a consistent and physically accurate implementation of the general framework of unified second-order time accurate integrators via the well-known GSSSS framework in the Discrete Element Method is presented.The improved tangential displacement evaluation in the present implementation of the discrete element method has been derived and implemented to preserve the consistency of the correct time level evaluation during the time integration process in calculating the algorithmic tangential displacement.Several numerical examples have been used to validate the proposed tangential displacement evaluation;this is in contrast to past practices which only seem to attain the first-order time accuracy due to inconsistent time level implementation with different algorithms for normal and tangential directions.The comparisons with the existing implementation and the superiority of the proposed implementation are given in terms of the convergence rate with improved numerical accuracy in time.Moreover,several schemes via the unified second-order time integrators within the framework of the GSSSS family have been carried out based on the proposed correct implementation.All the numerical results demonstrate that using the existing state-of-the-art implementation reduces the time accuracy to be first-order accurate in time,while the proposed implementation preserves the correct time accuracy to yield second-order.展开更多
By using cone theory and the MSnch fixed theorem combined with a monotone iterative technique, we investigate the existence of positive solutions for systems of second- order nonlinear singular differential equations ...By using cone theory and the MSnch fixed theorem combined with a monotone iterative technique, we investigate the existence of positive solutions for systems of second- order nonlinear singular differential equations with integral boundary conditions on infinite interval and establish the existence theorem of positive solutions and iterative sequence for approximating the positive solutions. The results in this paper improve some known results.展开更多
Polarization-dependent second harmonic generation is a widely utilized technique for characterizing symmetry.However,in collinear reflective geometry,the essential beam-splitting device significantly influences both t...Polarization-dependent second harmonic generation is a widely utilized technique for characterizing symmetry.However,in collinear reflective geometry,the essential beam-splitting device significantly influences both the polarization state of the fundamental and harmonic beams,thereby affecting the accuracy of the obtained second-order nonlinear susceptibility.Here,we propose a data correction method to solve this problem to obtain accurate secondorder nonlinear susceptibility.The feasibility and generality of the method are demonstrated through theoretical and experimental validation.展开更多
We theoretically study the effect of Kerr effect on the second-order nonlinearity induced transparency in a double-resonant optical cavity system.We show that in the presence of the Kerr effect,as the strength of the ...We theoretically study the effect of Kerr effect on the second-order nonlinearity induced transparency in a double-resonant optical cavity system.We show that in the presence of the Kerr effect,as the strength of the Kerr effect increases,the absorption curve exhibits an asymmetric-symmetric-asymmetric transition,and the zero absorption point shifts with the increase of the Kerr effect.Furthermore,by changing the strength of the Kerr effect,we can control the width of the transparent window,and the position of the zero-absorption point and meanwhile change the left and right width of the absorption peak.The asymmetry absorption curve can be employed to improve the quality factor of the cavity when the frequency detuning is tuned to be around the right peak.The simple dependence of the zeroabsorption point on the strength of Kerr effect suggests that the strength of Kerr effect can be measured by measuring the position of the zero-absorption point in a possible application.展开更多
To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregress...To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.展开更多
In the cascaded H-bridge inverter(CHBI)with supercapacitor and dc-dc stage,inherent second-order harmonic power flows through each submodule(SM),causing fluctuations in both the dc-link voltage and the dc-dc current.T...In the cascaded H-bridge inverter(CHBI)with supercapacitor and dc-dc stage,inherent second-order harmonic power flows through each submodule(SM),causing fluctuations in both the dc-link voltage and the dc-dc current.There exist limitations in handling these fluctuations at variable output frequencies when employing proportional-integral(PI)control to the dc-dc stage.This paper aims to coordinately control these second-order harmonic voltage and current fluctuations in the CHBI.The presented method configures a specific second-order harmonic voltage reference,equipped with a maximum voltage fluctuation constraint and a suitable phase,for the dc-dc stage.A PI-resonant controller is used to track the configured reference.This allows for regulating the second-order harmonic fluctuation in the average dc-link voltage among the SMs within a certain value.Importantly,the second-order harmonic fluctuation in the dc-dc current can also be reduced.Simulation and experimental results demonstrate the effectiveness of the presented method.展开更多
In this work,we propose a low-regularity Fourier integrator with almost mass conservation to solve the Davey-StewartsonⅡsystem(hyperbolic-elliptic case).Arbitrary order mass convergence could be achieved by the suita...In this work,we propose a low-regularity Fourier integrator with almost mass conservation to solve the Davey-StewartsonⅡsystem(hyperbolic-elliptic case).Arbitrary order mass convergence could be achieved by the suitable addition of correction terms,while keeping the first order accuracy in H~γ×H^(γ+1)for initial data in H^(γ+1)×H^(γ+1)withγ>1.The main theorem is that,up to some fixed time T,there exist constantsτ_(0)and C depending only on T and‖u‖_(L^(∞)((0,T);H^(γ+1)))such that,for any 0<τ≤τ_(0),we have that‖u(t_(n),·)-u^(n)‖H_γ≤C_(τ),‖v(t_(n),·)-v^(n)‖_(Hγ+1)≤C_(τ),where u^(n)and v^(n)denote the numerical solutions at t_(n)=nτ.Moreover,the mass of the numerical solution M(u^(n))satisfies that|M(u^(n))-M(u_0)|≤Cτ~5.展开更多
Simulations of contact problems involving at least one plastic solid may be costly due to their strong nonlinearity and requirements of stability.In this work,we develop an explicit asynchronous variational integrator...Simulations of contact problems involving at least one plastic solid may be costly due to their strong nonlinearity and requirements of stability.In this work,we develop an explicit asynchronous variational integrator(AVI)for inelastic non-frictional contact problems involving a plastic solid.The AVI assigns each element in the mesh an independent time step and updates the solution at the elements and nodes asynchronously.This asynchrony makes the AVI highly efficient in solving such bi-material problems.Taking advantage of the AVI,the constitutive update is locally performed in one element at a time,and contact constraints are also enforced on only one element.The time step of the contact element is subdivided into multiple segments,and the fields are updated accordingly.During a contact event,only one element involving a few degrees of freedom is considered,leading to high efficiency.The proposed formulation is first verified with a pure elastodynamics benchmark and further applied to a contact problem involving an elastoplastic solid with non-associative volumetric hardening.The numerical results indicate that the AVI exhibits excellent energy behaviors and has high computational efficiency.展开更多
This paper is concerned with the generalized nonlinear second-order equation.By the direct construction method,all of the first-order multipliers of the equation are obtained,and the corresponding complete conservatio...This paper is concerned with the generalized nonlinear second-order equation.By the direct construction method,all of the first-order multipliers of the equation are obtained,and the corresponding complete conservation laws(CLs) of such equations are provided.Furthermore,the integrability of the equation is considered in terms of the conservation laws.In addition,the relationship of multipliers and symmetries of the equations is investigated.展开更多
Complex network models are frequently employed for simulating and studyingdiverse real-world complex systems.Among these models,scale-free networks typically exhibit greater fragility to malicious attacks.Consequently...Complex network models are frequently employed for simulating and studyingdiverse real-world complex systems.Among these models,scale-free networks typically exhibit greater fragility to malicious attacks.Consequently,enhancing the robustness of scale-free networks has become a pressing issue.To address this problem,this paper proposes a Multi-Granularity Integration Algorithm(MGIA),which aims to improve the robustness of scale-free networks while keeping the initial degree of each node unchanged,ensuring network connectivity and avoiding the generation of multiple edges.The algorithm generates a multi-granularity structure from the initial network to be optimized,then uses different optimization strategies to optimize the networks at various granular layers in this structure,and finally realizes the information exchange between different granular layers,thereby further enhancing the optimization effect.We propose new network refresh,crossover,and mutation operators to ensure that the optimized network satisfies the given constraints.Meanwhile,we propose new network similarity and network dissimilarity evaluation metrics to improve the effectiveness of the optimization operators in the algorithm.In the experiments,the MGIA enhances the robustness of the scale-free network by 67.6%.This improvement is approximately 17.2%higher than the optimization effects achieved by eight currently existing complex network robustness optimization algorithms.展开更多
Understanding the neural underpinning of human gait and balance is one of the most pertinent challenges for 21st-century translational neuroscience due to the profound impact that falls and mobility disturbances have ...Understanding the neural underpinning of human gait and balance is one of the most pertinent challenges for 21st-century translational neuroscience due to the profound impact that falls and mobility disturbances have on our aging population.Posture and gait control does not happen automatically,as previously believed,but rather requires continuous involvement of central nervous mechanisms.To effectively exert control over the body,the brain must integrate multiple streams of sensory information,including visual,vestibular,and somatosensory signals.The mechanisms which underpin the integration of these multisensory signals are the principal topic of the present work.Existing multisensory integration theories focus on how failure of cognitive processes thought to be involved in multisensory integration leads to falls in older adults.Insufficient emphasis,however,has been placed on specific contributions of individual sensory modalities to multisensory integration processes and cross-modal interactions that occur between the sensory modalities in relation to gait and balance.In the present work,we review the contributions of somatosensory,visual,and vestibular modalities,along with their multisensory intersections to gait and balance in older adults and patients with Parkinson’s disease.We also review evidence of vestibular contributions to multisensory temporal binding windows,previously shown to be highly pertinent to fall risk in older adults.Lastly,we relate multisensory vestibular mechanisms to potential neural substrates,both at the level of neurobiology(concerning positron emission tomography imaging)and at the level of electrophysiology(concerning electroencephalography).We hope that this integrative review,drawing influence across multiple subdisciplines of neuroscience,paves the way for novel research directions and therapeutic neuromodulatory approaches,to improve the lives of older adults and patients with neurodegenerative diseases.展开更多
A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general para...A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general parametric solutions to this type of generalized matrix second-order Sylvester matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the fight factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass-dashpot system is utilized to illustrate the design procedure and show the effect of the proposed approach.展开更多
Astrocytes read and react to synaptic transmission through tripartite synapses,where the binding of neurotransmitters onto astrocytic receptors triggers an increase in intracellular calcium.Recent investigations have ...Astrocytes read and react to synaptic transmission through tripartite synapses,where the binding of neurotransmitters onto astrocytic receptors triggers an increase in intracellular calcium.Recent investigations have revealed that astrocytes exhibit two distinct states of intracellular calcium activity:(1)graded subcellular localized clusters with independently active microdomains,likely influenced by nearby synaptic events,and(2)whole-cell astrocyte calcium surges,believed to result from the coordinated activation of multiple synapses.Notably,astrocyte calcium responses are not solely graded;instead,a spatial threshold of intracellular calcium activity can be overcome to elicit an astrocyte calcium surge.Together these calcium responses,in turn,initiate downstream signaling pathways capable of modifying synaptic communication and overall network activity.In summary,astrocytes can function as integrators of local synaptic events,actively contributing to information processing within the brain.展开更多
This paper describes an intelligent integrated control of an acrobot, which is an underactuated mechanical system with second-order nonholonomic constraints. The control combines a model-free fuzzy control, a fuzzy sl...This paper describes an intelligent integrated control of an acrobot, which is an underactuated mechanical system with second-order nonholonomic constraints. The control combines a model-free fuzzy control, a fuzzy sliding-mode control and a model-based fuzzy control. The model-free fuzzy controller designed for the upswing ensures that the energy of the acrobot increases with each swing. Then the fuzzy sliding-mode controller is employed to control the movement that the acrobot enters the balance area from the swing-up area. The model-based fuzzy controller, which is based on a Takagi-Sugeno fuzzy model, is used to balance the acrobot. The stability of the fuzzy control system for balance control is guaranteed by a common symmetric positive matrix, which satisfies linear matrix inequalities.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12104232 and 12074156).
文摘In recent years,the study of higher-order topological states and their material realizations has become a research frontier in topological condensed matter physics.We demonstrate that twisted bilayer graphene with small twist angles behaves as a second-order topological insulator possessing topological corner charges.Using a tight-binding model,we compute the topological band indices and corner states of finite-sized twisted bilayer graphene flakes.It is found that for any small twist angle,whether commensurate or incommensurate,the gaps both below and above the flat bands are associated with nontrivial topological indices.Our results not only extend the concept of second-order band topology to arbitrary small twist angles but also confirm the existence of corner states at acute-angle corners.
基金supported by the National Natural Science Foundation of China under Grants 62476138 and 42375016.
文摘Continuous control protocols are extensively utilized in traditional MASs,in which information needs to be transmitted among agents consecutively,therefore resulting in excessive consumption of limited resources.To decrease the control cost,based on ISC,several LFC problems are investigated for second-order MASs without and with time delay,respectively.Firstly,an intermittent sampled controller is designed,and a sufficient and necessary condition is derived,under which state errors between the leader and all the followers approach zero asymptotically.Considering that time delay is inevitable,a new protocol is proposed to deal with the time-delay situation.The error system’s stability is analyzed using the Schur stability theorem,and sufficient and necessary conditions for LFC are obtained,which are closely associated with the coupling gain,the system parameters,and the network structure.Furthermore,for the case where the current position and velocity information are not available,a distributed protocol is designed that depends only on the sampled position information.The sufficient and necessary conditions for LFC are also given.The results show that second-order MASs can achieve the LFC if and only if the system parameters satisfy the inequalities proposed in the paper.Finally,the correctness of the obtained results is verified by numerical simulations.
基金Supported by the National Natural Science Foundation of China(No.U22A20246)the Key Project of Natural Science Foundation of Hebei Province of China(Basic Research Base Project)(No.A2023210064)the Science and Technology Program of Hebei Province of China(Nos.246Z1904G and 225676162GH)。
文摘The vehicle-road coupling dynamics problem is a prominent issue in transportation,drawing significant attention in recent years.These dynamic equations are characterized by high-dimensionality,coupling,and time-varying dynamics,making the exact solutions challenging to obtain.As a result,numerical integration methods are typically employed.However,conventional methods often suffer from low computational efficiency.To address this,this paper explores the application of the parameter freezing precise exponential integrator to vehicle-road coupling models.The model accounts for road roughness irregularities,incorporating all terms unrelated to the linear part into the algorithm's inhomogeneous vector.The general construction process of the algorithm is detailed.The validity of numerical results is verified through approximate analytical solutions(AASs),and the advantages of this method over traditional numerical integration methods are demonstrated.Multiple parameter freezing precise exponential integrator schemes are constructed based on the Runge-Kutta framework,with the fourth-order four-stage scheme identified as the optimal one.The study indicates that this method can quickly and accurately capture the dynamic system's vibration response,offering a new,efficient approach for numerical studies of high-dimensional vehicle-road coupling systems.
基金supported by the National Natural Science Foundation of China(Grant Nos.12174344 and 12175199)Foundation of Department of Science and Technology of Zhejiang Province(Grant No.2022R52047)。
文摘In this paper,we investigate the phenomena of electromagnetically induced transparency and the generation of second-order sideband in a Laguerre–Gaussian cavity optorotational system with a Kerr nonlinear medium.Using the perturbation method,we analyze the first-and second-order sideband generations in the output field from the system under the actions of a strong control field and a weak probe field.Numerical simulations show that the Kerr nonlinearity can lead to the occurrence of the asymmetric line shape in the transmission of the probe field.Comparing with traditional scheme for generating the second-order sideband,our spectral shape of the second-order sideband is amplified and becomes asymmetric,which has potential applications in precision measurement,high-sensitivity devices,and frequency conversion.
基金supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-DDRSP2503).
文摘This study develops a high-order computational scheme for analyzing unsteady tangent hyperbolic fluid flow with variable thermal conductivity,thermal radiation,and coupled heat andmass transfer effects.Amodified twostage Exponential Time Integrator is introduced for temporal discretization,providing second-order accuracy in time.A compact finite difference method is employed for spatial discretization,yielding sixth-order accuracy at most grid points.The proposed framework ensures numerical stability and convergence when solving stiff,nonlinear parabolic systems arising in fluid flow and heat transfer problems.The novelty of the work lies in combining exponential integrator schemes with compact high-order spatial discretization,enabling accurate and efficient simulations of tangent hyperbolic fluids under complex boundary conditions,such as oscillatory plates and varying thermal conductivity.This approach addresses limitations of classical Euler,Runge–Kutta,and spectral methods by significantly reducing numerical errors(up to 45%)and computational cost.Comprehensive parametric studies demonstrate how viscous dissipation,chemical reactions,the Weissenberg number,and the Hartmann number influence flow behaviour,heat transfer,and mass transfer.Notably,heat transfer rates increase by 18.6%with stronger viscous dissipation,while mass transfer rates rise by 21.3%with more intense chemical reactions.The real-world relevance of the study is underscored by its direct applications in polymer processing,heat exchanger design,radiative thermal management in aerospace,and biofluid transport in biomedical systems.The proposed scheme thus provides a robust numerical framework that not only advances the mathematical modelling of non-Newtonian fluid flows but also offers practical insights for engineering systems involving tangent hyperbolic fluids.
文摘In this work,a consistent and physically accurate implementation of the general framework of unified second-order time accurate integrators via the well-known GSSSS framework in the Discrete Element Method is presented.The improved tangential displacement evaluation in the present implementation of the discrete element method has been derived and implemented to preserve the consistency of the correct time level evaluation during the time integration process in calculating the algorithmic tangential displacement.Several numerical examples have been used to validate the proposed tangential displacement evaluation;this is in contrast to past practices which only seem to attain the first-order time accuracy due to inconsistent time level implementation with different algorithms for normal and tangential directions.The comparisons with the existing implementation and the superiority of the proposed implementation are given in terms of the convergence rate with improved numerical accuracy in time.Moreover,several schemes via the unified second-order time integrators within the framework of the GSSSS family have been carried out based on the proposed correct implementation.All the numerical results demonstrate that using the existing state-of-the-art implementation reduces the time accuracy to be first-order accurate in time,while the proposed implementation preserves the correct time accuracy to yield second-order.
基金SuppoSed by the NSF of Anhui Provincial Education Depaxtment(KJ2012A265,KJ2012B187)
文摘By using cone theory and the MSnch fixed theorem combined with a monotone iterative technique, we investigate the existence of positive solutions for systems of second- order nonlinear singular differential equations with integral boundary conditions on infinite interval and establish the existence theorem of positive solutions and iterative sequence for approximating the positive solutions. The results in this paper improve some known results.
基金This work was supported by the National Natural Science Foundation of China(No.U2230203)the Fundamental Research Funds for the Central Universities.
文摘Polarization-dependent second harmonic generation is a widely utilized technique for characterizing symmetry.However,in collinear reflective geometry,the essential beam-splitting device significantly influences both the polarization state of the fundamental and harmonic beams,thereby affecting the accuracy of the obtained second-order nonlinear susceptibility.Here,we propose a data correction method to solve this problem to obtain accurate secondorder nonlinear susceptibility.The feasibility and generality of the method are demonstrated through theoretical and experimental validation.
基金Supported by the Key Scientific Research Plan of Colleges and Universities in Henan Province(23B140006)the National Natural Science Foundation of China(11965017)。
文摘We theoretically study the effect of Kerr effect on the second-order nonlinearity induced transparency in a double-resonant optical cavity system.We show that in the presence of the Kerr effect,as the strength of the Kerr effect increases,the absorption curve exhibits an asymmetric-symmetric-asymmetric transition,and the zero absorption point shifts with the increase of the Kerr effect.Furthermore,by changing the strength of the Kerr effect,we can control the width of the transparent window,and the position of the zero-absorption point and meanwhile change the left and right width of the absorption peak.The asymmetry absorption curve can be employed to improve the quality factor of the cavity when the frequency detuning is tuned to be around the right peak.The simple dependence of the zeroabsorption point on the strength of Kerr effect suggests that the strength of Kerr effect can be measured by measuring the position of the zero-absorption point in a possible application.
基金The National Key Research and Development Program of China under contract No.2023YFC3107701the National Natural Science Foundation of China under contract No.42375143.
文摘To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.
基金supported by the National Key Research and Development Program of China under Grant 2023YFB2407400。
文摘In the cascaded H-bridge inverter(CHBI)with supercapacitor and dc-dc stage,inherent second-order harmonic power flows through each submodule(SM),causing fluctuations in both the dc-link voltage and the dc-dc current.There exist limitations in handling these fluctuations at variable output frequencies when employing proportional-integral(PI)control to the dc-dc stage.This paper aims to coordinately control these second-order harmonic voltage and current fluctuations in the CHBI.The presented method configures a specific second-order harmonic voltage reference,equipped with a maximum voltage fluctuation constraint and a suitable phase,for the dc-dc stage.A PI-resonant controller is used to track the configured reference.This allows for regulating the second-order harmonic fluctuation in the average dc-link voltage among the SMs within a certain value.Importantly,the second-order harmonic fluctuation in the dc-dc current can also be reduced.Simulation and experimental results demonstrate the effectiveness of the presented method.
基金supported by the NSFC(11901120)supported by the NSFC(12171356)the Science and Technology Program of Guangzhou,China(2024A04J4027)。
文摘In this work,we propose a low-regularity Fourier integrator with almost mass conservation to solve the Davey-StewartsonⅡsystem(hyperbolic-elliptic case).Arbitrary order mass convergence could be achieved by the suitable addition of correction terms,while keeping the first order accuracy in H~γ×H^(γ+1)for initial data in H^(γ+1)×H^(γ+1)withγ>1.The main theorem is that,up to some fixed time T,there exist constantsτ_(0)and C depending only on T and‖u‖_(L^(∞)((0,T);H^(γ+1)))such that,for any 0<τ≤τ_(0),we have that‖u(t_(n),·)-u^(n)‖H_γ≤C_(τ),‖v(t_(n),·)-v^(n)‖_(Hγ+1)≤C_(τ),where u^(n)and v^(n)denote the numerical solutions at t_(n)=nτ.Moreover,the mass of the numerical solution M(u^(n))satisfies that|M(u^(n))-M(u_0)|≤Cτ~5.
基金support from the Hui-Chun Chin and Tsung-Dao Lee Chinese Undergraduate Research Endowment(CURE).
文摘Simulations of contact problems involving at least one plastic solid may be costly due to their strong nonlinearity and requirements of stability.In this work,we develop an explicit asynchronous variational integrator(AVI)for inelastic non-frictional contact problems involving a plastic solid.The AVI assigns each element in the mesh an independent time step and updates the solution at the elements and nodes asynchronously.This asynchrony makes the AVI highly efficient in solving such bi-material problems.Taking advantage of the AVI,the constitutive update is locally performed in one element at a time,and contact constraints are also enforced on only one element.The time step of the contact element is subdivided into multiple segments,and the fields are updated accordingly.During a contact event,only one element involving a few degrees of freedom is considered,leading to high efficiency.The proposed formulation is first verified with a pure elastodynamics benchmark and further applied to a contact problem involving an elastoplastic solid with non-associative volumetric hardening.The numerical results indicate that the AVI exhibits excellent energy behaviors and has high computational efficiency.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11171041 and 10971018the Natural Science Foundation of Shandong Province under Grant No.ZR2010AM029+1 种基金the Promotive Research Fund for Young and Middle-Aged Scientists of Shandong Province under Grant No.BS2010SF001 the Doctoral Foundation of Binzhou University under Grant No.2009Y01
文摘This paper is concerned with the generalized nonlinear second-order equation.By the direct construction method,all of the first-order multipliers of the equation are obtained,and the corresponding complete conservation laws(CLs) of such equations are provided.Furthermore,the integrability of the equation is considered in terms of the conservation laws.In addition,the relationship of multipliers and symmetries of the equations is investigated.
基金National Natural Science Foundation of China(11971211,12171388).
文摘Complex network models are frequently employed for simulating and studyingdiverse real-world complex systems.Among these models,scale-free networks typically exhibit greater fragility to malicious attacks.Consequently,enhancing the robustness of scale-free networks has become a pressing issue.To address this problem,this paper proposes a Multi-Granularity Integration Algorithm(MGIA),which aims to improve the robustness of scale-free networks while keeping the initial degree of each node unchanged,ensuring network connectivity and avoiding the generation of multiple edges.The algorithm generates a multi-granularity structure from the initial network to be optimized,then uses different optimization strategies to optimize the networks at various granular layers in this structure,and finally realizes the information exchange between different granular layers,thereby further enhancing the optimization effect.We propose new network refresh,crossover,and mutation operators to ensure that the optimized network satisfies the given constraints.Meanwhile,we propose new network similarity and network dissimilarity evaluation metrics to improve the effectiveness of the optimization operators in the algorithm.In the experiments,the MGIA enhances the robustness of the scale-free network by 67.6%.This improvement is approximately 17.2%higher than the optimization effects achieved by eight currently existing complex network robustness optimization algorithms.
文摘Understanding the neural underpinning of human gait and balance is one of the most pertinent challenges for 21st-century translational neuroscience due to the profound impact that falls and mobility disturbances have on our aging population.Posture and gait control does not happen automatically,as previously believed,but rather requires continuous involvement of central nervous mechanisms.To effectively exert control over the body,the brain must integrate multiple streams of sensory information,including visual,vestibular,and somatosensory signals.The mechanisms which underpin the integration of these multisensory signals are the principal topic of the present work.Existing multisensory integration theories focus on how failure of cognitive processes thought to be involved in multisensory integration leads to falls in older adults.Insufficient emphasis,however,has been placed on specific contributions of individual sensory modalities to multisensory integration processes and cross-modal interactions that occur between the sensory modalities in relation to gait and balance.In the present work,we review the contributions of somatosensory,visual,and vestibular modalities,along with their multisensory intersections to gait and balance in older adults and patients with Parkinson’s disease.We also review evidence of vestibular contributions to multisensory temporal binding windows,previously shown to be highly pertinent to fall risk in older adults.Lastly,we relate multisensory vestibular mechanisms to potential neural substrates,both at the level of neurobiology(concerning positron emission tomography imaging)and at the level of electrophysiology(concerning electroencephalography).We hope that this integrative review,drawing influence across multiple subdisciplines of neuroscience,paves the way for novel research directions and therapeutic neuromodulatory approaches,to improve the lives of older adults and patients with neurodegenerative diseases.
基金This work was supported by the Chinese National Natural Science Foundation ( No. 69925308).
文摘A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general parametric solutions to this type of generalized matrix second-order Sylvester matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the fight factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass-dashpot system is utilized to illustrate the design procedure and show the effect of the proposed approach.
基金supported by NIH-NIA (1F31AG057155-01A1)University of Minnesota Doctoral Dissertation Fellowship (to JL)
文摘Astrocytes read and react to synaptic transmission through tripartite synapses,where the binding of neurotransmitters onto astrocytic receptors triggers an increase in intracellular calcium.Recent investigations have revealed that astrocytes exhibit two distinct states of intracellular calcium activity:(1)graded subcellular localized clusters with independently active microdomains,likely influenced by nearby synaptic events,and(2)whole-cell astrocyte calcium surges,believed to result from the coordinated activation of multiple synapses.Notably,astrocyte calcium responses are not solely graded;instead,a spatial threshold of intracellular calcium activity can be overcome to elicit an astrocyte calcium surge.Together these calcium responses,in turn,initiate downstream signaling pathways capable of modifying synaptic communication and overall network activity.In summary,astrocytes can function as integrators of local synaptic events,actively contributing to information processing within the brain.
文摘This paper describes an intelligent integrated control of an acrobot, which is an underactuated mechanical system with second-order nonholonomic constraints. The control combines a model-free fuzzy control, a fuzzy sliding-mode control and a model-based fuzzy control. The model-free fuzzy controller designed for the upswing ensures that the energy of the acrobot increases with each swing. Then the fuzzy sliding-mode controller is employed to control the movement that the acrobot enters the balance area from the swing-up area. The model-based fuzzy controller, which is based on a Takagi-Sugeno fuzzy model, is used to balance the acrobot. The stability of the fuzzy control system for balance control is guaranteed by a common symmetric positive matrix, which satisfies linear matrix inequalities.
