In this article,we consider a discrete right-definite Sturm-Liouville problems with two squared eigenparameter-dependent boundary conditions.By constructing some new Lagrange-type identities and two fundamental functi...In this article,we consider a discrete right-definite Sturm-Liouville problems with two squared eigenparameter-dependent boundary conditions.By constructing some new Lagrange-type identities and two fundamental functions,we obtain not only the existence,the simplicity,and the interlacing properties of the real eigenvalues,but also the oscillation properties,orthogonality of the eigenfunctions,and the expansion theorem.Finally,we also give a computation scheme for computing eigenvalues and eigenfunctions of specific eigenvalue problems.展开更多
In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hil...In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hilbert space,on which the concerned operator A is self-adjoint.Then we construct the fundamental solutions to the problem,obtain the necessary and sufficient conditions for eigenvalues,and prove that the eigenvalues are simple.Finally,we investigate Green’s functions of such problem.展开更多
In this paper,we consider incompressible Navier-Stokes/Cahn-Hilliard system with the generalized Navier boundary condition and the dynamic boundary condition in a channel,which can describe the interaction between a b...In this paper,we consider incompressible Navier-Stokes/Cahn-Hilliard system with the generalized Navier boundary condition and the dynamic boundary condition in a channel,which can describe the interaction between a binary material and the walls of the physical domain.We prove the global-in-time existence and uniqueness of strong solutions to this initial boundary value problem in a 2D channel domain.展开更多
Drains play an important role in seepage control in geotechnical engineering.The enormous number and one-dimensional(1D)geometry of drainage holes make their nature difficult to be accurately modeled in groundwater fl...Drains play an important role in seepage control in geotechnical engineering.The enormous number and one-dimensional(1D)geometry of drainage holes make their nature difficult to be accurately modeled in groundwater flow simulation.It has been well understood that drains function by presenting discharge boundaries,which can be characterized by water head,no-flux,unilateral or mixed water head-unilateral boundary condition.It has been found after years of practices that the flow simulation may become erroneous if the transitions among the drain boundary conditions are not properly considered.For this,a rigorous algorithm is proposed in this study to detect the onset of transitions among the water head,noflux and mixed water head-unilateral boundary conditions for downwards-drilled drainage holes,which theoretically completes the description of drain boundary conditions.After verification against a numerical example,the proposed algorithm is applied to numerical modeling of groundwater flow through a gravity dam foundation.The simulation shows that for hundreds of downwards-drilled drainage holes used to be prescribed with water head boundary condition,56%and 2%of them are transitioned to mixed water head-unilateral and no-flux boundary conditions,respectively.The phreatic surface around the drains will be overestimated by 25e33 m without the use of the mixed boundary condition.For the first time,this study underscores the importance of the mixed water head-unilateral boundary condition and the proposed transition algorithm in drain modeling,which may become more essential for simulation of transient flow because of groundwater dynamics.展开更多
This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the chara...This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the characteristic function and resolvent of this third-order differential operator.Secondly,by using the expression for the resolvent of the operator,we prove that the spectrum for this operator consists of simple eigenvalues and a finite number of eigenvalues with multiplicity 2.Finally,we solve the inverse problem for this operator,which states that the non-local potential function can be reconstructed from four spectra.Specially,we prove the Ambarzumyan theorem and indicate that odd or even potential functions can be reconstructed by three spectra.展开更多
We perform a comprehensive study of the electron-doped t-t′-J model on cylinders with density matrix renormalization group(DMRG).We conduct a systematic study on the finite-size and boundary condition effects on t-t...We perform a comprehensive study of the electron-doped t-t′-J model on cylinders with density matrix renormalization group(DMRG).We conduct a systematic study on the finite-size and boundary condition effects on t-t′-J model on cylinders.Periodic and anti-periodic boundary conditions are implemented along the circumference direction,with the system’s width extending up to as large as 8 lattice units.We study doping levels of 1/6,1/8,and 1/12,which represent the most interesting region in the phase diagram of electron-doped cuprates.We find that for width-4 and width-6 systems,the ground state for fixed doping switches between anti-ferromagnetic Neel state and stripe state under different boundary conditions and system widths,indicating the presence of large finite size effect in the t-t′-J model.We also have a careful analysis of the d-wave pairing correlations which also change quantitatively with boundary conditions and widths of the system.However,the pairing correlations are enhanced when the system becomes wider for all dopings,suggesting the existence of possible long-range superconducting order in the thermodynamic limit.The width-8 results are found to be dependent on the starting state in the DMRG calculation for the kept states we can reach.For the width-8 system,only Neel(stripe)state can be stabilized in DMRG calculation for 1/12(1/6)doping,while both stripe and Neel states are stable in the DMRG sweep for 1/8 doping,regardless of the boundary conditions.These results indicate that 1/8 doping is likely to lie on the boundary of a phase transition between the Neel phase with lower doping and the stripe phase with higher doping,consistent with the previous study.The sensitivity of the ground state on boundary conditions and size observed for narrow systems is similar to that found in the t′-Hubbard model,where the t′term introduces frustration and makes the stripe state fragile.The study of different boundary conditions provides a useful tool to check the finite size effect in the future DMRG calculations.展开更多
The impacts of lateral boundary conditions(LBCs)provided by numerical models and data-driven networks on convective-scale ensemble forecasts are investigated in this study.Four experiments are conducted on the Hangzho...The impacts of lateral boundary conditions(LBCs)provided by numerical models and data-driven networks on convective-scale ensemble forecasts are investigated in this study.Four experiments are conducted on the Hangzhou RDP(19th Hangzhou Asian Games Research Development Project on Convective-scale Ensemble Prediction and Application)testbed,with the LBCs respectively sourced from National Centers for Environmental Prediction(NCEP)Global Forecast System(GFS)forecasts with 33 vertical levels(Exp_GFS),Pangu forecasts with 13 vertical levels(Exp_Pangu),Fuxi forecasts with 13 vertical levels(Exp_Fuxi),and NCEP GFS forecasts with the vertical levels reduced to 13(the same as those of Exp_Pangu and Exp_Fuxi)(Exp_GFSRDV).In general,Exp_Pangu performs comparably to Exp_GFS,while Exp_Fuxi shows slightly inferior performance compared to Exp_Pangu,possibly due to its less accurate large-scale predictions.Therefore,the ability of using data-driven networks to efficiently provide LBCs for convective-scale ensemble forecasts has been demonstrated.Moreover,Exp_GFSRDV has the worst convective-scale forecasts among the four experiments,which indicates the potential improvement of using data-driven networks for LBCs by increasing the vertical levels of the networks.However,the ensemble spread of the four experiments barely increases with lead time.Thus,each experiment has insufficient ensemble spread to present realistic forecast uncertainties,which will be investigated in a future study.展开更多
In regions characterized with great mining depths,complex topography,and intense geological activities,solely relying on lateral pressure coefficients or linear boundary conditions for predicting the in situ stress fi...In regions characterized with great mining depths,complex topography,and intense geological activities,solely relying on lateral pressure coefficients or linear boundary conditions for predicting the in situ stress field of rock bodies can induce substantial deviations and limitations.This study focuses on a typical karst area in Southwest Guizhou,China as its research background.It employs a hybrid approach integrating machine learning,numerical simulations,and field experiments to develop an optimization algorithm for nonlinear prediction of the complex three-dimensional(3D)in situ stress fields.Through collecting and fitting analysis of in situ stress measurement data from the karst region,the distributions of in situ stresses with depth were identified with nonlinear boundary conditions.A prediction model for in situ stress was then established based on artificial neural network(ANN)and genetic algorithm(GA)approach,validated in the typical karst landscape mine,Jinfeng Gold Mine.The results demonstrate that the model's predictions align well with actual measurements,showcasing consistency and regularity.Specifically,the error between the predicted and actual values of the maximum horizontal principal stress was the smallest,with an absolute error 0.01-3 MPa and a relative error of 0.04-15.31%.This model accurately and effectively predicts in situ stresses in complex geological areas.展开更多
We investigate the integrability of the Rabi model,which is traditionally viewed as not Yang–Baxter-integrable despite its solvability.Building on efforts by Bogoliubov and Kulish(2013 J.Math.Sci.19214–30),Amico et ...We investigate the integrability of the Rabi model,which is traditionally viewed as not Yang–Baxter-integrable despite its solvability.Building on efforts by Bogoliubov and Kulish(2013 J.Math.Sci.19214–30),Amico et al(2007 Nucl.Phys.B 787283–300),and Batchelor and Zhou(2015 Phys.Rev.A 91053808),who explored special limiting cases of the model,we develop a spin–boson interaction Hamiltonian under more general boundary conditions,particularly focusing on open boundary conditions with off-diagonal terms.Our approach maintains the direction of the spin in the z direction and also preserves the boson particle number operator a^(†)a,marking a progression beyond previous efforts that have primarily explored reduced forms of the Rabi model from Yang–Baxter algebra.We also address the presence of‘unwanted’quadratic boson terms a^(2) and a^(†2),which share coefficients with the boson particle number operator.Interestingly,these terms vanish when spectral parameter u=±θ_(s),simplifying the model to a limiting case of operator-valued twists,a scenario previously discussed by Batchelor and Zhou(2015 Phys.Rev.A 91053808).展开更多
The influence of Impedance Boundary Condition (IBC) on transonic compressors is investigated. A systematic input–output analytical framework is developed, which treats the nonlinearities as unknown forcing terms. The...The influence of Impedance Boundary Condition (IBC) on transonic compressors is investigated. A systematic input–output analytical framework is developed, which treats the nonlinearities as unknown forcing terms. The framework is validated through the experiments of rotating inlet distortion within a low-speed compressor. The input–output method is subsequently applied to transonic compressors, including NASA Rotor37 and Stage35, wherein impedance optimization is studied along with the exploration of its fundamental mechanisms. The IBC is employed to model the effect of Casing Treatment (CT). The optimal complex impedance values are determined through predicted results and tested across a range of circumferential modes and forcing frequencies. The IBC significantly reduces the energy and Reynolds stress gain, notably at the first-order circumferential mode and within the Rotor Rotating Frequency (RRF) range. Output modes reveal that transonic compressors with fine-tuned impedance values exhibit a more confined perturbation distribution and redistribute the perturbations compared to the uncontrolled case. Additionally, the roles of resistance and reactance are elucidated through input–output analysis, and resistance determines the energy transfer direction between flow and pressure waves and modulates the amplitude, whereas reactance modifies the phase relationships and attenuates the perturbations.展开更多
In this paper,we investigate the blow-up phenomenon for a class of logarithmic viscoelastic equations with delay and nonlocal terms under acoustic boundary conditions.Using the energy method,we prove that nontrivial s...In this paper,we investigate the blow-up phenomenon for a class of logarithmic viscoelastic equations with delay and nonlocal terms under acoustic boundary conditions.Using the energy method,we prove that nontrivial solutions with negative initial energy will blow up in finite time,and provide an upper bound estimate for the blow-up time.Additionally,we also derive a lower bound estimate for the blow-up time.展开更多
In this study,we mainly discuss some spectral properties of the Dirac operator with eigenparameter-dependent boundary condition.Initially,we reformulate the spectral problem into linear operator eigenparameter problem...In this study,we mainly discuss some spectral properties of the Dirac operator with eigenparameter-dependent boundary condition.Initially,we reformulate the spectral problem into linear operator eigenparameter problem in a suitable Hilbert space,and obtain some pivotal properties of self-adjoint operator.Subsequently,by establishing the boundary condition space and constructing the embedded mapping,we show that the simple eigenvalue branch of this system is not only continuous,but also smooth.We then obtain the differential expressions of the eigenvalue branch in the sense of Frechet derivative.展开更多
Moving-load induced vibrations can,in certain instances,exceed those caused by equivalent static loads,especially at the critical velocity of moving loads.Suppressing these vibrations is of critical practical importan...Moving-load induced vibrations can,in certain instances,exceed those caused by equivalent static loads,especially at the critical velocity of moving loads.Suppressing these vibrations is of critical practical importance in various engineering fields,including the design of precision robotics and advanced aerospace structures where components are subject to moving loads.In this paper,an inertial nonlinear energy sink(NES)is used for the first time to reduce the vibration response of graphene platelet(GPL)-reinforced nanocomposite beams with elastic boundaries under moving loads.Based on the von Kármán nonlinear theory,the governing equations of the beam-NES system are derived using the Lagrange equation.The Newmark-Newton method,in conjunction with the Heaviside step function,is used to obtain the nonlinear responses of the beam under moving loads.The effects of the boundary spring stiffness,the GPL parameters,as well as the velocity and frequency of the moving loads on the beam response and the performance of the NES are thoroughly studied.The results of this work provide insights into applying NESs to suppress the nonlinear vibrations induced by moving loads in composite structures with elastic boundaries.展开更多
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary,subject to the kinematic and vorticity boundary conditio...We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary,subject to the kinematic and vorticity boundary conditions on the non-flat boundary.We observe that,under the nonhomogeneous boundary conditions,the pressure p can be still recovered by solving the Neumann problem for the Poisson equation.Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions.Based on this,we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition(without the incompressibility condition),which establishes a velocity mapping.Then we develop apriori estimates for the velocity mapping,especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions,which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem.Finally,we establish that,when the viscosity coefficient tends zero,the strong solutions of the initial-boundary value problem in R^n(n≥3)with nonhomogeneous vorticity boundary condition converge in L^2 to the corresponding Euler equations satisfying the kinematic condition.展开更多
We apply the newly proposed double absorbing boundary condition（DABC）（Hagstrom et al., 2014） to solve the boundary reflection problem in seismic finite-difference（FD） modeling. In the DABC scheme, the local high...We apply the newly proposed double absorbing boundary condition（DABC）（Hagstrom et al., 2014） to solve the boundary reflection problem in seismic finite-difference（FD） modeling. In the DABC scheme, the local high-order absorbing boundary condition is used on two parallel artificial boundaries, and thus double absorption is achieved. Using the general 2D acoustic wave propagation equations as an example, we use the DABC in seismic FD modeling, and discuss the derivation and implementation steps in detail. Compared with the perfectly matched layer（PML）, the complexity decreases, and the stability and fl exibility improve. A homogeneous model and the SEG salt model are selected for numerical experiments. The results show that absorption using the DABC is considerably improved relative to the Clayton–Engquist boundary condition and nearly the same as that in the PML.展开更多
The perfectly matched layer （PML） is a highly efficient absorbing boundary condition used for the numerical modeling of seismic wave equation. The article focuses on the application of this technique to finite-eleme...The perfectly matched layer （PML） is a highly efficient absorbing boundary condition used for the numerical modeling of seismic wave equation. The article focuses on the application of this technique to finite-element time-domain numerical modeling of elastic wave equation. However, the finite-element time-domain scheme is based on the second- order wave equation in displacement formulation. Thus, the first-order PML in velocity-stress formulation cannot be directly applied to this scheme. In this article, we derive the finite- element matrix equations of second-order PML in displacement formulation, and accomplish the implementation of PML in finite-element time-domain modeling of elastic wave equation. The PML has an approximate zero reflection coefficients for bulk and surface waves in the finite-element modeling of P-SV and SH wave propagation in the 2D homogeneous elastic media. The numerical experiments using a two-layer model with irregular topography validate the efficiency of PML in the modeling of seismic wave propagation in geological models with complex structures and heterogeneous media.展开更多
A compact four-component two-dimensional （2-D） finite-difference frequency domain （FDFD） method with the equivalent surface impedance boundary condition is used to analyze the dispersion characteristics of multila...A compact four-component two-dimensional （2-D） finite-difference frequency domain （FDFD） method with the equivalent surface impedance boundary condition is used to analyze the dispersion characteristics of multilayer metal-coated waveguides. According to the equivalent surface impedance boundary condition,the relationship between transverse field components on the boundary can be easily depicted. Once the eigen equation is solved,the propagation constant can be obtained as the eigen value for a given frequency. Results of the proposed method agaree well with those of high frequency structure simulator（HFSS）.展开更多
With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） meth...With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） method. The reflection of the ABC caused by both the truncated error and the phase velocity error is analyzed. Based on the phase velocity estimation and the nonuniform cell, two methods are studied and then adopted to improve the performance of the ABC. A calculation case of a rectangular waveguide which is a typical dispersive transmission line is carried out using the ADI-FDTD method with the improved ABC for evaluation. According to the calculated case, the comparison is given between the reflection coefficients of the ABC with and without the velocity estimation and also the comparison between the reflection coefficients of the ABC with and without the nonuniform processing. The reflection variation of the ABC under different time steps is also analyzed and the acceptable worsening will not obscure the improvement on the absorption. Numerical results obviously show that efficient improvement on the absorbing performance of the ABC is achieved based on these methods for the ADI-FDTD.展开更多
In this paper, the classical Ambarzumyan’s theorem for the regular SturmLiouville problem is extended to the case in which the boundary conditions are eigenparameter dependent. Specifically, we show that if the spect...In this paper, the classical Ambarzumyan’s theorem for the regular SturmLiouville problem is extended to the case in which the boundary conditions are eigenparameter dependent. Specifically, we show that if the spectrum of the operator D 2 ＋q with eigenparameter dependent boundary conditions is the same as the spectrum belonging to the zero potential, then the potential function q is actually zero.展开更多
基金The authors are supported by National Natural Sciences Foundation of China(11961060,11671322)the Key Project of Natural Sciences Foundation of Gansu Province(18JR3RA084).
文摘In this article,we consider a discrete right-definite Sturm-Liouville problems with two squared eigenparameter-dependent boundary conditions.By constructing some new Lagrange-type identities and two fundamental functions,we obtain not only the existence,the simplicity,and the interlacing properties of the real eigenvalues,but also the oscillation properties,orthogonality of the eigenfunctions,and the expansion theorem.Finally,we also give a computation scheme for computing eigenvalues and eigenfunctions of specific eigenvalue problems.
基金supported by the National Natural Science Foundation of China(No.12461086)the Natural Science Foundation of Hubei Province(No.2022CFC016)。
文摘In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hilbert space,on which the concerned operator A is self-adjoint.Then we construct the fundamental solutions to the problem,obtain the necessary and sufficient conditions for eigenvalues,and prove that the eigenvalues are simple.Finally,we investigate Green’s functions of such problem.
基金supported by the Key Project of the NSFC(12131010)the NSFC(12271032)+2 种基金supported by the NSFC(12371205)the NSF of Guangdong Province(2025A1515012026)supported by the NSF of Guangdong Province(2024A1515013238)。
文摘In this paper,we consider incompressible Navier-Stokes/Cahn-Hilliard system with the generalized Navier boundary condition and the dynamic boundary condition in a channel,which can describe the interaction between a binary material and the walls of the physical domain.We prove the global-in-time existence and uniqueness of strong solutions to this initial boundary value problem in a 2D channel domain.
基金Financial support from the National Natural Science Foundation of China(Grant Nos.51925906 and U2340228)the Natural Science Foundation of Hubei Province(Grant No.2022CFA028)is acknowledged.
文摘Drains play an important role in seepage control in geotechnical engineering.The enormous number and one-dimensional(1D)geometry of drainage holes make their nature difficult to be accurately modeled in groundwater flow simulation.It has been well understood that drains function by presenting discharge boundaries,which can be characterized by water head,no-flux,unilateral or mixed water head-unilateral boundary condition.It has been found after years of practices that the flow simulation may become erroneous if the transitions among the drain boundary conditions are not properly considered.For this,a rigorous algorithm is proposed in this study to detect the onset of transitions among the water head,noflux and mixed water head-unilateral boundary conditions for downwards-drilled drainage holes,which theoretically completes the description of drain boundary conditions.After verification against a numerical example,the proposed algorithm is applied to numerical modeling of groundwater flow through a gravity dam foundation.The simulation shows that for hundreds of downwards-drilled drainage holes used to be prescribed with water head boundary condition,56%and 2%of them are transitioned to mixed water head-unilateral and no-flux boundary conditions,respectively.The phreatic surface around the drains will be overestimated by 25e33 m without the use of the mixed boundary condition.For the first time,this study underscores the importance of the mixed water head-unilateral boundary condition and the proposed transition algorithm in drain modeling,which may become more essential for simulation of transient flow because of groundwater dynamics.
基金supported by the Tianjin Municipal Science and Technology Program of China(No.23JCZDJC00070)。
文摘This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the characteristic function and resolvent of this third-order differential operator.Secondly,by using the expression for the resolvent of the operator,we prove that the spectrum for this operator consists of simple eigenvalues and a finite number of eigenvalues with multiplicity 2.Finally,we solve the inverse problem for this operator,which states that the non-local potential function can be reconstructed from four spectra.Specially,we prove the Ambarzumyan theorem and indicate that odd or even potential functions can be reconstructed by three spectra.
基金supported by the National Key Research and Development Program of China(Grant No.2022YFA1405400)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301902),the National Natural Science Foundation of China(Grant No.12274290)the sponsor-ship from Yangyang Development Fund.
文摘We perform a comprehensive study of the electron-doped t-t′-J model on cylinders with density matrix renormalization group(DMRG).We conduct a systematic study on the finite-size and boundary condition effects on t-t′-J model on cylinders.Periodic and anti-periodic boundary conditions are implemented along the circumference direction,with the system’s width extending up to as large as 8 lattice units.We study doping levels of 1/6,1/8,and 1/12,which represent the most interesting region in the phase diagram of electron-doped cuprates.We find that for width-4 and width-6 systems,the ground state for fixed doping switches between anti-ferromagnetic Neel state and stripe state under different boundary conditions and system widths,indicating the presence of large finite size effect in the t-t′-J model.We also have a careful analysis of the d-wave pairing correlations which also change quantitatively with boundary conditions and widths of the system.However,the pairing correlations are enhanced when the system becomes wider for all dopings,suggesting the existence of possible long-range superconducting order in the thermodynamic limit.The width-8 results are found to be dependent on the starting state in the DMRG calculation for the kept states we can reach.For the width-8 system,only Neel(stripe)state can be stabilized in DMRG calculation for 1/12(1/6)doping,while both stripe and Neel states are stable in the DMRG sweep for 1/8 doping,regardless of the boundary conditions.These results indicate that 1/8 doping is likely to lie on the boundary of a phase transition between the Neel phase with lower doping and the stripe phase with higher doping,consistent with the previous study.The sensitivity of the ground state on boundary conditions and size observed for narrow systems is similar to that found in the t′-Hubbard model,where the t′term introduces frustration and makes the stripe state fragile.The study of different boundary conditions provides a useful tool to check the finite size effect in the future DMRG calculations.
基金supported by the Strategic Research and Consulting Project of the Chinese Academy of Engineering[grant number 2024-XBZD-14]the National Natural Science Foundation of China[grant numbers 42192553 and 41922036]the Fundamental Research Funds for the Central Universities–Cemac“GeoX”Interdisciplinary Program[grant number 020714380207]。
文摘The impacts of lateral boundary conditions(LBCs)provided by numerical models and data-driven networks on convective-scale ensemble forecasts are investigated in this study.Four experiments are conducted on the Hangzhou RDP(19th Hangzhou Asian Games Research Development Project on Convective-scale Ensemble Prediction and Application)testbed,with the LBCs respectively sourced from National Centers for Environmental Prediction(NCEP)Global Forecast System(GFS)forecasts with 33 vertical levels(Exp_GFS),Pangu forecasts with 13 vertical levels(Exp_Pangu),Fuxi forecasts with 13 vertical levels(Exp_Fuxi),and NCEP GFS forecasts with the vertical levels reduced to 13(the same as those of Exp_Pangu and Exp_Fuxi)(Exp_GFSRDV).In general,Exp_Pangu performs comparably to Exp_GFS,while Exp_Fuxi shows slightly inferior performance compared to Exp_Pangu,possibly due to its less accurate large-scale predictions.Therefore,the ability of using data-driven networks to efficiently provide LBCs for convective-scale ensemble forecasts has been demonstrated.Moreover,Exp_GFSRDV has the worst convective-scale forecasts among the four experiments,which indicates the potential improvement of using data-driven networks for LBCs by increasing the vertical levels of the networks.However,the ensemble spread of the four experiments barely increases with lead time.Thus,each experiment has insufficient ensemble spread to present realistic forecast uncertainties,which will be investigated in a future study.
基金financially supported by the National Natural Science Foundation of China(Grant No.52374118)the Science and Technology Support Project of Guizhou Province,China(Project Grant No.Qiankehe Support(2022)General 247).
文摘In regions characterized with great mining depths,complex topography,and intense geological activities,solely relying on lateral pressure coefficients or linear boundary conditions for predicting the in situ stress field of rock bodies can induce substantial deviations and limitations.This study focuses on a typical karst area in Southwest Guizhou,China as its research background.It employs a hybrid approach integrating machine learning,numerical simulations,and field experiments to develop an optimization algorithm for nonlinear prediction of the complex three-dimensional(3D)in situ stress fields.Through collecting and fitting analysis of in situ stress measurement data from the karst region,the distributions of in situ stresses with depth were identified with nonlinear boundary conditions.A prediction model for in situ stress was then established based on artificial neural network(ANN)and genetic algorithm(GA)approach,validated in the typical karst landscape mine,Jinfeng Gold Mine.The results demonstrate that the model's predictions align well with actual measurements,showcasing consistency and regularity.Specifically,the error between the predicted and actual values of the maximum horizontal principal stress was the smallest,with an absolute error 0.01-3 MPa and a relative error of 0.04-15.31%.This model accurately and effectively predicts in situ stresses in complex geological areas.
基金supported by the National Natural Science Foundation of China(Grant Nos.12275214,12247103,12047502)the Natural Science Basic Research Program of Shaanxi Province Grant Nos.2021JCW-19 and 2019JQ-107Shaanxi Key Laboratory for Theoretical Physics Frontiers in China.
文摘We investigate the integrability of the Rabi model,which is traditionally viewed as not Yang–Baxter-integrable despite its solvability.Building on efforts by Bogoliubov and Kulish(2013 J.Math.Sci.19214–30),Amico et al(2007 Nucl.Phys.B 787283–300),and Batchelor and Zhou(2015 Phys.Rev.A 91053808),who explored special limiting cases of the model,we develop a spin–boson interaction Hamiltonian under more general boundary conditions,particularly focusing on open boundary conditions with off-diagonal terms.Our approach maintains the direction of the spin in the z direction and also preserves the boson particle number operator a^(†)a,marking a progression beyond previous efforts that have primarily explored reduced forms of the Rabi model from Yang–Baxter algebra.We also address the presence of‘unwanted’quadratic boson terms a^(2) and a^(†2),which share coefficients with the boson particle number operator.Interestingly,these terms vanish when spectral parameter u=±θ_(s),simplifying the model to a limiting case of operator-valued twists,a scenario previously discussed by Batchelor and Zhou(2015 Phys.Rev.A 91053808).
基金co-supported by the National Natural Science Foundation of China(Nos.52325602,52306036 and 52306035)the National Science and Technology Major Project of China(No.Y2022-II-0003-0006 and Y2022-II-0002-0005)+1 种基金the project funded by China Postdoctoral Science Foundation(No.2022M720346)supported by the Key Laboratory of Pre-Research Management Centre of China(No.6142702200101).
文摘The influence of Impedance Boundary Condition (IBC) on transonic compressors is investigated. A systematic input–output analytical framework is developed, which treats the nonlinearities as unknown forcing terms. The framework is validated through the experiments of rotating inlet distortion within a low-speed compressor. The input–output method is subsequently applied to transonic compressors, including NASA Rotor37 and Stage35, wherein impedance optimization is studied along with the exploration of its fundamental mechanisms. The IBC is employed to model the effect of Casing Treatment (CT). The optimal complex impedance values are determined through predicted results and tested across a range of circumferential modes and forcing frequencies. The IBC significantly reduces the energy and Reynolds stress gain, notably at the first-order circumferential mode and within the Rotor Rotating Frequency (RRF) range. Output modes reveal that transonic compressors with fine-tuned impedance values exhibit a more confined perturbation distribution and redistribute the perturbations compared to the uncontrolled case. Additionally, the roles of resistance and reactance are elucidated through input–output analysis, and resistance determines the energy transfer direction between flow and pressure waves and modulates the amplitude, whereas reactance modifies the phase relationships and attenuates the perturbations.
基金supported by the National Natural Sciences Foundation of China(No.62363005)。
文摘In this paper,we investigate the blow-up phenomenon for a class of logarithmic viscoelastic equations with delay and nonlocal terms under acoustic boundary conditions.Using the energy method,we prove that nontrivial solutions with negative initial energy will blow up in finite time,and provide an upper bound estimate for the blow-up time.Additionally,we also derive a lower bound estimate for the blow-up time.
基金Supported by the National Natural Science Foundation of China(12461039)Excellent Graduate Innovation Star Scientific Research Project of Gansu Province of China(2025CXZX-273)。
文摘In this study,we mainly discuss some spectral properties of the Dirac operator with eigenparameter-dependent boundary condition.Initially,we reformulate the spectral problem into linear operator eigenparameter problem in a suitable Hilbert space,and obtain some pivotal properties of self-adjoint operator.Subsequently,by establishing the boundary condition space and constructing the embedded mapping,we show that the simple eigenvalue branch of this system is not only continuous,but also smooth.We then obtain the differential expressions of the eigenvalue branch in the sense of Frechet derivative.
基金Project supported by the National Natural Science Foundation of China(No.12472003)the Key Research Project of Zhejiang Market Supervision Administration(No.ZD2024013)the Technical Project of Research Institute of Highway Ministry of Transport of China(No.0225KF12SC1002)。
文摘Moving-load induced vibrations can,in certain instances,exceed those caused by equivalent static loads,especially at the critical velocity of moving loads.Suppressing these vibrations is of critical practical importance in various engineering fields,including the design of precision robotics and advanced aerospace structures where components are subject to moving loads.In this paper,an inertial nonlinear energy sink(NES)is used for the first time to reduce the vibration response of graphene platelet(GPL)-reinforced nanocomposite beams with elastic boundaries under moving loads.Based on the von Kármán nonlinear theory,the governing equations of the beam-NES system are derived using the Lagrange equation.The Newmark-Newton method,in conjunction with the Heaviside step function,is used to obtain the nonlinear responses of the beam under moving loads.The effects of the boundary spring stiffness,the GPL parameters,as well as the velocity and frequency of the moving loads on the beam response and the performance of the NES are thoroughly studied.The results of this work provide insights into applying NESs to suppress the nonlinear vibrations induced by moving loads in composite structures with elastic boundaries.
基金supported in part by the National Science Foundation under Grants DMS-0807551,DMS-0720925,and DMS-0505473the Natural Science Foundationof China(10728101)supported in part by EPSRC grant EP/F029578/1
文摘We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary,subject to the kinematic and vorticity boundary conditions on the non-flat boundary.We observe that,under the nonhomogeneous boundary conditions,the pressure p can be still recovered by solving the Neumann problem for the Poisson equation.Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions.Based on this,we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition(without the incompressibility condition),which establishes a velocity mapping.Then we develop apriori estimates for the velocity mapping,especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions,which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem.Finally,we establish that,when the viscosity coefficient tends zero,the strong solutions of the initial-boundary value problem in R^n(n≥3)with nonhomogeneous vorticity boundary condition converge in L^2 to the corresponding Euler equations satisfying the kinematic condition.
基金supported by the National Nature Science Foundation of China(Grant No.U1262208)the Important National Science & Technology Specific Projects(Grant No.2011ZX05019-008)
文摘We apply the newly proposed double absorbing boundary condition（DABC）（Hagstrom et al., 2014） to solve the boundary reflection problem in seismic finite-difference（FD） modeling. In the DABC scheme, the local high-order absorbing boundary condition is used on two parallel artificial boundaries, and thus double absorption is achieved. Using the general 2D acoustic wave propagation equations as an example, we use the DABC in seismic FD modeling, and discuss the derivation and implementation steps in detail. Compared with the perfectly matched layer（PML）, the complexity decreases, and the stability and fl exibility improve. A homogeneous model and the SEG salt model are selected for numerical experiments. The results show that absorption using the DABC is considerably improved relative to the Clayton–Engquist boundary condition and nearly the same as that in the PML.
基金sponsored by the National Natural Science Foundation of China Research(Grant No.41274138)the Science Foundation of China University of Petroleum(Beijing)(No.KYJJ2012-05-02)
文摘The perfectly matched layer （PML） is a highly efficient absorbing boundary condition used for the numerical modeling of seismic wave equation. The article focuses on the application of this technique to finite-element time-domain numerical modeling of elastic wave equation. However, the finite-element time-domain scheme is based on the second- order wave equation in displacement formulation. Thus, the first-order PML in velocity-stress formulation cannot be directly applied to this scheme. In this article, we derive the finite- element matrix equations of second-order PML in displacement formulation, and accomplish the implementation of PML in finite-element time-domain modeling of elastic wave equation. The PML has an approximate zero reflection coefficients for bulk and surface waves in the finite-element modeling of P-SV and SH wave propagation in the 2D homogeneous elastic media. The numerical experiments using a two-layer model with irregular topography validate the efficiency of PML in the modeling of seismic wave propagation in geological models with complex structures and heterogeneous media.
基金Supported by the Project Innovation of Graduate Students of Jiangsu Province of China(CX09B-079Z)the Basic Research Items of National Key Lab of Electronic Measurement Technology~~
文摘A compact four-component two-dimensional （2-D） finite-difference frequency domain （FDFD） method with the equivalent surface impedance boundary condition is used to analyze the dispersion characteristics of multilayer metal-coated waveguides. According to the equivalent surface impedance boundary condition,the relationship between transverse field components on the boundary can be easily depicted. Once the eigen equation is solved,the propagation constant can be obtained as the eigen value for a given frequency. Results of the proposed method agaree well with those of high frequency structure simulator（HFSS）.
基金The National Natural Science Foundation of China(No.60702027)the Free Research Fund of the National Mobile Communications Research Laboratory of Southeast University (No.2008B07)the National Basic Research Program of China(973 Program)(No.2007CB310603)
文摘With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） method. The reflection of the ABC caused by both the truncated error and the phase velocity error is analyzed. Based on the phase velocity estimation and the nonuniform cell, two methods are studied and then adopted to improve the performance of the ABC. A calculation case of a rectangular waveguide which is a typical dispersive transmission line is carried out using the ADI-FDTD method with the improved ABC for evaluation. According to the calculated case, the comparison is given between the reflection coefficients of the ABC with and without the velocity estimation and also the comparison between the reflection coefficients of the ABC with and without the nonuniform processing. The reflection variation of the ABC under different time steps is also analyzed and the acceptable worsening will not obscure the improvement on the absorption. Numerical results obviously show that efficient improvement on the absorbing performance of the ABC is achieved based on these methods for the ADI-FDTD.
基金supported by Natural Science Foun- dation of Jiangsu Province of China (BK 2010489)the Outstanding Plan-Zijin Star Foundation of Nanjing University of Science and Technology (AB 41366)+1 种基金NUST Research Funding (AE88787)the National Natural Science Foundation of China (11071119)
文摘In this paper, the classical Ambarzumyan’s theorem for the regular SturmLiouville problem is extended to the case in which the boundary conditions are eigenparameter dependent. Specifically, we show that if the spectrum of the operator D 2 ＋q with eigenparameter dependent boundary conditions is the same as the spectrum belonging to the zero potential, then the potential function q is actually zero.
