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
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
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
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
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
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 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
The determination of the ultimate load-bearing capacity of structures made of elastoplastic heterogeneous materials under varying loads is of great importance for engineering analysis and design. Therefore, it is nece...The determination of the ultimate load-bearing capacity of structures made of elastoplastic heterogeneous materials under varying loads is of great importance for engineering analysis and design. Therefore, it is necessary to accurately predict the shakedown domains of these materials. The static shakedown theorem, also known as Melan's theorem, is a fundamental method used to predict the shakedown domains of structures and materials. Within this method, a key aspect lies in the construction and application of an appropriate self-equilibrium stress field(SSF). In the structural shakedown analysis, the SSF is typically constructed by governing equations that satisfy no external force(NEF) boundary conditions. However, we discover that directly applying these governing equations is not suitable for the shakedown analysis of heterogeneous materials. Researchers must consider the requirements imposed by the Hill-Mandel condition for boundary conditions and the physical significance of representative volume elements(RVEs). This paper addresses this issue and demonstrates that the sizes of SSFs vary under different boundary conditions, such as uniform displacement boundary conditions(DBCs), uniform traction boundary conditions(TBCs), and periodic boundary conditions(PBCs). As a result, significant discrepancies arise in the predicted shakedown domain sizes of heterogeneous materials. Built on the demonstrated relationship between SSFs under different boundary conditions, this study explores the conservative relationships among different shakedown domains, and provides proof of the relationship between the elastic limit(EL) factors and the shakedown loading factors under the loading domain of two load vertices. By utilizing numerical examples, we highlight the conservatism present in certain results reported in the existing literature. Among the investigated boundary conditions, the obtained shakedown domain is the most conservative under TBCs.Conversely, utilizing PBCs to construct an SSF for the shakedown analysis leads to less conservative lower bounds, indicating that PBCs should be employed as the preferred boundary conditions for the shakedown analysis of heterogeneous materials.展开更多
The inverse spectral theory of a class of Atkinson-type Sturm-Liouville problems with non-self-adjoint boundary conditions containing the spectral parameter is investigated.Based on the so-called matrix representation...The inverse spectral theory of a class of Atkinson-type Sturm-Liouville problems with non-self-adjoint boundary conditions containing the spectral parameter is investigated.Based on the so-called matrix representations of such problems and a special class of inverse matrix eigenvalue problems,some of the coefficient functions of the corresponding Sturm-Liouville problems are constructed by using priori known two sets of complex numbers satisfying certain conditions.To best understand the result,an algorithm and some examples are posted.展开更多
This paper aims to investigate the multi-soliton solutions of the coupled Lakshmanan–Porsezian–Daniel equations with variable coefficients under nonzero boundary conditions.These equations are utilized to model the ...This paper aims to investigate the multi-soliton solutions of the coupled Lakshmanan–Porsezian–Daniel equations with variable coefficients under nonzero boundary conditions.These equations are utilized to model the phenomenon of nonlinear waves propagating simultaneously in non-uniform optical fibers.By analyzing the Lax pair and the Riemann–Hilbert problem,we aim to provide a comprehensive understanding of the dynamics and interactions of solitons of this system.Furthermore,we study the impacts of group velocity dispersion or the fourth-order dispersion on soliton behaviors.Through appropriate parameter selections,we observe various nonlinear phenomena,including the disappearance of solitons after interaction and their transformation into breather-like solitons,as well as the propagation of breathers with variable periodicity and interactions between solitons with variable periodicities.展开更多
We construct the Riemann-Hilbert problem of the Lakshmanan-Porsezian-Daniel equation with nonzero boundary conditions,and use the Laurent expansion and Taylor series expansion to obtain the exact formulas of the solit...We construct the Riemann-Hilbert problem of the Lakshmanan-Porsezian-Daniel equation with nonzero boundary conditions,and use the Laurent expansion and Taylor series expansion to obtain the exact formulas of the soliton solutions in the case of a higher-order pole and multiple higher-order poles.The dynamic behaviors of a simple pole,a second-order pole and a simple pole plus a second-order pole are demonstrated.展开更多
The purpose of this study is to determine a suitable modeling method to make computational fluid dynamics(CFD)simulation more efficient for aeroacoustics optimization of the bogie region of high-speed trains.To this e...The purpose of this study is to determine a suitable modeling method to make computational fluid dynamics(CFD)simulation more efficient for aeroacoustics optimization of the bogie region of high-speed trains.To this end,four modeling methods are considered,which involve different geometry simplifications and boundary condition specifications.The corresponding models are named the three-car marshalling model,computational domain shortening model,carbody shortening model,and sub-domain model.Combining the detached eddy simulation(DES)model and Ffowcs Williams-Hawkings(FW-H)equation,the unsteady flow field and far-field noise of the four models are predicted.To evaluate the effect of the different modeling methods,the time-averaged flow field,fluctuating flow field,and far-field noise results of the four models are compared and analyzed in detail with the results of the three-car marshalling model used as basis for comparison.The results show that the flow field results of the bogie region predicted by the four models have relatively high consistency.However,the usage of the non-time varying outlet boundary conditions in the computational domain shortening model and sub-domain model could affect the pressure fluctuation on the upstream carbody surface.When only the bogie region is used as the source surface,the differences between the far-field noise results of the three simplified models and the three-car marshalling model are all within 1 dB;when the train head is used as the source surface,the results of the carbody shortening model and the three-car marshalling model are more consistent.展开更多
In this article we study the existence of solutions for the Dirac systems with the chirality boundary condition.Using an analytic framework of proper products of fractional Sobolev spaces,the solutions existence resul...In this article we study the existence of solutions for the Dirac systems with the chirality boundary condition.Using an analytic framework of proper products of fractional Sobolev spaces,the solutions existence results of the coupled Dirac systems are obtained for nonlinearity with superquadratic growth rates.The results obtained by GONG and LU(2017)are extended to the case of chiral boundary condition.展开更多
The Riemann–Hilbert approach is demonstrated to investigate the defocusing Lakshmanan–Porsezian–Daniel equation under fully asymmetric nonzero boundary conditions.In contrast to the symmetry case,this paper focuses...The Riemann–Hilbert approach is demonstrated to investigate the defocusing Lakshmanan–Porsezian–Daniel equation under fully asymmetric nonzero boundary conditions.In contrast to the symmetry case,this paper focuses on the branch points related to the scattering problem rather than using the Riemann surfaces.For the direct problem,we analyze the Jost solution of lax pairs and some properties of scattering matrix,including two kinds of symmetries.The inverse problem at branch points can be presented,corresponding to the associated Riemann–Hilbert.Moreover,we investigate the time evolution problem and estimate the value of solving the solutions by Jost function.For the inverse problem,we construct it as a Riemann–Hilbert problem and formulate the reconstruction formula for the defocusing Lakshmanan–Porsezian–Daniel equation.The solutions of the Riemann–Hilbert problem can be constructed by estimating the solutions.Finally,we work out the solutions under fully asymmetric nonzero boundary conditions precisely via utilizing the Sokhotski–Plemelj formula and the square of the negative column transformation with the assistance of Riemann surfaces.These results are valuable for understanding physical phenomena and developing further applications of optical problems.展开更多
We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, ani...Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.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 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 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 (Nos. 52075070 and12302254)the Dalian City Supports Innovation and Entrepreneurship Projects for High-Level Talents (No. 2021RD16)the Liaoning Revitalization Talents Program (No. XLYC2002108)。
文摘The determination of the ultimate load-bearing capacity of structures made of elastoplastic heterogeneous materials under varying loads is of great importance for engineering analysis and design. Therefore, it is necessary to accurately predict the shakedown domains of these materials. The static shakedown theorem, also known as Melan's theorem, is a fundamental method used to predict the shakedown domains of structures and materials. Within this method, a key aspect lies in the construction and application of an appropriate self-equilibrium stress field(SSF). In the structural shakedown analysis, the SSF is typically constructed by governing equations that satisfy no external force(NEF) boundary conditions. However, we discover that directly applying these governing equations is not suitable for the shakedown analysis of heterogeneous materials. Researchers must consider the requirements imposed by the Hill-Mandel condition for boundary conditions and the physical significance of representative volume elements(RVEs). This paper addresses this issue and demonstrates that the sizes of SSFs vary under different boundary conditions, such as uniform displacement boundary conditions(DBCs), uniform traction boundary conditions(TBCs), and periodic boundary conditions(PBCs). As a result, significant discrepancies arise in the predicted shakedown domain sizes of heterogeneous materials. Built on the demonstrated relationship between SSFs under different boundary conditions, this study explores the conservative relationships among different shakedown domains, and provides proof of the relationship between the elastic limit(EL) factors and the shakedown loading factors under the loading domain of two load vertices. By utilizing numerical examples, we highlight the conservatism present in certain results reported in the existing literature. Among the investigated boundary conditions, the obtained shakedown domain is the most conservative under TBCs.Conversely, utilizing PBCs to construct an SSF for the shakedown analysis leads to less conservative lower bounds, indicating that PBCs should be employed as the preferred boundary conditions for the shakedown analysis of heterogeneous materials.
基金Supported by the National Natural Science Foundation of China (12261066, 11661059)the Natural Science Foundation of Inner Mongolia (2021MS01020)。
文摘The inverse spectral theory of a class of Atkinson-type Sturm-Liouville problems with non-self-adjoint boundary conditions containing the spectral parameter is investigated.Based on the so-called matrix representations of such problems and a special class of inverse matrix eigenvalue problems,some of the coefficient functions of the corresponding Sturm-Liouville problems are constructed by using priori known two sets of complex numbers satisfying certain conditions.To best understand the result,an algorithm and some examples are posted.
基金supported by the Natural Science Foundation of Hebei Province,China (Grant No.A2021502004)the Fundamental Research Funds for the Central Universities (Grant No.2024MS126).
文摘This paper aims to investigate the multi-soliton solutions of the coupled Lakshmanan–Porsezian–Daniel equations with variable coefficients under nonzero boundary conditions.These equations are utilized to model the phenomenon of nonlinear waves propagating simultaneously in non-uniform optical fibers.By analyzing the Lax pair and the Riemann–Hilbert problem,we aim to provide a comprehensive understanding of the dynamics and interactions of solitons of this system.Furthermore,we study the impacts of group velocity dispersion or the fourth-order dispersion on soliton behaviors.Through appropriate parameter selections,we observe various nonlinear phenomena,including the disappearance of solitons after interaction and their transformation into breather-like solitons,as well as the propagation of breathers with variable periodicity and interactions between solitons with variable periodicities.
基金supported by the National Natural Science Foundation of China under Grant Nos.12175111,12275144 and 12235007the KC Wong Magna Fund in Ningbo University。
文摘We construct the Riemann-Hilbert problem of the Lakshmanan-Porsezian-Daniel equation with nonzero boundary conditions,and use the Laurent expansion and Taylor series expansion to obtain the exact formulas of the soliton solutions in the case of a higher-order pole and multiple higher-order poles.The dynamic behaviors of a simple pole,a second-order pole and a simple pole plus a second-order pole are demonstrated.
基金National Natural Science Foundation of China(No.12172308)National Key Research and Development Program of China(No.2020YFA0710902).
文摘The purpose of this study is to determine a suitable modeling method to make computational fluid dynamics(CFD)simulation more efficient for aeroacoustics optimization of the bogie region of high-speed trains.To this end,four modeling methods are considered,which involve different geometry simplifications and boundary condition specifications.The corresponding models are named the three-car marshalling model,computational domain shortening model,carbody shortening model,and sub-domain model.Combining the detached eddy simulation(DES)model and Ffowcs Williams-Hawkings(FW-H)equation,the unsteady flow field and far-field noise of the four models are predicted.To evaluate the effect of the different modeling methods,the time-averaged flow field,fluctuating flow field,and far-field noise results of the four models are compared and analyzed in detail with the results of the three-car marshalling model used as basis for comparison.The results show that the flow field results of the bogie region predicted by the four models have relatively high consistency.However,the usage of the non-time varying outlet boundary conditions in the computational domain shortening model and sub-domain model could affect the pressure fluctuation on the upstream carbody surface.When only the bogie region is used as the source surface,the differences between the far-field noise results of the three simplified models and the three-car marshalling model are all within 1 dB;when the train head is used as the source surface,the results of the carbody shortening model and the three-car marshalling model are more consistent.
基金Supported by the National Natural Science Foundation of China(11801499)。
文摘In this article we study the existence of solutions for the Dirac systems with the chirality boundary condition.Using an analytic framework of proper products of fractional Sobolev spaces,the solutions existence results of the coupled Dirac systems are obtained for nonlinearity with superquadratic growth rates.The results obtained by GONG and LU(2017)are extended to the case of chiral boundary condition.
基金the Fundamental Research Funds for the Central Universities(Grant No.2024MS126).
文摘The Riemann–Hilbert approach is demonstrated to investigate the defocusing Lakshmanan–Porsezian–Daniel equation under fully asymmetric nonzero boundary conditions.In contrast to the symmetry case,this paper focuses on the branch points related to the scattering problem rather than using the Riemann surfaces.For the direct problem,we analyze the Jost solution of lax pairs and some properties of scattering matrix,including two kinds of symmetries.The inverse problem at branch points can be presented,corresponding to the associated Riemann–Hilbert.Moreover,we investigate the time evolution problem and estimate the value of solving the solutions by Jost function.For the inverse problem,we construct it as a Riemann–Hilbert problem and formulate the reconstruction formula for the defocusing Lakshmanan–Porsezian–Daniel equation.The solutions of the Riemann–Hilbert problem can be constructed by estimating the solutions.Finally,we work out the solutions under fully asymmetric nonzero boundary conditions precisely via utilizing the Sokhotski–Plemelj formula and the square of the negative column transformation with the assistance of Riemann surfaces.These results are valuable for understanding physical phenomena and developing further applications of optical problems.
文摘We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
文摘Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.
