In this paper,we define for the trace operator,the solution of certain models of vibrating plates standards with initial data in a strategic region spaces of weak regularities.Indeed,we know that the notion of regiona...In this paper,we define for the trace operator,the solution of certain models of vibrating plates standards with initial data in a strategic region spaces of weak regularities.Indeed,we know that the notion of regional controllability is more adapted to systems described by dynamic systems.Regional controllability results in a strategic area were established for vibrating plates by the Hilbertian Uniqueness Method.展开更多
Young's modulus and Poisson's ratio are crucial parameters for reservoir characterization and rock brittleness evaluation.Conventional methods often rely on indirect computation or approximations of the Zoeppr...Young's modulus and Poisson's ratio are crucial parameters for reservoir characterization and rock brittleness evaluation.Conventional methods often rely on indirect computation or approximations of the Zoeppritz equations to estimate Young's modulus,which can introduce cumulative errors and reduce the accuracy of inversion results.To address these issues,this paper introduces the analytical solution of the Zoeppritz equation into the inversion process.The equation is re-derived and expressed in terms of Young's modulus,Poisson's ratio,and density.Within the Bayesian framework,we construct an objective function for the joint inversion of PP and PS waves.Traditional gradient-based algorithms often suffer from low precision and the computational complexity.In this study,we address limitations of conventional approaches related to low precision and complicated code by using Circle chaotic mapping,Levy flights,and Gaussian mutation to optimize the quantum particle swarm optimization(QPSO),named improved quantum particle swarm optimization(IQPSO).The IQPSO demonstrates superior global optimization capabilities.We test the proposed inversion method with both synthetic and field data.The test results demonstrate the proposed method's feasibility and effectiveness,indicating an improvement in inversion accuracy over traditional methods.展开更多
We investigate the origin of the 1/3 magnetization plateau in the S=1/2 kagome antiferromagnetic Heisenberg model using the variational Monte Carlo and exact diagonalization methods,to account for the recent experimen...We investigate the origin of the 1/3 magnetization plateau in the S=1/2 kagome antiferromagnetic Heisenberg model using the variational Monte Carlo and exact diagonalization methods,to account for the recent experimental observations in YCu_(3)(OH)_(6+x)Br_(3-x)and YCu_(3)(OD)_(6+x)Br_(3-x).We identify three degenerate valencebond-solid(VBS)states forming a√3×√3 unit cell.These states exhibit David-star patterns in the spin moment distribution with only two fractional values-1/3 and 2/3,and are related through translational transformations.While the spin correlations in these VBS states are found to be short-range,resembling a quantum spin liquid,we show that they have a vanishing topological entanglement entropy and thus are topologically trivial many-body states.Our theoretical results provide strong evidence that the 1/3 magnetization plateau observed in recent experiments arises from these√3×√3 VBS states with fractional spin moments.展开更多
Due to their superior properties, the interest in nanostructures is increasing today in engineering. This study presents a new two-noded curved finite element for analyzing the in-plane static behaviors of curved nano...Due to their superior properties, the interest in nanostructures is increasing today in engineering. This study presents a new two-noded curved finite element for analyzing the in-plane static behaviors of curved nanobeams. Opposite to traditional curved finite elements developed by using approximate interpolation functions, the proposed curved finite element is developed by using exact analytical solutions. Although this approach was first introduced for analyzing the mechanical behaviors of macro-scale curved beams by adopting the local theory of elasticity, the exact analytical expressions used in this study were obtained from the solutions of governing equations that were expressed via the differential form of the nonlocal theory of elasticity. Therefore, the effects of shear strain and axial extension included in the analytical formulation are also inherited by the curved finite element developed here. The rigidity matrix and the consistent force vector are developed for a circular finite element. To demonstrate the applicability of the method, static analyses of various curved nanobeams subjected to different boundary conditions and loading scenarios are performed, and the obtained results are compared with the exact analytical ones. The presented study provides an accurate and low computational cost method for researchers to investigate the in-plane static behavior of curved nanobeams.展开更多
Pathological tremor is one of the cardinal symptoms in Parkinson's disease (PD).Tremor is comprised of involuntary,rhythmic,a nd oscillating movements that can vary according to the circumstances under which they ...Pathological tremor is one of the cardinal symptoms in Parkinson's disease (PD).Tremor is comprised of involuntary,rhythmic,a nd oscillating movements that can vary according to the circumstances under which they occur,the body parts that are involved,and the frequency at which they present.For example,tremors can be mild to severe,are stress sensitive,and can affect arms,legs,or the head (Dirkx and Bologna,2022).展开更多
The main focus of this paper is to address a generalized(2+1)-dimensional Hirota bilinear equation utilizing the bilinear neural network method.The paper presents the periodic solutions through a single-layer model of...The main focus of this paper is to address a generalized(2+1)-dimensional Hirota bilinear equation utilizing the bilinear neural network method.The paper presents the periodic solutions through a single-layer model of[3-4-1],followed by breather,lump and their interaction solutions by using double-layer models of[3-3-2-1]and[3-3-3-1],respectively.A significant innovation introduced in this work is the computation of periodic cross-rational solutions through the design of a novel[3-(2+2)-4-1]model,where a specific hidden layer is partitioned into two segments for subsequent operations.Three-dimensional and density figures of the solutions are given alongside an analysis of the dynamics of these solutions.展开更多
This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we obtain conservation vectors that...This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we obtain conservation vectors that are related and unrelated to symmetric information. In addition, some exact solutions with particular forms are obtained according to the method of conservation laws. These particular solutions are different from the group-invariant solutions.展开更多
Transcritical and supercritical fluids widely exist in aerospace propulsion systems,such as the coolant flow in the regenerative cooling channels of scramjet engines.To numerically simulate the coolant flow,we must ad...Transcritical and supercritical fluids widely exist in aerospace propulsion systems,such as the coolant flow in the regenerative cooling channels of scramjet engines.To numerically simulate the coolant flow,we must address the challenges in solving Riemann problems(RPs)for real fluids under complex flow conditions.In this study,an exact numerical solution for the one-dimensional RP of two-parameter fluids is developed.Due to the comprehensive resolution of fluid thermodynamics,the proposed solution framework is suitable for all forms of the two-parameter equation of state(EoS).The pressure splitting method is introduced to enable parallel calculation of RPs across multiple grid points.Theoretical analysis demonstrates the isentropic nature of weak waves in two-parameter fluids,ensuring that the same mathematical properties as ideal gas could be applied in Newton's iteration.A series of numerical cases validate the effectiveness of the proposed method.A comparative analysis is conducted on the exact Riemann solutions for the real fluid EoS,the ideal gas EoS,and the improved ideal gas EoS under supercritical and transcritical conditions.The results indicate that the improved one produces smaller errors in the calculation of momentum and energy fluxes.展开更多
This study explores the phenomenon of shape coexistence in nuclei around^(172)Hg,with a focus on the isotopes^(170)Pt,^(172)Hg,and^(174)Pb,as well as the^(170)Pt to^(180)Pt isotopic chain.Utilizing a macro-microscopic...This study explores the phenomenon of shape coexistence in nuclei around^(172)Hg,with a focus on the isotopes^(170)Pt,^(172)Hg,and^(174)Pb,as well as the^(170)Pt to^(180)Pt isotopic chain.Utilizing a macro-microscopic approach that incorporates the Lublin-Strasbourg Drop model combined with a Yukawa-Folded potential and pairing corrections,we analyze the potential energy surfaces(PESs)to understand the impact of pairing interaction.For^(170)Pt,the PES exhibited a prolate ground state,with additional triaxial and oblate-shaped isomers.In^(172)Hg,the ground-state deformation transitions from triaxial to oblate with increasing pairing interaction,demonstrating its nearlyγ-unstable nature.Three shape isomers(prolate,triaxial,and oblate)were observed,with increased pairing strength leading to the disappearance of the triaxial isomer.^(174)Pb exhibited a prolate ground state that became increasingly spherical with stronger pairing.While shape isomers were present at lower pairing strengths,robust shape coexistence was not observed.For realistic pairing interaction,the ground-state shapes transitioned from prolate in^(170)Pt to a coexistence ofγ-unstable and oblate shapes in^(172)Hg,ultimately approaching spherical symmetry in^(174)Pb.A comparison between Exact and Bardeen-Cooper-Schrieffer(BCS)pairing demonstrated that BCS pairing tends to smooth out shape coexistence and reduce the depth of the shape isomer,leading to less pronounced deformation features.The PESs for even-even^(170)-180 Pt isotopes revealed significant shape evolution.^(170)Pt showed a prolate ground state,whereas^(172)Pt exhibited both triaxial and prolate shape coexistence.In^(174)Pt,the ground state was triaxial,coexisted with a prolate minimum.For^(176)Pt,aγ-unstable ground state coexists with a prolate minimum.By 178 Pt and 180Pt,a dominant prolate minimum emerged.These results highlight the role of shape coexistence andγ-instability in the evolution of nuclear structure,especially in the mid-shell region.These findings highlight the importance of pairing interactions in nuclear deformation and shape coexistence,providing insights into the structural evolution of mid-shell nuclei.展开更多
The gravitational deflection of light signals restricted in the polar-axis plane of a moving Kerr–Newman(KN)black hole with a constant velocity along the polar axis is studied within the second post-Minkowskian(PM)ap...The gravitational deflection of light signals restricted in the polar-axis plane of a moving Kerr–Newman(KN)black hole with a constant velocity along the polar axis is studied within the second post-Minkowskian(PM)approximation.For this purpose,the Lorentz boosting technique is adopted to obtain the exact metric of a moving KN black hole with an arbitrary constant velocity in Kerr–Schild coordinates for the first time.Based on the weak field limit of the exact metric,we then derive the equations of motion of test particles constrained in the polaraxis plane of a moving KN source whose velocity is along the polar axis and collinear with its angular momentum.An iterative technique is utilized subsequently in the calculations of the null deflection angle up to the 2PM order caused by the moving lens,and this deflection angle is found to be spin-independent.Finally,we discuss the influence of the motion of the lens on the gravitational deflection and estimate the possibility of detecting this kinematical effect.Our work might be helpful for future astronomical observations.展开更多
A comprehensive understanding of exact seismic P-wave reflection and transmission(R/T)coefficients at imperfectly welded or non-welded contact interfaces holds paramount importance in the realm of seismic exploration....A comprehensive understanding of exact seismic P-wave reflection and transmission(R/T)coefficients at imperfectly welded or non-welded contact interfaces holds paramount importance in the realm of seismic exploration.Nonetheless,scant attention has been devoted in previous literature to the investigation of stress-dependent exact R/T coefficients in horizontal transversely isotropic(HTI)media,characterized by a horizontal symmetry axis,at such interfaces.Addressing this scholarly gap,we present exact R/T coefficient formulations specifically tailored to an imperfectly welded contact interface separating two HTI media under the influence of in-situ horizontal stress.We begin by deriving the equation of motion for a stressed HTI medium,utilizing the theoretical framework of acoustoelasticity to examine the impact of in-situ horizontal stress on the overarching elastic properties of HTI media.Precise boundary conditions are then established at the imperfectly welded contact interface by applying generalized stress-strain relationships and linear-slip theory,with the influence of in-situ horizontal stress on the interface further explored through the linear-slip model.By integrating these elements with the seismic wave displacement equation,we derive exact R/T coefficient formulations applicable to an imperfectly welded contact interface between two HTI media.Numerical analyses are conducted to elucidate the effects of in-situ horizontal stress on critical parameters such as rock density,seismic wave velocity,Thomsen-type anisotropy parameters,R/T coefficients,and seismic reflection responses at the imperfectly welded contact interface.Furthermore,the proposed formulations are frequency-dependent,with the imperfectly welded contact interface acting as a frequency-selective filter for both reflected and transmitted waves.Notably,under conditions of sufficiently large incident angles,the sensitivity of R/T coefficients to key influencing factors increases significantly.The derived R/T coefficient formulations and the accompanying numerical results offer valuable insights for fracture characterization,stress-dependent parameter inversion,and in-situ stress detection.展开更多
The(2+1)-dimensional integrable generalization of the Kaup-Kuper-shmidt(KK)equation is solved by the inverse spectral transform method in this paper.Several new long derivative operators V_(x),V_(y) and V_(t) and the ...The(2+1)-dimensional integrable generalization of the Kaup-Kuper-shmidt(KK)equation is solved by the inverse spectral transform method in this paper.Several new long derivative operators V_(x),V_(y) and V_(t) and the kernel functions K of ■-problem are introduced to construct a type of general solution of the KK equation.Based on these,several classes of the new exact solutions,with constant asymptotic values at infinity u|_(x^(2)+y^(2)→∞)→0,for the KK equation are constructed via the-dressing method.展开更多
In this paper,the exact boundary controllability of the higher-order KdVtype equation on torus is studied.That is,given the initial and final states in the appropriate space,by adding the appropriate control function ...In this paper,the exact boundary controllability of the higher-order KdVtype equation on torus is studied.That is,given the initial and final states in the appropriate space,by adding the appropriate control function on the boundary,the solution of the system can transition from the initial state to the specified final value.Firstly,we establish the observability inequality for the higher-order KdV-type equation by Ingham inequality.Then,based on the observability inequality,Hilbert uniqueness method and a integral identity we obtain the exact boundary controllability of the higher-order KdV-type equation.展开更多
文摘In this paper,we define for the trace operator,the solution of certain models of vibrating plates standards with initial data in a strategic region spaces of weak regularities.Indeed,we know that the notion of regional controllability is more adapted to systems described by dynamic systems.Regional controllability results in a strategic area were established for vibrating plates by the Hilbertian Uniqueness Method.
基金supported by Fundamental Research Funds for the Central Universities,CHD300102264715National Key Research and Development Program of China under Grant 2021YFA0716902Natural Science Basic Research Program of Shaanxi 2024JCYBMS-199。
文摘Young's modulus and Poisson's ratio are crucial parameters for reservoir characterization and rock brittleness evaluation.Conventional methods often rely on indirect computation or approximations of the Zoeppritz equations to estimate Young's modulus,which can introduce cumulative errors and reduce the accuracy of inversion results.To address these issues,this paper introduces the analytical solution of the Zoeppritz equation into the inversion process.The equation is re-derived and expressed in terms of Young's modulus,Poisson's ratio,and density.Within the Bayesian framework,we construct an objective function for the joint inversion of PP and PS waves.Traditional gradient-based algorithms often suffer from low precision and the computational complexity.In this study,we address limitations of conventional approaches related to low precision and complicated code by using Circle chaotic mapping,Levy flights,and Gaussian mutation to optimize the quantum particle swarm optimization(QPSO),named improved quantum particle swarm optimization(IQPSO).The IQPSO demonstrates superior global optimization capabilities.We test the proposed inversion method with both synthetic and field data.The test results demonstrate the proposed method's feasibility and effectiveness,indicating an improvement in inversion accuracy over traditional methods.
基金supported by the National Key Projects for Research and Development of China(Grant Nos.2021YFA1400400 and 2024YFA1408104)the National Natural Science Foundation of China(Grant Nos.12434005,12374137,and 92165205).
文摘We investigate the origin of the 1/3 magnetization plateau in the S=1/2 kagome antiferromagnetic Heisenberg model using the variational Monte Carlo and exact diagonalization methods,to account for the recent experimental observations in YCu_(3)(OH)_(6+x)Br_(3-x)and YCu_(3)(OD)_(6+x)Br_(3-x).We identify three degenerate valencebond-solid(VBS)states forming a√3×√3 unit cell.These states exhibit David-star patterns in the spin moment distribution with only two fractional values-1/3 and 2/3,and are related through translational transformations.While the spin correlations in these VBS states are found to be short-range,resembling a quantum spin liquid,we show that they have a vanishing topological entanglement entropy and thus are topologically trivial many-body states.Our theoretical results provide strong evidence that the 1/3 magnetization plateau observed in recent experiments arises from these√3×√3 VBS states with fractional spin moments.
基金supported by Scientific Research Projects Department of Istanbul Technical University.Project Number:MGA-2018-41546.Grant receiver:E.T.
文摘Due to their superior properties, the interest in nanostructures is increasing today in engineering. This study presents a new two-noded curved finite element for analyzing the in-plane static behaviors of curved nanobeams. Opposite to traditional curved finite elements developed by using approximate interpolation functions, the proposed curved finite element is developed by using exact analytical solutions. Although this approach was first introduced for analyzing the mechanical behaviors of macro-scale curved beams by adopting the local theory of elasticity, the exact analytical expressions used in this study were obtained from the solutions of governing equations that were expressed via the differential form of the nonlocal theory of elasticity. Therefore, the effects of shear strain and axial extension included in the analytical formulation are also inherited by the curved finite element developed here. The rigidity matrix and the consistent force vector are developed for a circular finite element. To demonstrate the applicability of the method, static analyses of various curved nanobeams subjected to different boundary conditions and loading scenarios are performed, and the obtained results are compared with the exact analytical ones. The presented study provides an accurate and low computational cost method for researchers to investigate the in-plane static behavior of curved nanobeams.
基金supported by the German Research Foundation (SFB-TR 295)(to MM)。
文摘Pathological tremor is one of the cardinal symptoms in Parkinson's disease (PD).Tremor is comprised of involuntary,rhythmic,a nd oscillating movements that can vary according to the circumstances under which they occur,the body parts that are involved,and the frequency at which they present.For example,tremors can be mild to severe,are stress sensitive,and can affect arms,legs,or the head (Dirkx and Bologna,2022).
基金supported by the National Natural Science Foundation of China under Grant No.12375006the Weimu Technology Company Limited of Hangzhou of China under Grant No.KYY-HX-20240495。
文摘The main focus of this paper is to address a generalized(2+1)-dimensional Hirota bilinear equation utilizing the bilinear neural network method.The paper presents the periodic solutions through a single-layer model of[3-4-1],followed by breather,lump and their interaction solutions by using double-layer models of[3-3-2-1]and[3-3-3-1],respectively.A significant innovation introduced in this work is the computation of periodic cross-rational solutions through the design of a novel[3-(2+2)-4-1]model,where a specific hidden layer is partitioned into two segments for subsequent operations.Three-dimensional and density figures of the solutions are given alongside an analysis of the dynamics of these solutions.
文摘This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we obtain conservation vectors that are related and unrelated to symmetric information. In addition, some exact solutions with particular forms are obtained according to the method of conservation laws. These particular solutions are different from the group-invariant solutions.
基金Project supported by the National Natural Science Foundation of China(No.12525202)。
文摘Transcritical and supercritical fluids widely exist in aerospace propulsion systems,such as the coolant flow in the regenerative cooling channels of scramjet engines.To numerically simulate the coolant flow,we must address the challenges in solving Riemann problems(RPs)for real fluids under complex flow conditions.In this study,an exact numerical solution for the one-dimensional RP of two-parameter fluids is developed.Due to the comprehensive resolution of fluid thermodynamics,the proposed solution framework is suitable for all forms of the two-parameter equation of state(EoS).The pressure splitting method is introduced to enable parallel calculation of RPs across multiple grid points.Theoretical analysis demonstrates the isentropic nature of weak waves in two-parameter fluids,ensuring that the same mathematical properties as ideal gas could be applied in Newton's iteration.A series of numerical cases validate the effectiveness of the proposed method.A comparative analysis is conducted on the exact Riemann solutions for the real fluid EoS,the ideal gas EoS,and the improved ideal gas EoS under supercritical and transcritical conditions.The results indicate that the improved one produces smaller errors in the calculation of momentum and energy fluxes.
基金supported by the National Natural Science Foundation of China(Nos.12275115 and 12175097)the National Science Centre of Poland(No.2023/49/B/ST2/01294).
文摘This study explores the phenomenon of shape coexistence in nuclei around^(172)Hg,with a focus on the isotopes^(170)Pt,^(172)Hg,and^(174)Pb,as well as the^(170)Pt to^(180)Pt isotopic chain.Utilizing a macro-microscopic approach that incorporates the Lublin-Strasbourg Drop model combined with a Yukawa-Folded potential and pairing corrections,we analyze the potential energy surfaces(PESs)to understand the impact of pairing interaction.For^(170)Pt,the PES exhibited a prolate ground state,with additional triaxial and oblate-shaped isomers.In^(172)Hg,the ground-state deformation transitions from triaxial to oblate with increasing pairing interaction,demonstrating its nearlyγ-unstable nature.Three shape isomers(prolate,triaxial,and oblate)were observed,with increased pairing strength leading to the disappearance of the triaxial isomer.^(174)Pb exhibited a prolate ground state that became increasingly spherical with stronger pairing.While shape isomers were present at lower pairing strengths,robust shape coexistence was not observed.For realistic pairing interaction,the ground-state shapes transitioned from prolate in^(170)Pt to a coexistence ofγ-unstable and oblate shapes in^(172)Hg,ultimately approaching spherical symmetry in^(174)Pb.A comparison between Exact and Bardeen-Cooper-Schrieffer(BCS)pairing demonstrated that BCS pairing tends to smooth out shape coexistence and reduce the depth of the shape isomer,leading to less pronounced deformation features.The PESs for even-even^(170)-180 Pt isotopes revealed significant shape evolution.^(170)Pt showed a prolate ground state,whereas^(172)Pt exhibited both triaxial and prolate shape coexistence.In^(174)Pt,the ground state was triaxial,coexisted with a prolate minimum.For^(176)Pt,aγ-unstable ground state coexists with a prolate minimum.By 178 Pt and 180Pt,a dominant prolate minimum emerged.These results highlight the role of shape coexistence andγ-instability in the evolution of nuclear structure,especially in the mid-shell region.These findings highlight the importance of pairing interactions in nuclear deformation and shape coexistence,providing insights into the structural evolution of mid-shell nuclei.
基金supported in part by the National Natural Science Foundation of China(grant Nos.11973025,12205139,12303079,12475057,and 12481540180)the Natural Science Foundation of Hunan Province(grant No.2022JJ40347)。
文摘The gravitational deflection of light signals restricted in the polar-axis plane of a moving Kerr–Newman(KN)black hole with a constant velocity along the polar axis is studied within the second post-Minkowskian(PM)approximation.For this purpose,the Lorentz boosting technique is adopted to obtain the exact metric of a moving KN black hole with an arbitrary constant velocity in Kerr–Schild coordinates for the first time.Based on the weak field limit of the exact metric,we then derive the equations of motion of test particles constrained in the polaraxis plane of a moving KN source whose velocity is along the polar axis and collinear with its angular momentum.An iterative technique is utilized subsequently in the calculations of the null deflection angle up to the 2PM order caused by the moving lens,and this deflection angle is found to be spin-independent.Finally,we discuss the influence of the motion of the lens on the gravitational deflection and estimate the possibility of detecting this kinematical effect.Our work might be helpful for future astronomical observations.
基金the sponsorship of the National Natural Science Foundation of China(42474172,42130810)the Science and Technology Innovation Program of Hunan Province(2022RC1238)+1 种基金the Natural Science Foundation of Hunan Province(2025JJ20036,2023JJ30663)the Changzhou Science and Technology Support Project(CE20235069)。
文摘A comprehensive understanding of exact seismic P-wave reflection and transmission(R/T)coefficients at imperfectly welded or non-welded contact interfaces holds paramount importance in the realm of seismic exploration.Nonetheless,scant attention has been devoted in previous literature to the investigation of stress-dependent exact R/T coefficients in horizontal transversely isotropic(HTI)media,characterized by a horizontal symmetry axis,at such interfaces.Addressing this scholarly gap,we present exact R/T coefficient formulations specifically tailored to an imperfectly welded contact interface separating two HTI media under the influence of in-situ horizontal stress.We begin by deriving the equation of motion for a stressed HTI medium,utilizing the theoretical framework of acoustoelasticity to examine the impact of in-situ horizontal stress on the overarching elastic properties of HTI media.Precise boundary conditions are then established at the imperfectly welded contact interface by applying generalized stress-strain relationships and linear-slip theory,with the influence of in-situ horizontal stress on the interface further explored through the linear-slip model.By integrating these elements with the seismic wave displacement equation,we derive exact R/T coefficient formulations applicable to an imperfectly welded contact interface between two HTI media.Numerical analyses are conducted to elucidate the effects of in-situ horizontal stress on critical parameters such as rock density,seismic wave velocity,Thomsen-type anisotropy parameters,R/T coefficients,and seismic reflection responses at the imperfectly welded contact interface.Furthermore,the proposed formulations are frequency-dependent,with the imperfectly welded contact interface acting as a frequency-selective filter for both reflected and transmitted waves.Notably,under conditions of sufficiently large incident angles,the sensitivity of R/T coefficients to key influencing factors increases significantly.The derived R/T coefficient formulations and the accompanying numerical results offer valuable insights for fracture characterization,stress-dependent parameter inversion,and in-situ stress detection.
基金supported by the National Natural Science Foundation of China(Grant Nos.12371256,11971475).
文摘The(2+1)-dimensional integrable generalization of the Kaup-Kuper-shmidt(KK)equation is solved by the inverse spectral transform method in this paper.Several new long derivative operators V_(x),V_(y) and V_(t) and the kernel functions K of ■-problem are introduced to construct a type of general solution of the KK equation.Based on these,several classes of the new exact solutions,with constant asymptotic values at infinity u|_(x^(2)+y^(2)→∞)→0,for the KK equation are constructed via the-dressing method.
文摘In this paper,the exact boundary controllability of the higher-order KdVtype equation on torus is studied.That is,given the initial and final states in the appropriate space,by adding the appropriate control function on the boundary,the solution of the system can transition from the initial state to the specified final value.Firstly,we establish the observability inequality for the higher-order KdV-type equation by Ingham inequality.Then,based on the observability inequality,Hilbert uniqueness method and a integral identity we obtain the exact boundary controllability of the higher-order KdV-type equation.
