This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is fir...This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using the integral equation method. We then proceed to establish two tools that play important roles for the inverse problem： one is a mixed reciprocity relation and the other is a priori estimates of the solution on some part of the interfaces between the layered media. For the inverse problem, we prove in this paper that both the penetrable interfaces and the possible inside inhomogeneity can be uniquely determined from a knowledge of the far field pattern for incident plane waves.展开更多
In the present study,the dynamic response of block foundations of different equivalent radius to mass（R;/m） ratios under coupled vibrations is investigated for various homogeneous and layered systems.The frequency-d...In the present study,the dynamic response of block foundations of different equivalent radius to mass（R;/m） ratios under coupled vibrations is investigated for various homogeneous and layered systems.The frequency-dependent stiffness and damping of foundation resting on homogeneous soils and rocks are determined using the half-space theory.The dynamic response characteristics of foundation resting on the layered system considering rock-rock combination are evaluated using finite element program with transmitting boundaries.Frequencies versus amplitude responses of block foundation are obtained for both translational and rotational motion.A new methodology is proposed for determination of dynamic response of block foundations resting on soil-rock and weathered rock-rock system in the form of equations and graphs.The variations of dimensionless natural frequency and dimensionless resonant amplitude with shear wave velocity ratio are investigated for different thicknesses of top soil/weathered rock layer.The dynamic behaviors of block foundations are also analyzed for different rock-rock systems by considering sandstone,shale and limestone underlain by basalt.The variations of stiffness,damping and amplitudes of block foundations with frequency are shown in this study for various rock—rock combinations.In the analysis,two resonant peaks are observed at two different frequencies for both translational and rotational motion.It is observed that the dimensionless resonant amplitudes decrease and natural frequencies increase with increase in shear wave velocity ratio.Finally,the parametric study is performed for block foundations with dimensions of 4 m × 3 m × 2 m and 8m×5m×2m by using generalized graphs.The variations of natural frequency and peak displacement amplitude are also studied for different top layer thicknesses and eccentric moments.展开更多
Based on composite materials, the equivalent elastic-plastic constitutive equations of multiphase solid are researched. According to the suggested definition of. constitutive equivalence it is demonstrated that the mu...Based on composite materials, the equivalent elastic-plastic constitutive equations of multiphase solid are researched. According to the suggested definition of. constitutive equivalence it is demonstrated that the multiphase solid, composed of several kinds of homogeneous elastic-plastic media that conform to the generalized normality rule, has the same type of constitutive equations as its constituents have that also conform to the generalized normality rule.展开更多
The results of measurements of the Hubble constant H<sub>0</sub>, which characterizes the expansion rate of the universe, show that the values of H<sub>0</sub> vary significantly depending on M...The results of measurements of the Hubble constant H<sub>0</sub>, which characterizes the expansion rate of the universe, show that the values of H<sub>0</sub> vary significantly depending on Methodology. The disagreement in the values of H<sub>0</sub> obtained by the various teams far exceeds the standard uncertainties provided with the values. This discrepancy is called the Hubble Tension. In this paper, we discuss Macrostructures of the World (Superclusters and Galaxies);explain their Origin and Evolution in frames of the developed Hypersphere World-Universe Model (WUM), which is an alternative to the prevailing Big Bang Model (BBM) [1];and provide the explanation of the Hubble Tension. The main difference between WUM and BBM is: Instead of the Infinite Homogeneous and Isotropic Universe around the Initial Singularity in BBM, in WUM, the 3D Finite Boundless World (a Hypersphere) presents a Patchwork Quilt of different Luminous Superclusters (10<sup>3</sup>), which emerged in various places of the World at different Cosmological times. In WUM, the Medium of the World is Homogeneous and Isotropic. The distribution of Macroobjects in the World is spatially Inhomogeneous and Anisotropic and temporally Non-simultaneous.展开更多
Higher-order topological insulators(HOTIs)can support boundary states at least two dimensions lower than the bulk,attracting intensive attention from both fundamental science and application sides.Lattice-based tight-...Higher-order topological insulators(HOTIs)can support boundary states at least two dimensions lower than the bulk,attracting intensive attention from both fundamental science and application sides.Lattice-based tight-binding models such as Benalcazar-Bernevig-Hughes model have driven significant advancements in realizing HOTIs across various physical systems.Here,beyond lattice model,we demonstrate that a cylinder with an arbitrary cross section,composed of a homogeneous electromagnetic medium featuring nontrivial second Chern numbers c_(2)=±1 in a synthetic five-dimensional space,can exhibit topologically protected HOTI-type hinge states in three-dimensional laboratory space.Interestingly,this hinge state is essentially a chiral zero mode arising from the interaction between Weyl arc surface states,guaranteed by a nontrivial c_(2),and an effective magnetic field induced by the curvature of the cylinder surface.Compared to conventional schemes to generate HOTIs,our approach is more robust,as it is an intrinsic topological phase and therefore does not rely on additional symmetry protections such as time-reversal,parity,or chiral symmetry.We experimentally realize such a cylinder using a photonic metamaterial and confirm the existence of hinge states via microwave near-field measurements.Our work introduces the concept of boundary gauge fields and establishes the link between synthetic-space c_(2) and real-space HOTI states,thereby generalizing HOTIs to cornerless systems.展开更多
基金the first author (XL) was supported by the China Postdoctoral Science Foundation (20100480494)the NSF of China (11101412)+1 种基金K.C. Wong Education Foundation, Hong Kongthe second author (BZ) was supported by the NSF of China (11071244,11161130002)
文摘This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using the integral equation method. We then proceed to establish two tools that play important roles for the inverse problem： one is a mixed reciprocity relation and the other is a priori estimates of the solution on some part of the interfaces between the layered media. For the inverse problem, we prove in this paper that both the penetrable interfaces and the possible inside inhomogeneity can be uniquely determined from a knowledge of the far field pattern for incident plane waves.
文摘In the present study,the dynamic response of block foundations of different equivalent radius to mass（R;/m） ratios under coupled vibrations is investigated for various homogeneous and layered systems.The frequency-dependent stiffness and damping of foundation resting on homogeneous soils and rocks are determined using the half-space theory.The dynamic response characteristics of foundation resting on the layered system considering rock-rock combination are evaluated using finite element program with transmitting boundaries.Frequencies versus amplitude responses of block foundation are obtained for both translational and rotational motion.A new methodology is proposed for determination of dynamic response of block foundations resting on soil-rock and weathered rock-rock system in the form of equations and graphs.The variations of dimensionless natural frequency and dimensionless resonant amplitude with shear wave velocity ratio are investigated for different thicknesses of top soil/weathered rock layer.The dynamic behaviors of block foundations are also analyzed for different rock-rock systems by considering sandstone,shale and limestone underlain by basalt.The variations of stiffness,damping and amplitudes of block foundations with frequency are shown in this study for various rock—rock combinations.In the analysis,two resonant peaks are observed at two different frequencies for both translational and rotational motion.It is observed that the dimensionless resonant amplitudes decrease and natural frequencies increase with increase in shear wave velocity ratio.Finally,the parametric study is performed for block foundations with dimensions of 4 m × 3 m × 2 m and 8m×5m×2m by using generalized graphs.The variations of natural frequency and peak displacement amplitude are also studied for different top layer thicknesses and eccentric moments.
文摘Based on composite materials, the equivalent elastic-plastic constitutive equations of multiphase solid are researched. According to the suggested definition of. constitutive equivalence it is demonstrated that the multiphase solid, composed of several kinds of homogeneous elastic-plastic media that conform to the generalized normality rule, has the same type of constitutive equations as its constituents have that also conform to the generalized normality rule.
文摘The results of measurements of the Hubble constant H<sub>0</sub>, which characterizes the expansion rate of the universe, show that the values of H<sub>0</sub> vary significantly depending on Methodology. The disagreement in the values of H<sub>0</sub> obtained by the various teams far exceeds the standard uncertainties provided with the values. This discrepancy is called the Hubble Tension. In this paper, we discuss Macrostructures of the World (Superclusters and Galaxies);explain their Origin and Evolution in frames of the developed Hypersphere World-Universe Model (WUM), which is an alternative to the prevailing Big Bang Model (BBM) [1];and provide the explanation of the Hubble Tension. The main difference between WUM and BBM is: Instead of the Infinite Homogeneous and Isotropic Universe around the Initial Singularity in BBM, in WUM, the 3D Finite Boundless World (a Hypersphere) presents a Patchwork Quilt of different Luminous Superclusters (10<sup>3</sup>), which emerged in various places of the World at different Cosmological times. In WUM, the Medium of the World is Homogeneous and Isotropic. The distribution of Macroobjects in the World is spatially Inhomogeneous and Anisotropic and temporally Non-simultaneous.
基金supported by National Key Research and Development Program of China(Grants No.2023YFA1407700,2023YFA1406901)National Natural Science Foundation China(Grants No.12374343)+2 种基金the start-up funding of Fudan University(JIH1232133Y)the New Cornerstone Science Foundation,the Research Grants Council of Hong Kong(AoE/P-502/20,STG3/E-704/23-N,17309021)Guangdong Provincial Quantum Science Strategic Initiative(GDZX2204004,GDZX2304001).
文摘Higher-order topological insulators(HOTIs)can support boundary states at least two dimensions lower than the bulk,attracting intensive attention from both fundamental science and application sides.Lattice-based tight-binding models such as Benalcazar-Bernevig-Hughes model have driven significant advancements in realizing HOTIs across various physical systems.Here,beyond lattice model,we demonstrate that a cylinder with an arbitrary cross section,composed of a homogeneous electromagnetic medium featuring nontrivial second Chern numbers c_(2)=±1 in a synthetic five-dimensional space,can exhibit topologically protected HOTI-type hinge states in three-dimensional laboratory space.Interestingly,this hinge state is essentially a chiral zero mode arising from the interaction between Weyl arc surface states,guaranteed by a nontrivial c_(2),and an effective magnetic field induced by the curvature of the cylinder surface.Compared to conventional schemes to generate HOTIs,our approach is more robust,as it is an intrinsic topological phase and therefore does not rely on additional symmetry protections such as time-reversal,parity,or chiral symmetry.We experimentally realize such a cylinder using a photonic metamaterial and confirm the existence of hinge states via microwave near-field measurements.Our work introduces the concept of boundary gauge fields and establishes the link between synthetic-space c_(2) and real-space HOTI states,thereby generalizing HOTIs to cornerless systems.
