Enhancing the Goos-Hänchen shift based on quasi-bound states in the continuum through material asymmetric dielectric compound gratings

Quasi-bound state in the continuum(QBIC)resonance is gradually attracting attention and being applied in Goos-Hänchen(GH)shift enhancement due to its high quality(Q)factor and superior optical confinement.Currently,symmetry-protected QBIC resonance is often achieved by breaking the geometric symmetry,but few cases are achieved by breaking the material symmetry.This paper proposes a dielectric compound grating to achieve a high Q factor and high-reflection symmetry-protectede QBIC resonance based on material asymmetry.Theoretical calculations show that the symmetry-protected QBIC resonance achieved by material asymmetry can significantly increase the GH shift up to-980 times the resonance wavelength,and the maximum GH shift is located at the reflection peak with unity reflectance.This paper provides a theoretical basis for designing and fabricating high-performance GH shift tunable metasurfaces/dielectric gratings in the future.

Nonlinear wave dispersion in monoatomic chains with lumped and distributed masses:discrete and continuum models

The main objective of this paper is to investigate the influence of inertia of nonlinear springs on the dispersion behavior of discrete monoatomic chains with lumped and distributed masses.The developed model can represent the wave propagation problem in a non-homogeneous material consisting of heavy inclusions embedded in a matrix.The inclusions are idealized by lumped masses,and the matrix between adjacent inclusions is modeled by a nonlinear spring with distributed masses.Additionally,the model is capable of depicting the wave propagation in bi-material bars,wherein the first material is represented by a rigid particle and the second one is represented by a nonlinear spring with distributed masses.The discrete model of the nonlinear monoatomic chain with lumped and distributed masses is first considered,and a closed-form expression of the dispersion relation is obtained by the second-order Lindstedt-Poincare method(LPM).Next,a continuum model for the nonlinear monoatomic chain is derived directly from its discrete lattice model by a suitable continualization technique.The subsequent use of the second-order method of multiple scales(MMS)facilitates the derivation of the corresponding nonlinear dispersion relation in a closed form.The novelties of the present study consist of(i)considering the inertia of nonlinear springs on the dispersion behavior of the discrete mass-spring chains;(ii)developing the second-order LPM for the wave propagation in the discrete chains;and(iii)deriving a continuum model for the nonlinear monoatomic chains with lumped and distributed masses.Finally,a parametric study is conducted to examine the effects of the design parameters and the distributed spring mass on the nonlinear dispersion relations and phase velocities obtained from both the discrete and continuum models.These parameters include the ratio of the spring mass to the lumped mass,the nonlinear stiffness coefficient of the spring,and the wave amplitude.

Static-to-kinematic modeling and experimental validation of tendon-driven quasi continuum manipulators with nonconstant subsegment stiffness

Continuum robots with high flexibility and compliance have the capability to operate in confined and cluttered environments. To enhance the load capacity while maintaining robot dexterity, we propose a novel non-constant subsegment stiffness structure for tendon-driven quasi continuum robots(TDQCRs) comprising rigid-flexible coupling subsegments.Aiming at real-time control applications, we present a novel static-to-kinematic modeling approach to gain a comprehensive understanding of the TDQCR model. The analytical subsegment-based kinematics for the multisection manipulator is derived based on screw theory and product of exponentials formula, and the static model considering gravity loading,actuation loading, and robot constitutive laws is established. Additionally, the effect of tension attenuation caused by routing channel friction is considered in the robot statics, resulting in improved model accuracy. The root-mean-square error between the outputs of the static model and the experimental system is less than 1.63% of the arm length(0.5 m). By employing the proposed static model, a mapping of bending angles between the configuration space and the subsegment space is established. Furthermore, motion control experiments are conducted on our TDQCR system, and the results demonstrate the effectiveness of the static-to-kinematic model.

Variation of soil-plant-atmosphere continuum stable isotope and water source in Qinghai spruce forest of the eastern Qilian Mountains

Understanding the hydrogen and oxygen stable isotope composition and characteristics of different water bodies in soil-plant-atmosphere continuum is of significance for revealing regional hydrological processes and water cycle mechanisms.In this study,we analyzed the stable isotopic composition,relationship and indicative significance of precipitation,soil water(0~100 cm depth)and xylem water of Qinghai spruce(Picea crassifolia)forest in the eastern Qilian Mountains,and explored the circulation process among different water bodies.The results show that the stable isotopes of precipitation vary greatly during the entire observation period.The values ofδ2H andδ^(18)O in the precipitation in the warm season are richer than those in the cold season,and the slope and intercept of local meteoric water line(LMWL,δ2H=6.79δ18O+7.13)are both smaller than global meteoric water line(GMWL,δ2H=8.17δ18O+10.56).The stable isotopes of soil water at different depths underwent different degrees of evaporative fractionation,and theδ18O andδ2H of shallow soil water varied greatly,while the deep soil water tended to be similar.The topsoil(0~10 cm)can respond quickly to precipitation,and the response of the deep soil has a time lag.In the whole growing season,0~30 cm and 60~100 cm soil water are the main water sources of Qinghai spruce.The water source of Qinghai spruce was from all soil layers in May and September,mainly from the shallow soil layer(0~30 cm)in August and October,and mainly from the deep soil layer(60~100 cm)in June and July.

General Kinetostatic Modeling and Deformation Analysis of a Two-Module Rod-Driven Continuum Robot with Friction Considered

Continuum robots actuated by flexible rods have large potential applications,such as detection and operation tasks in confined environments,since the push and pull actuation of flexible rods withstand tension and compressive force,and increase the structure's rigidity.In this paper,a generalized kinetostatics model for multi-module and multi-segment continuum robots considering the effect of friction based on the Cosserat rod theory is established.Then,the model is applied to a two-module rod-driven continuum robot with winding ropes to analyze its deformation and load characteristics.Four different in-plane configurations under the external load term as S1,S2,C1,and C2 are defined.Taking a bending plane as an example,the tip deformation along thex-axis of these shapes is simulated and compared,which shows that the load capacity of C1 and C2 is generally larger than that of S1 and S2.Furthermore,the deformation experiments and simulations show that the maximum error ratio without external loads relative to the total length is no more than 3%,and it is no more than 4.7%under the external load.The established kinetostatics model is proven sufficient to accurately analyze the rod-driven continuum robot with the consideration of internal friction.

Hybrid bound states in the continuum in terahertz metasurfaces

Bound states in the continuum(BICs)have exhibited extraordinary properties in photonics for enhanced light-matter interactions that enable appealing applications in nonlinear optics,biosensors,and ultrafast optical switches.The most common strategy to apply BICs in a metasurface is by breaking symmetry of resonators in the uniform array that leaks the otherwise uncoupled mode to free space and exhibits an inverse quadratic relationship between quality factor(Q)and asymmetry.Here,we propose a scheme to further reduce scattering losses and improve the robustness of symmetry-protected BICs by decreasing the radiation density with a hybrid BIC lattice.We observe a significant increase of radiative Q in the hybrid lattice compared to the uniform lattice with a factor larger than 14.6.In the hybrid BIC lattice,modes are transferred toГpoint inherited from high symmetric X,Y,and M points in the Brillouin zone that reveal as multiple Fano resonances in the far field and would find applications in hyperspectral sensing.This work initiates a novel and generalized path toward reducing scattering losses and improving the robustness of BICs in terms of lattice engineering that would release the rigid requirements of fabrication accuracy and benefit applications of photonics and optoelectronic devices.

Variable Curvature Modeling Method of Soft Continuum Robots with Constraints

The inherent compliance of continuum robots holds great promise in the fields of soft manipulation and safe human–robot interaction.This compliance reduces the risk of damage to the manipulated object and its surroundings.However,continuum robots possess theoretically infinite degrees of freedom,and this high flexibility usually leads to complex deformations when subjected to external forces and positional constraints.Describing these complex deformations is the main challenge in modeling continuum robots.In this study,we investigated a novel variable curvature modeling method for continuum robots,considering external forces and positional constraints.The robot configuration curve is described using the developed mechanical model,and then the robot is fitted to the curve.A ten-section continuum robot prototype with a length of 1 m was developed in order to validate the model.The feasibility and accuracy of the model were verified by the ability of the robot to reach target points and track complex trajectories with a load.This work was able to serve as a new perspective for the design analysis and motion control of continuum robots.

Alfvén continuum in the presence of a magnetic island in a cylinder configuration

In this work,the effect of a magnetic island on Alfvén waves is studied.A physical model is established wherein Alfvén waves propagate in the presence of a magnetic island in a cylindrical geometry.The structure of the Alfvén wave continuum is calculated by considering only the coupling caused by the periodicity in the helical angle of the magnetic island.The results show that the magnetic island can induce an upshift in the Alfvén continuum.Moreover,the coupling between different branches of the continuous spectrum becomes more significant with increasing continuum mode numbers near the boundary of the magnetic island.

Strain localization of Mohr-Coulomb soils with non-associated plasticity based on micropolar continuum theory

To address the problems of strain localization, the exact Mohr-Coulomb (MC) model is used based on second-order cone programming (mpcFEM-SOCP) in the framework of micropolar continuum finite element method. Using the uniaxial compression test, we focused on the earth pressure problem of rigid wall segment involving non-associated plasticity. The numerical results reveal that when mpcFEM-SOCP is applied, the problems of mesh dependency can be effectively addressed. For geotechnical strain localization analysis involving non-associated MC plasticity, mpcFEM-SOCP in conjunction with the pseudo-time discrete scheme can improve the numerical stability and avoid the unreasonable softening issue in the pressure-displacement curves, which may be encountered in the conventional FEM. It also shows that the pressure-displacement responses calculated by mpcFEM-SOCP with the pseudo-time discrete scheme are higher than those calculated by mpcFEM-SOCP with the Davis scheme. The inclination angle of shear band predicted by mpcFEM-SOCP with the pseudo-time discrete scheme agrees well with the theoretical solution of non-associated MC plasticity.

Fundamentals and applications of photonic waveguides with bound states in the continuum

Photonic waveguides are the most fundamental element for photonic integrated circuits(PICs).Waveguide properties,such as propagation loss,modal areas,nonlinear coefficients,etc.,directly determine the functionalities and performance of PICs.Recently,the emerging waveguides with bound states in the continuum(BICs)have opened new opportunities for PICs because of their special properties in resonance and radiation.Here,we review the recent progress of PICs composed of waveguides with BICs.First,fundamentals including background physics and design rules of a BIC-based waveguide will be introduced.Next,two types of BIC-based waveguide structures,including shallowly etched dielectric and hybrid waveguides,will be presented.Lastly,the challenges and opportunities of PICs with BICs will be discussed.

The Historical Logic on the Basic Theory of Physics—A Summary on the Cosmic Continuum Theory

Any scientific system has a unified basic theory. But physics has no unified basic theory in the modern sense. Classical mechanics, relativity and quantum mechanics have their own basic concepts, categories and principles, so none of them can be regarded as true basic theories of physics. Cosmic Continuum Theory holds that the continuity and discreteness of the universe are fundamental issues related to the unification of physics. Because the contradiction between quantum non-locality and local reality is the fundamental obstacle to the unification of physics, while locality and non-locality correspond to the continuity and discreteness of physical reality respectively. The cosmic continuum theory introduces mathematical continuum and axiomatic ideas to reconstruct the basic theory of physics, and by the correspondence of existence and its dimensions to achieve the unification of the essence of physical reality, by introducing the cosmic continuum hypothesis to achieve the unification of the continuity and discreteness of physical reality, by introducing axiomatic methods to achieve formal unification of the foundations on physics. From the perspective of Cosmic Continuum, classical mechanics, relativity and quantum mechanics are no longer the basic theories of physics, but three branch theories of physics that are respectively applicable to macroscopic, cosmoscopic and microcosmic systems.

The Primes and Their Subsets as Continuum like the Integers

The present paper gives the proof of the set of primes as a continuum. It starts with the density of the primes, and shortly recapitulates the prime-number-formula and the complete-prime-number-formula. Reflecting the series of the primes over any prime gives the double density of occupation of integer positions by the union of the series of multiples of the primes. The remaining free positions render it possible to prove Goldbach’s conjecture and the set of primes as a continuum. The theoretical evaluation is followed in annexes by numerical evaluation, demonstrating the theoretical results. The numerical evaluation results in different constants and relations, which represent inherent properties of the set of primes.

用Cluster-Continuum模型计算水溶液中VO_2^+/VO^(2+)电对溶剂化自由能

利用Cluster-Continuum模型,通过B3LYP方法计算出VO2+/VO2+电对的第一溶剂化层的水分子数分别为3和5个,并得到了水溶液中VO2+、VO2+离子的溶剂化自由能。利用此计算数值并通过热力学计算推算出VO2+/VO2+电对的标准反应电势为1.29V,与理论值相差不大。这表明利用Cluster-Continuum模型可以较为准确地描述VO2+、VO2+离子的溶剂化作用。

Thermodynamic Consistency of Plate and Shell Mathematical Models in the Context of Classical and Non-Classical Continuum Mechanics and a Thermodynamically Consistent New Thermoelastic Formulation

Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler’s equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic assumptions can be derived using the conservation and balance laws of classical or non-classical continuum mechanics. The mathematical models based on Kirchhoff hypothesis (classical plate theory, CPT) and first order shear deformation theory (FSDT) that are representative of most mathematical models for plates/shells are investigated in this paper for their thermodynamic consistency. This is followed by the details of a general and higher order thermodynamically consistent plate/shell thermoelastic mathematical model that is free of a priori consideration of kinematic assumptions and remains valid for very thin as well as thick plates/shells with comprehensive nonlinear constitutive theories based on integrity. Model problem studies are presented for small deformation behavior of linear elastic plates in the absence of thermal effects and the results are compared with CPT and FSDT mathematical models.

Motivation in Foreign Language Learning: Applying the Time Continuum Model of Motivation in FLL

The research is: by using Wdolkowski's Time Continuum Model throughout a lesson plan enables the teacher to increase students'motivation and help them move closer to success in a learning environment. This research supports the theory that instruction is a network of interactions between the teacher and learner that promotes a successful learning experience. It identifies a three-part learning sequence-a beginning, middle and an end. Each part has two of six key motivational factors that when applied correctly by the teacher will maximize the success and continued motivation of the learner.

ATOMISTIC/CONTINUUM SIMULATION OF INTERFACIAL FRACTURE PART Ⅱ:ATOMISTIC/DISLOCATION/CONTINUUM SIMULATION

Coupled atomistic/dislocation/continuum simulation of interfacialfracture is performed in this paper.The model consists of a nanoscopic core made byatomistic assembly and a surrounding elastic continuum with discrete dislocations.Atomistic dislocations nucleate from the crack tip and move to the continuum layerwhere they glide according to the dislocation dynamics curve.An atoms/continuumoverlapping belt is devised to facilitate the transition between the two scales.Thecontinuum constraint on the atomic assembly is imposed through the mechanics at-mosphere along the overlapping belt.Transmissions of mechanics parameters suchas displacements,stresses,masses and momenta across the belt are realized.Thepresent model allows us to explore interfacial fracture processes under different modemixity.The effect of atomistic zigzag interface on the fracture process is revealed:ithinders dislocation emission from the crack tip,especially under high mode mixity.

Verification of a laboratory-based dilation model for in situ conditions using continuum models

With respect to constitutive models for continuum modeling applications, the post-yield domain remains the area of greatest uncertainty. Recent studies based on laboratory testing have led to the development of a number of models for brittle rock dilation, which account for both the plastic shear strain and confining stress dependencies of this phenomenon. Although these models are useful in providing an improved understanding of how dilatancy evolves during a compression test, there has been relatively little work performed examining their validity for modeling brittle rock yield in situ. In this study, different constitutive models for rock dilation are reviewed and then tested, in the context of a number of case studies, using a continuum finite-difference approach(FLAC). The uncertainty associated with the modeling of brittle fracture localization is addressed, and the overall ability of mobilized dilation models to replicate in situ deformation measurements and yield patterns is evaluated.

Seepage simulation of high concrete-faced rockfill dams based on generalized equivalent continuum model

This research focused on the three-dimensional(3 D) seepage field simulation of a high concrete-faced rockfill dam(CFRD) under complex hydraulic conditions. A generalized equivalent continuum model of fractured rock mass was used for equivalent continuous seepage field analysis based on the improved node virtual flow method. Using a high CFRD as an example, the generalized equivalent continuum range was determined, and a finite element model was established based on the terrain and geological conditions, as well as structural face characteristics of the dam area. The equivalent seepage coefficients of different material zones or positions in the dam foundation were calculated with the Snow model or inverse analysis. Then, the 3 D seepage field in the dam area was calculated under the normal water storage conditions, and the corresponding water head distribution, seepage flow, seepage gradient, and seepage characteristics in the dam area were analyzed. The results show that the generalized equivalent continuum model can effectively simulate overall seepage patterns of the CFRD under complex hydraulic conditions and provide a reference for seepage analysis of similar CFRDs.

ON THE CONTINUUM MODELING OF CARBON NANOTUBES

We have recently proposed a nanoscale continuum theory for carbonnanotubes.The theory links continuum analysis with atomistic modeling by incor-porating interatomic potentials and atomic structures of carbon nanotubes directlyinto the constitutive law.Here we address two main issues involved in setting upthe nanoscale continuum theory for carbon nanotubes,namely the multi-body in-teratomic potentials and the lack of centrosymmetry in the nanotube structure.Weexplain the key ideas behind these issues in establishing a nanoscale continuum theoryin terms of interatomic potentials and atomic structures.

Path Planning of Continuum Robot Based on a New Improved Particle Swarm Optimization Algorithm

Continuum robot is a new type of biomimetic robot,which realizes the motion by bending some parts of its body.So its path planning becomes more difficult even compared with hyper-redundant robots.In this paper a circular arc spline interpolating method is proposed for the robot shape description,and a new two-stage position-selectable-updating particle swarm optimization(TPPSO)algorithm is put forward to solve this path planning problem.The algorithm decomposes the standard PSO velocity’s single-step updating formula into twostage multi-point updating,specifically adopting three points as candidates and selecting the best one as the updated position in the first half stage,and similarly taking seven points as candidates and selecting the best one as the final position in the last half stage.This scheme refines and widens each particle’s searching trajectory,increases the updating speed of the individual best,and improves the converging speed and precision.Aiming at the optimization objective to minimize the sum of all the motion displacements of every segmental points and all the axial stretching or contracting displacements of every segment,the TPPSO algorithm is used to solve the path planning problem.The detailed solution procedure is presented.Numerical examples of five path planning cases show that the proposed algorithm is simple,robust,and efficient.