A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions

In this paper,we develop the residual based a posteriori error estimates and the corresponding adaptive mesh refinement algorithm for atomistic/continuum(a/c)coupling with finite range interactions in two dimensions.We have systematically derived a new explicitly computable stress tensor formula for finite range in-teractions.In particular,we use the geometric reconstruction based consistent atomistic/continuum(GRAC)coupling scheme,which is quasi-optimal if the continuum model is discretized by P1 finite elements.The numerical results of the adaptive mesh refinement algorithm is consistent with the quasi-optimal a priori error estimates.

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

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

Continuum and Discrete Element Coupling Approach to Analyzing Seismic Responses of a Slope Covered by Deposits

Numerical analyses of earthquake effects on the deformation,stability,and load transfer of a slope covered by deposits are traditionally based on the assumption that the slope is a continuum.It would be problematic,however,to extend these approaches to the simulation of the slide,collapse and disintegration of the deposits under seismic loading.Contrary to this,a discrete element method(DEM) provides a means to consider large displacement and rotation of the non-continuum.To take the advantages of both methods of continuum and noncontinuum analyses,seismic responses of a slope covered by deposits are studied by coupling a twodimensional(2-D) finite difference method and a 2-D DEM,with the bedrock being modelled by the finite difference grids and the deposits being represented by disks.A smooth transition across the boundaries of the continuous/discontinuous domains is obtained by imposing the compatibility condition and equilibrium condition along their interfaces.In the course of computation,the same time-step value is chosen for both continuous and discontinuous domains.The free-field boundaries are adopted for lateral grids of bedrock domain to eliminate the radiation damping effect.When the static equilibrium under gravity load is obtained,dynamic calculation begins under excitation of the seismic wave input from the continuum model bottom.In this way,responses to the earthquake of a slope covered by deposits are analyzed dynamically.Combined with field monitoring data,deformation and stability of the slope are discussed.The effects of the relevant parameters of spectrum characteristic,duration,and peak acceleration of seismic waves are further investigated and explained from the simulations.

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CON-TINUUM THEORIES (Ⅱ)—MICROMORPHIC CONTINUUM THEORY AND COUPLE STRESS THEORY

The purpose is to reestablish the balance laws of momentum, angular momentum and energy and to derive the corresponding local and nonlocal balance equations for micromorphic continuum mechanics and couple stress theory. The desired results for micromorphic continuum mechanics and couple stress theory are naturally obtained via direct transitions and reductions from the coupled conservation law of energy for micropolar continuum theory, respectively. The basic balance laws and equations for micromorphic continuum mechanics and couple stress theory are constituted by combining these results derived here and the traditional conservation laws and equations of mass and microinertia and the entropy inequality. The incomplete degrees of the former related continuum theories are clarified. Finally, some special cases are conveniently derived.

Coupling reaction mechanism of 2-(2-bromo-4-fluorophenyl)-1-cyclohexen-1-yl trifluoromethane-sulfonate

The detailed mechanism of CuI-catalyzed C-O intramolecular coupling reaction of 2-(2-bromo-4-fluoro-phenyl)-1-cyclohexen-1-yl trifluoromethane–sulfonate was studied with the density functional theory(DFT). The geometries of the reactants,transition states, intermediates and products were optimized at the B3LYP/6-31+G* level. Meanwhile, the single point energy of species involved in gas and solvent at B3LYP/6-311+G* level was individually investigated. Polarizable continuum models(PCM)were applied to the dioxane and water solutions at the same level, respectively. Results show that the rate-limiting step, M3→TS3,does not change in different solutions. However, the activation energy in a dioxane solution is lower than that in water, which explains the previous experimental results. Compared with the non-catalyzed reaction process, the activation energy of the ratelimiting step is reduced by 56.53 kJ mol-1 in gas and 44.84 kJ mol 1in solvent, demonstrating a high catalytic efficiency of CuI.

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.

节理化炭质页岩地层隧道围岩大变形及控制技术研究

某高速铁路XHS隧道穿越节理化炭质页岩地层,在施工过程中围岩大变形、失稳坍塌现象显著,现场采用强支护和仰拱加深等措施后围岩变形控制效果不佳。针对XHS隧道节理化炭质页岩地层地质条件,结合现场监测手段、离散-连续耦合数值模拟分析围岩大变形及破坏特征,基于数值模拟提出以采取地层预加固为主的围岩变形控制措施,并通过现场试验探讨该控制措施的应用效果。研究结果表明:隧道开挖后,围岩变形具有变形量大、变形速率快的特点,围岩拱部沉降量大于水平收敛量且变形具有非对称的分布特征;受三台阶法多次开挖扰动影响,围岩卸荷范围动态发育并不断向全环扩展,松动区逐渐由浅部围岩向深部转移,并呈现出非对称的破坏特征,最终引发围岩大变形;采取地层预加固后,模型中围岩变形和松动区范围明显减小,围岩非对称变形破坏也得到了有效控制;在采用地层预加固、管棚超前支护、三台阶临时仰拱法开挖的控制措施后,围岩变形得到控制,施工效果良好,隧道恢复正常施工,保证了隧道的顺利贯通;以地层预加固为主的控制措施是此类节理化炭质页岩地层围岩变形控制的有效手段。

双层空竹超表面中基于BIC的局域太赫兹磁场增强的研究

设计了包含双层空竹的超表面,通过调节其晶格周期实现了不同阶晶格模式与超表面本征模式间的耦合,获得了3个强耦合区,并在两个晶格周期处实现了弗里德里希–温特根型连续域束缚态(Friedrich-Wintgen bound states in the continuum,FW-BIC)。基于耦合模理论对其进行分析,理论分析结果与模拟结果吻合,进一步证明了结构的有效性。讨论了在介质间隔层中基于强耦合和FW-BIC的局域磁场增强,发现最大磁场强度是入射太赫兹波磁场强度的41 209倍,且该值是单纯的由超表面电磁共振产生的磁场强度的4倍。这项研究将为强场太赫兹产生和太赫兹非线性研究提供参考。

Elastic scattering and total reaction cross sections of^(6)Li examined via a microscopic continuum discretized coupled-channels model

We present a systematic study of 6Li elastic scattering and total reaction cross sections at incident energies around the Coulomb barrier within the continuum discretized coupled-channels(CDCC)framework,where 6Li is treated in anα+d two-body model.Collisions with 27Al,64Zn,138Ba,and 208Pa are analyzed.The microscopic optical potentials(MOP)based on Skyrme nucleon-nucleon interaction forαand d are adopted in CDCC calculations and satisfactory agreement with the experimental data is obtained without any adjustment on MOPs.For comparison,αand d global phenomenological optical potentials(GOP)are also used in CDCC analysis and a reduction of no less than 50%on the surface imaginary part of deuteron GOP is required for describing the data.In all cases,the 6Li breakup effect is significant and provides repulsive correction to the folding model potential.The reduction on the surface imaginary part of GOP of deuteron reveals a strong suppression of the reaction probability of deuteron as a component of 6Li when compared with that of a free deuteron.Further investigation is performed by considering the d breakup process equivalently within the dynamic polarization potential approach,and the results show that d behaves in a manner similar to a tightly bound nucleus in 6Li induced reactions.

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅰ) —MICROPOLAR CONTINUA

Based on the restudies of existing polar continuum theories rather complete systems of basic balance laws and equations for micropolar continuum theory are presented. In these new systems not only the additional angular momentum, surface moment and body moment produced by the linear momentum, surface force and body force, respectively, but also the additional velocity produced by the angular velocity are considered. The new coupled balance laws of linear momentum, angular momentum and energy are reestablished. From them the new coupled local and nonlocal balance equations are naturally derived. Via contrast it can be clearly seen that the new results are believed to be rather general and complete.

基于力传递模型的连续体机器人驱动误差补偿研究

针对绳索传动系统中的非线性摩擦、驱动线伸长及关节间耦合效应导致的连续体机器人控制精度较低的问题,提出了一种考虑非线性摩擦的连续体机器人误差补偿方法。基于虚功原理构建包含关节间耦合作用的连续体机器人静力学模型,分析不同预紧力、不同包角等参数对绳-轮传动系统力传递效率的影响规律,并基于改进的Capstan方程建立包含绳索弯曲刚度及非线性摩擦的力传递模型,提出一种基于力传递模型的驱动误差补偿方法,通过运动实验对所建模型及控制方法进行验证。结果表明,补偿前后连续体机器人运动控制精度得到明显提高,平均位置误差由补偿前5.94 mm降低至补偿后3.15 mm,补偿率达46.97%。

滴线区原子核第一性原理Gamow壳模型研究

本文发展了第一性原理Gamow壳模型,并已经成功地用于描述滴线区原子核。该方法从现实核力出发,在Berggren基矢空间开展壳模型计算。由于Berggren基矢包含束缚态、共振态和散射连续态,所以Gamow壳模型可以很好处理连续谱耦合问题。在复动量平面,用多体微扰理论(即所谓的Q-box折叠图)导得价空间哈密顿量,然后进行含共振和连续谱耦合的壳模型计算。这样的第一性原理计算能够很好描述滴线区原子核的弱束缚特性和滴线外原子核的非束缚共振性质。本文综述了该方法在理论和技术层面的发展。作为计算例子,讨论了氧同位素及其镜像核之间的对称性破缺问题,分析了连续谱耦合效应对丰中子碳同位素激发能谱的重要影响。

基于Cosserat理论的仿生鱼骨连续型机器人静力学分析

连续型机器人具有良好的灵活性、柔顺性和人机安全性等优点,受生物鱼骨结构启发,提出了结构紧凑、质量轻、灵活性高的仿生鱼骨连续型机器人。但多节垂直交叉的刚柔软耦合结构模式使仿生鱼骨连续型机器人静力学的精确建模难度增加。本文基于Cosserat理论考虑了驱动绳索和弹性骨干的耦合作用对该机器人进行静力学分析,建立了仿生鱼骨连续型骨干的Cosserat-rod模型和驱动绳索的Cosserat-string模型以及二者的耦合模型,预测了一节仿生鱼骨单元以及垂直交叉串联布置的两节仿生鱼骨单元的变形规律。理论与实验结果相比,理论值误差在1.5 mm之内,为其长度的1.2%。本文为绳索驱动的刚柔软耦合连续型机器人的静力学建模提供了理论参考。

Modes of grain growth and mechanism of dislocation reaction under applied biaxial strain:Atomistic and continuum modeling

The phase field crystal method and Continuum Modeling are applied to study the cooperative dislocation motion of the grain boundary(GB)migration,the manner of the nucleation of the grain and of the grain growth in two dimensions(2 D)under the deviatoric deformation at high temperature.Three types of the nucleation modes of new finding are observed by the phase field crystal simulation:The first mode of the nucleation is generated by the GB splitting into two sub-GBs;the second mode is of the reaction of the sub-GB dislocations,such as,the generation and annihilation of a pair of partial Frank sessile dislocation in 2 D.The process can be considered as the nucleation of dynamic recrystallization;the third mode is caused by two oncoming rows of the dislocations of these sub-GBs,crossing and passing each other to form new gap which is the nucleation place of the new deformed grain.The research is shown that due to the nucleation of different modes the mechanism of the grain growth by means of the sub-GB migration is different,and therefore,the grain growth rates are also different.Under the deviatoric deformation of the applied biaxial strain,the grain growth is faster than that of the grain growth without external applied stress.It is observed that the cooperative dislocation motion of the GB migration under the deviatoric deformation accompanies with local plastic flow and the state of the stress of the system changes sharply.When the system is in the process of recrystallized grain growth,the system energy is in an unstable state due to the release of the strain energy to cause that the reverse movement of the plastic flow occurs.The area growth of the deformed grain is approximately proportional to the strain square and also to the time square.The rule of the time square of the deformed grain growth can also be deduced by establishing the continuum dynamic equation of the biaxial strain-driven migration of the GB.The copper metal is taken as an example of the calculation,and the obtained result is a good agreement with that of the experiment.

岩石风化程度对土岩双元基坑变形的影响

土岩双元基坑是指开挖深度范围内,上部为土层、下部为岩层的基坑。由于下部岩层的力学性质与上部土层差异较大,因此传统纯土体的一元结构基坑设计理论与经验对该类基坑的适用性较差。利用FLAC3D有限差分软件,建立不同岩石风化程度的土岩组合基坑计算模型,研究不同岩石风化情况下土岩双元基坑的变形规律,并用连续-离散耦合模型模拟土+破碎岩石基坑失稳过程。结果表明:若岩层完整,最大水平位移出现在土层中,岩层中水平位移很小;若岩层为破碎状,最大水平位移有可能出现在岩层中;岩层中的黏土夹层也可能是基坑最大变形出现的部位;破碎岩石内部的破坏是同土层同步发育的,最终二者一起发生整体滑移破坏。了解基坑的变形规律,有助于针对性地采取加固措施,对破坏区域的细观研究为基坑支护设计提供了依据。

Acoustic Purcell effect induced by quasibound state in the continuum

We study theoretically and experimentally the acoustic Purcell effect induced by quasi-bound states in the continuum(quasiBICs).A theoretical framework describing the acoustic Purcell effect of a resonant system is developed based on the system’s radiative and dissipative factors,which reveals the critical emission condition for achieving optimum Purcell factors.We show that the quasiBICs contribute to highly confined acoustic field and bring about greatly enhanced acoustic emission,leading to strong Purcell effect.Our concept is demonstrated via two coupled resonators supporting a Friedrich-Wintgen quasiBIC,and the theoretical results are validated by the experiments observing emission enhancement of the sound source by nearly two orders of magnitude.Our work bridges the gap between the acoustic Purcell effect and acoustic BICs essential for enhanced wave-matter interaction and acoustic emission,which may contribute to the research of high-intensity sound sources,high-quality-factor acoustic devices and nonlinear acoustics.

Towards the continuum coupling in nuclear lattice effective field theory Ⅰ: A three-particle model

Weakly bound states often occur in nuclear physics.To precisely understand their properties,the coupling to the continuum should be worked out explicitly.As the first step,we use a simple nuclear model in the continuum and on a lattice to investigate the influence of a third particle on a loosely bound state of a particle and a heavy core.Our approach is consistent with the Lüscher formalism.

Waves stranded at sea:bound states in the continuum in a strong coupling regime

What,exactly,is a bound state in the continuum(BIC)?A BIC is an unconventional state that remains localized even upon its coexistence with the continuum of radiating modes.In theory,a BIC is characterized by the infinite radiative quality factor and zero linewidth.1 Amongst the various types of BICs,the so-called Friedrich–Wintgen BIC arises due to the destructive interference of two resonances coupled to the same radiation channel.Once the eigenvalue of one of the resonances becomes purely real,the state turns into a BIC.Generally,Friedrich–Wintgen BICs lie in the vicinity of the frequency crossings of the uncoupled resonances.

半导体量子点结构的特性及力学研究进展

量子点结构具有独特而优异的光学和电学等性能,是当前国际研究的热点问题之一.量子点异质结构中的弹性场会对量子点结构的制备、加工及其光学和电学等物理性能产生重要影响.本文以此为背景,从低维量子限制系统所遵循的量子力学规律及其特点、半导体量子点的物理性能及表征、半导体量子点制备技术等方面较为全面地介绍半导体量子点结构的研究进展,并着重介绍在半导体量子点结构的力学研究方面以及力学性能与物理性能耦合研究等方面的一些研究结果.

隧道裂隙岩体温度-渗流耦合数学模型研究

随着越来越多特长深埋隧道工程的修建，围岩体所赋存复杂地质环境（ 渗流场、温度场与应力场等） 之间的相互影响作用已不容忽视。通过隧道裂隙围岩体渗透性能与热物理性能的等效连续化处理，初步建立了围岩体温度场与渗流场耦合作用数学模型，并应用于秦岭隧道工程。