Uniqueness of Solution to Systems of Elliptic Operators and Application to Asymptotic Synchronization of Linear Dissipative Systems II: Case of Multiple Feedback Dampings

In this paper, the authors consider the asymptotic synchronization of a linear dissipative system with multiple feedback dampings. They ?rst show that under the observability of a scalar equation, Kalman’s rank condition is su?cient for the uniqueness of solution to a complex system of elliptic equations with mixedobservations. The authors then establish a general theory on the asymptotic stability and the asymptotic synchronization for the corresponding evolutional system subjected to mixed dampings of various natures. Some classic models are presented to illustrate the ?eld of applications of the abstract theory.     

Imposing accurate wall boundary conditions in corrective‐matrix‐based moving particle semi‐implicit method for free surface flow

Corrective matrix that is derived to restore consistency of discretization schemes can significantly enhance accuracy for the inside particles in the Moving Particle Semi‐implicit method. In this situation, the error due to free surface and wall boundaries becomes dominant. Based on the recent study on Neumann boundary condition (Matsunaga et al, CMAME, 2020), the corrective matrix schemes in MPS are generalized to straightforwardly and accurately impose Neumann boundary condition. However, the new schemes can still easily trigger instability at free surface because of the biased error caused by the incomplete/biased neighbor support. Therefore, the existing stable schemes based on virtual particles and conservative gradient models are applied to free surface and nearby particles to produce a stable transitional layer at free surface. The new corrective matrix schemes are only applied to the particles under the stable transitional layer for improving the wall boundary conditions. Three numerical examples of free surface flows demonstrate that the proposed method can help to reduce the pressure/velocity fluctuations and hence enhance accuracy further.     

不同退火条件对PEALD制备的Ga2O3薄膜特性的影响

利用等离子增强原子层沉积技术(PEALD)在c面蓝宝石衬底上制备了氧化镓(Ga₂O₃)薄膜,研究了退火气氛(v(N₂)∶v(O₂)=1∶1(体积比)、空气和N₂)及退火时间对Ga₂O₃薄膜晶体结构、表面形貌和光学性质的影响。研究结果表明,退火前的氧化镓处于亚稳态,不同退火气氛下退火后晶体结构发生明显改变,而且退火气氛中N₂比例增加有利于Ga₂O₃重结晶。在N₂气氛下退火达到30 min,薄膜结构已由亚稳态转变成择优取向的β-Ga₂O₃。而且表面形貌分析表明,退火30 min后表面形貌开始趋于稳定,表面晶粒密度不再增加。另外实验样品在 400~800 nm的平均透射率几乎是100%,且光吸收边陡峭。采用N₂气氛退火,对于富氧环境下沉积的Ga₂O₃更利于薄膜表面原子迁移,以及择优取向Ga₂O₃重结晶。     

Solvent‐free ring‐opening polymerization of lactones with hydrogen‐bonding bisurea catalyst

Development of effective organocatalysts for the living ring‐opening polymerization (ROP) of lactones is highly desired for the preparation of biocompatible and biodegradable polyesters with controlled microstructures and physical properties. Herein, a new class of hydrogen‐bond donating bisurea catalysts is reported for the ROP of lactones under solvent‐free conditions. ROP of lactones mediated by the bisurea/7‐methyl‐1,5,7‐triazabicyclo[4.4.0]dec‐5‐ene (MTBD) catalyst exhibits a living/controlled manner, affording the polymers and copolymers with the well‐defined structure, predictable molecular weight, narrow molecular weight distribution, and high selectivity for monomer at low catalyst loadings at ambient temperature. The possible mechanism of bisurea/MTBD‐catalyzed ROP of lactones is proposed, in which the bisurea activates the carbonyl group of lactones while MTBD facilitates the nucleophilic attack of the initiating/propagating alcohol by hydrogen bonding. Moreover, the poly(ε‐caprolactone‐co‐δ‐valerolactone) [P(CL‐co‐VL)] random copolymers with various compositions were synthesized using the bisurea/MTBD catalyst. The measurements of thermal properties and crystalline structure demonstrate that the CL and VL units are cocrystallized in the crystalline phase of P(CL‐co‐VL) copolymers. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 90–100     

Weighted estimates for the multilinear maximal function on the upper half‐spaces

For a general dyadic grid, we give a Calderón–Zygmund type decomposition, which is the principle fact about the multilinear maximal function on the upper half‐spaces. Using the decomposition, we study the boundedness of . We obtain a natural extension to the multilinear setting of Muckenhoupt's weak‐type characterization. We also partially obtain characterizations of Muckenhoupt's strong‐type inequalities with one weight. Assuming the reverse Hölder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hytönen–Pérez type weighted estimates.     

Domain decomposition methods in a geometrical multiscale domain using finite volume schemes

The heat equation is solved by using a finite volume discretization in a domain that consists of a two-dimensional central node and several one-dimensional outgoing branches. Several interface connection options to match the submodels set on the node and on the branches, with or without continuity, are looked at. For each of them, a monolithic scheme is defined, and existence and uniqueness of the solution is proved. New schemes are deduced, which are obtained through domain decomposition methods in the form of interface systems, with one or two unknowns per interface. A comparative systematic study is carried out from an algebraic and numerical point of view according to the interface conditions: Dirichlet, Neumann, or Robin. An efficient diagonal preconditioning is proposed.     

核电结构土-结相互作用分析分区混合计算方法

土-结构相互作用分析是核电结构进行抗震设计和安全评估的重要环节.在核电结构的土-结相互作用分析中,阻尼和非线性是影响结构反应的重要因素. 若采用频域分析,可以方便考虑阻尼,但需通过等效线性化来考虑非线性,不适合于强震作用下的土体非线性.若采用时域分析的逐步积分方法,适合于考虑非线性,但材料阻尼一般采用瑞利阻尼模型,除了紧靠指定阻尼比的少数几个振型外,其他振型的反应将受到瑞利阻尼模型所确定的大阻尼所抑制,造成地震反应与真实情形有较大差异.若采用时域分析的模态叠加法,可合理计入阻尼效应,但模态叠加法不能考虑非线性.因此,如何合理考虑阻尼和非线性是核电结构土-结相互作用分析需要关注的问题.基于此,本文提出一种模态叠加和时步积分结合的土-结相互作用分区算法.其中,出于安全性考虑,地震作用下核电主体结构一般不允许进入非线性,因此结构可采用模态叠加方法,以便合理考虑结构阻尼;土体和基础采用显式时步积分法,可考虑土体非线性;通过人工边界条件考虑无限域的影响 (辐射阻尼).通过简单算例对该方法进行了验证,并用于CAP1400核电结构的土-结相互作用分析中,对比分析了采用模态阻尼和瑞利阻尼时核电结构和场地反应的差异,结果表明结构阻尼模型对场地的反应影响不大,但对结构反应影响明显,在实际工程中应合理选取阻尼模型.      

A 3D mesh deformation technique for irregular in‐flight ice accretion

Aircraft holding around busy airports may be requested to sustain as much as 45 min of icing before landing or being diverted to another airport. In this paper, a three‐dimensional mesh deformation scheme, based on a structural frame analogy, is proposed for the numerical simulation of ice accretion during extended exposure to adverse weather conditions. The goal is to provide an approach that is robust and efficient enough to delay or altogether avoid re‐meshing while preserving (enforcing) nearly orthogonal elements at the highly distorted ice surface. Robustness is achieved by suitably modifying the axial and torsional stiffness components of the frame elements in order to handle large and irregular grid displacements typical of in‐flight icing. Computational efficiency is obtained by applying the mesh displacement to an automatically selected small subset of the entire computational domain. The methodology is validated first in the case of deformations typical of fluid‐structure interaction problems, including wing bending, a helicopter rotor in forward flight, and the twisting of a high‐lift wing configuration. The approach is then assessed for aero‐icing on two swept wings and compared against experimental measurements where available. Copyright © 2015 John Wiley & Sons, Ltd.     

理想弹塑性固体Riemann问题的解结构与初值条件

针对理想弹塑性固体材料的一维Riemann问题，在不考虑真空的情况下，讨论其所有可能存在的解结构，给出每一种解结构下对应的初值条件且证明该系列初值条件的完备性，即任意给定的物理量初值均有且只有一种解结构与之对应.基于该理论，在设计精确或近似理想弹塑性Riemann问题求解器时，可以依据初值条件对任意物理量初值直接判断其对应的解结构，从而提高求解器的精度和效率.数值试验验证了该系列初值条件的正确性和有效性.     

Stokes equations under nonlinear slip boundary conditions coupled with the heat equation: A priori error analysis

In this work, we consider the heat equation coupled with Stokes equations under threshold type boundary condition. The conditions for existence and uniqueness of the weak solution are made clear. Next we formulate the finite element problem, recall the conditions of its solvability, and study its convergence by making use of Babuska–Brezzi's conditions for mixed problems. Third we formulate an Uzawa's type iterative algorithm that separates the fluid from heat conduction, study its feasibility, and convergence. Finally the theoretical findings are validated by numerical simulations.