Analysis of a micro–macro acceleration method with minimum relative entropy moment matching

We analyse convergence of a micro–macro acceleration method for the simulation of stochastic differential equations with time-scale separation. The method alternates short bursts of path simulations with the extrapolation of macroscopic state variables forward in time. After extrapolation, a new microscopic state is constructed, consistent with the extrapolated macroscopic state, that minimises the perturbation caused by the extrapolation in a relative entropy sense. We study local errors and numerical stability of the method to prove its convergence to the full microscopic dynamics when the extrapolation time step tends to zero and the number of macroscopic state variables tends to infinity.     

Synthesis of tertiary amine‐based pH‐responsive polymers by RAFT Polymerization

Well‐defined tertiary amine‐based pH‐responsive homopolymers and block copolymers were synthesized via reversible addition‐fragmentation chain transfer (RAFT) polymerization using 4‐cyanopentanoic acid dithiobenzoate (CPAD) as the RAFT agent for homopolymers and a poly(ethylene glycol) (PEG) macro‐RAFT agent for the block copolymers. ¹H NMR and gel permeation chromatography results confirmed the successful synthesis of these homopolymers and block copolymers. Kinetics studies indicated that the formation of both the homopolymers and the block copolymers were well defined. The pKa titration experiments suggested that the homopolymers and the related block copolymers have a similar pKa. The dynamic light scattering investigation showed that all of the block copolymers underwent a sharp transition from unimers to micelles around their pKa and the hydrodynamic diameter (D_h) was not only dependent on the molecular weight but also on the composition of the block copolymers. The polymer solution of PEG‐b‐PPPDEMA formed the largest micelle compare to the PEG‐b‐PDPAEMA and PEG‐b‐PDBAEMA with a similar molecular weight. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1010–1022     

Nanocrystalline cellulose/fluorinated polyacrylate latex via RAFT‐mediated surfactant‐free emulsion polymerization and its application as waterborne textile finishing agent

A simple method for nanocrystalline cellulose (NCC)/fluorinated polyacrylate was developed by RAFT‐mediated surfactant‐free emulsion polymerization, in which the nanocomposites formed a core‐shell spherical morphology. The influence of the content of NCC‐g‐(PAA‐b‐PHFBA) (AA was acrylic acid, HFBA was hexafluorobutyl acrylate) on the properties of latex and film were systematically studied. The monomer conversion, the tensile strength, and water–oil repellency of film increased first and then decreased, the latex particle size decreased first and then decreased, when the content of NCC‐g‐(PAA‐b‐PHFBA) increased from 1 to 6 wt %. Elongation at break and thermal stability distinctly decreased when the content of NCC‐g‐(PAA‐b‐PHFBA) gradually increased. XPS showed that the fluorine‐containing groups well concentrated at the film–air interfaces during the annealing process. SEM analysis revealed that the treated fiber had a rugged surface, and the treated fabric had an excellent water repellency. In addition, this green grafting method in water offered a new perspective for the fabrication of exceptional NCC‐based nanocomposites with NCC as the core and also helped to promote the potential applicability of NCC in a range of multipurpose applications. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 1305–1314     

Multi-scale and multi-order singularity approach to non-equilibrium mechanics: Coupling of atomic-micro-macro damage

Offered in this work is the development of a macro/meso/micro model that covers the lineal scale of 10⁻¹¹ to 10⁰ by application of the volume energy density function. Boundary constraints and defect geometries are shown to play a role at the smaller scale in the same way as those at the macroscopic scale. Different orders of stress (or energy density) singularities are used to describe the defect geometry and prevailing constraint via the boundary conditions in a way similar to singularity adopted in classical fracture mechanics. Two classes of singularities have been identified in addition to classical one without violating the finiteness conditions of the local displacement and energy density. Still the connection of results from the different scales is no small task and is made possible by application of a scale multiplier. It is determined by considering the interactive effects of the parameters at the different scales from the atomic to the macroscopic. Unlike the classical boundary value problem approach, application of the scale multiplier has led to closed-form asymptotic multiscale solutions that otherwise would not have been made possible. The procedure is demonstrated for the anti-plane shear of a macro-micro-atomic model that accounts for imperfection at the different scales Published in Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 3–22, January 2006.     

Macro‐hybrid mixed variational two‐phase flow through fractured porous media

Macro‐hybrid mixed variational models of two‐phase flow, through fractured porous media, are analyzed at the mesoscopic and macroscopic levels. The mesoscopic models are treated in terms of nonoverlapping domain decompositions, in such a manner that the porous rock matrix system and the fracture network interact across rock–rock, rock–fracture, and fracture–fracture interfaces, with flux transmission conditions dualized. Alternatively, the models are scaled to a macroscopic level via an asymptotic process, where the width of the fractures tends to zero, and the fracture network turns out to be an interface system of one less spatial dimension, with variable high permeability. The two‐phase flow is characterized by a fractional flow dual mixed variational model. Augmented two‐field and three‐field variational reformulations are presented for regularization, internal approximations, and macro‐hybrid mixed finite element implementation. Also abstract proximal‐point penalty‐duality algorithms are derived and analyzed for parallel computing. Copyright © 2016 John Wiley & Sons, Ltd.     

“宏观辨识与微观探析”视域下的初中化学教学*——中和反应

在“宏观辨识与微观探析”视域下进行中和反应教学,首先以常规实验为载体,从宏观视角认识中和反应的外在表现,然后以模型、动画为载体,从微观视角了解中和反应的微观过程,再以数字化实验为载体,从宏观与微观相结合的视角理解中和反应的内在本质,最后联系生产生活实际,体验中和反应的应用价值。这样设计,学生能深刻理解中和反应的本质,增进化学学科理解,培养化学学科核心素养。     

Free volume,molecular grains,self-organisation,and anisotropic entropy: machining materials

ABSTRACT

In this article, the relationship between molecular architecture and the formation of twist-bend phases is reviewed under the context of shape dependency. We conclude that the twist-bend phase is a universal phenomenon, which occurs in a wide variety of materials, for dimers through to main chain polymers. In the process, the chemical information on molecular design is effectively lost or irrelevant, and molecular topology takes precedence over electrostatic interactions in mesophase formation. As a consequence of this macro-scale material, engineering by shape alone becomes a possibility, potentially more phases may be realised, and entropy is anisotropic.     

A strategy for synthesis of ion‐bonded amphiphilic miktoarm star copolymers via supramolecular macro‐RAFT agent

Amphiphilic supramolecular miktoarm star copolymers linked by ionic bonds with controlled molecular weight and low polydispersity have been successfully synthesized via reversible addition‐fragmentation chain transfer (RAFT) polymerization using an ion‐bonded macromolecular RAFT agent (macro‐RAFT agent). Firstly, a new tetrafunctional initiator, dimethyl 4,6‐bis(bromomethyl)‐isophthalate, was synthesized and used as an initiator for atom transfer radical polymerization (ATRP) of styrene to form polystyrene (PSt) containing two ester groups at the middle of polymer chain. Then, the ester groups were converted into tertiary amino groups and the ion‐bonded supramolecular macro‐RAFT agent was obtained through the interaction between the tertiary amino group and 2‐dodecylsulfanylthiocarbonylsulfanyl‐2‐methyl propionic acid (DMP). Finally, ion‐bonded amphiphilic miktoarm star copolymer, (PSt)₂‐poly(N‐isopropyl‐acrylamide)₂, was prepared by RAFT polymerization of N‐isopropylacrylamide (NIPAM) in the presence of the supramolecular macro‐RAFT agent. The polymerization kinetics was investigated and the molecular weight and the architecture of the resulting star polymers were characterized by means of ¹H‐NMR, FTIR, and GPC techniques. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5805–5815, 2008     

Multiscale approach to micro/macro fatigue crack growth in 2024-T3 aluminum panel

When two contacting solid surfaces are tightly closed and invisible to the naked eye,the discontinuity is said to be microscopic regardless of whether its length is short or long.By this definition,it is not sufficient to distinguish the difference between a micro-and macro-crack by using the length parameter.Microcracks in high strength metal alloys have been known to be several centimeters or longer.Considered in this work is a dual scale fatigue crack growth model where the main crack can be micro or macro but there prevails an inherent microscopic tip region that is damaged depending on the irregularities of the microstructure.This region is referred to as the"micro-tip"and can be simulated by a sharp wedge with different angles in addition to mixed boundary conditions.The combination is sufficient to model microscopic entities in the form of voids,inclusions,precipitations,interfaces,in addition to subgrain imperfections,or cluster of dislocations.This is accomplished by using the method of"singularity representation"such that closed form asymptotic solutions can be obtained for the development of fatigue crack growth rate relations with three parameters.They include:(1)the crack surface tightness*represented by o/=0.3-0.5 for short cracks in region I,and 0.1-0.2 for long cracks in region II,(2)the micro/macro material properties reflected by the shear modulus ratio*(=micro/macro varying between 2 and 5)and(3)the most sensitive parameter d*being the micro-tip characteristic length d*(=d/do)whose magnitude decreases in the direction of region I II.The existing fatigue crack growth data for 2024-T3 and 7075-T6 aluminum sheets are used to reinterpret the two-parameter da/dN=C(K)nrelation where K has now been re-derived for a microcrack with surfaces tightly in contact.The contact force will depend on the mean stress m or mean stress ratio R as the primary parameter and on the stress amplitude a as the secondary parameter.     

Linear quantification calibration of crystallinity at subpercent and its evaluation based on spectral and spatial information inherited in Raman chemical images

In this paper, the author reported two methods to extract spectral or spatial information inherited in the Raman chemical images for linear quantification calibration of crystallinity. The two approaches reported quantification results according to the spectral mean score of overall pixels or the spatial percentage of the pixels with a score greater than and equal to the threshold of the chemical images, respectively. From this study, it can be concluded that, first, sampling method for data collection in mapping has to be optimized to achieve linear quantification calibration through simple univariate analysis approaches. Second, the ordinary way of evaluating/validating a linear quantification technique by best linear correlation coefficient (R²) and root‐mean‐square error of calibration is disputable and has to be reconsidered. Lastly, with further consideration of root‐mean‐square relative error of calibration and predicted crystallinity at subpercent, it was found that the spectral mean score method cannot generate reliable quantification results at subpercent crystallinity. Copyright © 2014 John Wiley & Sons, Ltd.