正交匹配追踪算法的迭代残差重建方法

正交匹配追踪(Orthogonal Matching Pursuit, OMP)算法是一种重要的压缩感知重构算法. OMP算法在每次迭代中选择与当前残差最相关的原子. 针对每次迭代需要重新计算残差的问题, 本文考虑偶数次迭代下残差未知的情况. 首先, 研究了奇数次迭代的残差与下一次迭代的残差之间的关系, 得到了一种偶数次迭代时选择原子的标准. 然后, 引入一种回溯机制来处理前面所得的迭代结果, 这种机制通过剔除其中多余的原子来实现精确重建. 据此, 提出了可减少计算残差的改进型正交匹配追踪算法.     

基于Kronecker型替换的黑盒多项式稀疏插值

本文基于新的Kronecker型替换,给出两个由黑盒表示的稀疏多项式的新确定性插值算法.令f∈R[x1,……,xn]是一个稀疏黑盒多项式,其次数上界为D.当R是C或者是有限域时,相对于已有算法,新算法具有更好的计算复杂度或者关于D的复杂度更低.特别地,对于一般黑盒模型,D是复杂度中的主要因素,而在所有的确定性算法中,本文的第二个算法的复杂度关于D是最低的.     

三维非连续变形分析方法碰撞分析及其应用

将具有完备动力学理论的非连续变形分析(DDA)方法应用于块体碰撞研究。基于三维DDA(3D DDA)方法,按时步输出块体碰撞过程速度变化和接触嵌入量,进而得到块体碰撞恢复系数、冲量、冲击力。以此为参考指标,采用斜抛、面-面对心等碰撞模型,验证3D DDA方法模拟块体碰撞的有效性,并将3D DDA方法应用于多米诺骨牌倾倒、滚石边坡成灾及防护等算例分析,探讨了多米诺骨牌倾倒机制、滚石启动及运动行为、滚石灾害防护方案。结果表明:多米诺骨牌间距越大,同一块体被碰撞时间越迟,其最终稳定时间也越迟,与下一块体碰撞的动能越大;滚石运动呈侧向平动及转动三维运动特征,每一次碰撞,均引起动能、轨迹或状态的显著变化;滚石拦挡设施弹簧刚度越大,越先达到最大冲击力,最大冲击力随弹簧刚度的增加而减小;可结合树木阻挡效应,耗散滚石动能,降低滚石飞跃高度,使滚石灾害减轻或控制在防护范围以内。     

Spectral estimates for saddle point matrices arising in weak constraint four‐dimensional variational data assimilation

We consider the large sparse symmetric linear systems of equations that arise in the solution of weak constraint four‐dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can be written as saddle point systems with a 3 × 3 block structure but block eliminations can be performed to reduce them to saddle point systems with a 2 × 2 block structure, or further to symmetric positive definite systems. In this article, we analyse how sensitive the spectra of these matrices are to the number of observations of the underlying dynamical system. We also obtain bounds on the eigenvalues of the matrices. Numerical experiments are used to confirm the theoretical analysis and bounds.     

Triphilic pentablock copolymers with perfluoroalkyl segment in central position

Adding perfluoroalkyl (PF) segments to amphiphilic copolymers yields triphilic copolymers with new application profiles. Usually, PF segments are attached as terminal blocks via Cu(I) catalyzed azide-alkyne cycloaddition (CuAAC). The purpose of the current study is to design new triphilic architectures with a PF segment in central position. The PF segment bearing bifunctional atom transfer radical polymerization (ATRP) initiator is employed for the fabrication of triphilic poly(propylene oxide)-b-poly(glycerol monomethacrylate)-b-PF-b-poly(glycerol monomethacrylate)-b-poly(propylene oxide) PPO-b-PGMA-b-PF-b-PGMA-b-PPO pentablock copolymers by a combined ATRP and CuAAC reaction approach. Differential scanning calorimetry indicates the PF-initiator to undergo a solid–solid phase transition at 63°C before the final crystal melting at 95°C. This is further corroborated by polarized optical microscopy and X-ray diffraction studies. The PF-initiator could successfully polymerize solketal methacrylate (SMA) under typical ATRP conditions producing well-defined Br-PSMA-b-PF-b-PSMA-Br triblock copolymers that are then converted into PPO-b-PSMA-b-PF-b-PSMA-b-PPO pentablock copolymer via CuAAC reaction. Subsequently, acid hydrolysis of the PSMA blocks afforded water soluble well-defined triphilic pentablock copolymers PPO-b-PGMA-b-PF-b-PGMA-b-PPO with fluorophilic central segment, hydrophilic middle blocks, and lipophilic outer blocks. The triphilic block copolymers could self-assemble, depending upon the preparatory protocol, into spherical and filament-like phase-separated nanostructures as revealed by transmission electron microscopy.     

Amphiphilic pentablock copolymers and their blends with PDMS for antibiofouling coatings

Well‐defined amphiphilic pentablock copolymers Siy‐(EGx‐FAz)₂ composed of polysiloxane (Si), polyethylene glycol (EG), and perfluorohexylethyl polyacrylate (FA) blocks are synthesized by ATRP of FA monomer starting from a difunctional bromo‐terminated macroinitiator. Diblock copolymers EGx‐FAz are also synthesized as model systems. The block copolymers are used, either alone or blended with a PDMS matrix in varied loadings, to prepare antibiofouling coatings. Angle‐resolved XPS and contact angle measurements show that the coating surface is highly enriched in fluorine content but undergoes reconstruction after contact with water. Protein adsorption experiments with human serum albumin and calf serum highlight that diblock copolymers resist protein adhesion better than do pentablock copolymers. Blending of the pentablock copolymer with PDMS results in increased protein adsorption. By contrast, the PDMS‐matrix coatings show high removal percentages of sporelings of the green fouling alga Ulva linza. © 2015 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 2015 , 53, 1213–1225     

Amphiphilic block copolymer self‐assemblies of poly(NVP)‐b‐poly(MDO‐co‐vinyl esters): Tunable dimensions and functionalities

Functional, degradable polymers were synthesized via the copolymerization of vinyl acetate (VAc) and 2‐methylene‐1,3‐dioxepane (MDO) using a macro‐xanthate CTA, poly(N‐vinylpyrrolidone), resulting in the formation of amphiphilic block copolymers of poly(NVP)‐b‐poly(MDO‐co‐VAc). The behavior of the block copolymers in water was investigated and resulted in the formation of self‐assembled nanoparticles containing a hydrophobic core and a hydrophilic corona. The size of the resultant nanoparticles was able to be tuned with variation of the hydrophilic and hydrophobic segments of the core and corona by changing the incorporation of the macro‐CTA as well as the monomer composition in the copolymers, as observed by Dynamic Light Scattering, Static Light Scattering, and Transmission Electron Microscopy analyses. The concept was further applied to a VAc derivative monomer, vinyl bromobutanoate, to incorporate further functionalities such as fluorescent dithiomaleimide groups throughout the polymer backbone using azidation and “click” chemistry as postpolymerization tools to create fluorescently labeled nanoparticles. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2699–2710     

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     

End group polarity and block symmetry effects on cloud point and hydrodynamic diameter of thermoresponsive block copolymers

Thermoresponsive block copolymers are of interest for delivery vehicles in the body. Often an interior domain is designed for the active agent and the exterior domain provides stability in the bloodstream, and may carry a targeting ligand. There is still much to learn about how block sequence and chain end identity affect micelle structure, size, and cloud points. Here, hydrophilic oligo(ethylene glycol) methyl ether acrylate and more hydrophobic di(ethylene glycol) methyl ether methacrylate monomers were polymerized to give amphiphilic block copolymers with amphiphilic chain ends. The block sequence and chain end identity were both controlled by appropriate choice of RAFT chain transfer agents to study the effect of ‘matched’ and ‘mismatched’ chain end polarity with amphiphilic block sequence. The affect of matching or mismatching chain end polarity and block sequence was studied on the hydrodynamic diameter, cloud point, and temperature range of the chain collapse on linear di‐ and triblock copolymers and star diblock polymers. The affects of matching or mismatching chain end polarity were significant with linear diblock copolymers but more complex with triblock and star copolymers. Explanations of these results may help guide others in designing thermoresponsive block copolymers. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2838–2848     

Facile non‐lithographic route to highly aligned silica nanopatterns using unidirectionally aligned polystyrene‐block‐polydimethylsiloxane films

Thin films (monolayer and bilayer) of cylinder forming polystyrene‐block‐polydimethylsiloxane (PS‐b‐PDMS) were shear aligned by the swelling and deswelling of a crosslinked PDMS pad that was physically adhered to the film during solvent vapor annealing. The nanostructures formed by self‐assembly were exposed to ultraviolet‐ozone to partially oxidize the PDMS, followed by calcination in air at 500 °C. In this process, the PS segments were fully decomposed, while the PDMS yielded silica nanostructures. The highly aligned PDMS cylinders were thus deposited as silica nanolines on the silicon substrate. Using a bilayer film, the center‐to‐center distance of these features were effectively halved from 38 to 19 nm. Similarly, by sequential shear‐alignment of two distinct layers, a rhombic array of silica nanolines was fabricated. This methodology provides a facile route to fabricating complex topographically patterned nanostructures. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1058–1064