Existence for evolutionary problems with linear growth by stability methods

We establish that solutions to the Cauchy–Dirichlet problem

${?}_{t}u?\mathrm{div}(D_{\xi }f(x,Du))=0$

for functionals $f:\mathrm{\Omega }\times {\mathbb{R}}^{N\times n}\to [0,\infty )$ of linear growth can be obtained as limits of solutions to flows with p-growth in the limit $p\downarrow 1$. The result can be interpreted on the one hand as a stability result. On the other hand it provides an existence result for general flows with linear growth.     

A priori bounds and multiplicity for fully nonlinear equations with quadratic growth in the gradient

We consider fully nonlinear uniformly elliptic equations with quadratic growth in the gradient, such as

$?F(x,u,Du,D^{2}u)=\lambda c(x)u+〈M(x)Du,Du〉+h(x)$

in a bounded domain with a Dirichlet boundary condition; here $\lambda \in \mathbb{R}$, $c,h\in L^p(\mathrm{\Omega })$, $p>n\ge 1$, $c?0$ and the matrix M satisfies $0<{\mu }_{1}I\le M\le {\mu }_{2}I$. Recently this problem was studied in the “coercive” case $\lambda c\le 0$, where uniqueness of solutions can be expected; and it was conjectured that the solution set is more complex for noncoercive equations. This conjecture was verified in 2015 by Arcoya, de Coster, Jeanjean and Tanaka for equations in divergence form, by exploiting the integral formulation of the problem. Here we show that similar phenomena occur for general, even fully nonlinear, equations in nondivergence form. We use different techniques based on the maximum principle.We develop a new method to obtain the crucial uniform a priori bounds, which permit to us to use degree theory. This method is based on basic regularity estimates such as half-Harnack inequalities, and on a Vázquez type strong maximum principle for our kind of equations.     

Nucleation of Hematite: A Nonclassical Mechanism

Hematite (α-Fe₂O₃) is thermodynamically stable under ambient conditions, of vast geological importance, and widely used in applications, for example, as corrosion protection and as a pigment. It forms at elevated temperatures, whereas room-temperature reactions typically yield metastable akaganéite or ferrihydrite. The mechanistic key changes underlying this observation were explored in the present study. The entropic contribution to the prenucleation hydrolysis reaction categorically implies the presence of prenucleation clusters (PNCs) as fundamental precursors. The formation of hematite is then due to a change in the reaction mechanism above approximately 50 °C, whereby the reaction limitation towards oxolation in phase-separated clusters is overcome. A model that rationalizes the occurrence of hematite, akaganéite, and ferrihydrite based on the chemistry of olation PNCs is proposed. Supersaturation and the temperature dependence of olation and oxolation rates from monomeric precursors are irrelevant in this nonclassical mechanism.     

Brake Orbits of First Order Convex Hamiltonian Systems with Particular Anisotropic Growth

Combining the dual least action principle with Mountain-pass lemma,we obtain the existence of brake orbits for first-order convex Hamiltonian systems with particular anisotropic growth.     

The oak (Quercus brantii) acorn as a growth promotor for rainbow trout (Oncorhynchus mykiss): growth performance,body composition,liver enzymes activity and blood biochemical parameters

Abstract

Medicinal plants play an important role in aquaculture as feed additives. This study aimed to investigate effects of alcoholic extract of acorn on growth performance, body composition, digestive enzymes activity and blood biochemical parameters of rainbow trout (O. mykiss) as a commercially important fish. Five dietary treatments were supplemented: 100, 200, 400 and 600?mg.kg^?1 of the extract. Fishes were fed twice per day for 8?weeks, and results showed that acorn extract positively affected all investigated parameters in rainbow trout fishes. Digestive enzymes activity and growth performance were increased, while activity of liver enzymes and cortisol were lowed in comparison to control individuals. Body composition of treated animals was also enhanced. Comparison between treated groups together with integrative biomarker response (IBR) values indicated greatest effects in animals fed with 400 and 600?mg.kg^?1 of the extract. Positive effects of the acorn represent promising start point for further studies.     

过载作用下聚乙烯疲劳裂纹扩展行为研究

论文针对中密度聚乙烯材料(MDPE)，采用平板试样进行了I型疲劳裂纹扩展和单次过载下裂纹扩展试验．发现与金属材料类似，单次拉伸过载对聚乙烯(PE)的疲劳裂纹扩展有明显的迟滞作用，降低了裂纹扩展速率．试验还通过变载荷刻线法获取疲劳裂纹扩展前缘的实际形貌和变化规律，对常规变载荷刻线方法进行了调整和验证，其修正方法对高分子材料的疲劳裂纹扩展前缘刻线具有较好的效果．通过观察发现含楔形塑性区的裂尖钝化是裂纹迟滞的主要原因．过载引入的塑性区内残余应力对裂纹迟滞也起了重要作用．论文利用Dugdale模型计算了塑性区尺寸，使用基于残余应力的Wheeler模型对过载迟滞进行了很好的拟合．     

PVT法氮化铝晶体铝面、氮面生长对比分析

在氮气环境下用PVT方法生长氮化铝过程中,氮面和铝面由于表面化学性质不同,生长的主要化学反应速度存在差异。原子在生长表面的迁移能力不同造成单晶表面生长方式差异较大。在基本相同条件下(生长温度、生长温差、生长气压、类似的籽晶、同一台生长设备)进行了铝、氮面氮化铝单晶晶体生长。为了更明显地表现铝氮面的差异,将同一片籽晶分为两半,翻转其中一半让铝氮面同时生长。铝面生长较好的区域形成了明显的晶畴,而氮面生长时生长较好的部分出现了明显的生长台阶,并出现了晶畴边界被生长台阶湮灭的生长现象,进一步通过AFM观测到铝面生长台阶平整但被缺陷所阻隔,晶畴发育明显为各晶畴独立生长。氮面生长台阶没有铝面规则但连续性较强,在原来晶畴边界位置也出现了连续的生长台阶(或台阶簇)。所以籽晶质量不高时氮面生长更容易提高晶体质量,后续的XRD测量结果也证明了氮面生长后的晶体质量明显高于铝面生长的晶体质量。     

6英寸低位错锗单晶生长热场设计

锗片作为衬底材料已在空间太阳电池领域得到广泛的应用,新型锗基空间太阳能电池对锗片的需求由4英寸(1英寸=2.54 cm)提高到6英寸后,低位错锗单晶的生长难度增大。本文设计开发了一种适用于直拉法生长大尺寸、低位错锗单晶的双加热器热场系统,模拟研究了不同形状主加热器的热场分布,从而得到最优的热场环境。研究发现:渐变长度为L/h=1/2、渐变率α为65°的渐变型主加热器热场结构能够获得最佳的热场分布,有利于低位错单晶的生长。经验证,生长的锗单晶热应力较低,位错密度在310～450 cm^-2范围内。     

Kinetic model for Ostwald's rule of stages with applications to Boc-diphenylalanine self-assembly

A kinetic model which describes Ostwald's rule of stages, during the process of crystal growth from solution, is reported here. Reaction equations for stages are given where the stages convert from one to another. The final stage reacts to release a portion of solute back into solution, while the remainder converts to the final equilibrium form. Additionally, a remnant of the solute that was not consumed by any of the transitional stages, ultimately is converted into the final product. This particular model was motivated by a recent report for Boc-diphenylalanine self-assembly where the dissolved peptide was observed to go through two polymorphic stages before reaching the equilibrium supramolecular assembly [A. Levin et al., Nat. Commun. 5, 5219, (2014)]. Kinetic data for the concentration of solute present during the process are listed in the above-mentioned report. We show here how the model, for , describes the time-dependent behavior of the solute decay during the growth process. After comparing the model to the experimental data, we are able to report values for all of the rate constants and propose a rule whereby the relative magnitudes of these constants can be used to predict whether a supersaturated substance will noticeably pass through transitional stages or simply convert from solute to the equilibrium solid form.     

Synthesis of well‐defined,soluble poly(3‐alkyl‐4‐benzamide) by chain‐growth condensation polymerization

Well‐defined poly(3‐alkyl‐4‐benzamide) was synthesized by means of chain‐growth condensation polymerization of phenyl 3‐octyl‐4‐(4‐octyloxybenzyl(OOB)amino)benzoate ( 1c ) from initiator 2 , followed by removal of the OOB groups on amide nitrogen of poly 1c . Polymerization of 1c with phenyl 4‐(trifluoromethyl)benzoate ( 2b ) in the presence of 1,1,1,3,3,3‐hexamethyldisilazide (LiHMDS) and LiCl in THF at ?10 °C gave poly 1c with a narrow molecular weight distribution (M_w/M_n ≤ 1.08) and a well‐defined molecular weight (M_n = 4480–12,700) determined by the feed ratio of monomer to initiator (from 10 to 30). The OOB groups of poly 1c were removed with H₂SO₄ to give the corresponding N‐unsubstituted poly(p‐benzamide) (poly 1c′ ) with low polydispersity. The solublity of poly 1c′ in polar organic solvents was dramatically higher than that of poly(p‐benzamide), demonstrating that introduction of an alkyl group on the aromatic ring is very effective for improving the solubility of poly(p‐benzamide). © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 360–365