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Daomin Cao Zhongyuan Liu Juncheng Wei 《Archive for Rational Mechanics and Analysis》2014,212(1):179-217
In this paper, we construct stationary classical solutions of the incompressible Euler equation approximating singular stationary solutions of this equation. This procedure is carried out by constructing solutions to the following elliptic problem $$\left\{\begin{array}{l@{\quad}l} -\varepsilon^2 \Delta u = \sum\limits_{i=1}^m \chi_{\Omega_i^{+}} \left(u - q - \frac{\kappa_i^{+}}{2\pi} {\rm ln} \frac{1}{\varepsilon}\right)_+^p\\ \quad - \sum_{j=1}^n \chi_{\Omega_j^{-}} \left(q - \frac{\kappa_j^{-}}{2\pi} {\rm \ln} \frac{1}{\varepsilon} - u\right)_+^p , \quad \quad x \in \Omega,\\ u = 0, \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad x \in \partial \Omega,\end{array}\right.$$ where p > 1, ${\Omega \subset \mathbb{R}^2}$ is a bounded domain, ${\Omega_i^{+}}$ and ${\Omega_j^{-}}$ are mutually disjoint subdomains of Ω and ${\chi_{\Omega_i^{+}} ({\rm resp}.\; \chi_{\Omega_j^{-}})}$ are characteristic functions of ${\Omega_i^{+}({\rm resp}. \;\Omega_j^{-}})$ , q is a harmonic function. We show that if Ω is a simply-connected smooth domain, then for any given C 1-stable critical point of Kirchhoff–Routh function ${\mathcal{W}\;(x_1^{+},\ldots, x_m^{+}, x_1^{-}, \ldots, x_n^{-})}$ with ${\kappa^{+}_i > 0\,(i = 1,\ldots, m)}$ and ${\kappa^{-}_j > 0\,(j = 1,\ldots,n)}$ , there is a stationary classical solution approximating stationary m + n points vortex solution of incompressible Euler equations with total vorticity ${\sum_{i=1}^m \kappa^{+}_i -\sum_{j=1}^n \kappa_j^{-}}$ . The case that n = 0 can be dealt with in the same way as well by taking each ${\Omega_j^{-}}$ as an empty set and set ${\chi_{\Omega_j^{-}} \equiv 0,\,\kappa^{-}_j=0}$ . 相似文献
23.
Hongjing Wu Liuding Wang Shaoli Guo Zhongyuan Shen 《Applied Physics A: Materials Science & Processing》2012,108(2):439-446
Microwave absorbing materials composed of ordered mesoporous carbon (OMC) as absorbent and paraffin as matrix were prepared, and their electromagnetic and microwave absorbing properties could be tuned by changing the weight fraction of OMC at 2–18 GHz. The minimum reflection loss (RL) value reached ?9.3 dB at 8.0 GHz and the absorption range with RL lower than ?5 dB was obtained at 5.8–14.4 GHz for a single-layer absorber filled with 1.98 wt.% OMC at 3.0 mm. If a double-layer structure was adopted, the total thickness of the absorber could be reduced below 2.0 mm and the effective absorption range (RL<?10 dB) could be obtained at 8.9–14.3 GHz with a minimal RL of ?28.5 dB at 10.6 GHz. This work demonstrated that dielectric composites could be used as excellent absorbers by adopting reasonable multilayer structures. 相似文献
24.
Chung KH So CM Wong SM Luk CH Zhou Z Lau CP Kwong FY 《Chemical communications (Cambridge, England)》2012,48(14):1967-1969
A new class of easily accessible hemilabile benzimidazolyl phosphine ligands has been developed. The ligand skeleton is prepared from commercially available and inexpensive o-phenylenediamine and 2-bromobenzoic acid. With catalyst loading down to 0.5 mol% palladium, excellent catalytic activity towards the Suzuki-Miyaura coupling of aryl mesylates is still observed. This represents the lowest catalyst loading achieved so far for this reaction in general. X-Ray crystallography shows that new ligand L2 is coordinated with Pd in a κ(2)-P,N fashion. 相似文献
25.
通过水杨醛与乙醇胺(或邻氨基酚)和乙酰丙酮氧化钼在无水乙醇中反应得到双核配合物1[MoO2·SAE]2(SAE为N-亚水杨醛基-2-氨基乙醇)和单核配合物2[MoO2·SAP·(C2H5OH)](SAP为N-亚水杨醛基-2-氨基苯酚)。并用元素分析,IR,1^HNMR和热分析进行表征,测定了配合物1的单晶结构。1晶体属正交晶系,空间群为Pbca.晶胞参数:a=1.31007(16)nm,b=0.89636(11)nm,c=1.6841(2)nm,Mr=582.22,V=1.9777(4)nm^3,Z=4,Dc=1,955Mg/m^3,R1=0.0293,ωR2=0.0819.$521Thereactionofsalicylalwith2-aminoethenol(or-2-aminophenol)and[MoO2(acac)2])acac=acetylacetonate)inabsoluteethanolgavedinuclearmolybdenumcomplex1[MoO2·SAE]2(SAE=N-salicylidene-2-aninophenol).andmononuclearcomplex2[MoO2·SAP·(C2H5OH)](SAP=N-salicylidene-2-aminophenol).Theyhavebeencharacterizedbyelementalanalysis,IR,1^HNMRandTGA.Thesinglecrystalstructureofcomplex1hasbeendetermined.Itbelongstoorthorhombic,spacegroupPbcawitha=1.31007(16)nm,b=0.89636(11)nm,c=1.6841(2)nm,Mr=582.22,V=1.9777(4)nm^3,Z=4,Dc=1,955Mg/m^3,R1=0.0293,ωR2=0.0819. 相似文献
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Conservation Quantities of the Explicit Symplectic Scheme for Time-evolution of Quantum System 总被引:2,自引:0,他引:2
Zhou Zhongyuan Ding Peizhu Institute of Atomic Molecular Physics Jilin University Changchun P R China Supported by National Natural Science Foundation of China State Commission of Science Technology Chinese Research Asso 《原子与分子物理学报》1997,(2)
ConservationQuantitiesoftheExplicitSymplecticSchemeforTime-evolutionofQuantumSystemZhouZhongyuanDingPeizhuInstituteofAtomican... 相似文献
28.
ThetheoryofnonlinearpolymerizationwasinitiatedbyFlory[1]andStockmayer[2].Forsimplifyingtheevaluationofaveragepolymerquantities,manyotherstatisticalmethodssuchastheprobabilityofgeneratingfunctionmethod[3],thelawoftotalprobabilitymethod[4,5]andtheothermethods[6… 相似文献
29.
采用CoulombBorn交换近似,在修改了有效核电荷的Z标度类氢模型下,计算了‘水窗’波段V20+离子精细结构能级间的电子碰撞激发截面 相似文献
30.
Small-amplitudesolitonsinnonlinear-saturationglassfibersSmall-amplitudesolitonsinnonlinear-saturationglassfibers¥YUZhongyuan;... 相似文献