Locking effects in the finite element approximation of elasticity problems

Summary We consider the finite element approximation of the 2D elasticity problem when the Poisson ratiov is close to 0.5. It is well-known that the performance of certain commonly used finite elements deteriorates asv0, a phenomenon calledlocking. We analyze this phenomenon and characterize the strength of the locking androbustness of varioush-version schemes using triangular and rectangular elements. We prove that thep-andh-p versions are free of locking with respect to the error in the energy norm. A generalization of our theory to the 3D problem is also discussed.The work of this author was supported in part by the Office of Naval Research under Naval Research Grant N00014-90-J-1030The work of this author was supported in part by the Air Force Office of Scientific Research, Air Force Systems Command, U.S. Air Force, under grant AFOSR 89-0252     

Convergence rate estimate for a domain decomposition method

Summary We provide a convergence rate analysis for a variant of the domain decomposition method introduced by Gropp and Keyes for solving the algebraic equations that arise from finite element discretization of nonsymmetric and indefinite elliptic problems with Dirichlet boundary conditions in ². We show that the convergence rate of the preconditioned GMRES method is nearly optimal in the sense that the rate of convergence depends only logarithmically on the mesh size and the number of substructures, if the global coarse mesh is fine enough.This author was supported by the National Science Foundation under contract numbers DCR-8521451 and ECS-8957475, by the IBM Corporation, and by the 3M Company, while in residence at Yale UniversityThis author was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy under Contract W-31-109-Eng-38This author was supported by the National Science Foundation under contract number ECS-8957475, by the IBM Corporation, and by the 3M Company     

C59N单分子整流器

通过将单个C59N分子置于双势垒隧道结中，从而利用单电子隧穿效应和C59N分子的特殊能级结构，我们成功地实现了一种新型的单分子整流器件．实验中这个整流器件的正向导通电压约为0．5-0．7V，反向击穿电压约为1．6—1．8V．理论分析表明，中性C59N分子的半占据费米能级以及在不同充电情况下费米能级的不对称移动是形成整流效应的主要原因．其构成原理也决定了该器件具有稳定、易重复的特点．     

On the implementation of Sμ U(2) action in the irreducible representations of twisted canonical commutation relations

The natural S U(2) action on the creation and annihilation operators satisfying twisted canonical commutation relations (TCCR) is investigated. It is shown that the Fock representation is the only covariant irreducible representation of TCCR.Partially supported by the program RP.1.10.     

Angular distribution and differential sputtering yields for low-energy light-ion irradiation of polycrystalline nickel and tungsten

Angular differential and total sputtering yields of polycrystalline nickel and tungsten have been measured for 1 and 4 keV H⁺ and 4 keV He⁺ ion bombardment at incidence angles between 0° and 80°. The differential sputtering yields (dY/dΩ) were determined with the aid of the collector technique, whereas the total yieldY was determined from the weight loss of the target during irradiation. Asymmetric angular distributions are observed at oblique angles of incidence, the emission maximum being shifted in forward direction (with respect to the incident ions). Even more pronounced than the change in shape of the emission distribution is an increase in the differential yield:dY/dΩ rises with increasing incidence angle over the whole range of ejection angles, the increase being most prominent in the direction of primary recoil emission. This effect is therefore ascribed to emission of surface atoms in direct projectile-surface atom collisions. On short term leave from Institut für Plasmaphysik der Kernforschungsanlage Jülich GmbH, D-5170, Jülich, Fed. Rep. Germany.     

Tautomeric populations of the charged species of 1,12‐diamino‐3,6,9‐triazadodecane (SpmTrien) studied with computer simulations and cluster expansions

Correct net charge and protonation pattern in the polyamine backbone is one of the major factors that define the interactions of this class of compounds. 1,12‐diamino‐3,6,9‐triazadodecane (SpmTrien) is a isosteric charge deficient analogue of naturally occurring spermine (Spm) with different biological features. The tautomeric populations of each SpmTrien charge state were estimated with computer simulations, molecular dynamics (MD) and quantum mechanical calculations, and cluster expansions separately. In the computer simulations, tautomeric populations of each charge state were obtained by constrained least‐squares fitting the theoretically calculated (GIAO B3LYP/6‐311 + G**) ¹⁵ N NMR chemical shieldings of SpmTrien tautomers to the experimentally measured chemical shifts. Theoretical chemical shieldings were calculated for water complexes of SpmTrien obtained from MD simulations in explicit water. Both methods gave highly similar realistic results. SpmTrien has many major populations of tautomers at biologically relevant charge states of three (+3) and four (+4) thus enabling a large variety of structures for specific ionic interactions. Copyright © 2013 John Wiley & Sons, Ltd.     

Effect of Non‐Ideal Mixed Solvents on Dimensions of Poly(N‐Vinylpyrrolidone) and Poly(Methyl Methacrylate) Coils

An addition of a small amount of non‐solvent tetrahydrofuran (THF) to good solvent water gave rise to a strong solvent power for poly(N‐vinylpyrrolidone) (PVP). It was found that PVP coils in mixtures of water and THF first swelled as the fraction of THF was increased, and then the coils contracted after a critical composition of the solvent mixture based on the measurement of dilute solution viscosities. It was reached that the power of the mixed solvents was not the simple average of the power of individual components. The influence of the non‐ideal mixing of water and THF on the power of these mixtures for PVP and the dimensions of PVP coils was taken into account. Especially the formation of pseudo‐clathrate hydrate structure with the composition φ _THF ≈ 0.44 was found to be an important factor to change the solvation and dimensions of PVP coils. Some other solvent mixtures for PVP and poly(methyl methacrylate) (PMMA) were also found to be non‐ideal mixtures. The viscosities of these solvent mixtures could show positive or negative deviation from the values obtained from the addition rule. It was shown again that the influence of the non‐ideality of these solvent mixtures on the dimensions of polymer coils was great. The action of mixed solvents changed the dimension of polymer coils, not only because of excluded volume effects but also because of the different molecular interactions present in these mixed solvents.     

Radioaktive und stabile Isotope bei der Lösung pflanzenphysiologischer Probleme

Es werden neuere Ergebnisse von Untersuchungen zur Biosynthese einiger Alkaloide und zum Stoffwechsel von Herbiziden mitgeteilt und diskutiert, die unter Verwendung von ¹⁴C, ³H und ¹⁵N durchgeführt wurden.     

Crack growth on the basal plane in single crystal zinc: experiments and computations

Crack propagation on the basal planes in zinc was examined by means of in situ fracture testing of pre-cracked single crystals, with specific attention paid to the fracture mechanism. During quasistatic loading, crack propagation occurred in short bursts of dynamic crack extension followed by periods of arrests, the latter accompanied by plastic deformation and blunting of the crack-tip. In situ observations confirmed nucleation and propagation of microcracks on parallel basal planes and plastic deformation and failure of the linking ligaments. Pre-existing twins in the crack path serve as potent crack arrestors. The crystallographic orientation of the crack growth direction on the basal plane was found to influence both the fracture load as well as the deformation at the crack-tip, producing fracture surfaces of noticeably different appearances. Finite element analysis incorporating crystal plasticity was used to identify dominant slip systems and the stress distribution around the crack-tip in plane stress and plane strain. The computational results are helpful in rationalizing the experimental observations including the mechanism of crack propagation, the orientation dependence of crack-tip plasticity and the fracture surface morphology.     

Vibrational Spectroscopic and Theoretical Studies of Urea Derivatives with Biochemical Interest: N,N′-Dimethylurea,N,N,N′,N′-Tetramethylurea,and N,N′-Dimethylpropyleneurea

Abstract

Mid-infrared, far-infrared, and Raman vibrational spectroscopic studies were combined with density functional theory (DFT) calculations and normal coordinate force field analyses for N,N′-dimethylurea (DMU), N,N,N′,N′-tetramethylurea (TMU), and N,N′-dimethylpropyleneurea (DMPU: IUPAC name 1,3-dimethyltetrahydropyrimidin-2(1H)-one). The equilibrium molecular geometry of DMU (all three conformers), TMU, and DMPU and the frequencies, intensities, and depolarization ratios of their fundamental infrared (IR) and Raman vibrational transitions were obtained by DFT calculations. The vibrational spectra were fully analyzed by normal coordinate methods as well. A starting force field for DMPU was obtained by adapting corresponding force constants for DMU and TMU, resulting after refinements in the stretching force constants C=O (7.69, 7.30, 7.68 N·cm^?1), C–N (5.16, 5.55, 5.05 N·cm^?1), and C-Me (5.93, 4.00, 4.22 N·cm^?1) for DMU, TMU, and DMPU, respectively. The dominating conformer of liquid DMU was identified as trans-trans, strong intermolecular hydrogen bonding was verified in solid DMU, and weak dipole–dipole association was found in liquid TMU and in DMPU. Special attention was paid to analyzing the methyl group frequencies, which revealed deviations from local C_3v symmetry. A linear correlation was found between the CH stretching force constants and the inverse of the CH bond lengths (1/r ²). The averaged NH stretching frequencies of gaseous, dissolved, and solid urea and of DMU, with variations for hydrogen bonding of different strength, are linearly correlated to the NH stretching force constants. Characteristic skeletal vibrations were assigned for a broad variety of urea derivatives and also for pyrimidine derivatives, which all contain the N₂C=O entity. The very strong IR bands of C=O stretching (1,676 ± 40 cm^?1) and asymmetric CN₂ stretching (1,478 ± 60 cm^?1), and the very intense Raman feature of symmetric CN₂ stretching or ring breathing (757 ± 80 cm^?1), can be recognized as fingerprint bands also for the pyrimidine derivatives cytosine, thymine, and uracil, which all are nucleobases in DNA and RNA nucleotides.