辛方法和弹性圆柱壳在内外压和轴向冲击下的动态屈曲

针对有内压或外压的弹性圆柱壳在轴向冲击载荷耦合作用下的动态屈曲问题,构造哈密顿体系,在辛空间中将临界载荷和动态屈曲模态归结为辛本征值和本征解问题,从而形成一种辛方法。该方法直接得到非轴对称的屈曲模态。数值结果给出了圆柱壳问题的临界载荷和屈曲模态以及一些规律。     

Grassmannians of 2-Sided Vector Spaces

Let k ? K be an extension of fields, and let A ? M _n (K) be a k-algebra. We study parameter spaces of m-dimensional subspaces of K ⁿ which are invariant under A. The space  _A (m, n), whose R-rational points are A-invariant, free rank m summands of R ⁿ , is well known. We construct a distinct parameter space,  _A (m, n), which is a fiber product of a Grassmannian and the projectivization of a vector space. We then study the intersection  _A (m, n) ∩  _A (m, n), which we denote by  _A (m, n). Under suitable hypotheses on A, we construct affine open subschemes of  _A (m, n) and  _A (m, n) which cover their K-rational points. We conclude by using  _A (m, n),  _A (m, n), and  _A (m, n) to construct parameter spaces of 2-sided subspaces of 2-sided vector spaces.     

Effect of electron inertia on large amplitude solitary waves in presence of kinematic viscosity in dusty plasma

Nonlinear dust acoustic solitary waves in a dusty plasma are studied for nonzero kinematic viscosity. Sagdeev’s potential can be obtain upto any order in ϕ. The existence of soliton solution is determined by pseudopotential approach. It is seen that the electron inertia has a significant effect on the existence of solitary waves in presence of kinematic viscosity.     

Ion acoustic solitary waves with adiabatic ions in magnetized electron-positron-ion plasmas

Linear and nonlinear ion acoustic waves in the presence of adiabatically heated ions in magnetized electron-positron-ion plasmas are studied. The Sagdeev potential approach is employed to obtain the energy integral equation in such a mulitcomponent plasma using fluid theory. It is found that electron density humps are formed in the subsonic region in magnetized electron-positron-ion plasmas. The amplitude of electron density hump is decreased with the increase of hot ion temperature in electron-positron-ion plasmas. However, the increase in positron concentration and obliqueness of the wave increases the amplitude of nonlinear structure. The increase in positron concentration also reduces the width of the nonlinear structure in a magnetized multicomponent plasma. The numerical solutions in the form of solitary pulses are also presented for different plasma cases. The results may be applicable to astrophysical plasma situations, where magnetized electron-positron-ion plasma with hot ions can exist.     

Mechanical properties of nanotubes of polyelectrolyte multilayers

The elastic properties of nanotubes fabricated by layer-by-layer (LbL) assembly of polyelectrolytes in the nanopores of polycarbonate track-etched membranes have been investigated by resonant contact Atomic Force Microscopy (AFM), for nanotube diameters in the range of 100 to 200 nm. The elastic modulus of the nanotubes was computed from the resonance frequencies of a cantilever resting on freely suspended LbL nanotubes. An average value of 115 MPa was found in air for Young's modulus of these nanostructures, well below the values reported for dry, flat multilayers, but in the range of values reported for water-swollen flat multilayers. These low values are most probably due to the lower degree of ionic cross-linking of LbL nanotubes and their consequently higher water content in air, resulting from the peculiar mode of growth of nanoconfined polyelectrolyte multilayers.     

iVI-TD-DFT: An iterative vector interaction method for exterior/interior roots of TD-DFT

The recently proposed iterative vector interaction (iVI) method for large Hermitian eigenvalue problems (Huang et al., J. Comput. Chem. 2017, 38, 2481) is extended to generalized eigenvalue problems, HC = SCE , with the metric S being either positive definite or not. Although, it works with a fixed-dimensional search subspace, iVI can converge quickly and monotonically from above to the exact exterior/interior roots. The algorithms are further specialized to nonrelativistic and relativistic time-dependent density functional theories (TD-DFT) by taking the orbital Hessian as the metric (i.e., the inverse TD-DFT eigenvalue problem) and incorporating explicitly the paired structure into the trial vectors. The efficacy of iVI-TD-DFT is demonstrated by various examples. © 2018 Wiley Periodicals, Inc.     

Selective Carbanion–Pyridine Coordination of a Reactive P,N Ligand to RhI

Ligands with reactive carbon sites in the periphery of a metal center have emerged as a powerful approach for metal–ligand bond activation. These reactive carbon sites are commonly generated by deprotonation strategies. Carbon–silicon bond cleavage is a potential alternative to access such constructs. Herein, the monodesilylation of bis-silyl-substituted P,N scaffold PN^Si2 in the coordination sphere of [Rh^I(Cl)(CO)( PN^Si2 )] ( 1 ) with sodium azide is disclosed. This affords a unique dinucleating anionic κ²-C,N-κ¹-P ligand with a carbanionic methine carbon atom directly bound to rhodium as part of a four-membered Rh-N-C-C rhodacycle. This dimer undergoes meta-pyridine C−H activation facilitated by weak bases, which leads to a desymmetrization of the system and provides a σ,π-bridging 3-pyridyl fragment bound to Rh^I. The facile Si−C cleavage strategy may pave the way to studying the reactivity and functionalization of a variety of κ²-C,N-coordinated pyridine scaffolds for selective transformations.     

Conversion issues between microwave radiance and brightness temperature

Microwave radiances are usually converted into brightness temperatures for data assimilation and retrievals. The Rayleigh-Jeans approximation has been believed to be a good approximation for the conversion at low frequencies, but inaccurate at high frequencies. However, the simplified radiative transfer models under the Rayleigh-Jeans approximation (hereafter referred as BT-RTE) have been successfully applied in radiance simulations for frequencies below 183 GHz, which has somewhat puzzled the radiative transfer community. This paper clarifies the confusion. In addition, the conversion formula for the third and the fourth Stokes components are derived.Simulations for a polarized sensor, the Special Sensor Microwave Imager and Sounder, show that the BT-RTE is generally accurate. Results for a polarimetric sensor, WINDSAT, show that the third and the fourth Stokes radiances should be converted using the exact conversion formula given in this study rather than using a direct Planck function conversion.