Generalized rayleigh principle and its applications

In this paper, we mainly deal with cigenvalue problems of non-self-adjoint operator. To begin with, the generalized Rayleigh variational principle, the idea of which was due to Morse and Feshbach, is examined in detail and proved more strictly in mathematics. Then, other three equivalent formulations of it are presented. While applying them to approximate calculation we find the condition under which the above variational method can be identified as the same with Galerkin's one. After that we illustrate the generalized variational principle by considering the hydrodynamic stability of plane Poiseuille flow and Bénard convection. Finally, the Rayleigh quotient method is extended to the cases of non-self-adjoint matrix in order to determine its strong eigenvalne in linear algebra.

Vertical transport and exchange of materials in the upper waters of the oceans (VERTEX): introduction to the program, hydrographic conditions and major component fluxes during VERTEX I

This paper introduces VERTEX, a multi-disciplinary research program dealing with various aspects of particle transport in the upper, high-energy layers (0-2000 m) of the ocean. Background information is presented on hydrography, biological composition of trapped particulates, and major component fluxes observed on a cruise off central California (VERTEX I). Organic C fluxes measured with two trap systems are compared with several other estimates taken from the literature. The intent of this overview paper is to provide a common setting in an economical manner, and avoid undue repetition of background and ancillary information in subsequent publications. (PDF is 43 pages).

Least Squares Estimation Principle and its Geometrical Interpretation

pdf contains 14 pages)

Study of the damage-induced anisotropy of quasi-brittle materials using the component assembling model

Damage-induced anisotropy of quasi-brittle materials is investigated using component assembling model in this study. Damage-induced anisotropy is one significant character of quasi-brittle materials coupled with nonlinearity and strain softening. Formulation of such complicated phenomena is a difficult problem till now. The present model is based on the component assembling concept, where constitutive equations of materials are formed by means of assembling two kinds of components' response functions. These two kinds of components, orientational and volumetric ones, are abstracted based on pair-functional potentials and the Cauchy - Born rule. Moreover, macroscopic damage of quasi-brittle materials can be reflected by stiffness changing of orientational components, which represent grouped atomic bonds along discrete directions. Simultaneously, anisotropic characters are captured by the naturally directional property of the orientational component. Initial damage surface in the axial-shear stress space is calculated and analyzed. Furthermore, the anisotropic quasi-brittle damage behaviors of concrete under uniaxial, proportional, and nonproportional combined loading are analyzed to elucidate the utility and limitations of the present damage model. The numerical results show good agreement with the experimental data and predicted results of the classical anisotropic damage models.

A comparative study of Young's modulus of single-walled carbon nanotube by CPMD, MD, and first principle simulations

Carbon nanotubes (CNTs), due to their exceptional magnetic, electrical and mechanical properties, are promising candidates for several technical applications ranging from nanoelectronic devices to composites. Young's modulus holds the special status in material properties and micro/nano-electromechanical systems (MEMS/NEMS) design. The excellently regular structures of CNTs facilitate accurate simulation of CNTs' behavior by applying a variety of theoretical methods. Here, three representative numerical methods, i.e., Car-Parrinello molecular dynamics (CPMD), density functional theory (DFT) and molecular dynamics (MD), were applied to calculate Young's modulus of single-walled carbon nanotube (SWCNT) with chirality (3,3). The comparative studies showed that the most accurate result is offered by time consuming DFT simulation. MID simulation produced a less accurate result due to neglecting electronic motions. Compared to the two preceding methods the best performance, with a balance between efficiency and precision, was deduced by CPMD.

Adsorption of formaldehyde molecule on the intrinsic and Al-doped graphene: a first principle study

To search for a high sensitivity sensor for formaldehyde (H2CO), We investigated the adsorption of H2CO on the intrinsic and Al-doped graphene sheets using density functional theory (DFT) calculations. Compared with the intrinsic graphene, the Al-doped graphene system has high binding energy value and short connecting distance, which are caused by the chemisorption of H2CO molecule. Furthermore, the density of states (DOS) results show that orbital hybridization could be seen between H2CO and Al-doped graphene sheet, while there is no evidence for hybridization between the H2CO molecule and the intrinsic graphene sheet. Therefore, Al-doped graphene is expected to be a novel chemical sensor for H2CO gas. We hope our calculations are useful for the application of graphene in chemical sensor.