Asymptotic analysis on weakly forced vibration of axially moving viscoelastic beam constituted by standard linear solid model

The weakly forced vibration of an axially moving viscoelastic beam is inves- tigated. The viscoelastic material of the beam is constituted by the standard linear solid model with the material time derivative involved. The nonlinear equations governing the transverse vibration are derived from the dynamical, constitutive, and geometrical relations. The method of multiple scales is used to determine the steady-state response. The modulation equation is derived from the solvability condition of eliminating secular terms. Closed-form expressions of the amplitude and existence condition of nontrivial steady-state response are derived from the modulation equation. The stability of non- trivial steady-state response is examined via the Routh-Hurwitz criterion.

Structure of Graphene, and Mechanical and Bonding Characteristics of Single Wall Carbon Nanotube by Linear Scaling Quantum Mechanical Method

Using a linear scaling self-consistent-charge density functional tight binding （SCC-DFTB） and an ab initio Omol method, the bonding characteristics and Young＇s modulus of （10, 0） and （10,10） single-walled carbon nanotubes are calculated. The structure of a graphene is also calculated. It is found that the C-C and C-H bond length, their distribution characteristics on the tube, and Young^s modulus of the tube by linear scaling SCC-DFTB are identical to those by ab initio, while the computing cost by the linear scaling SCC-DFTB is reduced by more than 30 times as compared with that by the Dmol for the （10,0） and （10,10） tubes. By computing the structure of a graphene it is also found that the linear scaling SCCDFTB is reliable and time-saving.

Linear Scaling Discontinuous Galerkin Density Matrix Minimization Method with Local Orbital Enriched Finite Element Basis:1-D Lattice Model System

In the first of a series of papers,wewill study a discontinuous Galerkin(DG)framework for many electron quantum systems.The salient feature of this framework is the flexibility of using hybrid physics-based local orbitals and accuracy-guaranteed piecewise polynomial basis in representing the Hamiltonian of the many body system.Such a flexibility is made possible by using the discontinuous Galerkin method to approximate the Hamiltonian matrix elements with proper constructions of numerical DG fluxes at the finite element interfaces.In this paper,we will apply the DG method to the density matrix minimization formulation,a popular approach in the density functional theory of many body Schrodinger equations.The density matrix minimization is to find the minima of the total energy,expressed as a functional of the density matrixρ(r,r′),approximated by the proposed enriched basis,together with two constraints of idempotency and electric neutrality.The idempotency will be handled with theMcWeeny’s purification while the neutrality is enforced by imposing the number of electrons with a penalty method.A conjugate gradient method(a Polak-Ribiere variant)is used to solve the minimization problem.Finally,the linear-scaling algorithm and the advantage of using the local orbital enriched finite element basis in the DG approximations are verified by studying examples of one dimensional lattice model systems.