Mortar element methods for parabolic problems

In this article a standard mortar finite element method and a mortar element method with Lagrange multiplier are used for spatial discretization of a class of parabolic initial‐boundary value problems. Optimal error estimates in L^∞(L²) and L^∞(H¹)‐norms for semidiscrete methods for both the cases are established. The key feature that we have adopted here is to introduce a modified elliptic projection. In the standard mortar element method, a completely discrete scheme using backward Euler scheme is discussed and optimal error estimates are derived. The results of numerical experiments support the theoretical results obtained in this article. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008     

General implementation of the relativistic coupled-cluster method

We report the development of a general order relativistic coupled-cluster (CC) code. Our implementation is based on Kramers-paired molecular spinors, utilizes double group symmetry, and is applicable with the full Dirac-Coulomb and several approximate relativistic Hamiltonians. The available methods include iterative and perturbative single-reference CC approaches with arbitrary excitations as well as a state-selective multi-reference CC ansatz. To illustrate the performance of the new code, benchmark calculations have been performed for the total energies, bond lengths, and vibrational frequencies of the monoxides of Group IVa elements. The trends due to the simultaneous inclusion of relativity as well as higher-order electron correlation effects are analyzed. The newly developed code significantly widens the scope of the ab initio relativistic calculations, for both molecules and atoms alike, surpassing the accuracy and reliability of the currently available implementations in the literature.     

Correction To: On post-resonance backward whirl in an overhung rotor with snubbing contact

Nonlinear Dynamics - On the title page, author Oleg Shiryavev should be spelled as Oleg Shiryayev.     

Conforming finite element methods for the von Kármán equations

In this paper, we consider canonical von Kármán equations that describe the bending of thin elastic plates defined on polygonal domains. A conforming finite element method is employed to approximate the displacement and Airy stress functions. Optimal order error estimates in energy, H ¹ and L ² norms are deduced. The results of numerical experiments confirm the theoretical results obtained.     

A Mixed Finite Element Method for Fourth Order Eigenvalue Problems

A new mixed finite element method for approximating eigenpairs of IV order elliptic eigenvalue problems with Dirichlet boundary conditions has been given. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A weight-function approach for determining watershed initial conditions for combustion waves

In many generic combustion models, one finds that a combustionwave will develop with a specific wave speed. However, thereare possible initial temperature profiles which do not evolveinto such waves, but rather die out to the ambient temperature.There can exist, in some models, a clear distinction betweenthose initial conditions that do evolve into combustion wavesand those that do not; this is sometimes referred to as thewatershed initial condition. When fuel consumption is consideredto be negligible, analytical methods can be used to obtain theexact watershed. In this paper, we consider the problem of determiningpseudo-watersheds and ascertaining the relationship betweenthese pseudo-watersheds and the exact watersheds. In the processa novel weight-function approach for infinite spatial domainsis developed.     

Bioactivity and mechanical properties of nickel‐incorporated hydrogenated carbon nanocomposite thin films

In this paper, the influence of nickel incorporation on the mechanical properties and the in vitro bioactivity of hydrogenated carbon thin films were investigated in detail. Amorphous hydrogenated carbon (a‐C:H) and nickel‐incorporated hydrogenated carbon (Ni/a‐C:H) thin films were deposited onto the Si substrates by using reactive biased target ion beam deposition technique. The films' chemical composition, surface roughness, microstructure and mechanical properties were investigated by using XPS, AFM, TEM, nanoindentation and nanoscratch test, respectively. XPS results have shown that the film surface is mainly composed of nickel, nickel oxide and nickel hydroxide, whereas at the core is nickel carbide (Ni₃C) only. The presence of Ni₃C has increased the sp² carbon content and as a result, the mechanical hardness of the film was decreased. However, Ni/a‐C:H films shows very low friction coefficient with higher scratch‐resistance behavior than that of pure a‐C:H film. In addition, in vitro bioactivity study has confirmed that it is possible to grow dense bone‐like apatite layer on Ni/a‐C:H films. Thus, the results have indicated the suitability of the films for bone‐related implant coating applications. Copyright © 2011 John Wiley & Sons, Ltd.