Existence of a Steady Flow of Stokes Fluid Past a Linear Elastic Structure Using Fictitious Domain

We use fictitious domain method with penalization for the Stokes equation in order to obtain approximate solutions in a fixed larger domain including the domain occupied by the structure. The coefficients of the fluid problem, excepting the penalizing term, are independent of the deformation of the structure. It is easy to check the inf-sup condition and the coercivity of the Stokes problem in the fixed domain. Subtracting the structure equations from the fictitious fluid equations in the structure domain, we obtain a weak formulation in a fixed domain, where the continuity of the stress at the interface does not appear explicitly. Existence of a solution is proved when the structure displacement is generated by a finite number of modes.     

Interwall conductance in double-walled armchair carbon nanotubes

The dependence of the interwall conductance on distance between walls and relative positions of walls are calculated at the low voltage by Bardeen method for (n,n)@(2n,2n) double-walled carbon nanotubes (DWCNTs) with n=5,6,…,10. The calculations show that interwall conductance does not depend on temperature (for T?500 K) and current-voltage characteristic is linear. The conductance decreases by 6 orders of magnitude when the interwall distance is doubled. Thus, depending on the interwall distance, DWCNTs can be used as temperature stable nanoresistors or nanocapacitors.     

Vibrational energy levels of methyl chloride calculated from full dimensional ab initio potential energy surface

The vibrational levels for two isotopic species of methyl chloride have been calculated in the region 0-3500 cm⁻¹ from the ab initio potential energy surface (PES). The isotopic shift of vibrational levels of molecules ¹²CH₃³⁵Cl and ¹²CH₃³⁷Cl has been calculated. The correlation consistent basis sets cc-pVTZ and cc-pVQZ are employed to calculate energy values for 7957 and 3758 points correspondingly from a large domain of the nine-dimensional internal coordinate space. The analytic global PES is fitted with the standard deviation of 4.5 cm⁻¹.     

Synthesis and structural consideration of 1‐chloro‐N,N′,N″‐tris(pentafluorophenyl)azagermatrane: Azagermatrane with the shortest intramolecular N → Ge bond

Two compounds of a novel‐type azagermatrane, N(CH₂CH₂NC₆F₅)₃Ge‐Hal: HalCl ( 1 ), Br ( 2 ), were prepared via a metathetical reaction of trilithium salt of tetramine, N[CH₂CH₂N(Li)C₆F₅]₃, with corresponding GeHal₄. A single crystal structure of 1 was determined by the X‐ray diffraction study: The compound shows the strongest transannular N_ax → Ge interaction (2.148(7) Å) among other studied azagermatranes. © 2008 Wiley Periodicals, Inc. Heteroatom Chem 19:738–741, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20476     

Delay differential equations for mode-locked semiconductor lasers

We propose a new model for passive mode locking that is a set of ordinary delay differential equations. We assume a ring-cavity geometry and Lorentzian spectral filtering of the pulses but do not use small gain and loss and weak saturation approximations. By means of a continuation method, we study mode-locking solutions and their stability. We find that stable mode locking can exist even when the nonlasing state between pulses becomes unstable.     

On minimal Hausdorff and minimal Urysohn functions

In this article, we extend the work on minimal Hausdorff functions initiated by Cammaroto, Fedorchuk and Porter in a 1998 paper. Also, minimal Urysohn functions are introduced and developed. The properties of heredity and productivity are examined and developed for both minimal Hausdorff and minimal Urysohn functions.