Modelling of CO2 laser welding of magnesium alloys

Laser welding is an important joining process for magnesium alloys. These materials are being increasingly used in different applications such as in aerospace, aircraft, automotive, electronics, etc. To date, carbon dioxide (CO₂) neodymium-doped yttrium aluminum garnet (Nd:YAG) and the high power diode laser have been extensively used to investigate the weldability of magnesium alloys. The present work describes an analytical thermal model for the weldability of magnesium alloys (WE43) using an industrial (CO₂) laser source. The main target of the project is to present to the industrial community a simple and rapid tool for the determination of the penetration depth and the bead width as a function of both the incident laser power and welding speed. The proposed model is based on the Davis thermal approach, largely considered for the characterization of the average radius of the liquid zone, aiming at predicting the joint shape. Moreover, since during the welding process considered in this study, a protecting gas is used to avoid joint oxidation, both thermal convection and radiation phenomena in the welding area have been estimated and introduced in our model for a better characterization of the welding process. The obtained results have been compared to the experimental ones and a satisfactory correlation has been observed, indicating the reliability of the model developed in this study.     

On oscillation of eigenfunctions of a fourth-order problem with spectral parameters in the boundary conditions

In the paper, we study the problem on the number of zeros of eigenfunctions of the fourth-order boundary-value problem with spectral and physical parameters in the boundary conditions. We show that the number of zeros of the eigenfunctions corresponding to eigenvalues of positive type behaves in a usual way (it is equal to the serial number of an eigenvalue increased by 1), but, however, the number of zeros of the eigenfunction corresponding to an eigenvalue of negative type can be arbitrary. In the case of a sufficient smoothness of coefficients of the differential expression, we write the asymptotics in the physical parameter for such a number. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 4, pp. 41–52, 2006.     

Strength considerations of optical waveguide fibers

An important aspect of optical waveguide fiber made of glass is whether it will break under a wide variety of service and manufacturing conditions. This paper covers some of the testing in which stress, length, time, and environment were vaned. The use of Weibull statistics with these data indicates that a statistically predictable behavior exists for populations of glass fibers. Extrapolation from short lengths and short times to very long lengths and very long times must be based on an understanding of the “constants” in the prediction equation. That is, these “constants” can be shown to vary when the three basic parameters cover orders of magnitude in range.     

A Deodhar-type stratification on the double flag variety

We describe a partition of the double flag variety G/B⁺ × G/B^- of a complex semisimple algebraic group G analogous to the Deodhar partition on the flag variety G/B⁺. This partition is a refinement of the stratification into orbits both for B⁺ × B^- and for the diagonal action of G, just as Deodhar's partition refines the orbits of B⁺ and B^-. We give a coordinate system on each stratum, and show that all strata are coisotropic subvarieties. Also, we discuss possible connections to the positive and cluster geometry of G/B⁺ × G/B^-, which would generalize results of Fomin and Zelevinsky on double Bruhat cells and Marsh and Rietsch on double Schubert cells.     

Core–shell‐type multiarm star polyethylenimine‐block‐poly(ε‐caprolactone): Synthesis and guest encapsulation potential

Novel multiarm star copolymers with poly(?‐caprolactone) (PCL) as the arms and hyperbranched polyethylenimine (HPEI) as the core have been successfully prepared by the tin(II) 2‐ethylhexanoate catalyzed ring‐opening polymerization of ?‐caprolactone (CL) with HPEI used directly as a macroinitiator. Not only primary but also secondary amine groups of HPEI participate in initiating the ring‐opening polymerization of CL with almost 100% initiation efficiency. The average degree of polymerization of the PCL arms can be controlled by the feed ratio of the monomers to the initiating sites. Because of the polarity difference of the PCL arms and HPEI core, the obtained multiarm star polymers display an inverted micellar structure with potential extraction and encapsulation of water‐soluble guests. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4165–4173, 2006     

Error quantification in strain mapping methods.

In this article a method for determining errors of the strain values when applying strain mapping techniques has been devised. This methodology starts with the generation of a thickness/defocus series of simulated high-resolution transmission electron microscopy images of InAsxP1-x/InP heterostructures and the application of geometric phase. To obtain optimal defocusing conditions, a comparison of different defocus values is carried out by the calculation of the strain profile standard deviations among different specimen thicknesses. Finally, based on the analogy of real state strain to a step response, a characterization of strain mapping error near an interface is proposed.     

Laser pulse control of exciton dynamics in a biological chromophore complex

Femtosecond laser pulse control of exciton dynamics in a biological chromophore complex is studied theoretically. The computations use the optimal control theory specified to open quantum systems and formulated in the framework of the rotating wave approximation. Based on the laser pulse induced formation of an excitonic wave packet the possibility to localize excitation energy at a certain chromophore within a photosynthetic antenna system (FMO complex of green bacteria) is investigated. Details of exciton dynamics driven by a polarization shaped pulse are discussed.     

Oxidative Coupling of Methane over W‐Mn/SiO2 Catalyst

W‐Mn/SiO₂ catalyst has been developed in our laboratory (LICP), which is active, selective and stable for oxidative coupling of methane (OCM) in fixed bed and fluidized bed reactors. The research results have been reproduced at different reaction conditions by two groups of J. H. Lunsford (JH‐LL) from Texas A & M University and R. M. Lambert (RMLL) from University of Cambridge respectively. The basic research aspects on this catalyst systems, reaction performances, structure characterization and reaction mechanism were reviewed. A model on two active sites related to W^6+/5+ and Mn^3+/2+ has been suggested for activation of methane and oxygen respectively.     

Idempotency of linear combinations of three idempotent matrices, two of which are commuting

The considerations of the present paper were inspired by Baksalary [O.M. Baksalary, Idempotency of linear combinations of three idempotent matrices, two of which are disjoint, Linear Algebra Appl. 388 (2004) 67-78] who characterized all situations in which a linear combination P=c₁P₁+c₂P₂+c₃P₃, with c_i, i=1,2,3, being nonzero complex scalars and P_i, i=1,2,3, being nonzero complex idempotent matrices such that two of them, P₁ and P₂ say, are disjoint, i.e., satisfy condition P₁P₂=0=P₂P₁, is an idempotent matrix. In the present paper, by utilizing different formalism than the one used by Baksalary, the results given in the above mentioned paper are generalized by weakening the assumption expressing the disjointness of P₁ and P₂ to the commutativity condition P₁P₂=P₂P₁.     

High-resolution infrared study of the 2ν3 (A1, E) and ν1 + ν3 (E) bands of NF3

The 2ν₃ overtone (A₁, E) and the ν₁ + ν₃ (E) combination bands of the oblate symmetric top ¹⁴NF₃ were studied by FTIR spectroscopy with a resolution of 2.5 × 10⁻³ cm⁻¹. Nearly 500 lines up to K_max/J_max = 30/43 were observed for the weak A₁ component reaching the v₃ = 2⁰ substate (1803.1302 cm⁻¹), the majority of which corresponded to reinforced K = 3p-type transitions. For the strong E component reaching the v₃ = 2^±2 substate (1810.4239 cm⁻¹), about 3550 transitions were assigned up to K_max/J_max = 65/69, favoring a clear observation of the ℓ(4, −2) and ℓ(4, 4) splittings within the kℓ = −2 and +4 sublevels, respectively. The two v₃ = 2 substates are linked by the ℓ(2, 2)- and ℓ(2, −1)-type interactions, providing severe crossings, respectively, at K′ = 6 and near K′ = 24 on the v₃ = 2⁺² side. A model working in the D-reduction and including all these ℓ-type interactions could reproduce together 3695 nonzero weighted experimental data (NZW) through 33 free parameters with a standard deviation of σ = 0.357 × 10⁻³  cm⁻¹. As for the ν₁ + ν₃ (E) combination band, about 3690 lines were assigned up to K_max/J_max = 45/55. Its v₁ = v₃ = 1 upper state (1931.577 5 cm⁻¹) was treated using the same model recently applied to the v₃ = 1 (E, 907.5413 cm⁻¹) state. It yielded 21 free parameters through 3282 NZW experimental data, adjusted with σ = 0.344 × 10⁻³  cm⁻¹ in the D-reduction. For the two excited states, the small and unobserved ℓ(0, 6) interaction was tested as useless. To confirm the adequacy of the vibrationally isolated models used, some other reductions of the Hamiltonian were tried. For the v₃ = 2 state, the D-, L-, and LD-reductions led to similar σ’s, while the Q one was not successful. For the v₁ = v₃ = 1 state, the D- and Q-reductions gave comparable σ’s, while the QD-reduction was not as good. The corresponding unitary equivalence relations are generally more nicely fulfilled for the v₃ = 2 state than for the v₁ = v₃ = 1 state. The three derivable anharmonicity constants in cm⁻¹ are x₃₃ = −4.1528, g₃₃ = +1.8235 and x₁₃ = −7.9652.