A Sixth-order P-stable Symmetric Multistep Method for Periodic Initial-value Problems of Second-order Differential Equations

A sixth-order P-stable symmetric multistep method for periodicinitial-value problem y = f(x, y) is suggested. It requiresthree function evaluations per iteration. The method can beconsidered as a stabilized modification of Lambert and Watson'ssixth-order implicit method which has a finite interval of periodicity.The method is illustrated for three numerical examples.     

Benchmarking and scaling studies of pseudospectral code Tarang for turbulence simulations

Tarang is a general-purpose pseudospectral parallel code for simulating flows involving fluids, magnetohydrodynamics, and Rayleigh–Bénard convection in turbulence and instability regimes. In this paper we present code validation and benchmarking results of Tarang. We performed our simulations on 1024³, 2048³, and 4096³ grids using the HPC system of IIT Kanpur and Shaheen of KAUST. We observe good ‘weak’ and ‘strong’ scaling for Tarang on these systems.     

Axioms of spheres in lightlike geometry of submanifolds

We prove that if an indefinite Kaehler manifold \(\bar {M}\) with lightlike submanifolds satisfies the axioms of holomorphic 2r-spheres, axioms of holomorphic 2r-planes, axioms of transversal r-spheres and axioms of transversal r-planes, then it is an indefinite complex space form.     

Laser shock peening of steam turbine blade for enhanced service life

Fretting-fatigue is an important factor influencing service life of turbine blades. The present paper describes laser shock peening of potential crack nucleation site in the root region of steam turbine blade for its enhanced service life. The experimental study, performed with an in-house developed 2.5 J/7 ns Nd:YAG laser demonstrated that laser peening introduced a residual surface compressive stress of ?260 to ?390 MPa. Case depth of laser peened surface layer was found to be more than 900 μm.     

Thermostable Broad Band Polarizing PVA-Film: Theoretical and Experimental Investigations

In the present work, for the first time on the basis of poly(vinyl alcohol)(PVA), 2-(4-dimethylaminostyryl)-1-ethylquinolinium iodide(quinaldine red(QR)) and trisodium(4 E)-5-oxo-1-(4-sulfonatophenyl)-4-[(4-sulfonatophenyl)hydrazono]-3 pyrazolecarboxylate(tartrazine(T)), thermostable polarizing film in a wide range of spectra(λ_(max) = 394～511 nm) with polarization efficiency(PE) = 98% in absorption maximum and stretching degree(Rs) = 3.5 was developed. The basic spectral-polarization parameters(polarization efficiency and transmittance) of oriented colored PVA-films were measured and discussed. During the work it was found that oriented PVA-films are the phenomenon of anisotropy of thermal conductivity(λⅡ/λl). It is a very important parameter for the development of thermostable PVA-polarizing films. For the first time quantum-chemical calculations using density functional theory(DFT) approach for structural analysis and electronic spectrum of the QR were carried out via the B3 LYP/dgdzvp and TDB3 LYP/dgdzvp methods. Interpretation of absorption strips in visible region of spectrum was also reported. The excitation energies, electronic transitions and oscillator strengths for the studied structures have also been calculated(B3 LYP/dgdzvp). The NBO analysis and Mulliken atomic charges of the QR were carried out.