Optimal time advancing dispersion relation preserving schemes

In this paper we examine the constrained optimization of explicit Runge–Kutta (RK) schemes coupled with central spatial discretization schemes to solve the one-dimensional convection equation. The constraints are defined with respect to the correct error propagation equation which goes beyond the traditional von Neumann analysis   developed in Sengupta et al. [T.K. Sengupta, A. Dipankar, P. Sagaut, Error dynamics: beyond von Neumann analysis, J. Comput. Phys. 226 (2007) 1211–1218]. The efficiency of these optimal schemes is demonstrated for the one-dimensional convection problem and also by solving the Navier–Stokes equations for a two-dimensional lid-driven cavity (LDC) problem. For the LDC problem, results for Re=1000$\mathit{Re}=1000$ are compared with results using spectral methods in Botella and Peyret [O. Botella, R. Peyret, Benchmark spectral results on the lid-driven cavity flow, Comput. Fluids 27 (1998) 421–433] to calibrate the method in solving the steady state problem. We also report the results of the same flow at Re=10,000$\mathit{Re}=10\text{,}000$ and compare them with some recent results to establish the correctness and accuracy of the scheme for solving unsteady flow problems. Finally, we also compare our results for a wave-packet propagation problem with another method developed for computational aeroacoustics.     

Symmetry analysis and optimal systems of generalized Chaplygin gas equations with a source term

The system of generalized Chaplygin gas equations with a coulomblike friction term has been investigated by using the famous Lie symmetry method. A direct and systematic algorithm based on the adjoint transformation and invariants of the admitted Lie algebras is then used to construct one- and two-dimensional optimal system of the Chaplygin gas equations. Inequivalent classes of group invariant solutions are then obtained using the one-dimensional optimal system. Further, the evolutionary behaviour of the weak discontinuity wave within the state characterized by one of the group invariant solutions is investigated in detail, and certain observations are noted in respect to their contrasting behaviour.     

The Schur multiplier of central product of groups

Let G be a central product of two groups H and K. We study second cohomology group of G, having coefficients in a divisible abelian group D with trivial G-action, in terms of the second cohomology groups of certain quotients of H and K. In particular, for $D={\mathbb{C}}^{?}$, some of our results provide a refinement of results from Wiegold (1971) [10] and Eckmann et al. (1973) [2].     

Optical behaviour of swift heavy ions irradiated poly(vinyl alcohol) films

Polyvinyl alcohol films were irradiated to 90 MeV O ⁶⁺ and 150 MeV Si ¹⁴⁺ ions at fluence ranging from 10¹⁰ to 10¹² ions/cm². The observed changes in optical energy gap of this polymer have been investigated and results are tried to be explained in terms of energy transferred by the incident ions. It has been noticed that the value of optical energy gap decreases with increasing energy loss during the ion–polymer interaction process.     

Defect centres and thermoluminescence in SrS:Bi phosphor

Thermoluminescence (TL) and electron spin resonance studies have been carried out on SrS:Bi phosphor. The TL glow curve is broad and indicates a dominant peak at 120 ^°C with two additional peaks, not clearly resolved, appearing as shoulders at around 180 and 250 ^°C. Two defect centres are observed at room temperature. One of them is characterized by an isotropic g-value 2.0034 and is assigned to an F⁺ centre. Step annealing measurements indicate a possible association between the F⁺ centre and the three TL peaks.     

On Central Automorphisms Fixing the Center Element-Wise

Let G be a finite p-group of nilpotency class 2. We find necessary and sufficient conditions on G such that each central automorphism of G fixes the center of G element-wise.     

Layer thinning transition in an achiral four-ring hockey stick shaped liquid crystal

Depolarized reflected light microscopy and high resolution optical reflectivity measurements have been conducted on free-standing films of an achiral four-ring hockey stick shaped liquid crystal exhibiting SmA-B2–SmX* transition sequence. A layer thinning transition above the bulk isotropic-SmA phase transition has been observed. This behaviour was highly irreproducible, indicating an irregular layer thinning transition. From optical reflectivity data, both thickness of the free-standing films and the smectic interlayer spacing were determined. This is the first report of the layer thinning transition in a hockey stick shaped liquid crystal.     

Fabrication of nanopatterned germanium surface by laser-induced etching: AFM, Raman and PL studies

Fabrication of the nanopatterned germanium (Ge) surface is done by laser-induced etching. Atomic force microscopy is utilized here to study the surface and sizes of Ge nanoparticles. Raman and photoluminescence (PL) spectroscopy have been used to characterize their vibrational and light emission properties. Wavelength-dependent Raman investigations of these nanopatterned Ge surface reveal spatial distribution of sizes of nanoparticles. Nanopatterned Ge structures (etched for 60 min) emit a broad PL band having two maxima at 2.1 and 2.35 eV.     

Polarized Raman scattering and lattice eigenmodes of antiferromagnetic NdFeO3

The first‐ and second‐order Raman‐active phonons in the orthorhombic Pbnm NdFeO₃ single crystals were studied by means of polarized Raman scattering and lattice dynamics computations (LDC). The zone‐center phonons of A_g symmetry were distinguished from the B_1g eigenmodes by performing polarized Raman scattering experiments using two parallel polarization configurations, X′(ZZ)X′ and Z(X′X′)Z. With the help of LDC, we were able to assign most of the observed Raman‐active modes, including phonons of B_2g and B_3g symmetry. The LDC results indicated that among the 16 force constants employed, the one corresponding to the stretching vibration between the central Fe cation and the axial oxygen atom in a FeO₆ octahedron unit had the largest value. This suggests that the B‐site Fe cation is more tightly bound to the axial O1 ion than the other two equatorial O2 ions. It was further shown that at higher wavenumbers, the displacement of oxygen atoms contributed dominantly to the zone‐center vibrations. Copyright © 2008 John Wiley & Sons, Ltd.