Self-consistent field theory of dilated atomic hamiltonians: Some remarks

The bi-variational SCF scheme for dilated closed shell atomic hamiltonians is studied and discussed. Applications to the Be atom are presented.     

Treatment of Be+ ( 1 s? 1)2S Auger resonance with different decouplings of the dilated electron propagator

The diagonal 2ph-TDA and quasiparticle decouplings of the dilated electron propagator (based on an underlying bi-variational SCF) are utilized to calculate energy and width of the Be⁺(1_s ⁻¹)²S Auger resonance for the first time. Comparison with experimental and other theoretical results reveals that the renormalized infinite order diagonal 2ph-TDA decoupling seems to offer a less balanced approach to the treatment of resonances than the second-order decoupling. The diagonal quasiparticle approximation to the self energy is seen to offer an effective and economic alternative to the non-diagonal propagator calculations.     

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].     

Cover-incomparability graphs and chordal graphs

The problem of recognizing cover-incomparability graphs (i.e. the graphs obtained from posets as the edge-union of their covering and incomparability graph) was shown to be NP-complete in general [J. Maxová, P. Pavlíkova, A. Turzík, On the complexity of cover-incomparability graphs of posets, Order 26 (2009) 229-236], while it is for instance clearly polynomial within trees. In this paper we concentrate on (classes of) chordal graphs, and show that any cover-incomparability graph that is a chordal graph is an interval graph. We characterize the posets whose cover-incomparability graph is a block graph, and a split graph, respectively, and also characterize the cover-incomparability graphs among block and split graphs, respectively. The latter characterizations yield linear time algorithms for the recognition of block and split graphs, respectively, that are cover-incomparability graphs.     

Effect of V cut in perforated twisted tape insert on heat transfer and fluid flow behavior of tube flow: An experimental study

ABSTRACT

Present study investigates the heat transfer and friction characteristics of heat exchanger tube fitted with perforated twisted tape (PTT) insert having V cuts. A copper tube of 1 m length and 0.032 m inner diameter is used as test section to collect the experimental data by varying the twist ratio of PTT from 2 to 6 for the Reynolds number range of 2,700–23,400. V cuts are introduced in the PTT and the V-cut relative pitch ratio is varied from 1 to 2. The maximum thermo-hydraulic performance parameter is found to be 1.58.     

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.