The third post-Newtonian gravitational wave polarizations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits

The gravitational waveform (GWF) generated by inspiralling compact binaries moving in quasi-circular orbits is computed at the third post-Newtonian (3PN) approximation to general relativity. Our motivation is two-fold: (i) to provide accurate templates for the data analysis of gravitational wave inspiral signals in laser interferometric detectors; (ii) to provide the associated spin-weighted spherical harmonic decomposition to facilitate comparison and match of the high post-Newtonian prediction for the inspiral waveform to the numerically-generated waveforms for the merger and ringdown. This extension of the GWF by half a PN order (with respect to previous work at 2.5PN order) is based on the algorithm of the multipolar post-Minkowskian formalism, and mandates the computation of the relations between the radiative, canonical and source multipole moments for general sources at 3PN order. We also obtain the 3PN extension of the source multipole moments in the case of compact binaries, and compute the contributions of hereditary terms (tails, tails-of-tails and memory integrals) up to 3PN order. The end results are given for both the complete plus and cross polarizations and the separate spin-weighted spherical harmonic modes.

The use of circular surface aerators in wastewater treatment tanks

Aeration experiments were conducted in different sized baffled and unbaffled circular surface aeration tanks to study their relative performance on oxygen transfer process while aerating the same volume of water. Experiments were carried out with the objective of ascertaining the effect of baffle on oxygen transfer coefficient k. Simulation equations govern the oxygen transfer coefficient with the theoretical power per unit volume, X and actual power per unit volume, P-V. It has been found that, for any given X, circular tanks with baffle produce higher values of k than unbaffled circular tanks, but in terms of actual power consumption unbaffled tanks consume less power when compared to baffled circular tanks to achieve the same value of k. It has been found that in terms of energy consumption, epsilon, baffled tanks consume more energy than unbaffled tanks at any value of X. This suggests that the unbaffled circular tank gives a better performance as far as energy consumption is concerned and hence better economy. An example illustrating the energy conservation to aerate the same volume of water in both types of aerators is given. (c) 2007 Society of Chemical Industry.

Stability of an unsupported vertical circular excavation in clays under undrained condition

By using the axisymmetric finite elements static limit analysis formulation, proposed recently by the authors, the stability numbers (gamma H/c(o)) for an unsupported vertical circular excavation in clays, whose cohesion increases with depth, have been determined under undrained condition; gamma = unit weight, H., height of the excavation and c(o) = cohesion along ground surface. The results are obtained for various values of H/b and m; where b = the radius of the excavation and m = a non-dimensional parameter which accounts for the rate of the increase of cohesion with depth. The values of the stability numbers increase continuously both with increases in H/b and m. The results obtained in this study compare well with those available in literature.(C) 2009 Elsevier Ltd. All rights reserved.

Size-dependent magnetic properties of iron carbide nanoparticles embedded in a carbon matrix

Here we report on the magnetic properties of iron carbide nanoparticles embedded in a carbon matrix. Granular distributions of nanoparticles in an inert matrix, of potential use in various applications, were prepared by pyrolysis of organic precursors using the thermally assisted chemical vapour deposition method. By varying the precursor concentration and preparation temperature, compositions with varying iron concentration and nanoparticle sizes were made. Powder x-ray diffraction, transmission electron microscopy and Mossbauer spectroscopy studies revealed the nanocrystalline iron carbide (Fe3C) presence in the partially graphitized matrix. The dependence of the magnetic properties on the particle size and temperature (10 K < T < 300 K) were studied using superconducting quantum interference device magnetometry. Based on the affect of surrounding carbon spins, the observed magnetic behaviour of the nanoparticle compositions, such as the temperature dependence of magnetization and coercivity, can be explained.

Magnetic trapping of Yb in the metastable P-3(2) state

We report magnetic trapping of Yb in the excited P-3(2) state. This state, with a lifetime of 15 s, could play an important role in studies ranging from optical clocks and quantum computation to the search for a permanent electric dipole moment. Yb atoms are first cooled and trapped in the ground state in a 399-nm magneto-optic trap. The cold atoms are then pumped into the excited state by driving the S-1(0) -> P-3(1) -> S-3(1) transition. Atoms in the P-3(2) state are magnetically trapped in a spherical quadrupole field with an axial gradient of 110 G/cm. We trap up to 10(6) atoms with a lifetime of 1.5 s.

Scattering polarization in the presence of magnetic and electric fields

The polarization of radiation by scattering on an atom embedded in combined external quadrupole electric and uniform magnetic fields is studied theoretically. Limiting cases of scattering under Zeeman effect, and Hanle effect in weak magnetic fields are discussed. The theory is general enough to handle scattering in intermediate magnetic fields (Hanle-Zeeman effect) and for arbitrary orientation of magnetic field. The quadrupolar electric field produces asymmetric line shifts, and causes interesting level-crossing phenomena either in the absence of an ambient magnetic field, or in its presence. It is shown that the quadrupolar electric field produces an additional depolarization in the Q/I profiles and rotation of the plane of polarization in the U/I profile over and above that arising from magnetic field itself. This characteristic may have a diagnostic potential to detect steady-state and time-varying electric fields that surround radiating atoms in solar atmospheric layers. (c) 2007 Elsevier Ltd. All rights reserved.

Unsteady mixed convection on the stagnation-point flow adjacent to a vertical plate with a magnetic field

An analysis is performed to study the unsteady combined forced and free convection flow (mixed convection flow) of a viscous incompressible electrically conducting fluid in the vicinity of an axisymmetric stagnation point adjacent to a heated vertical surface. The unsteadiness in the flow and temperature fields is due to the free stream velocity, which varies arbitrarily with time. Both constant wall temperature and constant heat flux conditions are considered in this analysis. By using suitable transformations, the Navier-Stokes and energy equations with four independent variables (x, y, z, t) are reduced to a system of partial differential equations with two independent variables (eta, tau). These transformations also uncouple the momentum and energy equations resulting in a primary axisymmetric flow, in an energy equation dependent on the primary flow and in a buoyancy-induced secondary flow dependent on both primary flow and energy. The resulting system of partial differential equations has been solved numerically by using both implicit finite-difference scheme and differential-difference method. An interesting result is that for a decelerating free stream velocity, flow reversal occurs in the primary flow after certain instant of time and the magnetic field delays or prevents the flow reversal. The surface heat transfer and the surface shear stress in the primary flow increase with the magnetic field, but the surface shear stress in the buoyancy-induced secondary flow decreases. Further the heat transfer increases with the Prandtl number, but the surface shear stress in the secondary flow decreases.

Studies in terpenoids-XIII. Magnetic anisotropy2 in and stereochemistry of some gem-dimethylcyclobutanoids related to pinonic acid

The chemical shifts of “axial” vs “equatorial” Me protons of some gem-dimethylcyclobutanoids derived from α-pinene, arising from magnetic anisotropy of the ring and as influenced by vicinal substituents, are discussed. Conformational aspects of some cis- and trans-pinonic, pinononic and pinic acids have been elucidated on the basis of NMR evidence.

2(n)-SEMA-a robust solid state nuclear magnetic resonance experiment for measuring heteronuclear dipolar couplings in static oriented systems using effective transverse spin-lock

Separated local field (SLF) spectroscopy is a powerful technique to measure heteronuclear dipolar couplings. The method provides site-specific dipolar couplings for oriented samples such as membrane proteins oriented in lipid bilayers and liquid crystals. A majority of the SLF techniques utilize the well-known Polarization Inversion Spin Exchange at Magic Angle (PISEMA) pulse scheme which employs spin exchange at the magic angle under Hartmann-Hahn match. Though PISEMA provides a relatively large scaling factor for the heteronuclear dipolar coupling and a better resolution along the dipolar dimension, it has a few shortcomings. One of the major problems with PISEMA is that the sequence is very much sensitive to proton carrier offset and the measured dipolar coupling changes dramatically with the change in the carrier frequency. The study presented here focuses on modified PISEMA sequences which are relatively insensitive to proton offsets over a large range. In the proposed sequences, the proton magnetization is cycled through two quadrants while the effective field is cycled through either two or four quadrants. The modified sequences have been named as 2(n)-SEMA where n represents the number of quadrants the effective field is cycled through. Experiments carried out on a liquid crystal and a single crystal of a model peptide demonstrate the usefulness of the modified sequences. A systematic study under various offsets and Hartmann-Hahn mismatch conditions has been carried out and the performance is compared with PISEMA under similar conditions.

Ring loading of a long, thin, circular cylindrical shell enclosing a soft, solid core: A recalculation by the love function method of elasticity.

The problem is solved using the Love function and Flügge shell theory. Numerical work has been done with a computer for various values of shell geometry parameters and elastic constants.

Steady flow of a maxwell fluid in a porous cylindrical annulus with circular cross-section

When a fluid with memory is injected into any flow region some assumptions regarding the initial state of stress have to be made in order to determine the state of stress at any subsequent instant. For a Maxwell fluid, it is assumed that the fluid near the surface of injection is suddenly stressed and responds by starting flow in accordance with the mechanical model chosen. The flow of a Maxwell fluid with a single relaxation time has been determined under the above assumption in the following two cases: (i) annulus between two porous concentric circular cylinders, and (ii) space between two porous and infinitely extending parallel plates. The nature of flow in the present case is similar to that of the Reiner-Rivlin fluids obtained by Narasimhan2).

Flow of an electrically conducting non-newtonian fluid between two rotating coaxial cones in the presence of external magnetic field due to an axial current

Bhatnagar and Rathna (Quar. Journ. Mech. Appl. Maths., 1963,16, 329) investigated the flows of Newtonian, Reiner-Rivlin and Rivlin-Ericksen fluids between two rotating coaxial cones. In case of the last two types of fluids, they predicted the breaking of secondary flow field in any meridian plane. We find that such breaking is avoided by the application of a sufficiently strong azimuthal magnetic field arising from a line current along the axis of the cones.