The Linearly Independent Non Orthogonal yet Energy Preserving (LINOEP) vectors

It is well known that, in any inner product space, a set of linearly independent (LI) vectors can be transformed to a set of orthogonal vectors, spanning the same space, by the Gram-Schmidt Orthogonalization Method (GSOM). In this paper, we propose a transformation from a set of LI vectors to a set of LI non orthogonal yet energy (square of the norm) preserving (LINOEP) vectors in an inner product space and we refer it as LINOEP method. We also show that there are various solutions to preserve the square of the norm.Comment: 6 pages, 2 figure

Dopant Induced Stabilization of Silicon Cluster at Finite Temperature

With the advances in miniaturization, understanding and controlling properties of significant technological systems like silicon in nano regime assumes considerable importance. It turns out that small silicon clusters in the size range of 15-20 atoms are unstable upon heating and in fact fragment in the temperature range of 1200 K to 1500 K. In the present work we demonstrate that it is possible to stabilize such clusters by introducing appropriate dopant (in this case Ti). Specifically, by using the first principle density functional simulations we show that Ti doped Si$_{16}$, having the Frank-Kasper geometry, remains stable till 2200 K and fragments only above 2600 K. The observed melting transition is a two step process. The first step is initiated by the surface melting around 600 K. The second step is the destruction of the cage which occurs around 2250 K giving rise to a peak in the heat capacity curve.Comment: 6 pages, 8 Figs. Submitted to PR

Wave propagation through a coherently amplifying random medium

We report a detailed and systematic numerical study of wave propagation through a coherently amplifying random one-dimensional medium. The coherent amplification is modeled by introducing a uniform imaginary part in the site energies of the disordered single-band tight binding Hamiltonian. Several distinct length scales (regimes), most of them new, are identified from the behavior of transmittance and reflectance as a function of the material parameters. We show that the transmittance is a non-self-averaging quantity with a well defined mean value. The stationary distribution of the super reflection differs qualitatively from the analytical results obtained within the random phase approximation in strong disorder and amplification regime. The study of the stationary distribution of the phase of the reflected wave reveals the reason for this discrepancy. The applicability of random phase approximation is discussed. We emphasize the dual role played by the lasing medium, as an amplifier as well as a reflector.Comment: 33 pages RevTex, 14 EPS figures included, Accepted for publication in IJMP-

Unusual Coupling Between Field-induced Spin Fluctuations and Spin Density Wave in Intermetallic CeAg2Ge2

We report on the experimental evidences for an unusual coupling between the magnetic field- induced fluctuations of correlated Ce-ions coinciding with the discontinuous movement of the underlying spin density wave in the intermetallic rare earth compound CeAg2Ge2. The measurements performed using neutron scattering and magnetic Gruneisen ratio methods suggest that the coupling onsets at H= 2.7 T, T < 3.8 K and persists to the lowest measurement temperature T ~ 0.05 K. These measurements suggest a new mechanism behind the spin fluctuations which can affect the intrinsic properties of the system.Comment: 4 pages, 4 figures, Strongly correlated electrons syste

Gamma-ray bursts as the birth-cries of black holes

The origin of cosmic gamma-ray bursts remains one of the most intriguing puzzles in astronomy. We suggest that purely general relativistic effects in the collapse of massive stars could account for these bursts. The late formation of closed trapped surfaces can occur naturally, allowing the escape of huge energy from curvature-generated fireballs, before these are hidden within a black hole.Comment: 4 pages Revtex, 1 figure. This essay received an honorable mention in the Gravity Research Foundation essay competitio

Leveraging Social Capital through Classroom Communities of Practice

Educators have advocated the use of informal complementary learning approaches such as Communities of Practice (CoPs) to support existing formal educational structures. They argue that educational structures need to leverage its social capital through informal learning to support the sociocultural approaches to instructions. The CoP concept has been successfully used in business and other organizational settings. However, its application in the educational setting has not been examined in a systematic and deliberate manner. This extended abstract establishes this primary research question by providing a preliminary literature review and also gives an overview of the planned research methodology

Spectral sensitivity of the photoreceptors responsible for phase shifting the circadian rhythm of activity in the bat, Hipposideros speoris

1. The spectral sensitivity of the photoreceptors responsible for phase shifting the circadian rhythm of flight activity in the bat,Hipposideros speoris was investigated. For this purpose we studied the phase shifts evoked with 15 min and 2.77 h pulses of monochromatic light at various phases of the rhythm freerunning in DD. 2. A PRC for the circadian rhythm of flight activity inH. speoris was constructed with white light pulses (1,000 lx for 15 min) against DD background (Fig. 1). In the first set of experiments 15 min monochromatic light pulses of varying intensities were administered to two phases of the rhythm: the phase of the rhythm at which maximal phase advances occur CT 4, and the phase of the rhythm at which maximal phase delays occur CT 18. The intensities of the 15 min monochromatic light pulses required to produce 50% of the phase shifts evoked with white light pulses (1,000 lx for 15 min) at these two phases were determined. The spectral sensitivity curve for advance phase shifts has a maximum at the wavelength 520 nm and the spectral sensitivity curve for delay phase shifts has a maximum at the wavelength 430 nm (Fig. 5). 3. In the second set of experiments 2.77 h monochromatic light pulses of equal energy of 100 &#956;W/cm2 were used. We studied the wavelength dependent phase shifts at four phases of the rhythm: CT 2, CT 4, CT 12 and CT 18. The pulses of 430 and 520 nm evoked unequivocal delay and advance phase shifts, respectively, at all four phases (Fig. 7). These results suggest that at this photopic level of pulse energy, there might be a clear antagonism between the two photoreceptor classes, one having a maximum at the wavelength 430 nm and the other having a maximum at the wavelength 520 nm. 4. We suggest that there may exist two different classes of photoreceptors in the retinas ofH. speoris. The S photoreceptors (short wavelength sensitive) having a maximum at the wavelength 430 nm and the M photoreceptors (middle wavelength sensitive) having a maximum at the wavelength 520 nm that mediate delay and advance phase shifts, respectively

Agricultural diversification in India and role of urbanization

Indian agriculture is diversifying during the last two decades towards High-Value Commodities (HVCs) i.e., fruits, vegetables, milk, meat, and fish products. The pace has been accelerated during the decade of 1990s. HVCs account for a large share in the total value of agricultural production. Supply and demand side factors coupled with infrastructural development and innovative institutions drive these changes. In this paper, the focus is on diversification towards HVCs in the context of urbanization. Group of urban districts (districts with >1.5 million urban population) have a higher share of HVCs compared to the urban-surrounded (near urban districts) and other districts (districts in the hinterland). Among the HVCs, vegetables and meat products have a higher share in urban districts compared to the other two groups. Milk production is more widespread due to excellent network of co-operatives and infrastructure facilities. Using GIS (geographic Information System) approach it was found that urban-surrounded districts with better road network connection to urban centers have been able to diversify towards HVC's to meet the demand in the urban centers. Model results further confirm these findings. Thus, urbanization is a strong demand side driver promoting HVCs. Since urban population is growing at more than 3% per annum, demand for HVCs will drive their production. The analysis has also brought out regional variations in HVCs across different districts in the country that has implications on regional development and planning, and consequently on public and private sector investment strategies.