A robust layer adapted difference method for singularly perturbed two-parameter parabolic problems

A finite difference method for a time-dependent singularly perturbed convection-diffusion-reaction problem involving two small parameters in one space dimension is considered. We use the classical implicit Euler method for time discretization and upwind scheme on the Shishkin-Bakhvalov mesh for spatial discretization. The method is analysed for convergence and is shown to be uniform with respect to both the perturbation parameters. The use of the Shishkin-Bakhvalov mesh gives first-order convergence unlike the Shishkin mesh where convergence is deteriorated due to the presence of a logarithmic factor. Numerical results are presented to validate the theoretical estimates obtained.

Disappearance of electron-hole asymmetry in nanoparticles of Nd1-xCaxMnO3(x=0.6, 0.4): magnetization and electron paramagnetic resonance evidence

We study and compare magnetic and electron paramagnetic resonance behaviors of bulk and nanoparticles of Nd1-xCaxMnO3 in hole doped (x = 0.4; NCMOH) and electron doped (x = 0.6; NCMOE) samples. NCMOH in bulk form shows a complex temperature dependence of magnetization M(T), with a charge ordering transition at similar to 250 K, an antiferromagnetic (AFM) transition at similar to 150 K, and a transition to a canted AFM phase/mixed phase at similar to 80 K. Bulk NCMOE behaves quite differently with just a charge ordering transition at similar to 280 K, thus providing a striking example of the so called electron-hole asymmetry. While our magnetization data on bulk samples are consistent with the earlier reports, the new results on the nanoparticles bring out drastic effects of size reduction. They show that M(T) behaviors of the two nanosamples are essentially similar in addition to the absence of the charge order in them thus providing strong evidence for vanishing of the electron-hole asymmetry in nanomanganites. This conclusion is further corroborated by electron paramagnetic resonance studies which show that the large difference in the ``g'' values and their temperature dependences found for the two bulk samples disappears as they approach a common behavior in the corresponding nanosamples. (C) 2015 AIP Publishing LLC.

Construction of Singer Subgroup Orbit Codes Based on Cyclic Difference Sets

A recent approach for the construction of constant dimension subspace codes, designed for error correction in random networks, is to consider the codes as orbits of suitable subgroups of the general linear group. In particular, a cyclic orbit code is the orbit of a cyclic subgroup. Hence a possible method to construct large cyclic orbit codes with a given minimum subspace distance is to select a subspace such that the orbit of the Singer subgroup satisfies the distance constraint. In this paper we propose a method where some basic properties of difference sets are employed to select such a subspace, thereby providing a systematic way of constructing cyclic orbit codes with specified parameters. We also present an explicit example of such a construction.

Exploring isospectral cantilever beams using electromagnetism inspired optimization technique

Isospectral beams have identical free vibration frequency spectrum for a specific boundary condition. The problem of finding non-uniform beams which are isospectral to a given uniform beam, with fixed-free boundary condition, leads to a multimodal optimization problem. The first Q natural frequencies of the given uniform Euler-Bernoulli beam are determined using analytical solution. The first Q natural frequencies of a non-uniform beam are obtained with the help of finite element modeling. In order to obtain the non-uniform beams isospectral to a given uniform beam, an error function is designed, which calculates the difference between the spectra of the given uniform beam and the non-uniform beam. In our study, this error function is minimized using electromagnetism inspired optimization technique, a population based iterative algorithm inspired by the attraction-repulsion physics of electromagnetism. Numerical results show the existence of the isospectral non-uniform beams for a given uniform beam, which occur as local minima. Non-uniform beams isospectral to a damaged beam, are also explored using the proposed methodology to illustrate the fact that accurate structural damage identification is difficult by just frequency measurements. (C) 2012 Elsevier B.V. All rights reserved.

The interface makes a difference: lanthanide ion coated vesicles hydrolyze phosphodiesters

Lanthanide ions are strong Lewis acids. Their complexation to a variety of ligands can further enhance their Lewis acidity allowing the hydrolysis of phosphoesters and even DNA. We show that the interaction of lanthanide ions with vesicles from zwitterionic phosphatidylcholine lipids gives supramolecular structures in which the metal ion is loosely coordinated to the surface. This assembly provides a high density of Lewis-acidic metal centres, which hydrolyze phosphodiesters with enhanced rates.

Vegetation structure and composition of tropical evergreen and deciduous forests in Uttara Kannada District, Western Ghats under different disturbance regimes

In the present paper, we present the structure and composition of tropical evergreen and deciduous forests in the Western Ghats monitored under a long-term programme involving Indian Institute of Science, Earthwatch and volunteer investigators from HSBC. Currently, there is limited evidence on the status and dynamics of tropical forests in the context of human disturbance and climate change. Observations made in this study show that the `more disturbed' evergreen and one of the deciduous plots have low species diversity compared to the less-disturbed forests. There are also variations in the size class structure in the more and `less disturbed' forests of all the locations. The variation is particularly noticeable in the DBH size class 10 - 15 cm category. When biomass stock estimates are considered, there was no significant difference between evergreen and deciduous forests. The difference in biomass stocks between `less disturbed' and `more disturbed' forests within a forest type is also low. Thus, the biomass and carbon stock has not been impacted despite the dependence of communities on the forests. Periodic and long-term monitoring of the status and dynamics of the forests is necessary in the context of potential increased human pressure and climate change. There is, therefore, a need to inform the communities of the impact of extraction and its effect on regeneration so as to motivate them to adopt what may be termed as ``adaptive resource management'', so as to sustain the flow of forest products.