{C}^0$ penalty methods for the fully nonlinear Monge-Ampère equation

In this paper, we develop and analyze C(0) penalty methods for the fully nonlinear Monge-Ampere equation det(D(2)u) = f in two dimensions. The key idea in designing our methods is to build discretizations such that the resulting discrete linearizations are symmetric, stable, and consistent with the continuous linearization. We are then able to show the well-posedness of the penalty method as well as quasi-optimal error estimates using the Banach fixed-point theorem as our main tool. Numerical experiments are presented which support the theoretical results.

A family of Runge-Kutta based explicit methods for rotational dynamics

The present paper develops a family of explicit algorithms for rotational dynamics and presents their comparison with several existing methods. For rotational motion the configuration space is a non-linear manifold, not a Euclidean vector space. As a consequence the rotation vector and its time derivatives correspond to different tangent spaces of rotation manifold at different time instants. This renders the usual integration algorithms for Euclidean space inapplicable for rotation. In the present algorithms this problem is circumvented by relating the equation of motion to a particular tangent space. It has been accomplished with the help of already existing relation between rotation increments which belongs to two different tangent spaces. The suggested method could in principle make any integration algorithm on Euclidean space, applicable to rotation. However, the present paper is restricted only within explicit Runge-Kutta enabled to handle rotation. The algorithms developed here are explicit and hence computationally cheaper than implicit methods. Moreover, they appear to have much higher local accuracy and hence accurate in predicting any constants of motion for reasonably longer time. The numerical results for solutions as well as constants of motion, indicate superior performance by most of our algorithms, when compared to some of the currently known algorithms, namely ALGO-C1, STW, LIEMID[EA], MCG, SUBCYC-M.

Crustal Deformation and Seismic History Associated with the 2004 Indian Ocean Earthquake: A Perspective from the Andaman–Nicobar Islands

The Indian Ocean earthquake of 26 December 2004 led to significant ground deformation in the Andaman and Nicobar region, accounting for ~800 km of the rupture. Part of this article deals with coseismic changes along these islands, observable from coastal morphology, biological indicators, and Global Positioning System (GPS) data. Our studies indicate that the islands south of 10° N latitude coseismically subsided by 1–1.5 m, both on their eastern and western margins, whereas those to the north showed a mixed response. The western margin of the Middle Andaman emerged by >1 m, and the eastern margin submerged by the same amount. In the North Andaman, both western and eastern margins emerged by >1 m. We also assess the pattern of long-term deformation (uplift/subsidence) and attempt to reconstruct earthquake/tsunami history, with the available data. Geological evidence for past submergence includes dead mangrove vegetation dating to 740 ± 100 yr B.P., near Port Blair and peat layers at 2–4 m and 10–15 m depths observed in core samples from nearby locations. Preliminary paleoseismological/tsunami evidence from the Andaman and Nicobar region and from the east coast of India, suggest at least one predecessor for the 2004 earthquake 900–1000 years ago. The history of earthquakes, although incomplete at this stage, seems to imply that the 2004-type earthquakes are infrequent and follow variable intervals

Multicomponent solids of lamotrigine with some selected coformers and their characterization by thermoanalytical, spectroscopic and X-ray diffraction methods

The present study investigates the structural and pharmaceutical properties of different multicomponent crystalline forms of lamotrigine (LTG) with some pharmaceutically acceptable coformers viz. nicotinamide (1), acetamide (2), acetic acid (3), 4-hydroxy-benzoic acid (4) and saccharin (5). The structurally homogeneous phases were characterized in the solid state by DSC/TGA, FT-IR and XRD (powder and single crystal structure analysis) as well as in the solution phase. Forms 1 and 2 were found to be cocrystal hydrate and cocrystal, respectively, while in forms 3, 4 and 5, proton transfer was observed from coformer to drug. The enthalpy of formation of multicomponent crystals from their components was determined from the enthalpy of solution of the cocrystals and the components separately. Higher exothermic values of the enthalpy of formation for molecular complexes 3, 4 and 5 suggest these to be more stable than 1 and 2. The solubility was measured in water as well as in phosphate buffers of varying pH. The salt solvate 3 exhibited the highest solubility of the drug in water as well as in buffers over the pH range 7-3 while the cocrystal hydrate 1 showed the maximum solubility in a buffer of pH 2. A significant lowering of the dosage profile of LTG was observed for 1, 3 and 5 in the animal activity studies on mice.

A comparison of three methods for downscaling daily precipitation in the Punjab region

Many downscaling techniques have been developed in the past few years for projection of station-scale hydrological variables from large-scale atmospheric variables simulated by general circulation models (GCMs) to assess the hydrological impacts of climate change. This article compares the performances of three downscaling methods, viz. conditional random field (CRF), K-nearest neighbour (KNN) and support vector machine (SVM) methods in downscaling precipitation in the Punjab region of India, belonging to the monsoon regime. The CRF model is a recently developed method for downscaling hydrological variables in a probabilistic framework, while the SVM model is a popular machine learning tool useful in terms of its ability to generalize and capture nonlinear relationships between predictors and predictand. The KNN model is an analogue-type method that queries days similar to a given feature vector from the training data and classifies future days by random sampling from a weighted set of K closest training examples. The models are applied for downscaling monsoon (June to September) daily precipitation at six locations in Punjab. Model performances with respect to reproduction of various statistics such as dry and wet spell length distributions, daily rainfall distribution, and intersite correlations are examined. It is found that the CRF and KNN models perform slightly better than the SVM model in reproducing most daily rainfall statistics. These models are then used to project future precipitation at the six locations. Output from the Canadian global climate model (CGCM3) GCM for three scenarios, viz. A1B, A2, and B1 is used for projection of future precipitation. The projections show a change in probability density functions of daily rainfall amount and changes in the wet and dry spell distributions of daily precipitation. Copyright (C) 2011 John Wiley & Sons, Ltd.