Spatially partitioned embedded Runge-Kutta Methods

We study spatially partitioned embedded Runge–Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different part of the spatial domain. Such methods may be convenient for problems in which the smoothness of the solution or the magnitudes of the PDE coefficients vary strongly in space. We focus on embedded partitioned methods as they offer greater efficiency and avoid the order reduction that may occur in non-embedded schemes. We demonstrate that the lack of conservation in partitioned schemes can lead to non-physical effects and propose conservative additive schemes based on partitioning the fluxes rather than the ordinary differential equations. A variety of SPERK schemes are presented, including an embedded pair suitable for the time evolution of fifth-order weighted non-oscillatory (WENO) spatial discretizations. Numerical experiments are provided to support the theory

Comparison of numerical methods for the calculation of cold atom collisions

Three different numerical techniques for solving a coupled channel Schroedinger equation are compared. This benchmark equation, which describes the collision between two ultracold atoms, consists of two channels, each containing the same diagonal Lennard-Jones potential, one of positive and the other of negative energy. The coupling potential is of an exponential form. The methods are i) a recently developed spectral type integral equation method based on Chebyshev expansions, ii) a finite element expansion, and iii) a combination of an improved Numerov finite difference method and a Gordon method. The computing time and the accuracy of the resulting phase shift is found to be comparable for methods i) and ii), achieving an accuracy of ten significant figures with a double precision calculation. Method iii) achieves seven significant figures. The scattering length and effective range are also obtained.Comment: 22 pages, 3 figures, submitted to J. Comput. Phys. documentstyle [thmsa,sw20aip]{article} in .te

Trace Element Estimation – Methods & Clinical Context

Understanding the effects of trace metals on human health is as complex as it is fascinating. As mentioned earlier, the high concentrations may prove toxic, as also, depletion in the concentration of the essential trace elements may cause various metabolic instabilities due to enzyme dysfunction. In the era of rapid industrialization and technological advances, it is imperative to watch keenly for contamination of the environment and its vital composition from heavy metal wastes emanating out of industries. Many metabolic disorders in man are accompanied by alterations in the concentration of one or more trace elements in some body fluid, especially blood serum or plasma It is thus important to update ourselves with various techniques available for such determinations, their operational aspects, advantages / disadvantages etc. More recently, element analysis from hair and nail has been stated as the best indices of such contamination and has also been discussed in this article