In this paper a three-step scheme is applied to solve the Camassa-Holm (CH) shallow water equation. The differential order of the CH equation has been reduced in order to facilitate development of numerical scheme in a comparatively smaller grid stencil. Here a three-point seventh-order spatially accurate upwinding combined compact difference (CCD) scheme is proposed to approximate the firstorder derivative term. We conduct modified equation analysis on the CCD scheme and eliminate the leading discretization error terms for accurately predicting unidirectional wave propagation. The Fourier analysis is carried out as well on the proposed numerical scheme to minimize the dispersive error. For preserving Hamiltonians in Camassa- Holm equation, a symplecticity conserving time integrator has been employed. The other main emphasis of the present study is the use of u–P–α formulation to get nondissipative CH solution for peakon-antipeakon and soliton-anticuspon head-on wave collision problems.

Energy filtered transmission electron microscopy techniques are regularly used to build elemental maps of spatially distributed nanoparticles in materials and biological specimens. When working with thick biological sections, electron energy loss spectroscopy techniques involving core-loss electrons often require exposures exceeding several minutes to provide sufficient signal to noise. Image quality with these long exposures is often compromised by specimen drift, which results in blurring and reduced resolution. To mitigate drift artifacts, a series of short exposure images can be acquired, aligned, and merged to form a single image. For samples where the target elements have extremely low signal yields, the use of charge coupled device (CCD)-based detectors for this purpose can be problematic. At short acquisition times, the images produced by CCDs can be noisy and may contain fixed pattern artifacts that impact subsequent correlative alignment. Here we report on the use of direct electron detection devices (DDD’s) to increase the signal to noise as compared with CCD’s. A 3× improvement in signal is reported with a DDD versus a comparably formatted CCD, with equivalent dose on each detector. With the fast rolling-readout design of the DDD, the duty cycle provides a major benefit, as there is no dead time between successive frames.

We present basic information about package SPHOTOM for an automatic multicolour photometry. This package is in development for the creation of a photometric pipe-line, which we plan to use in the near future with our new instruments. It could operate in two independent modes, (i) GUI mode, in which the user can select images and control functions of package through interface and (ii) command line mode, in which all processes are controlled using a main parameter file. SPHOTOM is developed as a universal package for Linux based systems with easy implementation for different observatories. The photometric part of the package is based on the Sextractor code, which allows us to detect all objects on the images and perform their photometry with different apertures. We can also perform astrometric solutions for all images for a correct cross-identification of the stars on the images. The result is a catalogue of all objects with their instrumental photometric measurements which are consequently used for a differential magnitudes calculations with one or more comparison stars, transformations to an international system, and determinations of colour indices.

The main goal of this work was to find dependencies between Fourier coefficients, which were developed by light curve fitting with Fourier polynomials. The light curves were acquired from the ASAS database (All Sky Automated Survey). In this statistical research it was necessary to sort and modify these data, because light curves of eclipsing binaries are just part of a bigger database, which contains the light curves of pulsating variable stars, novas etc. It was required to phase and normalize all of our light curves, that it could be possible to use a program to fit light curves with Fourier coefficients. Thereafter, we were looking for relations between Fourier coefficients.

The plume images of the laser produced silver plasma in the absence and presence of 0.45 T transverse magnetic field has been investigated under vacuum ~10−4 torr and in air. An Nd:YAG laser (1.064 µm, 1.1 MW, 9 ns) with intensity ~1012 Wcm−2 was used to generate plasma. A CCD image capture system was used for plasma imaging to explore the plume. A magnetic probe was employed to measure the variation in internal magnetic field of plasma with as well as without 0.45 T external transverse magnetic field. The X-ray emission from plasma in both the cases (with and without B field) was also monitored using two PIN photodiodes filtered with 24 µm Cu and 24 µm Al. The plume images in both the cases were then correlated with the time resolved soft X-ray emission. It was found that the self generated magnetic field of the plasma increases in the presence of magnetic field. Plume images reveal that the confinement of the plume takes place in the presence of magnetic field both in the cases of air and vacuum. Jet and spikes like structures were also observed due to plasma instabilities. Lobe formation in the plume at latter stages of plasma evolution was more prominent in air than under vacuum. X-ray emission signals exhibited an enhancement in the emission under transverse magnetic field. An increased rate of recombination due to high density as a result of plasma confinement across the applied magnetic field was found to be the main reason behind emission enhancement.