Solutions of Klein-Gordon Equation by the Laplace Decomposition Method and Modified Laplace Decomposition Method

In this article, the Laplace decomposition method and Modified Laplace decomposition method have been employed to obtain the exact and approximate solutions of the Klein-Gordon equation with the initial profile. An approximate solution obtained by these methods is in good agreement with the exact solution and shows that these approaches can solve linear and nonlinear problems very effectively and are capable to reduce the size of computational work.

Localized waves and mixed interaction solutions with dynamical analysis to the Gross-Pitaevskii equation in the Bose-Einstein condensate

We report a kind of breather, rogue wave and mixed interaction structures on a variational background height in the Gross-Pitaevskii equation in the Bose-Einstein condensate by the generalized Darboux transformation method, and the effects of related parameters on rogue wave structures are discussed. Numerical simulation can discuss the dynamics and stability of these solutions. We numerically confirm that these are correct, and can be reproduced from a deterministic initial profile. Results show that rogue waves and mixed interaction solutions can evolve with a small amplitude perturbation under the initial profile conditions, but breathers cannot. Therefore, these can be used to anticipate the feasibility of their experimental observation.

Soil Formation, Subaerial Sedimentation Processes and Ancient Cultures during MIS 2 and the Deglaciation Phase MIS 1 in the Baikal–Yenisei Siberia (Russia)

The time of Sartan glaciation in the Baikal–Yenisei Siberia, is comparable with that of MIS 2 and the deglaciation phase MIS 1. Loess loams, aeolian–colluvial sands and sandy loams represent subaerial sediments. There are four subhorizons (sr1, sr2, sr3 and sr4) in the Sartan horizon (sr). Sedimentary and soil-forming processes at different stratigraphic levels are considered. Differing soil formation types of cold periods are distinguished. Soils of the interstadial type with the A-C profile are represented only in the Early Sartan section of this paper. The soils of the pleniglacial type are discussed throughout the section. Their initial profile is O-C, TJ-C and W-C. Plant detritus remnants or poor thin humus horizons are preserved in places from the upper horizons. We propose for the first time for the interphasial soil formation type of cold stages to be distinguished. This is represented in the sections by the preserved BCm, BCg, Cm and Cg horizons of 15–20 cm thick. The upper horizons are absent in most sections. According to the surviving fragments, these were organogenous (O, TJ and T) and organomineral (AO and W) horizons. The sedimentation and soil formation features are considered from the perspective reconstruction of the Sartan natural and climatic conditions. Buried Sartan soils often contain cultural layers. Soil formation shows a well-defined periodicity of natural condition stabilization, which allowed ancient populations to adapt actively to various situations. Archaeologists’ interest in fossil soils is based on the ability of soils to “record” information about the natural and climatic conditions of human habitation.

Grid method for solution of 2D Riemann type problem with two discontinuities having an initial condition

This study aims to obtain the numerical solution of the Cauchy problem for 2D conservation law equation with one arbitrary discontinuity having an initial profile. For this aim, a special auxiliary problem allowing to construct a sensitive method is developed in order to get a weak solution of the main problem. Proposed auxiliary problem also permits us to find entropy condition which guarantees uniqueness of the solution for the auxiliary problem. To compare the numerical solution with the exact solution theoretical structure of the problem under consideration is examined, and then the interplay of shock and rarefaction waves is investigated.

Forecast of low clouds over a snow surface in the Arctic using WRF model

The Swedish Armed Forces configuration of the Weather Research and Forecasting Model (WRF) has problems in forecasting low clouds in stably stratified conditions when the ground is covered by snow. Reforecasts for January and February 2018, together with observations from Sodankylä in northern Finland, are analyzed to find the cause. The investigation is done iteratively between the Single Column Model (SCM), applied at Sodankylä, and the full 3D version. Our experiments show that the forecast error arises due to inadequate initialization of Stratocumulus (Sc) clouds in WRF using the ECMWF global model, Integrated Forecast System (IFS). By including bulk liquid water and bulk ice water content, from IFS in the initial profile, the downwelling long wave radiation increases and prevents the near surface temperature from dropping abnormally. This, in turn, prevents artificial clouds from forming at the first model level. When no clouds are present in the IFS initial profile, the Sc clouds can be initialized using information from the observed vertical profiles. Generally, initialization of Sc clouds in WRF improves the forecast substantially.

Mathematical models of the evolution of classical and solitary cylindrical waves

The evolution of nonlinear elastic cylindrical displacement waves for initial profiles in the form of a Hankel and Macdonald functions is analyzed theoretically and numerically. The difference between the two waves is that the MacDonald function has no hump, decreases monotonically and has a concave downward profile, and the Hankel function is a harmonic attenuating wave. The main novelty is that the evolution of cylindrical waves is studied for two different approaches to the solution of a nonlinear equation. Some significant differences of these waves are shown. First, the features of the Hankel wave, a harmonic wave (symmetrical profile), are briefly described. Then, theoretically and numerically, a single wave with an initial profile in the form of a MacDonald function is analyzed in more detail. Distortion of the initial profile due to the nonlinear interaction of the wave itself and the increase in the maximum amplitude during wave propagation is common to these profiles. Significant features of the McDonald wave are shown - an uncharacteristic initial profile (a profile without a classical hump) evolves in an uncharacteristic way - the profile becomes much steeper and remains convex downwards. Keywords: classical and solitary cylindrical waves; five-constant Murnaghan potential; approximate methods; Hankel and Macdonald initial wave profiles; evolution.

Silicon twisted cone structure produced by optical vortex pulse with structure evaluation by radiation hydrodynamic simulation

We demonstrate a radiation hydrodynamic simulation of optical vortex pulse-ablated microcone structures on silicon (Si) substrates. Doughnut-shaped craters were formed by single pulse irradiation on the Si substrate, and a twisted cone structure with a height of 3.5 µm was created at the center of the irradiation spot by the circularly polarized optical vortex pulse. A two-dimensional (2-D) radiation hydrodynamic simulation reproduced the cone structure well with a height of 3 µm. The central part of the incident laser power was lowered from the initial profile due to plasma shielding over the laser pulse duration for an inverted double-well laser profile. The acute tip shape of the silicon surface can survive over the laser irradiation period.

Atypical evolution of solitary wave propagating in nonlinear elastic medium

The atypical evolution of a solitary cylindrical wave that propagates in the nonlinear elastic medium and has the initial profile in the form of the Macdonald function is described and commented. In the analysis, the approximate method of restriction on the gradient of a deformation is used, and three first approximations are taken into account. Two examples of typical wave evolution — harmoniс and bell-shaped waves — are shown and commented, where the first three approximations are also taken into account. The numerical modeling showed that the atypical initial profile (profile without a hump) evolves atypically — the profile becomes essentially steeper, saving the concavity, and the wave bottom decreases almost two times.

IMPROVEMENT OF SELF-ALIGNED DOUBLE PATTERNING USING SPIN-ON-CARBON MATERIAL

In this paper the advantages of using self-aligned double patterning in conjunction with extreme ultraviolet photolithography were analyzed, and a promising spin-on-carbon material used as the layer for the original pattern of the structure to be formed was identified. In addition, a method to treat and protect the shape of the initial profile of regular structure lines by using a direct current superposition on a capacitively-coupled plasma chamber was presented.