The EHTA for Two Shallow Water Wave Equations

Abstract In this paper, two shallow water wave equations are studied by using the extended homoclinic test approach (EHTA). The new exact solutions for the shallow water wave equations are obtained. Their dynamic properties of some exact solutions are discussed and their profiles of these solutions are given by using of software Maple. Mathematics Subject Classification: 35B05, 35B10, 35B1

Exact periodic cross-kink wave solutions and breather type of two-solitary wave solutions for the (3 + 1)-dimensional potential-YTSF equation

AbstractIn this paper, the (3+1)-dimensional potential-YTSF equation is investigated. Exact solutions with three-wave form including periodic cross-kink wave, periodic two-solitary wave and breather type of two-solitary wave solutions are obtained using Hirota’s bilinear form and generalized three-wave approach with the aid of symbolic computation. Moreover, the properties for some new solutions are shown with some figures

Relaxation in Disordered Systems

The relaxation behaviour of various statistical and thermodynamic many body systems like percolating networks, magnetic systems, spin glasses, ordinary glasses, polymers, powders or sand-pile, neural network etc are reviewed. Various theoretical models to explain these behaviours are briefly sketched

Steady flow of some non-newtonian fluids through a porous medium by using adomian decomposition method

Non-Newtonian fluids are employed in a wide range of industrial applications. Non-Newtonian fluids that shows characteristics of both elastic and viscous fluids as a result of shear stress, are referred to as viscoelastic fluids. Constitutive equations of the viscoelastic fluids, flow patterns and viscous response are important challenges that need to be considered when modelling the flow in a porous medium. The predominant idea of this thesis is to find the analytical solutions of viscoelastic fluid in a porous medium. The primary goal of this research is to create a one-dimensional simulation for three different kinds of viscoelastic fluids, namely, Johnson-Segalman, Powell-Eyring, and Sisko fluids, in a porous medium. Further, Darcy’s law is selected for simulating permeable media saturated by viscoelastic fluid. The effect of external magnetic field is an additional feature to the innovation of the constructed mathematical models. The system of nonlinear coupled partial differential equations supported by related boundary conditions are solved analytically by using the Adomian decomposition method (ADM). In the analysis, the impact of various physical parameters on velocity and temperature are scrutinized and the results are exhibited graphically. The wall shear stress versus governing constraints are also evaluated, and their results are summarised in the form of tables and graphs. The results demonstrated that for both isothermal and non-isothermal circumstances, the inclination angle causes a variation in shear stress. It is also observed that the viscosity and shear stress have a direct connection in the absence of a heating effect. Moreover, the viscosity of the non-isothermal state is sensitive to temperature variations for both lift and drainage problems. The findings validated the efficacy of the suggested technique, and the solutions are successfully approximated to the exact solutions

Water waves over a muddy seabed

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2008.Includes bibliographical references (p. 199-200).A generalized viscoelastic model is used to describe the rheological properties of mud and is fitted to the available experimental data, so that its constitutive coefficients are just material properties independent of the frequency of the external forcing. We integrate this model into a perturbation analysis to solve the interaction between a thin layer of viscoelastic mud and sinusoidal waves propagating on top of a water layer of intermediate depth. In contrast with the previous studies the analysis is done for decaying water waves and a rheological model with frequency independent coefficients. The leading order motion and the mean second order motion inside the mud layer is determined analytically together with the first two orders motion in water. The analysis is done in a fixed Eulerian frame and it is shown that both a mean horizontal displacement and a Eulerian mean horizontal velocity exists inside the mud layer at the second order. The effect of elasticity and viscosity on the damping of water waves and on the mean motion of the mud is studied. It is shown that a light mud with a high proportion of elasticity will significantly modify the leading order movement through damping. The results are applied to solve analytically the problem of the evolution of the narrow-banded waves propagating on top of a semi-infinite mud layer. It is shown that the presence of the mud layer gives rise to a negative mean current in water layer and to free waves generated at the edge of the mud layer and propagating at the dimensional velocity ....by Mikhael Krotov.S.M

High frequency backscatter from the polar and auroral e-region ionosphere

Thesis (Ph.D.) University of Alaska Fairbanks, 2017The Earth's ionosphere contains collisional and partially-ionized plasma. The electric field, produced by the interaction between the Earth's magnetosphere and the solar wind, drives the plasma bulk motion, also known as convection, in the F-region of the ionosphere. It can also destabilize the plasma in the E-region, producing irregularities or waves. Intermediatescale waves with wavelengths of hundreds of meters can cause scintillation and fading of the Global Navigation Satellite System (GNSS) signals, whereas the small-scale waves (< 100 m) can scatter radar signals, making possible detection of these plasma structures and measurements of their characteristics such as their phase velocity and intensity. In this work, production of the decameter-scale (10 m) irregularities in the ionospheric E-region (100-120 km in altitude) at high latitudes is investigated both theoretically, using linear fluid theory of plasma instability processes that generate small-scale plasma waves, and experimentally, by analyzing data collected with the newly-deployed high-southern-latitude radars within the Super Dual Auroral Radar Network (SuperDARN). The theoretical part of this work focuses on symmetry properties of the general dispersion relation that describes wave propagation in the collisional plasma in the two-stream and gradient-drift instability regimes. The instability growth rate and phase velocity are examined under the presence of a background parallel electric field, whose influence is demonstrated to break the spatial symmetry of the wave propagation patterns. In the observational part of this thesis, a novel dual radar setup is used to examine E-region irregularities in the magnetic polar cap by probing the E-region along the same line from opposite directions. The phase velocity analysis together with raytracing simulations demonstrated that, in the polar cap, the radar backscatter is primarily controlled by the plasma density conditions. In particular, when the E-region layer is strong and stratified, the radar backscatter properties are controlled by the convection velocity, whereas for a tilted E-layer, the height and aspect angle conditions are more important. Finally, the fundamental dependence of the E-region irregularity phase velocity on the component of the plasma convection is investigated using two new SuperDARN radars at high southern latitudes where plasma convection estimates are accurately deduced from all SuperDARN radars in the southern hemisphere. Statistical analysis is presented showing that the predominance of the E-region echoes of a particular polarity is strongly dictated by the orientation of the convection plasma ow which itself has a significant asymmetry towards westward zonal flow