Characteristic behaviour of plasma fluctuations inside a plasma bubble in presence of a magnetic field due to the formation of a potential well

Experiments were carried out to observe the effect of a magnetic field and grid biasing voltage in presence of a plasma bubble in a magnetized, filamentary discharge plasma system. A spherical mesh grid of 80% optical transparency was negatively biased and introduced into the plasma for creating a plasma bubble. Diagnostics via an electrical Langmuir probe and a hot emissive probe were extensively used for scanning the plasma bubble. Plasma floating potential fluctuations were measured at three different positions of the plasma bubble. The instability in the pattern showed the dynamic transition from periodic to chaotic for increasing magnetic fields. Time scale analysis using continuous wavelet transform was carried out to identify the presence of non‐linearity from the contour plots. The mechanisms of the low‐frequency instabilities along with the transition to chaos could be qualitatively explained. Non‐linear techniques such as fast Fourier transform, phase space plot, and recurrence plot were used to explore the dynamics of the system appearing during plasma fluctuations. In order to demonstrate the observed chaotic phenomena in this study, characteristics of chaos such as the Lyapunov exponent were obtained from experimental time series data. The experimentally observed potential structure is confirmed with numerical analysis based on fluid hydrodynamics.     

Keller–Osserman estimates and removability result for the anisotropic porous medium equation with gradient absorption term

We study “large” nonnegative solutions for a class of quasilinear equations model of which is We give a sufficient condition on the exponents and for the removability of isolated singularities.     

A cost‐effective curvature calculation approach for interfacial flows on unstructured meshes

We present a simple and cost‐effective curvature calculation approach for simulations of interfacial flows on structured and unstructured grids. The interface is defined using volume fractions, and the interface curvature is obtained as a function of the gradients of volume fractions. The gradient computation is based on a recently proposed gradient recovery method that mimicks the least squares approach without the need to solve a system of equations and is quite easy to implement on arbitrary polygonal meshes. The resulting interface curvature is used in a continuum surface force formulation within the framework of a well‐balanced finite‐volume algorithm to simulate multiphase flows dominated by surface tension. We show that the proposed curvature calculation is at least as accurate as some of the existing approaches on unstructured meshes while being straightforward to implement on any mesh topology. Numerical investigations also show that spurious currents in stationary problems that are dependent on the curvature calculation methodology are also acceptably low using the proposed approach. Studies on capillary waves and rising bubbles in viscous flows lend credence to the ability of the proposed method as an inexpensive, robust, and reasonably accurate approach for curvature calculation and numerical simulation of multiphase flows.     

A higher resolution edge‐based finite volume method for the simulation of the oil–water displacement in heterogeneous and anisotropic porous media using a modified IMPES method

In this article, we present a higher‐order finite volume method with a ‘Modified Implicit Pressure Explicit Saturation’ (MIMPES) formulation to model the 2D incompressible and immiscible two‐phase flow of oil and water in heterogeneous and anisotropic porous media. We used a median‐dual vertex‐centered finite volume method with an edge‐based data structure to discretize both, the elliptic pressure and the hyperbolic saturation equations. In the classical IMPES approach, first, the pressure equation is solved implicitly from an initial saturation distribution; then, the velocity field is computed explicitly from the pressure field, and finally, the saturation equation is solved explicitly. This saturation field is then used to re‐compute the pressure field, and the process follows until the end of the simulation is reached. Because of the explicit solution of the saturation equation, severe time restrictions are imposed on the simulation. In order to circumvent this problem, an edge‐based implementation of the MIMPES method of Hurtado and co‐workers was developed. In the MIMPES approach, the pressure equation is solved, and the velocity field is computed less frequently than the saturation field, using the fact that, usually, the velocity field varies slowly throughout the simulation. The solution of the pressure equation is performed using a modification of Crumpton's two‐step approach, which was designed to handle material discontinuity properly. The saturation equation is solved explicitly using an edge‐based implementation of a modified second‐order monotonic upstream scheme for conservation laws type method. Some examples are presented in order to validate the proposed formulation. Our results match quite well with others found in literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Brake Orbits of First Order Convex Hamiltonian Systems with Particular Anisotropic Growth

Combining the dual least action principle with Mountain-pass lemma,we obtain the existence of brake orbits for first-order convex Hamiltonian systems with particular anisotropic growth.     

A mixed hp FEM for the approximation of fourth‐order singularly perturbed problems on smooth domains

We consider fourth‐order singularly perturbed problems posed on smooth domains and the approximation of their solution by a mixed Finite Element Method on the so‐called Spectral Boundary Layer Mesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at an exponential rate when the error is measured in the energy norm. Numerical examples illustrate our theoretical findings.     

The local ultraconvergence of high‐order finite element method for second‐order elliptic problems with constant coefficients over a rectangular partition

In this article, we will discuss the local ultraconvergence of high‐degree finite element method based on a rectangular partition for the second‐degree elliptic problem with constant coefficients in Ω ? ?² , u( y ) = 0 on ?Ω . Based on suitable regularity, ultraconvergence of the displacement of the extrapolated kth (k ≥ 3) degree finite element solution has been obtained by an extrapolation technique. Finally, numerical experiments are applied to demonstrate our theoretical findings.     

Evaluation of RBFs for volume data interpolation in CFD

A greedy method for choosing an optimum reduced set of control points is integrated with RBF interpolation and evaluated for the purpose of interpolating large‐volume data sets in CFD. Given a function defined at a set of points, the greedy method selects a small subset of these points that is sufficient to keep the interpolation error at all the remaining points below a chosen bound. This is equivalent to a type of data compression and would have useful storage, post‐processing, and computational applications in CFD. To test the method in terms of both the point selection scheme and the suitability of reduced control point volume interpolation, a trial application of the interpolation to velocity fields in CFD volume meshes is considered. To optimise the point selection process, and attempt to be able to capture multiple length scales, a variable support radius formulation has also been included. Structured and unstructured mesh cases are considered for aerofoils, a wing case and a wing‐body case. For smooth volume functions, the method is shown to work well, producing accurate velocity interpolations using a very small number of the cells in the mesh. For general complex fields including large gradients, the method is still shown to be effective, although large gradients require more interpolation points to be used.Copyright © 2013 John Wiley & Sons, Ltd.     

Azimuthal orientational correlations due to excluded volume epitaxy in growing anisotropic grains

The microstructure of anisotropically shaped grains can strongly influence a range of material properties, including transport, mechanical and electro-optical. A grain-structure-related phenomenon, known as excluded volume epitaxy (EVE), is reported in this study. EVE is a local, inter-grain orientational correlations effect, which results from a combination of continuous nucleation of anisotropic grains and impingement of growing grains. Due to EVE, anisotropically shaped grains have a tendency to be similarly aligned in a local neighbourhood, despite the absence of any forced global orientation in the sample. The effect has been repeatedly observed by the authors in block copolymers, as illustrated by a representative TEM image. Optical microscopy of anisotropically shaped non-polymeric crystals revealed the generality of this effect. The simulation study revealed a tendency for azimuthal, inter-grain orientational correlation and re-confirmed the experimental observation of EVE.