Design of Gas - Surfactant Injection for Carbon Dioxide Storage in a North Sea Aquifer using Streamline-Based Simulation

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Extractions of some new travelling wave solutions to the conformable Date-Jimbo-Kashiwara-Miwa equation

In this paper, complex and combined dark-bright characteristic properties of nonlinear Date-Jimbo-Kashiwara-Miwa equation with conformable are extracted by using two powerful analytical approaches. Many graphical representations such as 2D, 3D and contour are also reported. Finally, general conclusions of about the novel findings are introduced at the end of this manuscript

Global Wilson-Fisher fixed points

The Wilson-Fisher fixed point with $O(N)$ universality in three dimensions is studied using the renormalisation group. It is shown how a combination of analytical and numerical techniques determine global fixed point solutions to leading order in the derivative expansion for real or purely imaginary fields with moderate numerical effort. Universal and non-universal quantitites such as scaling exponents and mass ratios are computed, for all $N$, together with local fixed point coordinates, radii of convergence, and parameters which control the asymptotic behaviour of the effective action. We also explain when and why finite-$N$ results do not converge pointwise towards the exact infinite-$N$ limit. In the regime of purely imaginary fields, a new link between singularities of fixed point effective actions and singularities of their counterparts by Polchinski are established. Implications for other theories are indicated.Comment: 28 pages, 10 figures, v2: explanations and refs added, to appear (NPB

Reproducibility, accuracy and performance of the Feltor code and library on parallel computer architectures

Feltor is a modular and free scientific software package. It allows developing platform independent code that runs on a variety of parallel computer architectures ranging from laptop CPUs to multi-GPU distributed memory systems. Feltor consists of both a numerical library and a collection of application codes built on top of the library. Its main target are two- and three-dimensional drift- and gyro-fluid simulations with discontinuous Galerkin methods as the main numerical discretization technique. We observe that numerical simulations of a recently developed gyro-fluid model produce non-deterministic results in parallel computations. First, we show how we restore accuracy and bitwise reproducibility algorithmically and programmatically. In particular, we adopt an implementation of the exactly rounded dot product based on long accumulators, which avoids accuracy losses especially in parallel applications. However, reproducibility and accuracy alone fail to indicate correct simulation behaviour. In fact, in the physical model slightly different initial conditions lead to vastly different end states. This behaviour translates to its numerical representation. Pointwise convergence, even in principle, becomes impossible for long simulation times. In a second part, we explore important performance tuning considerations. We identify latency and memory bandwidth as the main performance indicators of our routines. Based on these, we propose a parallel performance model that predicts the execution time of algorithms implemented in Feltor and test our model on a selection of parallel hardware architectures. We are able to predict the execution time with a relative error of less than 25% for problem sizes between 0.1 and 1000 MB. Finally, we find that the product of latency and bandwidth gives a minimum array size per compute node to achieve a scaling efficiency above 50% (both strong and weak)

Non-Commutative (Softly Broken) Supersymmetric Yang-Mills-Chern-Simons

We study d=2+1 non-commutative U(1) YMCS, concentrating on the one-loop corrections to the propagator and to the dispersion relations. Unlike its commutative counterpart, this model presents divergences and hence an IR/UV mechanism, which we regularize by adding a Majorana gaugino of mass m_f, that provides (softly broken) supersymmetry. The perturbative vacuum becomes stable for a wide range of coupling and mass values, and tachyonic modes are generated only in two regions of the parameters space. One such region corresponds to removing the supersymmetric regulator (m_f >> m_g), restoring the well-known IR/UV mixing phenomenon. The other one (for m_f ~ m_g/2 and large \theta) is novel and peculiar of this model. The two tachyonic regions turn out to be very different in nature. We conclude with some remarks on the theory's off-shell unitarity.Comment: 42 pages, 11 figures, uses Axodraw. Bibliography revise

New solution for well test analysis in reservoirs with permeability discontinuities

Abstract unavailable please refer to PDF

On optical solutions to the Kadomtsev–Petviashviliequation with a local Conformable derivativeitle

In fact, due to the existence of this category of equations, our understanding of many phenomena around us becomes more complete. In this paper, we study an integrable partial differential equation called the Kadomtsev–Petviashvili equation with a local conformable derivative. This equation is used to describe nonlinear motion. In order to solve the equation, it is first necessary to convert the form of the equation from a partial derivative to an equation with ordinary derivatives using a suitable variable change. The resulting form will then be the basis of our work to determine the main solutions. All the solutions reported in the paper for the present equation are quite different from the previous findings in other papers. All necessary calculations are provided using symbolic computing software in Maple

Propagation of an Optical Vortex in Fiber Arrays with Triangular Lattices

The propagation of optical vortices (OVs) in linear and nonlinear media is an important field of research in science and engineering. The most important goal is to explore the properties of guiding dynamics for potential applications such as sensing, all-optical switching, frequency mixing and modulation. In this dissertation, we present analytical methods and numerical techniques to investigate the propagation of an optical vortex in fiber array waveguides. Analytically, we model wave propagation in a waveguide by coupled mode Equations as a simplified approximation. The beam propagation method (BPM) is also employed to numerically solve the paraxial wave Equation by finite difference (FD) techniques. We will investigate the propagation of fields in a 2D triangular lattice with different core arrangements in the optical waveguide. In order to eliminate wave reflections at the boundaries of the computational area, the transparent boundary condition (TBC) is applied. In our explorations for the propagation properties of an optical vortex in a linear and a non-linear triangular lattice medium, images are numerically generated for the field phase and intensity in addition to the interferogram of the vortex field with a reference plane or Gaussian field. The finite difference beam propagation method (FD-BPM) with transparent boundary condition (TBC) is a robust approach to numerically deal with optical field propagations in waveguides. In a fiber array arranged in triangular lattices, new vortices vary with respect to the propagation distance and the number of cores in the fiber array for both linear and nonlinear regimes. With more cores and longer propagation distances, more vortices are created. However, they do not always survive and may disappear while other new vortices are formed at other points. In a linear triangular lattice, the results demonstrated that the number of vortices may increase or decrease with respect to the number of cores in the array lattice. In a nonlinear triangular lattice, however, the number of vortices tends to increase as the core radius increases and decrease as the distance between cores increases. Investigations revealed that new vortices are generated due to the effects of the phase spiral around the new points of zero intensity. These points are formed due to the mode coupling of the optical field between the cores inside the array. In order to understand the dynamics of vortex generation, we examine vortex density, defined as the total number of vortices per unit area of the fiber array. This parameter is to be explored versus the propagation distance, the core radius size and the distance between cores. The Shack-Hartmann wavefront sensor can be employed to find the vortex density and the locations of vortices. Simulation results revealed that the vortex density increases with respect to propagation distance until saturation. It also increases with an increasing radius size but decreases with increasing distance between the array cores for linear and nonlinear regimes