Search

In this paper, we present two computational methods for performing simulations of pollution propagation described by advection-diffusion equations. The first method employs graph grammars to describe the generation process of the computational mesh used in simulations with the meshless solver of the three-dimensional finite element method. The graph transformation rules express the three-dimensional Rivara longest-edge refinement algorithm. This solver is used for an exemplary application: performing three-dimensional simulations of pollution generation by the coal-burning power plant and its propagation in the city of Longyearbyen, the capital of Spitsbergen. The second computational code is based on the Physics Informed Neural Networks method. It is used to calculate the dissipation of the pollution along the valley in which the city of Longyearbyen is located. We discuss the instantiation and execution of the PINN method using Google Colab implementation. We discuss the benefits and limitations of the PINN implementation., Comment: 34 pages, 21 figures, 1 table

The Northern European Enclosure Dam (NEED) is a hypothetical project to prevent flooding in European countries following the rising ocean level due to melting arctic glaciers. This project involves the construction of two large dams between Scotland and Norway, as well as England and France. The anticipated cost of this project is 250 to 500 billion euros. In this paper, we present the simulation of the aftermath of flooding on the European coastline caused by a catastrophic break of this hypothetical dam. From our simulation results, we can observe that there is a traveling wave after the accident, with a velocity of around 10 kilometers per hour, raising the sea level permanently inside the dammed region. This observation implies a need to construct additional dams or barriers protecting the northern coastline of the Netherlands and the interior of the Baltic Sea. Our simulations have been obtained using the following building blocks. First, a graph transformation model was applied to generate an adaptive mesh approximating the topography of the Earth. We employ the composition graph grammar model for breaking triangular elements in the mesh without the generation of hanging nodes. Second, the wave equation is formulated in a spherical latitude-longitude system of coordinates and solved by a high-order time integration scheme using the generalized $\alpha$ method., Comment: 24 pages, 32 figures, 1 table

The inversion of cause and effect in the classic description of electromagnetism, gives rise to a conceptual error which is at the bottom of many paradoxes and exceptions. At present, the curious fact that unipolar induction or the Faraday Disc constitutes an exception to the Faraday induction law is generally accepted. When we establish the correct cause and effect relationship a close connection appears between mechanics and electromagnetism, as does a new induction law for which paradoxes or exceptions do not occur. Some paradoxical experiments in unipolar induction involving the unique geometry of the spiral are described demonstrating the inversion of cause and effect. The emf and torque of the Faraday Disc and the conducting spiral is due to the continuous variation of the electromagnetic angular moment of the continuous current. This experiments confirm the Lorentz Force and invalidate Faradays Induction Law. They show how in a closed circuit emf and unipolar torque are not produced by the variation in magnetic flux, which is constant, but by two variations in the electromagnetic angular moment. The three possible ways of varying the electromagnetic angular moment generated by the circulation of the charges gives rise to the different forms of electromagnetic induction., Comment: 23 pages, 11 figures, 11 equations