1,354,861 research outputs found
Light and Matter, Two Sides of the Same Coin
No full textWith an opinionated and irreverent tone, the author debunks most of the current theories in the field of modern physics, appealing to the scientific method and common sense. At the same time, in strict compliance with the already known experimental evidence, he proposes his own version of the facts, aimed at rationalizing and unifying the various aspects in which the nature that surrounds us manifests itself. The result is a possible model of the universe where events are all connected by a common thread, even if distributed on different scales, ranging from the subatomic to that of galaxies. In this perspective, in the middle, the living cell profits from a substrate and a habitat that have favoured its very existence. Reading of this book does not require any advanced scientific knowledge and is therefore accessible to non-experts, provided they are equipped with the necessary dose of eccentricity that allows them to appreciate these provocative pages
Some remarks about the collocation method on a modified Legendre grid
No full textWe compare the results obtained by applying the standard collocation method at the Legendre Gauss-Lobatto nodes, for a model problem simulating a steady advection-diffusion equation, with those obtained by collocating at a new set of nodes. These nodes are derived from a suitable modification of the Legendre grid, according to the magnitude of the ratio between the advective and the diffusive parts of the differential operator
The Space-Time Metric Outside a Pulsating Charged Sphere
No full textWe consider the problem of determining the dynamics of the electromagnetic field generated outside a ball whose charge changes depending on time. We are in conditions of perfect symmetry and the electric field is considered to be radial. This is not a simplification since, under such a hypothesis, the magnetic field does not develop. Thus, it is first necessary to find out the appropriate modeling equations. These are obtained by writing a suitable energy tensor that combines the classical electromagnetic stress-energy tensor with a special kind of mass tensor. The next step is to show that it is possible to solve Einstein’s equations by plugging the new tensor on the right-hand side. Interesting connections with some classical solutions related to black holes are finally established
Approximation by the Legendre collocation method of a model problem in electrophysiology
No full textAbstractWe examine the polynomial approximation of the solution of a nonlinear differential problem modelling the evolution of the potential inside an electrically stimulated neuron. The collocation method at the Legendre Gauss-Lobatto nodes is used for the discretization with respect to the space variable
Ball Lightning as Plasma Vortexes: A Reinforcement of the Conjecture
No full textThe idea that ball lightning is a plasma manifestation has been put forth by many authors. One of the major drawbacks of this approach concerns with the stability of these structures. After showing the theoretical existence of pure rotating electromagnetic waves in equilibrium, we argue that these can reasonably provide a robust stabilizing scaffolding for the development of ball lightning phenomena
Finite-difference preconditioners for superconsistent pseudospectral approximations
No full textThe superconsistent collocation method, which is based on a collocation grid different from the one used to represent the solution, has proven to be very accurate in the resolution of various functional equations. Excellent results can be also obtained for what concerns preconditioning. Some analysis and numerous experiments, regarding the use of finite-differences preconditioners, for matrices arising from pseudospectral approximations of advection-diffusion boundary value problems, are presented and discussed, both in the case of Legendre and Chebyshev representation nodes
High Frequency Electrical Oscillations in Cavities
No full textIf the interior of a conducting cavity (such as a capacitor or a coaxial cable) is supplied with a very high-frequency electric signal, the information between the walls propagates with an appreciable delay, due to the finiteness of the speed of light. The configuration is typical of cavities having size larger than the wavelength of the injected signal. Such a non rare situation, in practice, may cause a break down of the performances of the device. We show that the classical Coulomb’s law and Maxwell’s equations do not correctly predict this behavior. Therefore, we provide an extension of the modeling equations that allows for a more reliable determination of the electromagnetic field during the evolution process. The main issue is that, even in vacuum (no dielectric inside the device), the fast variation of the signal produces sinks and sources in the electric field, giving rise to zones where the divergence is not zero. These regions are well balanced, so that their average in the domain is zero. However, this behavior escapes the usual treatment with classical electromagnetism
Pseudospectral approximation of a PDE defined on a triangle
No full textA scheme for the approximation by collocation method of an elliptic equation defined on a triangle is proposed. Different solution techniques are examined
A fast solver for elliptic boundary-value problems in the square
No full textWe approximate the solution of advection-diffusion equations by collocation at a special grid related to the differential operator and the classical Legendre grid
Spectral elements for transport-dominated equations
No full textThe book deals with the numerical approximation of various PDEs using the spectral element method, with particular emphasis for elliptic equations dominated by first-order terms. It provides a simple introduction to spectral elements with additional new tools (upwind grids and preconditioners). Applications to fluid dynamics and semiconductor devices are considered, as well as in other models were transport-diffusion equations arise. The aim is to provide the reader with both introductive and more advanced material on spectral Legendre collocation methods. The book however does not cover all the aspects of spectral methods. Engineers, physicists and applied mathematicians may study how to implement the collocation method and use the results to improve their computational codes
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