Search results for " coordinate system"
showing 7 items of 77 documents
Genericity of dimension drop on self-affine sets
2017
We prove that generically, for a self-affine set in $\mathbb{R}^d$, removing one of the affine maps which defines the set results in a strict reduction of the Hausdorff dimension. This gives a partial positive answer to a folklore open question.
Improved tau polarisation measurement
1996
Using 22 pb−1 of data collected at LEP in 1992 on the peak of the Z resonance, the ALEPH collaboration has measured the polarisation of the tau leptons decaying into $$ev\bar v, \mu v\bar v$$ ,πν, ρν and a1 ν from their individual decay product distributions. The measurement of the tau polarisation as a function of the production polar angle yields the two parametersN τ andN e, where, in terms of the axial and vector couplingsg Al andg Vl,N l=2g Vl gAl/(g Vl 2 +g 2 ). This analysis follows to a large extent the methods devised for the 1990 and 1991 data but with improvements which bring a better understanding of the systematic uncertainties. Combining the 1992 measurements with our previous…
Higher-order Hamilton–Jacobi perturbation theory for anisotropic heterogeneous media: dynamic ray tracing in Cartesian coordinates
2018
With a Hamilton–Jacobi equation in Cartesian coordinates as a starting point, it is common to use a system of ordinary differential equations describing the continuation of first-order derivatives of phase-space perturbations along a reference ray. Such derivatives can be exploited for calculating geometrical spreading on the reference ray and for establishing a framework for second-order extrapolation of traveltime to points outside the reference ray. The continuation of first-order derivatives of phase-space perturbations has historically been referred to as dynamic ray tracing. The reason for this is its importance in the process of calculating amplitudes along the reference ray. We exte…
Cartesian Psychology – Could There Be One?
2008
The chapter examines what it would mean to talk about “psychology” in Descartes’ terms and argues that within the Cartesian framework we cannot really formulate the questions that are posed by contemporary psychologists. This results from the fact that psychological topics can be found on all three levels of Cartesian science: in metaphysics, in physics and finally in the applied sciences, such as medicine and morals. The aim is to show that the sensory and vegetative functions are often taken together by Descartes. Therefore, the Cartesian system does not recognize any principal difference between sensory functions, such as vision, and vegetative functions, such as digestion. Humans can be…
A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries
2021
Author(s): Gulizzi, Vincenzo; Almgren, Ann S; Bell, John B | Abstract: We present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a shock-capturing Finite Volume (FV) scheme coupled via an $hp$ adaptive mesh refinement ($hp$-AMR) strategy that offers high-order accurate resolution of the embedded geometries. The $hp$-AMR strategy is based on a multi-level block-structured domain partition in which each level is represented by block-structured Cartesian grids and the embedded geometry is represented implicitly by a…
<p>Problemas descriptivos y pensamiento numérico: el caso de las cien aves de corral</p>
2016
Bajo el marco metodológico del análisis didáctico y del análisis histórico-epistemológico se presenta un estudio sobre los problemas descriptivos clásicos que emanan del de “las cien aves de corral”. Se presenta una aproximación global a su larga evolución histórica como objeto de enseñanza, se da cuenta de algunas de sus lecturas analíticas, aritméticas y cartesianas, y se analizan sus métodos y reglas de resolución. Descriptive problems and numerical thinking: The case of one hundred poultryUnder the methodological framework of the didactic analysis and historical-epistemological analysis a study of the classical descriptive problems that emanate from the “hundred poultry” is presented. A…
Collision Avoidance with Potential Fields Based on Parallel Processing of 3D-Point Cloud Data on the GPU
2014
In this paper we present an experimental study on real-time collision avoidance with potential fields that are based on 3D point cloud data and processed on the Graphics Processing Unit (GPU). The virtual forces from the potential fields serve two purposes. First, they are used for changing the reference trajectory. Second they are projected to and applied on torque control level for generating according nullspace behavior together with a Cartesian impedance main control loop. The GPU algorithm creates a map representation that is quickly accessible. In addition, outliers and the robot structure are efficiently removed from the data, and the resolution of the representation can be easily ad…