Three-Dimensional Version of Hill’s Problem with Variable Mass

2021 ◽  
Vol 47 (4) ◽  
pp. 262-276
Author(s):  
Ferdous Bouaziz-Kellil
Keyword(s):  
Variable Mass ◽  
Three Dimensional ◽  
Hill’S Problem ◽  
Dimensional Version ◽  
Hill's Problem

scholarly journals Geometry of the 3D Pythagoras' Theorem

2016 ◽  
Vol 8 (6) ◽  
pp. 78 ◽  
Author(s):  
Luis Teia
Keyword(s):  
Three Dimensional ◽  
Transformation Process ◽  
Two Dimensional ◽  
Natural Evolution ◽  
Dimensional Version ◽  
Pythagoras Theorem

This paper explains step-by-step how to construct the 3D Pythagoras' theorem by geometric manipulation of the two dimensional version. In it is shown how $x+y=z$ (1D Pythagoras' theorem) transforms into $x^2+y^2=z^2$ (2D Pythagoras' theorem) via two steps: a 90-degree rotation, and a perpendicular extrusion. Similarly, the 2D Pythagoras' theorem transforms into 3D using the same steps. Octahedrons emerge naturally during this transformation process. Hence, each of the two dimensional elements has a direct three dimensional equivalent. Just like squares govern the 2D, octahedrons are the basic elements that govern the geometry of the 3D Pythagoras' theorem. As a conclusion, the geometry of the 3D Pythagoras' theorem is a natural evolution of the 1D and 2D. This interdimensional evolution begs the question -- Is there a bigger theorem at play that encompasses all three?

scholarly journals Simulation of denitrification and ozone loss for the Arctic winter 2002/2003

2005 ◽  
Vol 5 (6) ◽  
pp. 1437-1448 ◽  
Author(s):  
J.-U. Grooß ◽  
G. Günther ◽  
R. Müller ◽  
P. Konopka ◽  
S. Bausch ◽  
...  
Keyword(s):  
Inorganic Nitrogen ◽  
Potential Temperature ◽  
Three Dimensional ◽  
Lagrangian Model ◽  
The Arctic ◽  
Particle Nucleation ◽  
Ozone Loss ◽  
Dimensional Version ◽  
Total Inorganic Nitrogen ◽  
Catalytic Cycles

Abstract. We present simulations with the Chemical Lagrangian Model of the Stratosphere (CLaMS) for the Arctic winter 2002/2003. We integrated a Lagrangian denitrification scheme into the three-dimensional version of CLaMS that calculates the growth and sedimentation of nitric acid trihydrate (NAT) particles along individual particle trajectories. From those, we derive the HNO3 downward flux resulting from different particle nucleation assumptions. The simulation results show a clear vertical redistribution of total inorganic nitrogen ( ), with a maximum vortex average permanent removal of over 5ppb in late December between 500 and 550K and a corresponding increase of of over 2ppb below about 450K. The simulated vertical redistribution of is compared with balloon observations by MkIV and in-situ observations from the high altitude aircraft Geophysica. Assuming a globally uniform NAT particle nucleation rate of 7.8x10-6cm-3h-1 in the model, the observed denitrification is well reproduced. In the investigated winter 2002/2003, the denitrification has only moderate impact (≤14%) on the simulated vortex average ozone loss of about 1.1ppm near the 460K level. At higher altitudes, above 600K potential temperature, the simulations show significant ozone depletion through -catalytic cycles due to the unusual early exposure of vortex air to sunlight.

scholarly journals A mass-conserving and multi-tracer efficient transport scheme in the online integrated Enviro-HIRLAM model

2013 ◽  
Vol 6 (4) ◽  
pp. 1029-1042 ◽  
Author(s):  
B. Sørensen ◽  
E. Kaas ◽  
U. S. Korsholm
Keyword(s):  
Prediction Model ◽  
Weather Prediction ◽  
Three Dimensional ◽  
Chemical Species ◽  
Numerical Weather Prediction Model ◽  
Computationally Efficient ◽  
Long Time ◽  
Dimensional Version ◽  
The Stability ◽  
Lagrangian Scheme

Abstract. In this paper a new advection scheme for the online coupled chemical–weather prediction model Enviro-HIRLAM is presented. The new scheme is based on the locally mass-conserving semi-Lagrangian method (LMCSL), where the original two-dimensional scheme has been extended to a fully three-dimensional version. This means that the three-dimensional semi-implicit semi-Lagrangian scheme which is currently used in Enviro-HIRLAM is largely unchanged. The HIRLAM model is a computationally efficient hydrostatic operational short-term numerical weather prediction model, which is used as the base for the online integrated Enviro-HIRLAM. The new scheme is shown to be efficient, mass conserving, and shape preserving, while only requiring minor alterations to the original code. It still retains the stability at long time steps, which the semi-Lagrangian schemes are known for, while handling the emissions of chemical species accurately. Several mass-conserving filters have been tested to assess the optimal balance of accuracy vs. efficiency.

Development of the Life Project Reflexivity Scale: A New Career Intervention Inventory

2018 ◽  
Vol 27 (2) ◽  
pp. 358-370 ◽  
Author(s):  
Annamaria Di Fabio ◽  
Jacobus Gideon Maree ◽  
Maureen E. Kenny
Keyword(s):  
Factor Analysis ◽  
Three Dimensional ◽  
Reliability And Validity ◽  
Well Being ◽  
Career Intervention ◽  
Life Project ◽  
Group Settings ◽  
Confirmatory Factor ◽  
Dimensional Version ◽  
Italian Context

This article describes the Life Project Reflexivity Scale ( LPRS), a questionnaire constructed for use with Italian students to assess the development of reflexivity, which is increasingly vital for personal and professional progress and well-being. The instrument was administered to 502 Italian university students. A three-dimensional version of the scale was identified through exploratory factor analysis and supported by confirmatory factor analysis. Inter-item factor and scale correlations and reliability coefficients were calculated. We concluded that evidence supports the reliability and validity of the LPRS as a useful instrument for measuring life project reflexivity (people’s reflexivity regarding their future career–life–personal projects) in the Italian context. In addition to sound psychometric properties, the LPRS takes little time to administer and can be completed in large group settings with relative ease. More research is needed to more fully assess its validity and its potential for use in other countries.

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