scholarly journals Comparisons of the Cubed-Sphere Gravity Model with the Spherical Harmonics

2010 ◽  
Vol 33 (2) ◽  
pp. 415-425 ◽  
Author(s):  
Brandon A. Jones ◽  
George H. Born ◽  
Gregory Beylkin
Keyword(s):  
Gravity Model ◽  
Spherical Harmonics ◽  
Cubed Sphere

scholarly journals Weakly Orthogonal Spherical Harmonics in a Non-Polar Spherical Coordinates and its Application to Functions on Cubed-Sphere

2012 ◽  
Vol 17 (2) ◽  
pp. 200
Author(s):  
M.A.A.M. Faham ◽  
H.M. Nasir
Keyword(s):  
Fourier Series ◽  
Coordinate System ◽  
Spherical Harmonics ◽  
Spherical Coordinate System ◽  
Spherical Functions ◽  
Spherical Coordinates ◽  
Spherical Coordinate ◽  
Linear Relations ◽  
Inner Products ◽  
Cubed Sphere

In a recent paper (Nasir, 2007), a set of weakly orthogonal and completely orthogonal spherical harmonics in a non-polar spherical coordinate system based on a cubed-sphere was constructed. In this work, we explore some linear relations between these two sets of spherical harmonics. Moreover, a power representation for the set of weakly orthogonal spherical harmonics corresponding to a mode is presented. We also determine the norm of the orthogonal spherical harmonics and hence the inner products for the weakly orthogonal spherical harmonics. As an immediate application of these properties, we present a Fourier series formulation of spherical functions defined on the cubed-sphere.  

Sequential Orbit Determination with the Cubed-Sphere Gravity Model

2012 ◽  
Vol 49 (1) ◽  
pp. 145-156
Author(s):  
Brandon A. Jones ◽  
George H. Born ◽  
Gregory Beylkin
Keyword(s):  
Gravity Model ◽  
Orbit Determination ◽  
Cubed Sphere

Interpolating data on the Cubed Sphere with Spherical Harmonics

2021 ◽  
Author(s):  
Jean-Pierre Croisille ◽  
Jean-Baptiste Bellet ◽  
Matthieu Brachet
Keyword(s):  
Numerical Simulation ◽  
Symmetry Group ◽  
Spherical Harmonics ◽  
Recent Progress ◽  
Quadrature Rules ◽  
Geometrical Properties ◽  
Truncation Scheme ◽  
Cubed Sphere

<p>The Cubed Sphere is a grid commonly used in numerical simulation in climatology. In this talk we present recent progress<br>on the algebraic and geometrical properties of this highly symmetrical grid.<br>First, an analysis of the symmetry group of the Cubed Sphere will be presented: this group <br>is identified as the group of the Cube, [1]. Furthermore, we show how to construct a discrete Spherical Harmonics (SH) basis associated to <br>the Cubed Sphere. This basis displays a truncation scheme relating the zonal and longitudinal <br>mode numbers reminiscent of the rhomboidal truncation on the Lon-Lat grid.<br>The new analysis allows to derive new quadrature rules of  interest for applications in any kind of spherical modelling. In addition,<br>we will comment on applications in mathematical climatology and meteorology, [2].</p><p>[1] J.-B. Bellet, Symmetry group of the equiangular Cubed Sphere, preprint, IECL, Univ. Lorraine, 2020, submitted</p><p>[2] J.-B. Bellet, M. Brachet and J.-P. Croisille, Spherical Harmonics on The Cubed Sphere, IECL, Univ. Lorraine, 2021, Preprint.</p>

Zonal and tesseral harmonic perturbations of an artificial satellite

1966 ◽  
Vol 25 ◽  
pp. 323-325 ◽  
Author(s):  
B. Garfinkel
Keyword(s):  
Angular Velocity ◽  
Spherical Harmonics ◽  
Artificial Satellite ◽  
Compact Form ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Secular Variations ◽  
Tesseral Harmonics

The paper extends the known solution of the Main Problem to include the effects of the higher spherical harmonics of the geopotential. The von Zeipel method is used to calculate the secular variations of orderJmand the long-periodic variations of ordersJm/J2andnJm,λ/ω. HereJmandJm,λare the coefficients of the zonal and the tesseral harmonics respectively, withJm,0=Jm, andωis the angular velocity of the Earth's rotation. With the aid of the theory of spherical harmonics the results are expressed in a most compact form.

Nearly spherical vesicle shapes calculated by use of spherical harmonics : axisymmetric and nonaxisymmetric shapes and their stability

1992 ◽  
Vol 2 (5) ◽  
pp. 1081-1108 ◽  
Author(s):  
V. Heinrich ◽  
M. Brumen ◽  
R. Heinrich ◽  
S. Svetina ◽  
B. Žekš
Keyword(s):  
Spherical Harmonics ◽  
Spherical Vesicle ◽  
Vesicle Shapes

Internal migration in Italy. Long-run analysis of push and pull factors across regions and macro-areas of the country.

2016 ◽  
Vol 13 (3) ◽  
pp. 443-454
Author(s):  
Piras Romano
Keyword(s):  
Gravity Model ◽  
Internal Migration ◽  
Empirical Studies ◽  
Great Majority ◽  
Pull Factors ◽  
Push And Pull Factors ◽  
Long Run ◽  
Italian Regions ◽  
Migration Flows ◽  
Push And Pull

The great majority of empirical studies on internal migration across Italian regions either ignores the long-run perspective of the phenomenon or do not consider push and pull factors separately. In addition, Centre-North to South flows, intra-South and intra-Centre-North migration have not been studied. We aim to fill this gap and tackle interregional migration flows from different geographical perspectives. We apply four panel data estimators with different statistical assumptions and show that long-run migration flows from the Mezzogiorno towards Centre-Northern regions are well explained by a gravity model in which per capita GDP, unemployment and population play a major role. On the contrary, migration flows from Centre-North to South has probably much to do with other social and demographic factors. Finally, intra Centre-North and intra South migration flows roughly obey to the gravity model, though not all explicative variables are relevant.

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