scholarly journals The topographic bias in gravimetric geoid determination revisited

2019 ◽  
Vol 9 (1) ◽  
pp. 59-64
Author(s):  
Lars E. Sjöberg
Keyword(s):  
Density Distribution ◽  
Geoid Determination ◽  
The Other ◽  
Harmonic Potential ◽  
Gravimetric Geoid ◽  
Potential Bias ◽  
Computation Point ◽  
Density Distributions ◽  
Topographic Bias ◽  
Topographic Potential

Abstract The topographic potential bias at geoid level is the error of the analytically continued geopotential from or above the Earth’s surface to the geoid. We show that the topographic potential can be expressed as the sum of two Bouguer shell components, where the density distribution of one is spherical symmetric and the other is harmonic at any point along the normal to a sphere through the computation point. As a harmonic potential does not affect the bias, the resulting topographic bias is that of the first component, i.e. the spherical symmetric Bouguer shell. This implies that the so-called terrain potential is not likely to contribute significantly to the bias. We present three examples of the geoid bias for different topographic density distributions.

scholarly journals Solving the Topographic Potential Bias as an Initial Value Problem

2009 ◽  
Vol 44 (3) ◽  
pp. 75-84 ◽  
Author(s):  
L. Sjöberg
Keyword(s):  
Initial Value Problem ◽  
Potential Bias ◽  
Initial Value ◽  
Disturbing Potential ◽  
Computation Point ◽  
The Earth ◽  
Terrain Effect ◽  
Topographic Potential ◽  
The Difference ◽  
The Masses

Solving the Topographic Potential Bias as an Initial Value ProblemIf the gravitational potential or the disturbing potential of the Earth be downward continued by harmonic continuation inside the Earth's topography, it will be biased, the bias being the difference between the downward continued fictitious, harmonic potential and the real potential inside the masses. We use initial value problem techniques to solve for the bias. First, the solution is derived for a constant topographic density, in which case the bias can be expressed by a very simple formula related with the topographic height above the computation point. Second, for an arbitrary density distribution the bias becomes an integral along the vertical from the computation point to the Earth's surface. No topographic masses, except those along the vertical through the computation point, affect the bias. (To be exact, only the direct and indirect effects of an arbitrarily small but finite volume of mass around the surface point along the radius must be considered.) This implies that the frequently computed terrain effect is not needed (except, possibly, for an arbitrarily small inner-zone around the computation point) for computing the geoid by the method of analytical continuation.

One-Dimensional Density Distributions of Powder Media in Dies Subjected to Multishock Compactions

1988 ◽  
Vol 110 (4) ◽  
pp. 355-360 ◽  
Author(s):  
Y. Sano
Keyword(s):  
Shock Wave ◽  
Density Distribution ◽  
Friction Force ◽  
The Other ◽  
Wall Friction ◽  
Uniform Density ◽  
Simple Type ◽  
One Dimensional ◽  
Density Distributions ◽  
The One

A theoretical attempt to clarify the reason why the compacts of powder media have uniform density distributions as the density of the compacts becomes high, is made for the compaction of the copper powder medium of a simple type by punch impaction. Based on the one-dimensional equation of motion including the effect of die wall friction force, there are two main factors which influence the density distribution of the medium during the compaction process; one is the propagation of the shock wave passing through the medium, while the other is the friction force between the circumferential surface of the medium and the die wall. The equation reveals that the effect of the force increases little as the density becomes high as a result of the repetitive traveling of the shock wave between the punch and plug. The propagation or more definitely the repetitive traveling, on the other hand, increasingly unformalizes the density distribution during the process as the number of the traveling increases. Owing to the aforementioned effects of the two factors on the density distribution during the process, the high density compacts become uniform.

scholarly journals On the topographic bias and density distribution in modelling the geoid and orthometric heights

2018 ◽  
Vol 8 (1) ◽  
pp. 30-33 ◽  
Author(s):  
Lars E. Sjöberg
Keyword(s):  
Density Distribution ◽  
Mass Distribution ◽  
Geoid Height ◽  
Analytical Continuation ◽  
Orthometric Height ◽  
Gravimetric Geoid ◽  
Mountainous Regions ◽  
Imprecise Information ◽  
Topographic Bias ◽  
The Difference

Abstract It is well known that the success in precise determinations of the gravimetric geoid height (N) and the orthometric height (H) rely on the knowledge of the topographic mass distribution. We show that the residual topographic bias due to an imprecise information on the topographic density is practically the same for N and H, but with opposite signs. This result is demonstrated both for the Helmert orthometric height and for a more precise orthometric height derived by analytical continuation of the external geopotential to the geoid. This result leads to the conclusion that precise gravimetric geoid heights cannot be validated by GNSS-levelling geoid heights in mountainous regions for the errors caused by the incorrect modelling of the topographic mass distribution, because this uncertainty is hidden in the difference between the two geoid estimators.

scholarly journals Die zeitliche Änderung der radialen Elektronendichteverteilung beim Theta-Pinch

1963 ◽  
Vol 18 (8-9) ◽  
pp. 895-900
Author(s):  
Franz Peter Küpper
Keyword(s):  
Density Distribution ◽  
Electron Density ◽  
Electron Density Distribution ◽  
Electron Distribution ◽  
Radial Symmetry ◽  
Zero Order ◽  
Time Interval ◽  
Interferometric Method ◽  
Density Distributions ◽  
Theta Pinch

In a θ-pinch the radial symmetry of the electron density distribution as a function of time has been measured by a MACH—ZEHNDER interferometer. In a time interval of 400 nsec during a discharge an image converter made three pictures (exposure times of 10 nsec each) . Up to 100 nsec after the first compression, the experimental results show different density distributions for the cases of trapped parallel and antiparallel magnetic fields. Complete radial symmetry of the electron density distribution was not found.Another interferometric method for measuring the radial symmetry of the electron distribution by observing “zero order” fringes is described.

AVERAGE PROPERTY OF FRAGMENTATION REACTION AND MOMENTUM DISSIPATION INDUCED BY HALO-NUCLEI IN HEAVY ION COLLISIONS

2006 ◽  
Vol 15 (05) ◽  
pp. 1069-1086
Author(s):  
JIAN-YE LIU ◽  
WEN-JUN GUO ◽  
ZHONG-ZHOU REN ◽  
WEI ZUO ◽  
XI-GUO LEE ◽  
...  
Keyword(s):  
Density Distribution ◽  
Heavy Ion Collisions ◽  
Halo Nucleus ◽  
Heavy Ion ◽  
Halo Nuclei ◽  
Fragmentation Reaction ◽  
Quantum Molecular Dynamics ◽  
Nuclear Stopping ◽  
Density Distributions ◽  
Ion Collisions

We study systematically the average property of fragmentation reaction and momentum dissipation induced by halo-nuclei in intermediate energy heavy ion collisions for different colliding systems and different beam energies within the isospin dependent quantum molecular dynamics model (IQMD). This study is based on the extended halo-nucleus density distributions, which indicates the average property of loosely inner halo nucleus structure, because the interaction potential and in-medium nucleon-nucleon cross section in IQMD model depend on the density distribution. In order to study the average properties of fragmentation reaction and momentum dissipation induced by halo-nuclei we also compare the results for the halo-nuclear colliding systems with those for corresponding stable colliding systems with same mass under the same incident channel condition. We find that the effect of extended halo density distribution on the fragment multiplicity and nuclear stopping (momentum dissipation) are important for the different beam energies and different colliding systems. For example the extended halo density distributions increase the fragment multiplicity but decrease the nuclear stopping for all of incident channel conditions in this paper.

scholarly journals Phenomenological nuclear density distributions

2020 ◽  
Vol 4 ◽  
pp. 85
Author(s):  
G. A. Lalazissis ◽  
C. P. Panos
Keyword(s):  
Experimental Data ◽  
Density Distribution ◽  
Electron Scattering ◽  
Nuclear Density ◽  
Practical Application ◽  
Density Distributions ◽  
Pionic Atoms

A recently proposed semiphenomenological density distribution for neutrons and protons in nuclei is discussed. This density was derived using the separation energies of the last neutron or proton. A com­parison is made with the symmetrised Fermi density distribution with parameters determined by fitting electron scattering experimental data and with a Fermi density with parameters coming from a recent anal­ysis of pionic atoms. Theoretical expressions for rms radii for neutron, proton and matter distributions are proposed, which give the average trend of the variation of these quantities as functions of Ν, Ζ and A respectively. To facilitate the use of the new density all the parameters needed in a practical application are tabulated for a series of nuclei. Some applications of the new density are also discussed.

Density functional theory study on the structural, reactivity, and electronic properties of all mono-, di-, tri-, tetra-, and penta-fluoroanilines as monomers for conducting polymers

2012 ◽  
Vol 90 (10) ◽  
pp. 902-914 ◽  
Author(s):  
Hossein Shirani Il Beigi
Keyword(s):  
Density Functional Theory ◽  
Conducting Polymers ◽  
Structural Properties ◽  
Density Functional ◽  
Dipole Moments ◽  
Radical Cations ◽  
The Other ◽  
Functional Theory ◽  
Density Distributions ◽  
Electric Polarizabilities

Electrical and structural properties of mono-, di-, tri-, tetra-, and penta-fluoroanilines as candidate monomers for new conducting polymers have been investigated using hybrid density functional theory (B3LYP/6–311+G**) based methods. The effects of the number and position of the fluorine atoms on the electrical and structural properties of fluoroanilines and their radical cations have also been investigated. The values of the vibrational frequencies, charge and spin-density distributions, ionization potentials, dipole moments, electric polarizabilities, HOMO-LUMO gaps, and the NICS values of these compounds have been calculated and analyzed as well. The results showed that the double bonds in 2-fluoroaniline and 2,5-difluoroaniline are more delocalized compared with other fluoroanilines; therefore, these molecules have the most aptitude for the electropolymerization reactions. The frequency analysis showed that the electrochemical stability of 2-fluoroaniline is greater than the other fluoroanilines. Also, this molecule possesses the largest NICS value compared to the other fluoroanilines. Consequently, 2-fluoroaniline has the largest ring current and the highest conductivity among all other monomers. Based on the results obtained, 2-fluoroaniline and 2,5-difluoroaniline are the best candidate monomers among all fluoroanilines for the synthesis of corresponding conducting polymers.

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