scholarly journals Square Roots of Kepler Ellipses, Electrons and Rydberg Atoms in a Magnetic Field

2020 ◽  
Vol 65 (10) ◽  
pp. 835
Author(s):  
Yu. P. Stepanovsky
Keyword(s):  
Magnetic Field ◽  
Solar System ◽  
Radio Telescope ◽  
Rydberg Atoms ◽  
Kepler Problem ◽  
Energy Spectra ◽  
Square Root ◽  
Hydrogen Atoms ◽  
Eccentric Anomaly ◽  
Square Roots

Young Kepler’s daring ideas on the structure of the Solar system are applied to the analysis of planetary distances in the exoplanetary system HD 10180. Using Zhukovsky’s transformation, the essence of the spinor regularization of Kepler’s problem is explained as extracting the square root of an ellipse and using a Kepler eccentric anomaly instead of the usual time. The achievements of Kharkiv radio astronomers in the search for radio recombination lines of Rydberg carbon atoms at the UTR-2 radio telescope are considered. A generalized spinor regularization of the Kepler problem is used to analyze the energy spectra of Rydberg hydrogen atoms in a magnetic field.

Scaled energy spectra of non-hydrogenic Rydberg atoms in a magnetic field

1994 ◽  
Vol 27 (13) ◽  
pp. 2771-2784 ◽  
Author(s):  
D Delande ◽  
K T Taylor ◽  
M H Halley ◽  
T van der Veldt ◽  
W Vassen ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Rydberg Atoms ◽  
Energy Spectra ◽  
Scaled Energy

scholarly journals Simulations of Switchback, Fragmentation and Sunspot Pair in δ-Sunspots during Magnetic Flux Emergence

Sensors ◽  
2021 ◽  
Vol 21 (2) ◽  
pp. 586
Author(s):  
Che-Jui Chang ◽  
Jean-Fu Kiang
Keyword(s):  
Magnetic Field ◽  
Solar System ◽  
Field Strength ◽  
Magnetic Flux ◽  
Initial Conditions ◽  
Observation Data ◽  
Flux Emergence ◽  
Polarity Inversion ◽  
Simulation Results ◽  
Spot Type

Strong flares and coronal mass ejections (CMEs), launched from δ-sunspots, are the most catastrophic energy-releasing events in the solar system. The formations of δ-sunspots and relevant polarity inversion lines (PILs) are crucial for the understanding of flare eruptions and CMEs. In this work, the kink-stable, spot-spot-type δ-sunspots induced by flux emergence are simulated, under different subphotospheric initial conditions of magnetic field strength, radius, twist, and depth. The time evolution of various plasma variables of the δ-sunspots are simulated and compared with the observation data, including magnetic bipolar structures, relevant PILs, and temperature. The simulation results show that magnetic polarities display switchbacks at a certain stage and then split into numerous fragments. The simulated fragmentation phenomenon in some δ-sunspots may provide leads for future observations in the field.

scholarly journals Algebraic singularities of scattering amplitudes from tropical geometry

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
James Drummond ◽  
Jack Foster ◽  
Ömer Gürdoğan ◽  
Chrysostomos Kalousios
Keyword(s):  
Scattering Amplitudes ◽  
Natural Language ◽  
Tropical Geometry ◽  
Cluster Algebras ◽  
Finite Alphabet ◽  
Square Root ◽  
Finite Sets ◽  
Yang Mills ◽  
Square Roots ◽  
Algebraic Singularities

Abstract We address the appearance of algebraic singularities in the symbol alphabet of scattering amplitudes in the context of planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory. We argue that connections between cluster algebras and tropical geometry provide a natural language for postulating a finite alphabet for scattering amplitudes beyond six and seven points where the corresponding Grassmannian cluster algebras are finite. As well as generating natural finite sets of letters, the tropical fans we discuss provide letters containing square roots. Remarkably, the minimal fan we consider provides all the square root letters recently discovered in an explicit two-loop eight-point NMHV calculation.

scholarly journals Finding of principle square root of a real number by using interpolation method

2018 ◽  
Vol 7 (1) ◽  
pp. 77-83
Author(s):  
Rajendra Prasad Regmi
Keyword(s):  
Real Number ◽  
Positive Real Number ◽  
Interpolation Method ◽  
Square Root ◽  
Real Numbers ◽  
Positive Real ◽  
Unknown Quantity ◽  
Square Roots

There are various methods of finding the square roots of positive real number. This paper deals with finding the principle square root of positive real numbers by using Lagrange’s and Newton’s interpolation method. The interpolation method is the process of finding the values of unknown quantity (y) between two known quantities.

Planet Earth – our oasis in space

2004 ◽  
Vol 12 (1) ◽  
pp. 111-119
Author(s):  
SIEGFRIED J. BAUER
Keyword(s):  
Magnetic Field ◽  
Solar System ◽  
Internal Structure ◽  
Solid Surface ◽  
Liquid Water ◽  
Atmospheric Environment ◽  
Suitable Habitat ◽  
The Earth

Planet Earth is unique in our solar system as an abode of life. In contrast to its planetary neighbours, the presence of liquid water, a benign atmospheric environment, a solid surface and an internal structure providing a protective magnetic field make it a suitable habitat for man. While natural forces have shaped the Earth over millennia, man through his technological prowess may become a threat to this oasis of life in the solar system.

An early solar system magnetic field recorded in CM chondrites

2015 ◽  
Vol 410 ◽  
pp. 62-74 ◽  
Author(s):  
C. Cournede ◽  
J. Gattacceca ◽  
M. Gounelle ◽  
P. Rochette ◽  
B.P. Weiss ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Solar System ◽  
Early Solar System

scholarly journals Excitation And Ionization By Auroral Protons

1966 ◽  
Vol 19 (3) ◽  
pp. 309 ◽  
Keyword(s):  
Magnetic Field ◽  
Energy Range ◽  
Pitch Angle ◽  
Proton Energy ◽  
Ionization Rate ◽  
Energy Spectra ◽  
Proton Fluxes ◽  
Atmospheric Ionization ◽  
The Magnetic Field

Height distributions are presented for the atmospheric ionization rate and Balmer radiation resulting from precipitation of auroral protons. These results have been computed assuming proton fluxes with several different energy spectra and pitch-angle distributions about the magnetic field, the total proton energy range being restricted to 1-1000 keY.

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