scholarly journals The Vogt-Russell Theorem, and New Results on an Old Problem

1978 ◽  
Vol 80 ◽  
pp. 303-311
Author(s):  
Helmuth Kähler
Keyword(s):  
Existence And Uniqueness ◽  
Thermal Equilibrium ◽  
Equilibrium Configuration ◽  
Mathematical Proof ◽  
Stellar Structure

Half a centry ago Henry Norris Russell and Heinrich Vogt independently made a conjecture concerning the structure of spherical stars which are in hydrostatic and thermal equilibrium (Russell, 1927; Vogt, 1926). This conjecture has later come to be known as the Vogt-Russell theorem and is usually formulated as follows: The structure of a star is uniquely determined by the mass and the composition. In other words, the statement claims the existence and uniqueness of a stellar equilibrium configuration for given parameters mass and composition, and you may find what is called a mathematical proof in many textbooks on stellar structure.

Theoretical Underpinnings: Modeling Stars

2017 ◽  
Author(s):  
Sarbani Basu ◽  
William J. Chaplin
Keyword(s):  
Thermal Equilibrium ◽  
Total Mass ◽  
Stellar Structure ◽  
Conservation Of Mass ◽  
Elemental Abundances ◽  
The Core ◽  
Self Consistent ◽  
Consistent Manner ◽  
Independent Variable ◽  
Stellar Oscillation

This chapter provides a brief description of the process of constructing models for the interpretation of stellar oscillation data. The equations of stellar structure are basically statements of conservation—of mass, momentum, and energy—along with the conditions required for thermal equilibrium. The equations of stellar structure are written with mass as the independent variable. Here, a star is divided into many mass shells, from the center at m = 0 to the surface at m = M, where M is the total mass of the star, and a model is obtained by solving the set of equations at each mass shell in a self-consistent manner. In addition, the chapter considers energy generation and how energy is transported from the core to the surface, as well as how elemental abundances change as a function of time.

scholarly journals Storage of Magnetic Flux in the Overshoot Region

1993 ◽  
Vol 157 ◽  
pp. 41-44
Author(s):  
F. Moreno-Insertis ◽  
M. Schüssler ◽  
A. Ferriz-Mas
Keyword(s):  
Field Strength ◽  
Magnetic Flux ◽  
Thermal Equilibrium ◽  
Convection Zone ◽  
Equilibrium Configuration ◽  
Solar Rotation ◽  
Inertial Forces ◽  
High Latitudes ◽  
Flux Tubes ◽  
Combined Action

The combined action of the subadiabatic ambient stratification in the overshoot region below the convection zone and the inertial forces associated with the solar rotation is shown to lead to the suppression of the escape of magnetic flux in the form of toroidal flux tubes both toward the surface and toward higher latitudes. We show that a flux ring initially in thermal equilibrium with its environment and rotating with the ambient angular velocity moves radially and latitudinally towards an equilibrium configuration of lower internal temperature and larger internal rotation rate with respect to the surrounding, field-free gas. We conclude that flux rings with B≲ 105 G can be kept within the overshoot region if the superadiabaticity is sufficiently negative, i.e. δ = ▿ – ▿ad≲–10−5; below that field strength the poleward drift is also reduced to a latitudinal oscillation of moderate amplitude, δθ ≲ 20 deg. Flux rings with significantly larger field strength cannot be kept in the equatorial parts of the overshoot region: their equilibrium configuration is located at high latitudes far outside the solar activity belts and, at any rate, requires unrealistic values of δ.

Mathematical proof that rocked number theory will be published

Nature ◽  
2020 ◽  
Vol 580 (7802) ◽  
pp. 177-177
Author(s):  
Davide Castelvecchi
Keyword(s):  
Number Theory ◽  
Mathematical Proof

Hypothesis on the Solvability of Parabolic Equations with nonlocal Condition

2002 ◽  
Vol 7 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Mifodijus Sapagovas
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Numerical Algorithms ◽  
Uniqueness Of The Solution

Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself.

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