scholarly journals Mass Distribution and Gravitational Potential of the Milky Way

2017 ◽  
Vol 26 (1) ◽  
pp. 1-6
Author(s):  
Slobodan Ninković
Keyword(s):  
Exact Solution ◽  
Poisson Equation ◽  
Mass Distribution ◽  
Milky Way ◽  
Dark Halo ◽  
New Formalism ◽  
The Poisson Equation ◽  
Cumulative Mass ◽  
First Time ◽  
Special Case

AbstractModels of mass distribution in the Milky Way are discussed where those yielding the potential analytically are preferred. It is noted that there are three main contributors to the Milky Way potential: bulge, disc and dark halo. In the case of the disc the Miyamoto-Nagai formula, as simple enough, has shown as a very good solution, but it has not been able to satisfy all requirements. Therefore, improvements, such as adding new terms or combining several Miyamoto-Nagai terms, have been attempted. Unlike the disc, in studying the bulge and dark halo the flattening is usually neglected, which offers the possibility of obtaining an exact solution of the Poisson equation. It is emphasized that the Hernquist formula, used very often for the bulge potential, is a special case of another formula and the properties of that formula are analysed. In the case of the dark halo, the slopes of its cumulative mass for the inner and outer parts are explained through a new formalism presented here for the first time.

scholarly journals PENYELESAIAN PERSAMAAN POISSON MENGGUNAKAN METODE HOMOTOPI PERTUBASI

2021 ◽  
Vol 13 (2) ◽  
pp. 105
Author(s):  
Mashuri Mashuri ◽  
Sulistiowati Nur Rahmi ◽  
Marwah Daud Wijayanti ◽  
Alviana Pratama Putri
Keyword(s):  
Exact Solution ◽  
Power Series ◽  
Poisson Equation ◽  
Homotopy Method ◽  
Initial Condition ◽  
The Poisson Equation

In this paper, we discuss the solution of the Poisson equation with some initial condition.  We use the homotopy pertubation method to get the solution.. The homotopy pertubation method is a combination of the homotopy method and the pertubation method. The solution of the equation is assumed to be in the form of a power series. The result is  by using the homotopy pertubation method for the diffution equation, the solution  is the same with the exact solution.  

scholarly journals An approach in studying gyrostat motion with variable gyrostatic moment

2021 ◽  
Vol 31 (1) ◽  
pp. 102-115
Author(s):  
G.V. Gorr
Keyword(s):  
Fixed Point ◽  
Explicit Form ◽  
Poisson Equation ◽  
Mass Distribution ◽  
Equations Of Motion ◽  
Order System ◽  
Constant Multiplier ◽  
The Poisson Equation ◽  
Spherical Mass ◽  
Fifth Order

The problem of the motion of a gyrostat with a fixed point and a variable gyrostatic moment under the action of gravity force is considered. A new method for integrating the equations of motion of a system consisting of a carrier body and three rotors that rotate around the main axes is proposed. The method can be attributed to the method of variation of the constant in the function for the gyrostatic moment, which linearly depends on the vector of vertical. In case of a constant multiplier, the gyrostatic moment satisfies the Poisson equation, and its variation is found from the integral of areas. The original equations have been reduced to a fifth-order system. New solutions of these equations are obtained in the case of a spherical mass distribution for the gyrostat and for the precessional motions of a carrier body. An explicit form of the gyrostatic moment is established for the case of three invariant relations.

scholarly journals General model of vertical distribution of stars in the Milky Way using complete Jeans equations

2019 ◽  
Vol 492 (1) ◽  
pp. 628-633 ◽  
Author(s):  
Suchira Sarkar ◽  
Chanda J Jog
Keyword(s):  
Vertical Distribution ◽  
Density Distribution ◽  
Poisson Equation ◽  
Milky Way ◽  
High Resolution Data ◽  
The Poisson Equation ◽  
Stellar Velocity ◽  
Vertical Density ◽  
Isothermal Case ◽  
The Vertical Distribution

ABSTRACT The self-consistent vertical density distribution in a thin, isothermal disc is typically given by a sech2 law, as shown in the classic work by Spitzer. This is obtained assuming that the radial and vertical motions are decoupled and only the vertical term is used in the Poisson equation. We argue that in the region of low density as in the outer disc this treatment is no longer valid. We develop a general, complete model that includes both radial and vertical terms in the Poisson equation and write these in terms of the full radial and vertical Jeans equations which take account of the non-flat observed rotation curve, the random motions, and the cross term that indicates the tilted stellar velocity ellipsoid. We apply it to the Milky Way and show that these additional effects change the resulting density distribution significantly, such that the mid-plane density is higher and the disc thickness (HWHM) is lower by 30–40 per cent in the outer Galaxy. Further, the vertical distribution is no longer given as a sech2 function even for an isothermal case. These predicted differences are now within the verification limit of new, high-resolution data for example from Gaia and hence could be confirmed.

scholarly journals Convergence properties of the Broyden-like method for mixed linear–nonlinear systems of equations

2021 ◽  
Author(s):  
Florian Mannel
Keyword(s):  
Linear Independence ◽  
Affine Subspace ◽  
Systems Of Equations ◽  
Nonlinear Systems Of Equations ◽  
Convergence Properties ◽  
Initial Matrix ◽  
First Time ◽  
Special Case ◽  
Dimensional Mapping ◽  
Finite Number Of Iterations

AbstractWe consider the Broyden-like method for a nonlinear mapping $F:\mathbb {R}^{n}\rightarrow \mathbb {R}^{n}$ F : ℝ n → ℝ n that has some affine component functions, using an initial matrix B0 that agrees with the Jacobian of F in the rows that correspond to affine components of F. We show that in this setting, the iterates belong to an affine subspace and can be viewed as outcome of the Broyden-like method applied to a lower-dimensional mapping $G:\mathbb {R}^{d}\rightarrow \mathbb {R}^{d}$ G : ℝ d → ℝ d , where d is the dimension of the affine subspace. We use this subspace property to make some small contributions to the decades-old question of whether the Broyden-like matrices converge: First, we observe that the only available result concerning this question cannot be applied if the iterates belong to a subspace because the required uniform linear independence does not hold. By generalizing the notion of uniform linear independence to subspaces, we can extend the available result to this setting. Second, we infer from the extended result that if at most one component of F is nonlinear while the others are affine and the associated n − 1 rows of the Jacobian of F agree with those of B0, then the Broyden-like matrices converge if the iterates converge; this holds whether the Jacobian at the root is invertible or not. In particular, this is the first time that convergence of the Broyden-like matrices is proven for n > 1, albeit for a special case only. Third, under the additional assumption that the Broyden-like method turns into Broyden’s method after a finite number of iterations, we prove that the convergence order of iterates and matrix updates is bounded from below by $\frac {\sqrt {5}+1}{2}$ 5 + 1 2 if the Jacobian at the root is invertible. If the nonlinear component of F is actually affine, we show finite convergence. We provide high-precision numerical experiments to confirm the results.

scholarly journals Modified differential transform method for solving linear and nonlinear pantograph type of differential and Volterra integro-differential equations with proportional delays

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Seyyedeh Roodabeh Moosavi Noori ◽  
Nasir Taghizadeh
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Differential Transform Method ◽  
Hybrid Technique ◽  
Transform Method ◽  
Proportional Delays ◽  
Differential Transform ◽  
Computational Work ◽  
Linear And Nonlinear ◽  
First Time

AbstractIn this study, a hybrid technique for improving the differential transform method (DTM), namely the modified differential transform method (MDTM) expressed as a combination of the differential transform method, Laplace transforms, and the Padé approximant (LPDTM) is employed for the first time to ascertain exact solutions of linear and nonlinear pantograph type of differential and Volterra integro-differential equations (DEs and VIDEs) with proportional delays. The advantage of this method is its simple and trusty procedure, it solves the equations straightforward and directly without requiring large computational work, perturbations or linearization, and enlarges the domain of convergence, and leads to the exact solution. Also, to validate the reliability and efficiency of the method, some examples and numerical results are provided.

scholarly journals Measurement of the cosmic ray proton spectrum from 40 GeV to 100 TeV with the DAMPE satellite

2019 ◽  
Vol 5 (9) ◽  
pp. eaax3793 ◽  
Author(s):  
◽  
Q. An ◽  
R. Asfandiyarov ◽  
P. Azzarello ◽  
P. Bernardini ◽  
...  
Keyword(s):  
Cosmic Rays ◽  
Cosmic Radiation ◽  
Precise Measurement ◽  
Milky Way ◽  
Spectral Feature ◽  
Dark Matter Particle ◽  
Cosmic Ray ◽  
Galactic Cosmic Rays ◽  
Proton Spectrum ◽  
First Time

The precise measurement of the spectrum of protons, the most abundant component of the cosmic radiation, is necessary to understand the source and acceleration of cosmic rays in the Milky Way. This work reports the measurement of the cosmic ray proton fluxes with kinetic energies from 40 GeV to 100 TeV, with 2 1/2 years of data recorded by the DArk Matter Particle Explorer (DAMPE). This is the first time that an experiment directly measures the cosmic ray protons up to ~100 TeV with high statistics. The measured spectrum confirms the spectral hardening at ~300 GeV found by previous experiments and reveals a softening at ~13.6 TeV, with the spectral index changing from ~2.60 to ~2.85. Our result suggests the existence of a new spectral feature of cosmic rays at energies lower than the so-called knee and sheds new light on the origin of Galactic cosmic rays.

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