A new class of analytic solutions in the optimal turn problem for a spherically symmetric body

2012 ◽  
Vol 47 (2) ◽  
pp. 167-177 ◽  
Author(s):  
A. V. Molodenkov ◽  
Ya. G. Sapunkov
Keyword(s):  
Analytic Solutions ◽  
Symmetric Body ◽  
Spherically Symmetric ◽  
New Class ◽  
Optimal Turn

scholarly journals A new class of discontinuous solar wind solutions

2020 ◽  
Vol 496 (2) ◽  
pp. 1023-1034
Author(s):  
Bidzina M Shergelashvili ◽  
Velentin N Melnik ◽  
Grigol Dididze ◽  
Horst Fichtner ◽  
Günter Brenn ◽  
...  
Keyword(s):  
Solar Wind ◽  
External Source ◽  
Analytic Solutions ◽  
Governing Equations ◽  
Discontinuous Solutions ◽  
One Dimensional ◽  
Heating Source ◽  
New Class ◽  
Localized Heating ◽  
Physical Quantities

ABSTRACT A new class of one-dimensional solar wind models is developed within the general polytropic, single-fluid hydrodynamic framework. The particular case of quasi-adiabatic radial expansion with a localized heating source is considered. We consider analytical solutions with continuous Mach number over the entire radial domain while allowing for jumps in the flow velocity, density, and temperature, provided that there exists an external source of energy in the vicinity of the critical point that supports such jumps in physical quantities. This is substantially distinct from both the standard Parker solar wind model and the original nozzle solutions, where such discontinuous solutions are not permissible. We obtain novel sample analytic solutions of the governing equations corresponding to both slow and fast winds.

scholarly journals Exact analytic solutions for nonlinear waves in cold plasmas

2008 ◽  
Vol 74 (4) ◽  
pp. 569-573 ◽  
Author(s):  
G. ROWLANDS ◽  
G. BRODIN ◽  
L. STENFLO
Keyword(s):  
Wave Breaking ◽  
Electron Plasma ◽  
Analytic Solutions ◽  
Field Amplitude ◽  
Cold Electron ◽  
Electric Field Amplitude ◽  
New Class ◽  
Exact Analytic Solutions ◽  
Lagrangian Variables ◽  
Cold Plasmas

AbstractLarge amplitude plasma oscillations are studied in a cold electron plasma. Using Lagrangian variables, a new class of exact analytical solutions is found. It turns out that the electric field amplitude is limited either by wave breaking or by the condition that the electron density always has to stay positive. The range of possible amplitudes is determined analytically.

Spherically Symmetric Vibration of an Elastic Spherical Shell Subject to a Radial and Time-Dependent Body-Force Field

1971 ◽  
Vol 38 (3) ◽  
pp. 702-705 ◽  
Author(s):  
J. M. McKinney
Keyword(s):  
Continuous Function ◽  
Spherical Shell ◽  
Force Field ◽  
Body Force ◽  
Time Dependent ◽  
Symmetric Body ◽  
Spherically Symmetric ◽  
Symmetric Vibration ◽  
Elastic Spherical Shell

A solution, exact within the framework of linear elastokinetics, is obtained for a vibrating, elastic, arbitrarily thick spherical shell subject only to a spherically symmetric body force field of the form FR(r, τ) = Fr(r)Ft(τ). Fr(r) is taken in the form of a polynomial whereas Ft(τ) is restricted only to being a sectionally continuous function of time.

scholarly journals Self-Similar Cosmological Models with a Cosmical Constant

1988 ◽  
Vol 130 ◽  
pp. 516-516
Author(s):  
Robin M. Green ◽  
David Alexander
Keyword(s):  
Analytic Solutions ◽  
Cosmological Models ◽  
Spherically Symmetric ◽  
Self Similarity ◽  
General Behaviour ◽  
Similarity Variable ◽  
Fundamental Scale ◽  
Self Similar

The presence of the cosmical constant introduces a fundamental scale and prevents there being any simple self-symmetry. Henriksen, Emslie and Wesson (HEW), who studied spherically-symmetric models with a positive cosmical constant, have, however, demonstrated the possible existence of a self-similarity of the second kind and identified the similarity variable. They obtained interesting analytic solutions which are homogeneous in density, but not in pressure. We have extended this work and investigated the general behaviour of these cosmological models which possess a self-similarity of the second kind and in which the requirement of homogeneity is relaxed.

scholarly journals Finite-Energy Dressed String-Inspired Dirac-Like Monopoles

Universe ◽  
2018 ◽  
Vol 5 (1) ◽  
pp. 8 ◽  
Author(s):  
Nikolaos E. Mavromatos ◽  
Sarben Sarkar
Keyword(s):  
Differential Equations ◽  
Shooting Method ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Finite Energy ◽  
Spherically Symmetric ◽  
New Class ◽  
The Standard Model ◽  
Monopole Solution ◽  
Asymptotic Analyses

On extending the Standard Model (SM) Lagrangian, through a non-linear Born–Infeld (BI) hypercharge term with a parameter β (of dimensions of [mass] 2 ), a finite energy monopole solution was claimed by Arunasalam and Kobakhidze. We report on a new class of solutions within this framework that was missed in the earlier analysis. This new class was discovered on performing consistent analytic asymptotic analyses of the nonlinear differential equations describing the model; the shooting method used in numerical solutions to boundary value problems for ordinary differential equations is replaced in our approach by a method that uses diagonal Padé approximants. Our work uses the ansatz proposed by Cho and Maison to generate a static and spherically-symmetric monopole with finite energy and differs from that used in the solution of Arunasalam and Kobakhidze. Estimates of the total energy of the monopole are given, and detection prospects at colliders are briefly discussed.

scholarly journals REISSNER–NORDSTRÖM SPACE–TIME IN THE TETRAD THEORY OF GRAVITATION

2007 ◽  
Vol 16 (01) ◽  
pp. 65-79 ◽  
Author(s):  
GAMAL G. L. NASHED ◽  
TAKESHI SHIRAFUJI
Keyword(s):  
Exact Solutions ◽  
Arbitrary Function ◽  
Energy Content ◽  
Analytic Solutions ◽  
Spherically Symmetric ◽  
Theory Of Gravitation ◽  
Momentum Complex ◽  
Charged Source ◽  
Superpotential Method ◽  
Tetrad Theory

We give two classes of spherically symmetric exact solutions of the coupled gravitational and electromagnetic fields with charged source in the tetrad theory of gravitation. The first solution depends on an arbitrary function H(R,t). The second solution depends on a constant parameter η. These solutions reproduce the same metric, i.e. the Reissner–Nordström metric. If the arbitrary function which characterizes the first solution and the arbitrary constant of the second solution are set to be zero, then the two exact solutions will coincide with each other. We then calculate the energy content associated with these analytic solutions using the superpotential method. In particular, we examine whether these solutions meet the condition, which Møller required for a consistent energy–momentum complex, namely, we check whether the total four-momentum of an isolated system behaves as a four-vector under Lorentz transformations. It is then found that the arbitrary function should decrease faster than [Formula: see text] for R → ∞. It is also shown that the second exact solution meets the Møller's condition.

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