scholarly journals Spherically symmetric solutions of multidimensional zero-pressure gas dynamics system

2014 ◽  
Vol 11 (02) ◽  
pp. 269-293 ◽  
Author(s):  
Anupam Pal Choudhury ◽  
K. T. Joseph ◽  
Manas R. Sahoo
Keyword(s):  
Asymptotic Behavior ◽  
Gas Dynamics ◽  
Explicit Solutions ◽  
Spherically Symmetric ◽  
Spherically Symmetric Solutions ◽  
Different Types ◽  
Explicit Formulae

We derive explicit formulae for spherically symmetric solutions to the system of multidimensional zero-pressure gas dynamics and its adhesion approximation. The asymptotic behavior of the explicit solutions of the adhesion approximation is studied here. We observe that the radial components of the velocity and density satisfy a simpler equation, which enables us to get explicit formulae for different types of domains and study its asymptotic behavior. A class of solutions to the inviscid system with conditions on the mass instead of conditions at origin is also analyzed here.

Spherically symmetric solutions of the equations of gas dynamics

1953 ◽  
Vol 220 (1142) ◽  
pp. 339-355 ◽  
Keyword(s):  
Differential Equation ◽  
Contact Surface ◽  
Gas Dynamics ◽  
Spherically Symmetric ◽  
Arbitrary Boundary ◽  
Shock Surface ◽  
Equations Of Gas Dynamics ◽  
Special Character ◽  
Spherically Symmetric Solutions ◽  
Explicit Formulae

The method developed by the author is adapted to the case of spherically symmetric gas motions. The pressure, density and velocity of the gas are shown to involve one arbitrary function Ф; if Ф = f ( t ) w ( rt -α ), where f and w are arbitrary functions, explicit formulae for the pressure, density and velocity are worked out. Amongst motions of this kind, those in which the velocity is proportional to r , are selected for detailed investigation. Cases in which the gas motion is adiabatic are determined; in one type w is a known function of rt -α , while f is the solution of a certain differential equation; in a second type, f is known but w remains arbitrary. Boundary conditions are then applied, first, on the assumption that the boundary is approximately a contact surface and that the motion is of the first type; secondly, when the boundary is a true shock surface and the motion has a special character and is common to both types. Primakoff's solution is obtained in the second case. The author’s method is contrasted with the conventional ones.

scholarly journals FERMIONS IN THE BACKGROUND OF DILATONIC SPHALERONS

1994 ◽  
Vol 09 (40) ◽  
pp. 3731-3739 ◽  
Author(s):  
GEORGE LAVRELASHVILI
Keyword(s):  
Gauge Field ◽  
Field Potential ◽  
Spherically Symmetric ◽  
Yang Mills ◽  
Zero Modes ◽  
Discrete Sequence ◽  
Number Of Zeros ◽  
Spherically Symmetric Solutions ◽  
Static Spherically Symmetric Solutions

We discuss the properties and interpretation of a discrete sequence of a static spherically symmetric solutions of the Yang-Mills dilaton theory. This sequence is parametrized by the number of zeros, n, of a component of the gauge field potential. It is demonstrated that solutions with odd n possess all the properties of the sphaleron. It is shown that there are normalizable fermion zero modes in the background of these solutions. The question of instability is critically analyzed.

scholarly journals New Iterative Method for Fractional Gas Dynamics and Coupled Burger’s Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Mohamed S. Al-luhaibi
Keyword(s):  
Iterative Method ◽  
Analytical Solutions ◽  
Gas Dynamics ◽  
Time Derivative ◽  
Explicit Solutions ◽  
Fractional Partial Differential Equations ◽  
Approximate Analytical Solutions ◽  
Fractional Time Derivative ◽  
Burger's Equations ◽  
New Iterative Method

This paper presents the approximate analytical solutions to solve the nonlinear gas dynamics and coupled Burger’s equations with fractional time derivative. By using initial values, the explicit solutions of the equations are solved by using a reliable algorithm. Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations.

On a Voronoi aggregative process related to a bivariate Poisson process

1996 ◽  
Vol 28 (04) ◽  
pp. 965-981 ◽  
Author(s):  
S. G. Foss ◽  
S. A. Zuyev
Keyword(s):  
Asymptotic Behavior ◽  
Lower Bounds ◽  
Distribution Functions ◽  
Poisson Processes ◽  
Upper And Lower Bounds ◽  
Additive Functionals ◽  
Second Moments ◽  
Explicit Formulae ◽  
Bivariate Poisson Process ◽  
Sum Of Distances

We consider two independent homogeneous Poisson processes Π0 and Π1 in the plane with intensities λ0 and λ1, respectively. We study additive functionals of the set of Π0-particles within a typical Voronoi Π1-cell. We find the first and the second moments of these variables as well as upper and lower bounds on their distribution functions, implying an exponential asymptotic behavior of their tails. Explicit formulae are given for the number and the sum of distances from Π0-particles to the nucleus within a typical Voronoi Π1-cell.

scholarly journals Intersecting Electric and Magnetic p-branes: Spherically Symmetric Solutions

1999 ◽  
Vol 31 (11) ◽  
pp. 1681-1702 ◽  
Author(s):  
K. A. Bronnikov ◽  
U. Kasper ◽  
M. Rainer
Keyword(s):  
Spherically Symmetric ◽  
Spherically Symmetric Solutions
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