Interaction between a weak discontinuity wave and a blast wave: Search for critical times for transmitted waves in self-similar flows

1982 ◽  
Vol 69 (1) ◽  
pp. 119-135 ◽  
Author(s):  
N. Virgopia ◽  
F. Ferraioli
Keyword(s):  
Blast Wave ◽  
Weak Discontinuity ◽  
Transmitted Waves ◽  
Self Similar ◽  
Similar Flows ◽  
Critical Times

Rotational λ – hypersurfaces in Euclidean spaces

2021 ◽  
Vol 30 (1) ◽  
pp. 29-40
Author(s):  
KADRI ARSLAN ◽  
ALIM SUTVEREN ◽  
BETUL BULCA
Keyword(s):  
Present Article ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Special Solution ◽  
Euclidean Spaces ◽  
Self Similar ◽  
The Mean ◽  
Similar Flows

Self-similar flows arise as special solution of the mean curvature flow that preserves the shape of the evolving submanifold. In addition, \lambda -hypersurfaces are the generalization of self-similar hypersurfaces. In the present article we consider \lambda -hypersurfaces in Euclidean spaces which are the generalization of self-shrinkers. We obtained some results related with rotational hypersurfaces in Euclidean 4-space \mathbb{R}^{4} to become self-shrinkers. Furthermore, we classify the general rotational \lambda -hypersurfaces with constant mean curvature. As an application, we give some examples of self-shrinkers and rotational \lambda -hypersurfaces in \mathbb{R}^{4}.

scholarly journals Mathematical Theory of Cylindrical Isothermal Blast Waves in a Magnetic Field

1981 ◽  
Vol 34 (3) ◽  
pp. 279 ◽  
Author(s):  
I Lerche
Keyword(s):  
Magnetic Field ◽  
Supernova Remnants ◽  
Magnetic Pressure ◽  
Blast Waves ◽  
Physical Domain ◽  
Fluid Flow Velocity ◽  
Magnetic Tension ◽  
Self Similar ◽  
The Magnetic Field ◽  
Similar Flows

An investigation is made of the self-similar flow behind a cylindrical blast wave from a line explosion (situated on r = 0, using conventional cylindrical coordinates r, 4>, z) in a medium whose density and magnetic field both vary as r -w ahead of the blast front, with the assumption that the flow is isothermal. The magnetic field can have components in both the azimuthal B(jJ and longitudinal B, directions. It is found that: (i) For B(jJ =f:. 0 =f:. B, a continuous single-valued solution with a velocity field representing outflow of material away from the line of explosion does not exist for OJ OJ > 0 the governing equation possesses a set of movable critical points. In this case it is shown that the fluid flow velocity is bracketed between two curves and that the asymptotes of the velocity curve on the shock are intersected by, or are tangent to, the two curves. Thus a solution always exists in the physical domain r ~ o. The overall conclusion from the investigation is that the behaviour of isothermal blast waves in the presence of an ambient magnetic field differs substantially from the behaviour calculated for no magnetic field. These results have an impact upon previous applications of the theory of self-similar flows to evolving supernova remnants without allowance for the dynamical influence of magnetic pressure and magnetic tension.

Self-similar flows with increasing energy—2. Isothermal flow

1972 ◽  
Vol 10 (11) ◽  
pp. 963-973 ◽  
Author(s):  
Melam P. Ranga Rao ◽  
Sharad C. Purohit
Keyword(s):  
Isothermal Flow ◽  
Self Similar ◽  
Similar Flows

Self-similar, time-dependent flows with a free surface

1976 ◽  
Vol 73 (4) ◽  
pp. 603-620 ◽  
Author(s):  
Michael S. Longuet-Higgins
Keyword(s):  
Free Surface ◽  
Rational Functions ◽  
Rigid Wall ◽  
The Other ◽  
Three Dimensions ◽  
Simple Derivation ◽  
Similar Time ◽  
Self Similar ◽  
Parabolic Flow ◽  
Similar Flows

A simple derivation is given of the parabolic flow first described by John (1953) in semi-Lagrangian form. It is shown that the scale of the flow decreases liket−3, and the free surface contracts about a point which lies one-third of the way from the vertex of the parabola to the focus.The flow is an exact limiting form of either a Dirichlet ellipse or hyperbola, as the timettends to infinity.Two other self-similar flows, in three dimensions, are derived. In one, the free surface is a paraboloid of revolution, which contracts liket−2about a point lying one-quarter the distance from the vertex to the focus. In the other, the flow is non-axisymmetric, and the free surface contracts liket−5.The parabolic flow is shown to be one of a general class of self-similar flows in the plane, described by rational functions of degreen. The parabola corresponds ton= 2. Whenn= 3 there are two new flows. In one of these the scale varies ast12/7and the free surface has the appearance of a trough filling up. In the other, the free surface resembles flow round the end of a rigid wall; the scale varies ast−4·17.

Mixed hyperbolic-elliptic systems in self-similar flows

2001 ◽  
Vol 32 (3) ◽  
pp. 377-399 ◽  
Author(s):  
Sunčica Čanić ◽  
Barbara Lee Keyfitz ◽  
Eun Heui Kim
Keyword(s):  
Elliptic Systems ◽  
Self Similar ◽  
Similar Flows

scholarly journals Mathematical Theory of One-dimensional Isothermal Blast Waves in a Magnetic Field

1979 ◽  
Vol 32 (5) ◽  
pp. 491 ◽  
Author(s):  
I Lerche
Keyword(s):  
Magnetic Field ◽  
Fluid Flow ◽  
Critical Point ◽  
Blast Wave ◽  
Supernova Remnants ◽  
Magnetic Energy ◽  
Flow Speed ◽  
Blast Waves ◽  
One Dimensional ◽  
Self Similar

An investigation is made of the self-similar flow behind a one-dimensional blast wave from a planar explosion (situated on z = 0) in a medium whose density and magnetic field vary with distance as Z-W ahead of the blast front, with the assumption that the flow is isothermal. It is found that; if OJ OJ > 0 the governing equation possesses a set of movable critical points. For a weak, but nonzero, magnetic field it is shown that the value of the smallest critical point does not lie in the physical domain z > O. The post-shock fluid flow then cannot intersect the critical point, and is smoothly continuous. It is shown that to be physically acceptable, the fluid flow speed must pass through the origin. It is also shown that OJ must be less than t for the magnetic energy swept up by the blast wave to remain finite. The overall conclusion from the investigation is that the behaviour of isothermal blast waves in the presence of an ambient magnetic field differs substantially from the behaviour calculated for no magnetic field. These results point to the inadequacy of previous attempts to apply the theory of self-similar flows to evolving supernova remnants without making any allowance for the dynamical influence of magnetic field pressure.

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