scholarly journals Self-similar solutions of fully nonlinear curvature flows

2011 ◽  
pp. 317-333
Author(s):  
James A. McCoy
Keyword(s):  
Fully Nonlinear ◽  
Self Similar ◽  
Similar Solutions

scholarly journals Self-similar solutions to fully nonlinear curvature flows by high powers of curvature

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Shanze Gao ◽  
Haizhong Li ◽  
Xianfeng Wang
Keyword(s):  
Large Family ◽  
Concave Function ◽  
Principal Curvatures ◽  
Fully Nonlinear ◽  
Strictly Convex ◽  
Self Similar ◽  
Speed Function ◽  
Similar Solutions ◽  
Convex Hypersurfaces

Abstract In this paper, we investigate closed strictly convex hypersurfaces in ℝ n + 1 {\mathbb{R}^{n+1}} which shrink self-similarly under a large family of fully nonlinear curvature flows by high powers of curvature. When the speed function is given by powers of a homogeneous of degree 1 and inverse concave function of the principal curvatures with power greater than 1, we prove that the only such hypersurfaces are round spheres. We also prove that slices are the only closed strictly convex self-similar solutions to such curvature flows in the hemisphere 𝕊 + n + 1 {\mathbb{S}^{n+1}_{+}} with power greater than or equal to 1.

scholarly journals A laser experiment for studying radiative shocks in astrophysics

2002 ◽  
Vol 20 (2) ◽  
pp. 263-268 ◽  
Author(s):  
X. FLEURY ◽  
S. BOUQUET ◽  
C. STEHLÉ ◽  
M. KOENIG ◽  
D. BATANI ◽  
...  
Keyword(s):  
Laser Pulse ◽  
Pulse Duration ◽  
Experimental Results ◽  
Laboratory Astrophysics ◽  
Laser Pulse Duration ◽  
Radiative Shocks ◽  
Self Similar ◽  
Laser Experiment ◽  
Similar Solutions

In this article, we present a laboratory astrophysics experiment on radiative shocks and its interpretation using simple modelization. The experiment is performed with a 100-J laser (pulse duration of about 0.5 ns) which irradiates a 1-mm3 xenon gas-filled cell. Descriptions of both the experiment and the associated diagnostics are given. The apparition of a radiation precursor in the unshocked material is evidenced from interferometry diagrams. A model including self-similar solutions and numerical ones is derived and fairly good agreements are obtained between the theoretical and the experimental results.

Self-similar solutions to stellar winds with cosmic rays

2005 ◽  
Vol 35 (12) ◽  
pp. 2115-2118 ◽  
Author(s):  
Chung-Ming Ko ◽  
Min-Hsu Chu
Keyword(s):  
Cosmic Rays ◽  
Stellar Winds ◽  
Self Similar ◽  
Similar Solutions

On a self-similar solution for the decay of turbulent bursts

1992 ◽  
Vol 3 (4) ◽  
pp. 319-341 ◽  
Author(s):  
S. P. Hastings ◽  
L. A. Peletier
Keyword(s):  
Asymptotic Behaviour ◽  
Physical Parameter ◽  
Dimensional Analysis ◽  
Existence And Uniqueness ◽  
The Self ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Eigenvalue Parameter ◽  
Self Similar ◽  
Similar Solutions

We discuss the self-similar solutions of the second kind associated with the propagation of turbulent bursts in a fluid at rest. Such solutions involve an eigenvalue parameter μ, which cannot be determined from dimensional analysis. Existence and uniqueness are established and the dependence of μ on a physical parameter λ in the problem is studied: estimates are obtained and the asymptotic behaviour as λ → ∞ is established.

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