On the galloping instability of two-dimensional bodies having elliptical cross-sections

On the galloping instability of two-dimensional bodies having elliptical cross-sections

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Approximation of Two-dimensional Cross-sections of Convex Bodies by Disks and Ellipses

In connection with the well-known Dvoretsky theorem, the following question arises: How close to a disk or to an ellipse can a two-dimensional crosssection through an interior point O of a convex body K ⊂ Rn be? In the present paper, the attention is focused on a few (close to prime) dimensions n for which this problem can be solved exactly. Asymptotically, this problem was solved by the author...

Asymptotics of Cross Sections for Convex Bodies

For normed isotropic convex bodies in R n we investigate the behaviour of the (n ? 1)-dimensional volume of intersections with hyperplanes orthogonal to a xed direction, considered as a function of the distance of the hyperplane to the origin. It is a conjecture that for arbitrary normed isotropic convex bodies and random directions this function { with high probability { is close to a Gaussian...

Galloping instability of viscous shock waves

Motivated by physical and numerical observations of time oscillatory “galloping”, “spinning”, and “cellular” instabilities of detonation waves, we study Poincaré–Hopf bifurcation of traveling-wave solutions of viscous conservation laws. The main difficulty is the absence of a spectral gap between oscillatory modes and essential spectrum, preventing standard reduction to a finite-dimensional cen...