Orientation dynamics of two-dimensional concavo-convex bodies
نویسندگان
چکیده
We study the complex orientation dynamics of a settling body with concave and convex surfaces using particle-resolving direct numerical simulations, find multiple bifurcations as Reynolds number is varied from O(1) to O(20). The irregularly shaped solid bodies in this range numbers relevant such phenomena tumbling ice particles atmospheric clouds, plant animal microorganisms ocean.
منابع مشابه
Random Aspects of High-dimensional Convex Bodies
In this paper we study geometry of compact, not necessarily centrally symmetric, convex bodies in R. Over the years, local theory of Banach spaces developed many sophisticated methods to study centrally symmetric convex bodies; and already some time ago it became clear that many results, if valid for arbitrary convex bodies, may be of interest in other areas of mathematics. In recent years many...
متن کاملApproximation 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...
متن کاملLattice Coverings and Gaussian Measures of n-Dimensional Convex Bodies
Let ‖ · ‖ be the euclidean norm on R and γn the (standard) Gaussian measure on R with density (2π)e 2/2. Let θ (≃ 1.3489795) be defined by γ1([−θ/2, θ/2]) = 1/2 and let L be a lattice in R n generated by vectors of norm ≤ θ. Then, for any closed convex set V in R with γn(V ) ≥ 1 2 and for any a ∈ R, (a + L) ∩ V 6= φ. The above statement can be viewed as a “nonsymmetric” version of Minkowski The...
متن کاملHigh Dimensional Random Sections of Isotropic Convex Bodies
We study two properties of random high dimensional sections of convex bodies. In the first part of the paper we estimate the central section function |K ∩F⊥| n−k for random F ∈ Gn,k and K ⊂ R n a centrally symmetric isotropic convex body. This partially answers a question raised by V. Milman and A. Pajor (see [MP], p.88). In the second part we show that every symmetric convex body has random hi...
متن کاملO ct 2 01 7 EXTREMAL KÄHLER - EINSTEIN METRIC FOR TWO - DIMENSIONAL CONVEX BODIES
Given a convex body K ⊂ Rn with the barycenter at the origin we consider the corresponding Kähler-Einstein equation e = detDΦ. If K is a simplex, then the Ricci tensor of the Hessian metric DΦ is constant and equals n−1 4(n+1) . We conjecture that the Ricci tensor of D Φ for arbitrary K is uniformly bounded by n−1 4(n+1) and verify this conjecture in the two-dimensional case. The general case r...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical review fluids
سال: 2023
ISSN: ['2469-9918', '2469-990X']
DOI: https://doi.org/10.1103/physrevfluids.8.l062301