---
res:
bibo_abstract:
- 'We consider the hollow on the half-plane {(x, y) : y ≤ 0} ⊂ ℝ2 defined by a function
u : (-1, 1) → ℝ, u(x) < 0, and a vertical flow of point particles incident
on the hollow. It is assumed that u satisfies the so-called single impact condition
(SIC): each incident particle is elastically reflected by graph(u) and goes away
without hitting the graph of u anymore. We solve the problem: find the function
u minimizing the force of resistance created by the flow. We show that the graph
of the minimizer is formed by two arcs of parabolas symmetric to each other with
respect to the y-axis. Assuming that the resistance of u ≡ 0 equals 1, we show
that the minimal resistance equals π/2 - 2arctan(1/2) ≈ 0.6435. This result completes
the previously obtained result [SIAM J. Math. Anal., 46 (2014), pp. 2730-2742]
stating in particular that the minimal resistance of a hollow in higher dimensions
equals 0.5. We additionally consider a similar problem of minimal resistance,
where the hollow in the half-space {(x1,...,xd,y) : y ≤ 0} ⊂ ℝd+1 is defined by
a radial function U satisfying the SIC, U(x) = u(|x|), with x = (x1,...,xd), u(ξ)
< 0 for 0 ≤ ξ < 1, and u(ξ) = 0 for ξ ≥ 1, and the flow is parallel to the
y-axis. The minimal resistance is greater than 0.5 (and coincides with 0.6435
when d = 1) and converges to 0.5 as d → ∞.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Arseniy
foaf_name: Akopyan, Arseniy
foaf_surname: Akopyan
foaf_workInfoHomepage: http://www.librecat.org/personId=430D2C90-F248-11E8-B48F-1D18A9856A87
- foaf_Person:
foaf_givenName: Alexander
foaf_name: Plakhov, Alexander
foaf_surname: Plakhov
bibo_doi: 10.1137/140993843
bibo_issue: '4'
bibo_volume: 47
dct_date: 2015^xs_gYear
dct_language: eng
dct_publisher: SIAM@
dct_title: Minimal resistance of curves under the single impact assumption@
...