Exact results for the jammed state of binary mixtures of superdisks on the plane

2016 ◽  
Vol 441 ◽  
pp. 93-99 ◽  
Author(s):  
N.M. Švrakić ◽  
Branislav N. Aleksić ◽  
Milivoj R. Belić
Keyword(s):  
Binary Mixtures ◽  
Exact Results ◽  
Jammed State

Thermodynamic properties of binary mixtures containing thiaalkanes

1980 ◽  
Vol 77 ◽  
pp. 445-449 ◽  
Author(s):  
Zohra Ferhat-Hamida ◽  
Robert Philippe ◽  
Jean-Claude Merlin ◽  
V. Kehiaian
Keyword(s):  
Thermodynamic Properties ◽  
Binary Mixtures

Erratum - Frustration in periodic systems : exact results for some 2D ising models

1979 ◽  
Vol 40 (10) ◽  
pp. 1024-1024
Author(s):  
G. André ◽  
R. Bidaux ◽  
J.-P. Carton ◽  
R. Conte ◽  
L. de Seze
Keyword(s):  
Ising Models ◽  
Periodic Systems ◽  
Exact Results

Almost empty polygons

2003 ◽  
Vol 40 (3) ◽  
pp. 269-286 ◽  
Author(s):  
H. Nyklová
Keyword(s):  
Exact Results ◽  
Point Sets ◽  
Planar Point ◽  
Convex Position ◽  
Vertex Set ◽  
Point Set ◽  
Empty Polygons

In this paper we study a problem related to the classical Erdos--Szekeres Theorem on finding points in convex position in planar point sets. We study for which n and k there exists a number h(n,k) such that in every planar point set X of size h(n,k) or larger, no three points on a line, we can find n points forming a vertex set of a convex n-gon with at most k points of X in its interior. Recall that h(n,0) does not exist for n = 7 by a result of Horton. In this paper we prove the following results. First, using Horton's construction with no empty 7-gon we obtain that h(n,k) does not exist for k = 2(n+6)/4-n-3. Then we give some exact results for convex hexagons: every point set containing a convex hexagon contains a convex hexagon with at most seven points inside it, and any such set of at least 19 points contains a convex hexagon with at most five points inside it.

Sign in / Sign up

Export Citation Format

Share Document