The robust assembly of small symmetric nano-shells

Highly symmetric nano-shells are found in many biological systems, such as clathrin cages and viral shells. Several studies have shown that symmetric shells appear in nature as a result of the free energy minimization of a generic interaction between their constituent subunits. We examine the physical basis for the formation of symmetric shells, and using a minimal model we demonstrate that these structures can readily grow from identical subunits under non equilibrium conditions. Our model of nano-shell assembly shows that the spontaneous curvature regulates the size of the shell while the mechanical properties of the subunit determines the symmetry of the assembled structure. Understanding the minimum requirements for the formation of closed nano-shells is a necessary step towards engineering of nano-containers, which will have far reaching impact in both material science and medicine.Comment: 12 pages, 12 figure

Online Circle and Sphere Packing

In this paper we consider the Online Bin Packing Problem in three variants: Circles in Squares, Circles in Isosceles Right Triangles, and Spheres in Cubes. The two first ones receive an online sequence of circles (items) of different radii while the third one receive an online sequence of spheres (items) of different radii, and they want to pack the items into the minimum number of unit squares, isosceles right triangles of leg length one, and unit cubes, respectively. For Online Circle Packing in Squares, we improve the previous best-known competitive ratio for the bounded space version, when at most a constant number of bins can be open at any given time, from 2.439 to 2.3536. For Online Circle Packing in Isosceles Right Triangles and Online Sphere Packing in Cubes we show bounded space algorithms of asymptotic competitive ratios 2.5490 and 3.5316, respectively, as well as lower bounds of 2.1193 and 2.7707 on the competitive ratio of any online bounded space algorithm for these two problems. We also considered the online unbounded space variant of these three problems which admits a small reorganization of the items inside the bin after their packing, and we present algorithms of competitive ratios 2.3105, 2.5094, and 3.5146 for Circles in Squares, Circles in Isosceles Right Triangles, and Spheres in Cubes, respectively

Signature of nearly icosahedral structures in liquid and supercooled liquid Copper

A growing body of experiments display indirect evidence of icosahedral structures in supercooled liquid metals. Computer simulations provide more direct evidence but generally rely on approximate interatomic potentials of unproven accuracy. We use first-principles molecular dynamics simulations to generate realistic atomic configurations, providing structural detail not directly available from experiment, based on interatomic forces that are more reliable than conventional simulations. We analyze liquid copper, for which recent experimental results are available for comparison, to quantify the degree of local icosahedral and polytetrahedral order

Ground state of a large number of particles on a frozen topography

Problems consisting in finding the ground state of particles interacting with a given potential constrained to move on a particular geometry are surprisingly difficult. Explicit solutions have been found for small numbers of particles by the use of numerical methods in some particular cases such as particles on a sphere and to a much lesser extent on a torus. In this paper we propose a general solution to the problem in the opposite limit of a very large number of particles M by expressing the energy as an expansion in M whose coefficients can be minimized by a geometrical ansatz. The solution is remarkably universal with respect to the geometry and the interaction potential. Explicit solutions for the sphere and the torus are provided. The paper concludes with several predictions that could be verified by further theoretical or numerical work.Comment: 9 pages, 9 figures, LaTeX fil

Random sequential adsorption of rounded rectangles, isosceles and right triangles

We studied random sequential adsorption (RSA) of three classes of polygons with rounded corners: rectangles, isosceles triangles, and orthogonal triangles. Using the algorithm that enables the generation of strictly saturated RSA packing, we systematically determined the mean saturated packing fraction for RSA configurations built by these shapes. The main aim was to find the figure that forms the densest random configuration. Although for rounded rectangles the packing fractions were lower than for discorectangles, the densities reached for some rounded isosceles and right triangles exceeded the highest known two-dimensional packing fraction for configurations built of unoriented monodisperse objects. The microstructural properties of several packings were discussed in terms of the two-point density autocorrelation function