Minimal cones on hypercubes

It is shown that in dimension greater than 4, the minimal area hypersurface separating the faces of a hypercube is the cone over the edges of the hypercube. This constrasts with the cases of two and three dimensions, where the cone is not minimal. For example, a soap film on a cubical frame has a small rounded square in the center. In dimensions over 6, the cone is minimal even if the area separating opposite faces is given zero weight. The proof uses the maximal flow problem that is dual to the minimal surface problem

Instability of the wet cube cone soap film

A dry conical soap film on a cubical frame is well known not to be stable. Recent experimental evidence seems to indicate that adding liquid to form Plateau borders stabilizes the conical film, perhaps to arbitrarily low liquid volumes. This paper presents numerical simulation evidence that the wet cone is unstable for low enough liquid volume, with the critical volume fraction being about 0.000274

The Surface Evolver

The Surface Evolver is a computer program that minimizes the energy of a surface subject to constraints. The surface is represented as a simplicial complex. The energy can include surface tension, gravity, and other forms. Constraints can be geometrical constraints on vertex positions or constraints on integrated quantities such as body volumes. The minimization is done by evolving the surface down the energy gradient. This paper describes the mathematical model used and the operations available to interactively modify the surface

Sedimentation Coefficients of the Virions of Soil-Borne Wheat Mosaic Virus

The sedimentation coefficient of virion I of soil-borne wheat mosaic virus was estimated to be 219S, the same, within error, as the sedimentation coefficient of the dimer of virion II, estimated to be 218S. The monomer of virion II sedimented at 177S, and was 138 nm long. Another strain of the virus had a virion II (designated lIb) that was 92 nm long and sedimented at 159S. The two virus strains coexist in some fields

Aggregates of two-dimensional vesicles: Rouleaux and sheets

Using both numerical and variational minimization of the bending and adhesion energy of two-dimensional lipid vesicles, we study their aggregation, and we find that the stable aggregates include an infinite number of vesicles and that they arrange either in a columnar or in a sheet-like structure. We calculate the stability diagram and we discuss the modes of transformation between the two types of aggregates, showing that they include disintegration as well as intercalation.Comment: 4 figure

Dense Regular Packings of Irregular Non-Convex Particles

We present a new numerical scheme to study systems of non-convex, irregular, and punctured particles in an efficient manner. We employ this method to analyze regular packings of odd-shaped bodies, not only from a nanoparticle but also both from a computational geometry perspective. Besides determining close-packed structures for many shapes, we also discover a new denser configuration for Truncated Tetrahedra. Moreover, we consider recently synthesized nanoparticles and colloids, where we focus on the excluded volume interactions, to show the applicability of our method in the investigation of their crystal structures and phase behavior. Extensions to the presented scheme include the incorporation of soft particle-particle interactions, the study of quasicrystalline systems, and random packings.Comment: 4 pages, 3 figure

Tensor virial equation of evolving surfaces in sintering of aggregates of particles by diffusion

The moment of inertia tensor is a quantity that characterizes the morphology of aggregates of particles. The deviatoric components indicate the anisotropy of the aggregate, and its compactness is described by the isotropic component, i.e. the second moment of inertia, which is related to the radius of gyration. The equation of motion of the moment of inertia tensor is proposed for the sintering and coalescence of crystalline particles by bulk diffusion and surface diffusion. Simulations of the evolution of aggregates of particles (linear chains, rings and branched chains) show that the aggregates become more compact and more isotropic structures, driven by the surface energy tensor or the surface force density. The tensor virial equation for diffusion is applicable also to evolution of pores, precipitates and inclusions embedded in a surrounding matrix

Unconventional agriculture how farmer-to-farmer networks support sustainable communities: a study of the Sustainable Farming Association of Minnesota

As the public’s interest in local and sustainably-produced food continues to grow, farmer organizations throughout the country are working to develop and spread more sustainable methods of farming for producers. To better understand how these groups can promote alternatives to industrialized food systems, I conducted a study of the Sustainable Farming Association of Minnesota (SFA). SFA is farmer-led and encompasses a state-level organization along with nine geographic chapters across Minnesota. Their organizational structure serves as the framework of their “community network” through which they connect farmers and disseminate the wisdom of their sustainable farming communities. My study involved interviews with members of three local SFA chapters, observations of chapter activities, and an interview with SFA’s Network Coordinator. Through this research, I was able to observe how interdependent relationships between local SFA chapter members, as well as between local chapters and the state-level SFA, support sustainable agriculture within the state

A Triangular Tessellation Scheme for the Adsorption Free Energy at the Liquid-Liquid Interface: Towards Non-Convex Patterned Colloids

We introduce a new numerical technique, namely triangular tessellation, to calculate the free energy associated with the adsorption of a colloidal particle at a flat interface. The theory and numerical scheme presented here are sufficiently general to handle non-convex patchy colloids with arbitrary surface patterns characterized by a wetting angle, e.g., amphiphilicity. We ignore interfacial deformation due to capillary, electrostatic, or gravitational forces, but the method can be extended to take such effects into account. It is verified that the numerical method presented is accurate and sufficiently stable to be applied to more general situations than presented in this paper. The merits of the tessellation method prove to outweigh those of traditionally used semi-analytic approaches, especially when it comes to generality and applicability.Comment: 21 pages, 11 figures, 0 table

Computation of equilibrium foam structure using the Surface Evolver

The Surface Evolver has been used to minimise the surface area of various ordered structures for monodisperse foam. Additional features have enabled its application to foams of arbitrary liquid fraction. Early results for the case of dry foam (negligible liquid fraction) produced a structure haveing lower surface area, or energy, than Kelvin\u27s 1887 minimal tetrakaidecahedron. The calculations reported here show that this remains the case when the liquid fraction is finite, up to about 11%, at which point an f.c.c arrangement of the cells becomes preferable