Narrow Results

Applications of the cellular Potts model to investigate cellular structures are becoming widely spread in the scientific literature. Despite its realism and generality, the standard Monte Carlo algorithm used to evolve this model in the scientific literature lacks computational efficiency. As an alternative we introduce the Random Walker algorithm that is a modified Monte Carlo procedure of simpler parallelization. We test it in cell sorting and foam coarsening simulations obtaining velocity increase factors of 10 and 3 times, respectively, in relation to the standard algorithm. The results obtained with these simulations are equivalent to those obtained with the standard algorithm.

We show how to use Bar-Natan's "divide and conquer" approach to computation to efficiently compute the universal sl(2) dotted foam cohomology groups, even for big knots and links. We also describe a purely topological version of the sl(2) foam theory, in the sense that no dots are needed on foams.

We generalize the Khovanov–Rozansky cohomology theory for n = 2 by using a homogeneous potential that depends on two parameters, to obtain the universal Khovanov-Rozansky sl(2)-link cohomology. This theory is equivalent to the universal sl(2)-link cohomology using foams, after tensoring both theories with appropriate rings.

In the study of knotted trivalent graphs and their higher dimensional analogue, knotted foams, some of the moves have alternative interpretations. Here three interpretations are given. (1) As the boundaries of chains in a homology theory, (2) as a system of abstract tensor relations, and (3) as a collection of polyhedra that include the permutohedron. The homological interpretation will allow for a solution to the abstract tensor system.

Micro-arc oxidation (MAO) coatings were prepared on closed-cell aluminum foams. The microstructure, elemental distribution and phase composition of the MAO coatings were analyzed by scanning electron microscopy (SEM), energy-dispersive spectroscopy (EDS) and X-ray diffraction (XRD), respectively. The corrosion resistances and compressive properties of the uncoated and coated aluminum foams were studied by electrochemical polarization test and mechanical test, respectively. The results show that the MAO coatings cover the surfaces of closed-cell aluminum foams. The average thickness of the MAO coatings is 7 μm. The MAO coatings are mainly composed of γ-Al₂O₃ phase. The corrosion resistances of the closed-cell aluminum foams are improved by MAO treatment. The as-received foams show a low corrosion potential (-1.36 V), on contrary, the MAO coated foams get an increase corrosion potential (-0.78 V). But the MAO coated foams show the marginal variation in compressive strengths when the thickness of the coatings could be negligible compared with the total thickness of the foams.

The geometry of soap films, bubble clusters and foams has a nice mathematical description, though many open problems remain. Recently, computer simulations, and their graphical output, have led to some new insights.

Numerical prediction of mixed-mode failure along interfaces between polymeric foams and metals in foam-filled composite structures can be facilitated if interfacial cohesive laws are known. In this paper, we characterize the cohesive behavior of the interface between a polyurethane (PU) closed-cell foam and galvanized mild steel by extending an experimental approach suggested by [Lundsgaard–Larsen et al. [2008] Engineering Fracture Mechanics 75(8), 2514–2530]. A simplified approach for calculating the fracture energy and for extracting cohesive relations from the fracture energy-total crack opening displacement data is presented. We find that there is a substantial amount of normal separation in tests that are designed to be purely mode II, and a small amount of tangential motion in tests designed to be purely mode I. The interfacial cohesive laws extracted from our experiments suggest that the normal traction depends not only the normal and tangential displacements but also the tangential traction.

The objective of this work is to numerically study the individual and mixed mode fracture behavior of open-cell foams. Three-dimensional tetrakaidecahedron model is adopted and finite element method is employed in analysis. The overall elastic properties of open-cell foams are numerically obtained. Then, modes I, II, III and mixed mode I–II fracture behavior of open-cell foams are numerically predicted respectively, in which both solid/hollow and square/circular strut cross-sections are considered. It is seen that the relationship between the overall critical stress intensity factor and the relative density of foam obeys power law for individual crack problems. Effects of the shape and the topology of strut cross-section are discussed in detail. For mixed mode I–II crack problem, the relationship between K_I/K_IC and K_II/K_IIC is obtained and the effect of the shape of strut cross-section is discussed.

Intrinsic coalescence (corresponding to the opening of a hole in a surfactant monolayer) is important only for poor surfactants. With good surfactants, and in usual industrial conditions, coalescence is extrinsic, and mainly due to dirt particles. In the present note, we first analyze the motions of one dirt particle inside an initially monodisperse O/W emulsion. The particle remains trapped at the surface of a growing oil droplet, of size R(t) ~ t^⅓. If we now go to a very dilute system of dirt particles, we expect that they generate first a collection of large drops. Ultimately, these large drops come into contact, and one may end up with an oil matrix containing droplets of the O/W emulsion.