Related papers: Optimal Three-Material Wheel Assemblage of Conduct…
Experiments on isotropic compression of a granular assembly of spheres show that the shear and bulk moduli vary with the confining pressure faster than the 1/3 power law predicted by Hertz-Mindlin effective medium theories (EMT) of contact…
In high-contrast composite materials, the electric field concentration is a common phenomenon when two inclusions are close to touch. It is important from an engineering point of view to study the dependence of the electric field on the…
Self-assembly of complex and functional materials remains a grand challenge in soft material science. Efficient assembly depends on a delicate balance between thermodynamic and kinetic effects, requiring fine-tuning affinities and…
It is shown that a compound elastic structure, which displays a dynamic instability, may be designed as the union (or 'fusion') of two structures which are stable when separately analyzed. The compound elastic structure has two degrees of…
A two-dimensional three-phase conducting composite with coated circular inclusions, periodically distributed in a parallelogram, is studied. The phases are assumed to be isotropic, and perfect contact conditions at the interfaces are…
We study the structural properties of multi-period martingale optimal transport (MOT). We develop new tools to address these problems, and use them to prove several uniqueness and structural results on three-period martingale optimal…
Asymptotic homogenisation is used to systematically derive reduced-order macroscopic models of conductive behaviour in spirally-wound layered materials in which the layers have very different conductivities. The problem is motivated by the…
We consider a gradient estimate for a conductivity problem whose inclusions are two neighboring insulators in three dimensions. When inclusions with an extreme conductivity (insulators or perfect conductors) are closely located, the…
We consider the problem of isotropic effective conductivity $\sigma_e(\sigma_1,\ldots,\sigma_n)$ in two-dimensional three- and four-phase symmetric composites with a partial isotropic conductivity $\sigma_j$ of the $j$-th phase. The upper…
3D printing mechanically flexible composite materials with high electrical conductivity is currently hindered by the need to use high loading of conductive filler, which severely limits flexibility. Here, microstructural patterning of…
Algebraic expressions are found for the effective conductivities of some infinite tessellations composed of conducting square, triangular, or hexagonal tiles. A tessellation is further characterized by the number N of different colors…
This article combines shape optimization and homogenization techniques by looking for the optimal design of the microstructure in composite materials and of scaffolds. The development of materials with specific properties is of huge…
A class of optimal three-weight cyclic codes of dimension 3 over any finite field was presented by Vega [Finite Fields Appl., 42 (2016) 23-38]. Shortly thereafter, Heng and Yue [IEEE Trans. Inf. Theory, 62(8) (2016) 4501-4513] generalized…
Designing and optimizing different flows in networks is a relevant problem in many contexts. While a number of methods have been proposed in the physics and optimal transport literature for the one-commodity case, we lack similar results…
Experimentally it is known that the bulk modulus, K, and shear modulus, \mu, of a granular assembly of elastic spheres increase with pressure, p, faster than the p^1/3 law predicted by effective medium theory (EMT) based on Hertz-Mindlin…
The response of a neo-Hookean fiber composite undergoing finite out-of-plane shear deformation is examined. To this end an explicit close form solution for the out-of-plane shear response of a cylindrical composite element is introduced. We…
Assemblies of purely repulsive and frictionless particles, such as emulsions or hard spheres, display very curious properties near their jamming transition, which occurs at the random close packing for mono-disperse spheres. Although such…
A CaTherine wheel is a surjective continuous map $f:S^1 \to S^2$ such that for every closed interval $I\subset S^1$ the image $f(I)$ is homeomorphic to a disk, and $f(\partial I)$ is contained in the boundary of this disk. CaTherine wheels…
The giant $\{ \mathrm{Mn}_{70} \}$ and $\{ \mathrm{Mn}_{84} \}$ wheels are the largest nuclearity single-molecule magnets synthesized to date and understanding their magnetic properties poses a challenge to theory. Starting from first…
The effective quasistatic conductivity of composite polymeric electrolytes is studied in terms of a hard-core--penetrable-layer model. Used to incorporate the interface phenomena (such as amorphization of the polymer matrix around filler…