Related papers: Compressing thin spheres in the complement of a li…
We extend the weak-strong uniqueness principle to general models of compressible viscous fluids near/on the vacuum. In particular, the physically relevant case of positive density with polynomial decay at infinity is considered.
A two phase elastic composite with weakly compressible elastic inclusions is considered. The homogenised two-scale limit problem is found, via a version of the method of two-scale convergence, and analysed. The microscopic part of the…
We consider a thin multi-domain of $\mathbb R^N$, with $N\geq 2$, consisting of a vertical rod upon a horizontal disk. In this thin multi-domain, we introduce a bulk energy density of the kind $W(D^2U)$, where $W$ is a continuous function…
S. Blank solved the question of classifying immersed circles in $\mathbb{R}^{2}$ that extend to immersed disks, and how many topologically inequivalent disks can be extended. The quetions of various cases in $2$-dimension have already been…
Many multiprocessor systems have interconnection networks as underlying topologies and an interconnection network is usually represented by a graph where nodes represent processors and links represent communication links between processors.…
We study the existence of incompressible embeddings of surfaces into the genus two handlebody. We show that for every compact surface with boundary, orientable or not, there is an incompressible embedding of the surface into the genus two…
A shape of a combinatorial polytope is a convex embedding into Euclidean space. We provide necessary and sufficient conditions for a piecewise linear map between two shapes of the same polytope to be a compression (respectively a weak…
In this thesis, we use normal surface theory to understand certain properties of minimal triangulations of compact orientable 3-manifolds. We describe the collapsing process of normal 2-spheres and disks. Using some geometrical…
The hyperbolic volume of a link complement is known to be unchanged when a half-twist is added to a link diagram, and a suitable 3-punctured sphere is present in the complement. We generalize this to the simplicial volume of link…
We introduce systematically with the help of Weyl operators novel classes of multipartite and multidimensional states which are all bound entangled for arbitrary dimension. We find that the entanglement is bound due to different reasons:…
A sphere packing of the three-dimensional Euclidean space is compact if it has only tetrahedral holes, that is, any local maximum of the distance to the spheres is at equal distance to exactly four spheres. This papers describes all the…
We study numerically how multiple deformable capsules squeeze into a constriction. This situation is largely encountered in microfluidic chips designed to manipulate living cells, which are soft entities. We use fully three-dimensional…
Many objects in nature and industry are wrapped in a thin sheet to enhance their chemical, mechanical, or optical properties. There are similarly a variety of methods for wrapping, from pressing a film onto a hard substrate, to using…
Confinement is a versatile and well-established tool to study the properties of polymers either to understand biological processes or to develop new nano-biomaterials. We investigate the conformations of a semiflexible polymer ring in weak…
Suppose a knot in a $3$-manifold is in $n$-bridge position. We consider a reduction of the knot along a bridge disk $D$ and show that the result is an $(n-1)$-bridge position if and only if there is a bridge disk $E$ such that $(D, E)$ is a…
We exhibit several families of planar graphs that are minor-minimal intrinsically spherical $3$-linked. A graph is intrinsically spherical 3-linked if it is planar graph that has, in every spherical embedding, a non-split 3-link consisting…
We show that if a knot or link has n thin levels when put in thin position then its exterior contains a collection of n disjoint, non-parallel, planar, meridional, essential surfaces. A corollary is that there are at least n/3 tetrahedra in…
It is shown that a suspension of particles in a partially-filled, horizontal, rotating cylinder is linearly unstable towards axial segregation and an undulation of the free surface at large enough particle concentrations. Relying on the…
We give a method for searching for thin positions of a given link.
Surface incompressibility, also called inextensibility, imposes a zero-surface-divergence constraint on the velocity of a closed deformable material surface. The well-posedness of the mechanical problem under such constraint depends on an…