Related papers: Chain union closures
The aim in packing problems is to decide if a given set of pieces can be placed inside a given container. A packing problem is defined by the types of pieces and containers to be handled, and the motions that are allowed to move the pieces.…
Totally symmetric sets are a recently introduced tool for studying homomorphisms between groups. In this paper, we give full classifications of totally symmetric sets in certain families of groups and bound their sizes in others. As a…
When are athermal soft sphere packings jammed ? Any experimentally relevant definition must at the very least require a jammed packing to resist shear. We demonstrate that widely used (numerical) protocols in which particles are compressed…
We study the effects of random bonds on spin chains that have an excitation gap in the absence of randomness. The dimerized spin-1/2 chain is our principal example. Using an asymptotically exact real space decimation renormalization group…
Random packings of granular chains are presented as a model polymer system to investigate the contribution of entanglements to strain-stiffening in the absence of Brownian motion. The chain packings are sheared in triaxial compression…
Spherical confinement can act either stabilizing or destabilizing on the collapsed state of a semi-flexible polymer. General free-energy arguments suggest that the order of the unconstrained collapse transition is the distinguishing factor:…
The equilibrium partitioning of linear polymer chains into flexible polymer networks is governed by intricate entropic constraints arising from configurational degrees of freedom of both chains and network, yet a quantitative understanding…
We prove the non-linear stability of a large class of spherically symmetric equilibrium solutions of both the collisonless Boltzmann equation and of the Euler equations in MOND. This is the first such stability result that is proven with…
In this paper, we introduce a notion called "Approximate Ultrametricity" which encapsulates the phenomenology of a sequence of random probability measures having supports that behave like ultrametric spaces insofar as they decompose into…
Theoretical background is provided towards the mathematical foundation of the minimum enclosing ball problem. This problem concerns the determination of the unique spherical surface of smallest radius enclosing a given bounded set in the…
We study symmetrization procedures within the class $\mathcal S_n$ of \emph{ball-bodies}, i.e.\ intersections of unit Euclidean balls (equivalently, summands of the Euclidean unit ball, or $c$-convex sets via the $c$-duality $A\mapsto…
If the n-dimensional unit sphere is covered by finitely many spherically convex bodies, then the sum of the inradii of these bodies is at least {\pi}. This bound is sharp, and the equality case is characterized.
We use a hybrid Monte Carlo algorithm to simulate the shaking of spheres at different vibrational amplitudes, and find that spontaneous crystallisation occurs in specific dynamical regimes. Several crystallising transitions are typically…
It is well known that the vertices of any Euclidean simplicial regular polytope determine an optimal packing of equal spherical balls. We prove a stability version of optimal order of this result.
Entanglement plays a prominent role in the study of condensed matter many-body systems: Entanglement measures not only quantify the possible use of these systems in quantum information protocols, but also shed light on their physics.…
In this paper we introduce the concept of completeness of sets. We study this property on the set of integers. We examine how this property is preserved as we carry out various operations compatible with sets. We also introduce the problem…
Let B be a thick spherical building equipped with its natural CAT(1) metric and let M be a proper, convex subset of B. If M is open or if M is a closed ball of radius pi/2, then the maximal subcomplex supported by the complement of M is…
Chain distance between points in a metric space is defined as the infimum of epsilon such that there is an epsilon-chain connecting these points. We call a mapping of a metric compact into the real line a chain development if it preserves…
We study the stability of supersymmetry breaking vacuum in the presence of cosmic strings arising in the messenger sector. For certain ranges of the couplings, the desired supersymmetry breaking vacua become unstable against decay into…
Linear topological spaces with partial ordering (linear kinematics) are studied. They are defined by a set of 8 axioms implying that topology, linear structure and ordering are compatible with each other. Most of the results are valid for…