The cyclic and dihedral groups can be made to act on the set Acyc(Y ) of acyclic orientations of an undirected graph Y , and this gives rise to the equivalence relations ∼κ and ∼δ, respectively. These two actions and their corresponding equivalence classes are closely related to combinatorial problems arising in the context of Coxeter groups, sequential dynamical systems, the chip-firing game, ...

Given an undirected graph, one can assign directions to each of the edges of the graph, thus orienting the graph. To be as egalitarian as possible, one may wish to find an orientation such that no vertex is unfairly hit with too many arcs directed into it. We discuss how this objective arises in problems resulting from telecommunications. We give optimal, polynomial-time algorithms for: finding...

A tree-composition is a tree-like family that serves to describe the obstacles to k-edge-connected orientability of mixed graphs. Here we derive a structural result on tree-compositions that gives rise to a simple algorithm for computing an obstacle when the orientation does not exist. As another application, we show a min–max theorem on the minimal in-degree of a given node set in a k-edge-con...

CRACKS in ductile single crystals are analyzed here for geometries and orientations such that twodimensional states of anti-plane shear constitute possible deformation fields. The crystals are modelled as ideally plastic and yield according to critical resolved shear stresses on their slip systems. Restrictions on the asymptotic forms of stress and deformation fields at crack tips are establish...

Intermolecular features like hydrogen bonding and π-type interactions play pivotal roles in stabilizing molecular structures in ionic liquids with planar rings and hydrogen-bond donors and acceptors. However, the delicate interplay among these interactions is complicated and depends on specific ion types. In this work, ab initio molecular dynamics simulations were performed to reveal competitiv...

In this paper we study influenza viral membrane deformation related to the refolding of Hemagglutinin (HA) protein. The focus of the paper is to understand membrane deformation and budding due to experimentally observed linear HA-protein clusters, which have not been mathematically studied before. The viral membrane is modeled as a two dimensional incompressible lipid bilayer with bending rigid...

Electrical steels are important alloys widely used in electrical instruments. The magnetic properties and low core loss of grain oriented silicon steels are closely related to the sharpness of Goss texture ({110} ).The direction of is the softest direction for magnetism.  In this work, the microstructure and dependence of orientation density along the major texture fibers on the applied cold ro...

Formation of stray grain defects particularly around re-entrant features of the turbine blade airfoils is one of the major problems in directional and single crystal solidification processes. In this work, directional solidification tests of the GTD-111 Ni-based superalloy were conducted at different withdrawal velocities of 3, 6 and 9 mm.min-1 using various stepped cylindrical and cubic design...