We analyze the structure of reduced expressions in the Coxeter groups An, Bn and Dn. Several special classes of elements are singled out for their connections with symmetric functions or the theory of P -partitions. Membership in these special classes is characterized in a variety of ways, including forbidden patterns, forbidden subwords, and by the form of canonically chosen reduced words.

We introduce and study a class of simplicial complexes, the orphan complexes, associated to simple graphs whose family of (open or closed) vertex-neighborhoods are anti-Sperner. Under suitable restrictions, we show that orphan complexes of such graphs are always shellable and provide a characterization of graphs in terms of induced forbidden subgraphs contained in this restricted subfamily.

In this paper we demonstrate that several theorems from [1] and [3] do not hold as they are stated. These are the theorems regarding forbidden subposet characterizations of certain classes of coverincomparability graphs. In this paper we correct a mistake in the main theorem of [1], reformulate the corresponding statements and present corrected proofs. We further characterize posets whose cover...

One-dimensional magnetic nanowires have been introduced into polydimethylsiloxane PDMS to form polymer based nanocomposites. In contrast to the conventional nanofillers such as carbon nanotubes, carbon nanofibers, nanoparticles, and layer-structured materials, these well-defined anisotropic metallic nanowires are highly conductive and have much weaker van der Waals interactions. Moreover, compo...

Macrophage cell lines like J774 cells are ideal model systems for establishing the biophysical foundations of autonomous deformation and motility of immune cells. To aid comparative studies on these and other types of motile cells, we report measurements of the cortical tension and cytoplasmic viscosity of J774 macrophages using micropipette aspiration. Passive J774 cells cultured in suspension...

Metallic foams with pore sizes from 250 lm to 2 mm have been a subject of research for over two decades due to their high surface area, which allows for a variety of applications, such as thermal and sound insulation. Recently, processing of metallic foams at the nanoscale (pores sizes less than 100 nm) has opened the door to new and interesting applications, such as sensors and actuators. In g...

Silica aerogels are nanoporous ultralight new materials with extraordinary material properties. In this study, the mechanical properties of silica aerogels, e.g. Young’s modulus, Poisson’s ratio and constitutive relation, are investigated using Molecular Dynamics (MD) simulations and theoretical analysis. In molecular dynamics simulations, an improved process of negative pressure rupturing meth...

Mechanics are increasingly recognized to play an important role in modulating brain form and function. Computational simulations are a powerful tool to predict the mechanical behavior of the human brain in health and disease. The success of these simulations depends critically on the underlying constitutive model and on the reliable identification of its material parameters. Thus, there is an u...

Human movements are physical processes combining the classical mechanics of the human body moving in space and the biomechanics of the muscles generating the forces acting on the body under sophisticated sensory-motor control. The characterization of the performance of human movements is a problem with important applications in clinical and sports research. One way to characterize movement perf...