Introduction. Dedekind has determined all groups whose subgroups are all normal (see, e.g., [5, Theorem 12.5.4]). Partially generalizing this, Wielandt showed that a finite group is nilpotent, if and only if all its subgroups are subnormal, and also if and only if all maximal subgroups are normal [5, Corollary 10.3.1, 10.3.4]. Huppert [7, Sätze 23, 24] has shown that if all 2nd-maximal subgroup...

We have reached our goal of implementing a computationally cheap algorithm for realtime rendering of realistic two-dimensional fire. The fire is simulated using computational fluid dynamics, vorticity confinement, and combustion modelling and visualized using black-body radiation. Small rotationally homogenous fires like torches and candles viewed in front are the best candidates when using thi...

Densely packed systems of thermal particles in curved geometries are frequently encountered in biological and microfluidic systems. In 2D systems, at sufficiently high surface coverage, diffusive motion is widely known to be strongly affected by physical confinement, e.g., by the walls. In this work, we explore the effects of confinement by shape, not rigid boundaries, on the diffusion of discs...

Geocell structures consist of a series of interconnected single cells, made from different polymer materials. The cell walls completely encase the infill material and provide an all-around confinement to the soil. The confinement effect is based on three main mechanisms: active earth pressure within loaded cell, passive earth resistance in the adjacent cells and hoop stresses in the cell walls....

Synthetic microswimmers are envisioned to be useful in numerous applications, many of which occur in tightly confined spaces. It is therefore important to understand how confinement influences swimmer dynamics. Here we study the motility of bimetallic microswimmers in linear and curved channels. Our experiments show swimmer velocities increase, up to 5 times, with the degree of confinement, and...

Using a Landau-de Gennes approach, we study the impact of confinement topology, geometry and external fields on the spatial positioning of nematic topological defects (TDs). In quasi two-dimensional systems we demonstrate that a confinement-enforced total topological charge of m > 1/2 decays into elementary TDs bearing a charge of m = 1/2. These assemble close to the bounding substrate to enabl...

This paper presents the results of modeling tests of the Effect of Confinement Pressure on footing bearing capacity of two kinds of square and strip footing. Footings bearing capacity depends upon many factors including soil kind, depth, form and kind of loading. Soil behavior is variable regarding the kind of loading and the kind of deformations in that can have great importance in the amount ...