The concept of minimum length, widely accepted as a low-energy effect quantum gravity, manifests itself in mechanics through generalized uncertainty principles. Curved momentum space, on the other hand, is at heart similar applications such doubly special relativity. We introduce duality between theories yielding principles and nontrivial space. In particular, we find canonically conjugate vari...

Monochromatic x-ray imaging has been shown to increase contrast and reduce dose relative to conventional broadband imaging. However, clinical sources with very narrow energy bandwidth tend to have limited intensity and field of view. In this study, focused fan beam monochromatic radiation was obtained using doubly curved monochromator crystals. While these optics have been in use for microanaly...

In the present manuscript, a Layer-Wise (LW) generalized model is proposed for linear static analysis of doublycurved shells constrained with general boundary conditions under influence concentrated and surface loads. The unknown field variable modelled employing polynomials various orders, each them defined within layer structure. As particular case LW model, an Equivalent Single Layer (ESL) f...

We consider an ideal gas of infinitely rigid rods near a perfectly repulsive wall, and show that the interfacial tension of a surface with rods on one side is lower when the surface bends towards the rods. Surprisingly we find that rods on both sides of surfaces also lower the energy when the surface bends. We compute the partition functions of rods confined to spherical and cylindrical open sh...

In this note we give a correspondence between three kinds of pictures. First, we consider pictures with the “Droste-effect”: a scaling symmetry. These are drawn on a plane with a special point, which is the center of the scaling symmetry. Then we use the complex exponential map to transform these pictures to doubly periodic pictures, commonly known as wallpaper pictures, which are drawn on the ...

The draping process of non-crimp fabrics (NCF) on a doubly curved mould determines the fibre distribution and hence the processing and performance of the NCF product. A composite Finite Element (FE) model is developed to simulate the draping process of NCFs on arbitrary geometries. Tool-part interaction is taken into account. Problem regions with possible fibre buckling can be indicated and the...

Despite the common use of the blooming metaphor, its floral inspiration remains poorly understood. Here we study the physical process of blooming in the asiatic lily Lilium casablanca. Our observations show that the edges of the petals wrinkle as the flower opens, suggesting that differential growth drives the deployment of these laminar shell-like structures. We use a combination of surgical m...

The inherent advantages of thermoplastics over the traditional thermoset composite systems are well recognized in the aeronautics community. The main advantages are the much faster processing and the higher toughness. The current advanced thermoplastic material systems provide excellent mechanical performance but their main disadvantage is the difficult processing. Ideally, future aircraft subc...

Agent-based modelling (ABM) is a complex problem-solving approach that can be employed in early-stage parametric design, and certain design applications may benefit from such bottom-up strategy. This research investigates the potential of ABM for structural optimization. A case study form-found cantilevered truss presented has doubly curved shape over regular grid, resulting individual members ...