Related papers: Geometric deformations of sodalite frameworks
Glass is a microscopically disordered, solid form of matter that results when a fluid is cooled or compressed in such a fashion that it does not crystallise. Almost all types of materials are capable of glass formation -- polymers, metal…
Liquid droplets on fiber are often observed both in nature and in different engineering applications, like a fog harvesting mesh. Knowledge about drop-on-fiber morphology and its shedding under the influence of gravity can allow for the…
In structural rigidity, one studies frameworks of bars and joints in Euclidean space. Such a framework is an articulated structure consisting of rigid bars, joined together at joints around which the bars may rotate. In this paper, we will…
The constitutive characterization of the uniformity and homogeneity of binary elastic composites is presented in terms of a combination of the material groupoids of the individual constituents. The incorporation of these two groupoids…
Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…
An increasing variety of crystal structures has been observed in soft condensed matter over the past two decades, surpassing most expectations for the diversity of arrangements accessible through classical driving forces. Here, we survey…
Recent years have seen a large increase in the number of reported framework materials, including the nowadays-ubiquitous metal-organic frameworks (MOFs). Many of these materials show flexibility and stimuli-responsiveness, i.e. their…
Scattering structure factors provide essential insight into material properties and are routinely obtained in experiments, computer simulations, and theoretical analyses. Different approaches favor different geometries of the material. In…
Symmetry equations are obtained for the rigidity matrix of a bar-joint framework in R^d. These form the basis for a short proof of the Fowler-Guest symmetry group generalisation of the Calladine-Maxwell counting rules. Similar symmetry…
The transport and deformation of confined droplets and flexible capsules are central to diverse phenomena and applications, from biological flows in microcapillaries to industrial processes in porous media. Inspired by experiments, we…
We formulate a mathematical theory of auxetic behavior based on one-parameter deformations of periodic frameworks. Our approach is purely geometric, relies on the evolution of the periodicity lattice and works in any dimension. We…
We introduce a geometric framework to study Newton's equations on infinite-dimensional configuration spaces of diffeomorphisms and smooth probability densities. It turns out that several important PDEs of hydrodynamical origin can be…
Materials exhibit geometric structures across mesoscopic to microscopic scales, influencing macroscale properties such as appearance, mechanical strength, and thermal behavior. Capturing and modeling these multiscale structures is…
Metal--organic frameworks (MOFs) are a family of chemically diverse materials, with applications in a wide range of fields covering engineering, physics, chemistry, biology and medicine. Research so far has focused almost entirely on…
This paper presents a modeling framework---mathematical model and computational framework---to study the response of a plastic material due to the presence and transport of a chemical species in the host material. Such a modeling framework…
Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is…
The discrete Gaussian model for the surface of a crystal deposited on a disordered substrate is studied by Monte Carlo simulations. A continuous transition is found from a phase with a thermally-induced roughness to a glassy one in which…
We develop a numerical a framework to study phoretic particle dynamics in two dimensions. The particles are modeled as chemically active rigid circles, which can emit or absorb a solute into surrounding fluid. The interaction between…
We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise…
A phenomenological free energy model is proposed to describe the behavior of smectic liquid crystals, an intermediate phase that exhibits orientational order and layering at the molecular scale. Advantageous properties render the functional…