We present observations of the formation of plate-like snow crystals that provide evidence for an edge-enhancing crystal growth instability. This instability arises when the condensation coefficient describing the growth of an ice prism facet increases as the width of the facet becomes narrower. Coupled with the effects of particle diffusion, this phenomenon causes thin plate-like crystals to d...

Non-Euclidean plates are a subset of the class of elastic bodies having no stress-free configuration. Such bodies exhibit residual stress when relaxed from all external constraints, and may assume complicated equilibrium shapes even in the absence of external forces. In this work we present a mathematical framework for such bodies in terms of a covariant theory of linear elasticity, valid for l...

We study a vectorial approximation problem based on thin plate spline with tension involving two positive parameters one for a control of the oscillations and the other one allows a control on the divergence and rotational components of the field. The existence and uniqueness of the solution is proved and the solution is explicitly given. We study the limit problems and the convergence problem ...

We describe a model-based method of generating realistic mass lesions and placing them in appropriate locations on normal mammogram backgrounds. These lesions are highly irregular in shape and have no consistent internal landmarks. Thin plate splines are used both in modelling the background to each lesion, and to warp examples when training an appearance model.

The residual stresses of the thin-walled injection molding are investigated in this study. It was realized that the behavior of residual stresses in injection molding parts was affected by different process conditions such as melt temperature, mold temperature, packing pressure and filling time. The layer removal method was used to measure the residual stresses at a thin-walled test sample by a...

Curved thin sheets are ubiquitously found in nature and manmade structures from macro- to nanoscale. Within the framework of classical thin plate theory, the stiffness of thin sheets is independent of its bending state for small deflections. This assumption, however, goes against intuition. Simple experiments with a cantilever sheet made of paper show that the cantilever stiffness largely incre...