The shape-dependent universality of the excess percolation cluster number and cross-configuration probability on a torus is discussed. Besides the aspect ratio of the torus, the universality class depends upon the twist in the periodic boundary conditions, which for example are generally introduced when triangular lattices are used in simulations.

The production of small fluid droplets relies on an instability of solutions to the Young-Laplace equation. We ask whether smaller droplets can be produced by changing the shape of the nozzle. At a given critical pressure, the circular nozzle actually produces the largest droplet. The droplet volume can be decreased by up to 18% using a triangular nozzle with stretched corners.

This paper proposes a practical, topologically robust and ranging error resistive shape modeling procedure that approximates a real 3D object with the matrix-formatted organized meshing for the 3D shape processing. A geometric model with desired meshing, not limited to triangular one, but also quadrilateral, hexagonal or n-gonal mesh, is directly reconstructed based on a solid modeling approach...

The paper deals with a fast computational method for discretized optimal shape design problems governed by 2–dimensional magnetostatics. We discretize the underlying state problem using linear Lagrange triangular finite elements and in the optimization we eliminate the state problem for each shape design. The shape to be optimized is the interface between the ferromagnetic and air domain. The n...

Microcantilever platforms with integrated piezoresistors have found versatile applications in the field of clinical analysis and diagnostics. Even though treatise encompasses numerous design details of the cantilever based biochemical sensors, a majority of them focus on the generic slender rectangular cantilever platform mainly due to its evolution from the atomic force microscope (AFM). The r...

Understanding the localized surface plasmon resonance (LSPR) of differently shaped plasmonic nanoparticles benefits screening and designing highly sensitive single nanoparticle sensors. Herein, in the present work, we systematically investigated the shape-dependent scattering light colours and refractive index (RI) sensitivity of Ag nanoparticles (AgNPs) at the single nanoparticle level using c...

Constructing a 3D papercraft model from its unfolding has been fun for both children and adults since we can reproduce virtual 3D models in the real world. However, facilitating the papercraft construction process is still a challenging problem, especially when the shape of the input model is complex in the sense that it has large variation in its surface curvature. This paper presents a new he...