Operator representations of the cross product ∗-algebra O(S2 qc)⋊Uq(su2) of the Hopf ∗-algebra Uq(su2) and its module ∗-algebras O(S2 qc) of Podles’ spheres are studied. Two classes of representations are described by explicit formulas for the actions of the generators.

Super water-repellent surfaces occur naturally on plants and aquatic insects and are created in the laboratory by combining micro or nano-scale surface topographic features with hydrophobic surface chemistry. When such types of water-repellent surfaces are submerged they can retain a film of air (a plastron). In this work, we report measurements of the terminal velocity of solid acrylic spheres...

We investigate the possibility of using magnetorheological polydimethylsiloxane (MR-PDMS) spheres as micro-optical resonators. In particular, the effect of a magnetic field on the whispering gallery modes (WGM) of these resonators is studied. The applied field induces mechanical deformation, causing shifts in the WGM. The microspheres are made of PDMS with embedded magnetically polarizable part...

This paper reviews recent developments in Morphology—Dependent Resonance (MDR)—based sensors for aerospace applications. The sensor concept is based on the detection of small shifts of optical resonances (also called the whispering gallery modes or WGM) of dielectric spheres caused by external effects. Recent developments in MDR-based micro-optical sensors for temperature, force, pressure and c...

Nano- and micro-sized ZnO spheres were fabricated via a simple solvothermal synthesis using two different precursors, while diethanolamine was used to control the morphology. The applied solvent composition, precursor ratio treatment temperature mathematically correlated with diameter of spheres. crystallite size could be easily controlled by adjusting temperature, providing flexibility during ...

The acoustical macro-behavior of mineral open-cell foam samples is modeled from microstructure morphology using a three-dimensional idealized periodic unit-cell (3D-PUC). The 3D-PUC is based on a regular arrangement of spheres allowed to interpenetrate during the foaming process. Identification and sizing of the 3D-PUC is made from x-ray computed microtomography and manufacturing process inform...

In the introduction a brief recollection is made of how one of us (RKC), accidentally, got into this field of linear and nonlinear spectroscopy of a dielectric micro-particle that can be treated as a micro-cavity or a micro-resonator. The basic principles of whispering gallery modes (WGMs) and their relationship with electromagnetic theory are presented. To simplify the mathematics, we only dis...

Nanoparticle shape can improve drug delivery, based in part on recent fi ndings that fl exible, worm-like nanocarriers (Worms) increase the amount of drug delivered to tumors and shrink the tumors more effectively than spherical micelles (Spheres). Here, all-atom molecular dynamics (MD) simulations are used to build a rational coarse grain (rCG) model that helps clarify shape-dependent effects ...

Given a sphere of radius r > 1 in the n-dimensional Euclidean space, we study the coverings of this sphere with unit spheres. Our goal is to design a covering of the lowest covering density, which defines the average number of unit spheres covering a point in a bigger sphere. For growing n, we obtain the covering density of (n lnn)/2. This new upper bound is half the order n lnn established in ...

Abstract Crystallization of granular assemblies has broad implications for rapid and scalable creation architected materials with applications ranging from structural to microarchitected battery electrodes. While significant advances have been made in understanding colloidal self‐assembly at nano micro scale, the governing mechanisms organization dry hard spheres remain unclear. Here, we invest...