Related papers: Exploring non-Euclidean photonics: Pseudosphere mi…
We study properties of non-minimal biharmonic hypersurfaces of spheres. The main result is a CMC Unique Continuation Theorem for biharmonic hypersurfaces of spheres. We then deduce new rigidity theorems to support the Conjecture that…
In the perturbative approach, substructures in the lens can be reduced to their effect on the two perturbative fields $f_1$ and $\frac{d f_0}{d\theta}$. A simple generic model of elliptical lens with a substructure situated near the…
Let $M^n$ be an $n$-dimensional complete and locally conformally flat hypersurface in the unit sphere $\mathbb{S}^{n+1}$ with constant scalar curvature $n(n-1)$. We show that if the total curvature $\left( \int _ { M } | H | ^ { n } d v…
A method of scanning mid-IR-laser microscopy has recently been proposed for the investigation of large-scale electrically and recombination-active defects in semiconductors and non-destructive inspection of semiconductor materials and…
In this article we study the shape of a compact surface of constant mean curvature of Euclidean space whose boundary is contained in a round sphere. We consider the case that the boundary is prescribed or that the surface meets the sphere…
We will obtain the warped product decompositions of spaces of constant curvature (with arbitrary signature) in their natural models as subsets of pseudo-Euclidean space. This generalizes the corresponding result by S. Nolker to arbitrary…
We consider geodesics on the surfaces obtained by weak deformations of the standard 2D-sphere. The dynamics of a particle on the surface can be asymptotically described by the averaged evolution of the particle's angular momentum. It is…
We have used scanning probe microscopy to investigate self-assembled monolayers of chemically synthesized peptides. We find that the peptides form a dense uniform monolayer, above which is found a sparse additional layer. Using scanning…
In this paper, we study biconservative hypersurfaces of index 2 in $\mathbb E^{5}_{2}$. We give the complete classification of biconservative hypersurfaces with diagonalizable shape operator at exactly three distinct principal curvatures.…
We introduce a system of light driven microscopic autonomous moving particles that move on a flat surface. The design is simple, yet effective: Micrometer sized objects with wedge shape are produced by photopolymerization, they are covered…
Photomechanically active materials undergo reversible deformation on illumination, making them ideal for remote, tether-free actuation. Much of the work on these materials has focused on one-dimensional structures, such as strips. In this…
It is proposed that a lattice, with constituent masses and spring constants, may be considered as a model system for topological matter. For instance, a relative variation of the inter- and intra-unit cell spring constants can be used to…
We explore geometric properties of circular analogues of tractrices and pseudospheres in $\mathbb R^3$.
It is proved some results about existence and non existence of unit normal sections of submanifolds of the Euclidean space and sphere which associated Gauss maps are harmonic. Some applications to CMC hypersurfaces of the sphere and…
When a single time-like vector is distinguished geometrically to present the only preferred direction in extending the pseudoeuclidean geometry, the hyperboloid may not be regarded as an exact carrier of the unit-vector image. So under…
A homogeneous negative permeability sphere can support magnetic localized surface plasmons (MLSPs). Generally, negative permeability materials are metamaterial (MM) structures exhibiting very deep subwavelength spatial scales, whose effects…
A pseudo-edge graph of a convex polyhedron K is a 3-connected embedded graph in K whose vertices coincide with those of K, whose edges are distance minimizing geodesics, and whose faces are convex. We construct a convex polyhedron K in…
We describe a micro-fabrication method to create concave features with ultra-low surface roughness in silica, either on the end facets of optical fibers or on flat substrates. The machining uses a single focused CO2 laser pulse. Parameters…
The motion of submerged magnetic microspheres rolling at a glass-water interface has been studied using magnetic rotation and optical tweezers combined with bright-field microscopy particle tracking techniques. Individual microspheres of…
We study the classical geodesic motions of nonzero rest mass test particles and photons in five-dimensional warped product spaces. We show that it is possible to obtain a general picture of these motions, using the natural decoupling that…