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We investigate morphologies of semiflexible polymer rings, such as circular DNA, which are adsorbed onto topographically or chemically structured substrate surfaces. We classify all equilibrium morphologies for two striped surface…
The second order optical response of centrosymmetric materials manifests itself mostly at their surface, being strongly suppressed in their bulk. However, the overall surface response is also suppressed in nanoparticles with a…
We consider the optimal covering of fractal sets in a two-dimensional space using ellipses which become increasingly anisotropic as their size is reduced. If the semi-minor axis is \epsilon and the semi-major axis is \delta, we set…
The living body is composed of innumerable fine and complex structures and although these structures have been studied in the past, a vast amount of information pertaining to them still remains unknown. When attempting to observe these…
The incorporation of graphene-related materials as nanofiller can produce multifunctional foams with enhanced specific properties and density reduction. Herein we report on the preparation of microcellular thermoplastic…
We show that any noncompact oriented surface is homeomorphic to the leaf of a minimal foliation of a closed $3$-manifold. These foliations are (or are covered by) suspensions of continuous minimal actions of surface groups on the circle.…
Many organisms form colonies for a transient period of time to withstand environmental pressure. Bacterial biofilms are a prototypical example of such behavior. Despite significant interest across disciplines, physical mechanisms governing…
Electrostatic force microscopy (EFM) can image nanoscale objects buried below the surface. Here, we theoretically show that this capability can be used to obtain nanotomographic information, i.e., the physical dimensions and dielectric…
We study automorphism groups of fibered surfaces for finite cyclic covering fibrations of an elliptic surface. We estimate the order of a finite subgroup of automorphism groups in terms of the genus of the fiber, the genus of the base…
Vesicles prepared in water from a series of diblock copolymers and termed "polymersomes" are physically characterized. With increasing molecular weight $\bar{M}_n$, the hydrophobic core thickness $d$ for the self-assembled bilayers of…
An increasing number of large molecules have been positively identified in space. Many of these molecules are of biological interest and thus provide insight into prebiotic organic chemistry in the protoplanetary nebula. Among these…
A partial cube is a graph having an isometric embedding in a hypercube. Partial cubes are characterized by a natural equivalence relation on the edges, whose classes are called zones. The number of zones determines the minimal dimension of…
This paper considers membranes of globular structure in the framework of the cell model technique. Coupled micropolar and Brinkman-type equations are used to model the flow of micropolar fluid through a spherical cell, consisting of solid…
We report on a new, single-step and scalable method to fabricate highly ordered, multi-directional and complex surface structures that mimic the unique morphological features of certain species found in nature. Biomimetic surface…
The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of…
During development, organisms acquire three-dimensional shapes with important physiological consequences. While the basic mechanisms underlying morphogenesis are known in eukaryotes, it is often difficult to manipulate them in vivo. To…
The industrial implementation of biofuel production from lignocellulosic biomass faces a number of economic obstacles. One of these is the cost of enzymes, typically used for cellulose hydrolysis. Nature provides some hints towards the…
Supported Lipid Bilayers (SLBs) are model membranes formed at solid substrate surfaces. This architecture renders the membrane experimentally accessible to surface sensitive techniques used to study their properties, including Atomic Force…
We investigate the maximal solid tubes around short simple geodesics in hyperbolic three-manifolds and how complex length of curves relate to closed, incompressible, least area minimal surfaces. As applications, we prove, there are some…
In this paper, a new class of optical fibers is studied, i.e. microstructured fibers or photonic crystal fibers (PCF). The main objective is to characterize these fibers using different dispersion diagrams and present an interface that…