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We consider the number of configurations of a surface in two dimensions that has a prescribed length and encloses a prescribed perimeter with respect to a baseline. An approximate analytical treatment in a semi--continuum compares…
Hypothesis: Slippery Omniphobic Covalently Attached Liquids (SOCAL) have been proposed for making omnirepellent thin films of self-assembled dimethylsiloxane polymer brushes grafted from silica surfaces. Smooth and flat at very small scale,…
Generic polyhedra are interesting mathematical objects to study in their own right. In this paper, we initialize a systematic study of two-dimensional generic polyhedra with an eye towards applications to low-dimensional topology,…
The microstructure, electronic structure, and chemical bonding of chromium carbide thin films with different carbon contents have been investigated with high-resolution transmission electron microscopy, electron energy loss spectroscopy and…
An electrokinetic (zeta) potential of charged permeable porous films on solid supports generally exceeds their surface potential, which often builds up to a quite high value itself. Recent work provided a quantitative understanding of zeta…
Interfaces are a most common motif in complex systems. To understand how the presence of interfaces affect hydrophobic phenomena, we use molecular simulations and theory to study hydration of solutes at interfaces. The solutes range in size…
Environmental fate and toxicity of microplastic particles is dominated by their surface properties. In the environment an adsorbed layer of biomolecules and natural organic matter forms the so-called eco-corona. A quantitative description…
The properties of polymeric nanofibers can be tailored and enhanced by properly managing the structure of the polymeric molecules at the nanoscale. Although electrospun polymer fibers are increasingly exploited in many technological…
The bending rigidity $k_c$ of bilayer vesicles self-assembled from amphiphilic diblock copolymers has been measured using single and dual-micropipet techniques. These copolymers are nearly a factor of 5 greater in hydrophobic membrane…
Associated with isoparametric foliations of unit spheres, there are two classes of minimal surfaces $-$ minimal isoparametric hypersurfaces and focal submanifolds. By virtue of their rich structures, we find new series of minimizing cones.…
Several bacteria and bacteria strands form biofilms in different environmental conditions, e.g. pH, temperature, nutrients, etc. Biofilm growth, therefore, is an extremely robust process. Because of this, while biofilm growth is a complex…
In this paper, we develop a general mathematical framework for enhanced hydrodynamic near-cloaking of electro-osmotic flow for more complex shapes, which is obtained by simultaneously perturbing the inner and outer boundaries of the perfect…
The adsorption of a collagen fragment on both a hydrophobic, hydrogen-terminated and a hydrophilic, natively oxidised Si surface is investigated using all-atom molecular dynamics. While favourable direct protein-surface interactions via…
Biofilms, bacteria cells surrounded by a self-produced polymeric matrix, are common on medical devices and lead to many hospital infections. The biofilm lifecycle includes disassembly and dispersion, where bacteria clusters detach from the…
We investigate the existence of minimal hypersurfaces in $\mathbb{S}^{n+1}$ that are generated by the isoparametric foliation of a subsphere $\mathbb{S}^n$. By considering a generalized rotational ansatz formed by the union of homothetic…
A suspension of nanoparticles with very low volume fraction is found to assemble into a macroscopic cellular phase under the collective influence of AC and DC voltages. Systematic study of this phase transition shows that it was the result…
Insects like dragonflies and cicadas possess nanoprotusions on their wings that rupture bacterial membranes upon contact, inspiring synthetic antibacterial surfaces mimicking this phenomenon. Designing such biomimetic surfaces requires…
We propose a general parametrizable model to capture the dynamic interaction among bacteria in the formation of micro-colonies. micro-colonies represent the first social step towards the formation of structured multicellular communities…
We study the topology of small covers from their fundamental groups. We find a way to obtain explicit presentations of the fundamental group of a small cover. Then we use these presentations to study the relations between the fundamental…
Functionality of living cells is inherently linked to subunits with dimensions on the nanoscale. In case of osteoblasts the cell surface plays a particularly important role for adhesion and spreading which are crucial properties with regard…