Related papers: Is there an Optimal Substrate Geometry for Wetting…
The sliced Wasserstein metric compares probability measures on $\mathbb{R}^d$ by taking averages of the Wasserstein distances between projections of the measures to lines. The distance has found a range of applications in statistics and…
The superhydrophobic leaves of a lotus plant and other natural surfaces with self-cleaning function have been studied intensively for the development of artificial biomimetic surfaces. Surface roughness generated by hierarchical structures…
The implementation of boundary conditions is among the most challenging parts of modeling fluid flow through channels and complex media. Here, we show that the existing methods to deal with liquid-wall interactions using multicomponent…
We study the geometry of the Thurston metric on the Teichm\"uller space $\mathcal{T}(S)$ of hyperbolic structures on a surface $S$. Some of our results on the coarse geometry of this metric apply to arbitrary surfaces $S$ of finite type;…
Consider the classical $(2+1)$-dimensional Solid-On-Solid model above a hard wall on an $L\times L$ box of $\bbZ^2$. The model describes a crystal surface by assigning a non-negative integer height $\eta_x$ to each site $x$ in the box and 0…
We consider the local theory of constant mean curvature surfaces that satisfy one or two integrable boundary conditions and determine the corresponding potentials for the generalized Weierstrass representation.
The optimal exponentials of the thickness in the geometry rigidity inequality of shells represent the geometry rigidity of the shells. We obtain that the lower bounds of the optimal exponentials are $4/3,$ $3/2,$ and $1,$ for the hyperbolic…
We present in this Letter a free-energy approach to the dynamics of a fluid near a nanostructured surface. The model accounts both for the static phase equilibrium in the vicinity of the surface (wetting angles, Cassie-Wenzel transition)…
This work constructs Jonson-Lindenstrauss embeddings with best accuracy, as measured by variance, mean-squared error and exponential concentration of the length distortion. Lower bounds for any data and embedding dimensions are determined,…
For over 200 years, wettability has made significant contributions to understanding the properties of objects, advancing technological progress. Theoretical model of the contact angle (CA) for evaluating wettability has constantly been…
Various recent experiments hint at a geometry dependence of scaling relations in Rayleigh-B\'enard convection. Aspect ratio and shape dependences have been found. In this paper a mechanism is offered which can account for such dependences.…
A type of super-hydrophobic surface consists of a solid plane boundary with an array of grooves which, due to the effect of surface tension, prevent a complete wetting of the wall. The effect is greatest when the grooves are aligned with…
This paper investigates the geometric inverse problem of recovering the bottom shape from surface measurements of water waves. Using the general water-waves system on a bounded subdomain of the fluid domain, we address this inverse problem,…
A partially-wetting liquid can deform the underlying elastic substrate upon which it rests. This situation requires the development of theoretical models to describe the wetting forces imparted by the drop onto the solid substrate,…
We propose a simplified description of fluid adsorption on heterogenenous micropatterned substrates. Using this approach, we are able to rederive results obtained earlier using effective interfacial Hamiltonian methods and predict a number…
Length spectral rigidity is the question of under what circumstances the geometry of a surface can be determined, up to isotopy, by knowing only the lengths of its closed geodesics. It is known that this can be done for negatively curved…
We study the influence of the surface orientation on the wetting behavior of bcc binary alloys, using a semi-infinite lattice model equivalent to a nearest-neighbor Ising antiferromagnet in an external field. The salient feature of the…
We use a conformal mapping method introduced in a companion paper to study the properties of bi-harmonic fields in the vicinity of rough boundaries. We focus our analysis on two different situations where such bi-harmonic problems are…
We consider two stacked ultra-thin layers of different liquids on a solid substrate. Using long-wave theory, we derive coupled evolution equations for the free liquid-liquid and liquid-gas interfaces. Linear and non-linear analyses show…
We present a projector quantum Monte Carlo study of the topological properties of the valence-bond-solid ground state in the $J$-$Q_3$ spin model on the square lattice. The winding number is a topological number counting the number of…