Related papers: Is there an Optimal Substrate Geometry for Wetting…
A statistical analysis of the wall roughness effect is carried out to determine the impact of the shape uncertainty on the Poiseuille number and Nusselt number of laminar forced convection. The focus is on the fully developed regime in a…
As a first step towards a microscopic understanding of the effective interaction between colloidal particles suspended in a solvent we study the wetting behavior of one-component fluids at spheres and fibers. We describe these phenomena…
Superomniphobic textures are at the frontier of surface design for vast arrays of applications. Despite recent significant advances in fabrication methods for reentrant and doubly reentrant microstructures, design optimisation remains a…
A liquid in contact with a textured surface can be found in two states, Wenzel and Cassie. In the Wenzel state the liquid completely wets the corrugations while in the Cassie state the liquid is suspended over the corrugations with air or…
In recent years, new methods have been developed to synthesize complex porous and micro-structured geometry in a variety of ways. In this work, we take these approaches one step further and present these methods as an efficacious design…
A basic feature of Teichm\"uller theory of Riemann surfaces is the interplay of two dimensional hyperbolic geometry, the behavior of geodesic-length functions and Weil-Petersson geometry. Let $\mathcal{T}_g$ $(g\geq 2)$ be the Teichm\"uller…
This work focuses on the numerical modelling of confined concretes when subjected to multiaxial loading accounting for a nonlinear material response. Particularly, an improved return mapping procedure is here presented to cope with the…
We investigate a mathematical theory for the erosion of sediment which begins with the study of a non-linear, parabolic, weighted 4-Laplace equation on a rectangular domain corresponding to a base segment of an extended landscape. Imposing…
We study the solid-on-solid interface model above a horizontal wall in three dimensional space, with an attractive interaction when the interface is in contact with the wall, at low temperatures. The system presents a sequence of layering…
We consider curves which go around Whitney umbrella. Then we consider the geodesic and the normal curvatures, ruled surfaces generated by the normal vector and normal developable surfaces with respect to the tangent and bi-tangent vectors…
Recent studies of elasto-capillary phenomena have triggered interest in a basic variant of the classical Young-Laplace-Dupr\'e (YLD) problem: The capillary interaction between a liquid drop and a thin solid sheet of low bending stiffness.…
In this article, we derive a mathematical model for a shell (i.e. a thin elastic body) bonded to an elastic foundation by modifying Koiter's linear shell equations. We prove the existence and the uniqueness of solutions, and we explicitly…
We investigate through numerical simulations of the Navier-Stokes equations the influence of the surface roughness on the fluid flow through fracture joints. Using the Hurst exponent $H$ to characterize the roughness of the self-affine…
Geometry plays a fundamental role in a wide range of physical responses, from anomalous transport coefficients to their related sum rules. Notable examples include the quantization of the Hall conductivity and the Souza-Wilkens-Martin (SWM)…
Superantiwettability, including superhydrophobicity, is an enhanced effect of surface ruggedness via the Cassie-Baxter wetting state, and has many applications such as antifouling, drop manipulation, and self-cleaning. However,…
We report measurements of the hydrodynamic drag force acting on a smooth sphere falling down under gravity to a plane decorated with microscopic periodic grooves. Both surfaces are lyophilic, so that a liquid (silicone oil) invades the…
Based on a microscopic density functional theory we investigate the morphology of thin liquidlike wetting films adsorbed on substrates endowed with well-defined chemical heterogeneities. As paradigmatic cases we focus on a single chemical…
In this paper, we are interested in shape optimization problems involving the ge ometry (normal, curvatures) of the surfaces. We consider a class of hypersurface s in $\mathbb{R}^{n}$ satisfying a uniform ball condition and we prove the…
We derive constraints on the existence of walls for Bridgeland stability conditions for general projective surfaces. We show that in suitable planes of stability conditions the walls are bounded and derive conditions for when the number of…
The main goal of this paper is to present a series of inequalities connecting the surface area measure of a convex body and surface area measure of its projections and sections. We present a solution of a question from S. Campi, P.…