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We present a unique experimental configuration that allows us to determine the interfacial forces on nearly parallel plates made from the thinnest possible mechanical structures, single and few layer graphene membranes. Our approach…
We study rigidity problems for Riemannian and semi-Riemannian manifolds with metrics of low regularity. Specifically, we prove a version of the Cheeger-Gromoll splitting theorem \cite{CheegerGromoll72splitting} for Riemannian metrics and…
Surface roughness plays a crucial role in the accuracy of indentation experiments used to measure the elastic properties of materials. In this study, we present a computational analysis of how surface roughness, represented explicitly by…
Starting from Enskog equation of hard spheres of mass m and diameter D under the gravity g, we first derive the exact equation of motion for the equilibrium density profile at a temperature T and examine its solutions via the gradient…
We prove a rigidity result in the sphere which allows us to generalize a result about smooth convex hypersurfaces in the sphere by Do Carmo-Warner to convex $C^2$-hypersurfaces. We apply these results to prove $C^{1,\beta}$-convergence of…
Suspended graphene sheets exhibit correlated random deformations that can be studied under the framework of rough surfaces with a Hurst (roughness) exponent $0.72 \pm 0.01$. Here, we show that, independent of the temperature, the iso-height…
The surface stability of two interacting (for example, by van der Waals forces) incompressible thin films, one bonded to a substrate and the other to a contactor, is studied extending the work of Shenoy and Sharma, Physical Review Letters…
We prove stability estimates for the Brunn-Minkowski inequality for convex sets. Unlike existing stability results, our estimates improve as the dimension grows. Our results are equivalent to a thin shell bound, which is one of the central…
We study theoretically and numerically the elastic properties of hard sphere glasses, and provide a real-space description of their mechanical stability. In contrast to repulsive particles at zero-temperature, we argue that the presence of…
This paper is devoted to rigidity results for some elliptic PDEs and related interpolation inequalities of Sobolev type on smooth compact connected Riemannian manifolds without boundaries. Rigidity means that the PDE has no other solution…
The known ground state of ultrathin smectic films confined to the surface of a sphere is described by four +1/2 defects assembled on a great circle and a director which follows geodesic lines. Using a simple perturbative approach we show…
Let $F$ be a Bedford-McMullen carpet defined by independent exponents. We prove that $\overline{\dim}_B (\ell \cap F) \leq \max \lbrace \dim^* F -1,0 \rbrace$ for all lines $\ell$ not parallel to the principal axes, where $\dim^*$ is…
A method of modifying the roughness of soda-lime glass spheres is presented, with the purpose of tuning inter-particle friction. The effect of chemical etching on the surface topography and the bulk frictional properties of grains is…
We present a physical model for turbulent friction on rough surfaces with regularly distributed roughness elements. Wall shear stresses are expressed as functions of physical quantities. Surfaces with varying roughness densities and…
Surface roughness is a key factor when it comes to friction and wear, as well as to other physical properties. These phenomena are controlled by mechanisms acting at small scales, in which the topography of apparently-flat surfaces is…
Triangular lattice models for pattern formation by hard-core soft-shell particles at interfaces are introduced and studied in order to determine the effect of the shell thickness and structure. In model I, we consider particles with…
Monte Carlo simulations are employed to investigate the surface growth generated by deposition of particles of different sizes on a substrate, in one and two dimensions. The particles have a linear form, and occupy an integer number of…
We consider shells in three dimensional Euclidean space which have bounded principal curvatures. We prove Korn's interpolation (or the so called first and a half\footnote{The inequality first introduced in [6]}) and second inequalities on…
Normal contact behaviour between non adhesive fractal rough particles is studied using a finite element method (FEM). A series of spherical grain surfaces with distinguished roughness features are generated by means of Spherical Harmonics.…
We study the structure of thick discs in extraordinary depth by reaching a surface brightness limit of $\mu_{r_{\rm deep}} \sim$28.5$-$29~mag arcsec$^{-2}$ with combined $g$,$r$,$i$ band images from the IAC Stripe 82 Legacy Project. We…