Related papers: Conformal Invariance of Graphene Sheets
It has recently been demonstrated that difference frequency mixing (DFM) can generate surface plasmons in graphene [1]. Here, we present detailed calculations comparing the contributions to this effect from substrate and from graphene…
Equilibrium and non-equilibrium growth phenomena, e.g., surface growth, generically yields self-affine distributions. Analysis of statistical properties of these distributions appears essential in understanding statistical mechanics of…
The inertial subrange of turbulent scales is commonly reflected by a power law signature in ensemble statistics such as the energy spectrum and structure functions - both in theory and from observations. Despite promising findings on the…
The scaling properties of post-mortem fracture surfaces of brittle (silica glass), ductile (aluminum alloy) and quasi-brittle (mortar and wood) materials have been investigated. These surfaces, studied far from the initiation, were shown to…
We analyze experimentally the behavior of a non-Brownian, iso-dense suspension of spheres submitted to periodic square wave oscillations of the flow in a Hele-Shaw cell of gap $H$. We do observe an instability of the initially homogeneous…
Interfacial phenomena associated with fluid adsorption in two dimensional systems has recently been shown to exhibit hidden symmetries, or covariances, which precisely relate local adsorption properties in different confining geometries. We…
We note that in a system far from equilibrium the interface roughening may depend on the system size which plays the role of control parameter. To detect the size effect on the interface roughness, we study the scaling properties of rough…
A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…
We characterize the carrier density profile of the ground state of graphene in the presence of particle-particle interaction and random charged impurity for zero gate voltage. We provide detailed analysis on the resulting spatially…
The electrical properties of graphene depend sensitively on the substrate. For example, recent measurements of epitaxial graphene on SiC show resistance arising from steps on the substrate. Here we calculate the deformation of graphene at…
We consider the multi-time correlation and covariance structure of a random surface growth with a wall introduced in arXiv:0904.2607. It is shown that the correlation functions associated with the model along space-like paths have…
We handshake statistical mechanics with continuum mechanics to develop a methodology for consistent evaluation of the continuum scale properties of graphene. The scope is kept limited to elastic modulus, $E$, which has been reported to vary…
In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…
We formulate a nonlinear continuum model of a graphene sheet supported by a flat rigid substrate. The sheet is parallel to the substrate and loaded on a pair of opposite edges. A typical cross-section of the sheet is modeled as an elastica.…
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…
Flows of granular media down a rough inclined plane demonstrate a number of nonlocal phenomena. We apply the recently proposed nonlocal granular fluidity model to this geometry and find that the model captures many of these effects.…
The geometry of two-dimensional crystalline membranes dictates their mechanical, electronic and chemical properties. The local geometry of a surface is determined from the two invariants of the metric and the curvature tensors. Here we…
The amount of rippling in graphene sheets is related to the interactions with the substrate or with the suspending structure. Here, we report on an irreversibility in the response to forces that act on suspended graphene sheets. This may…
The roughness properties of two-dimensional fracture surfaces as created by the slow failure of random fuse networks are considered and compared to yield surfaces of perfect plasticity with similar disorder. By studying systems up to a…
Stylolites are natural pressure-dissolution surfaces in sedimentary rocks. We present 3D high resolution measurements at laboratory scales of their complex roughness. The topography is shown to be described by a self-affine scaling…