Related papers: Conformal Invariance of Graphene Sheets
We study the local and global roughness scaling in growth models with grains at the film surfaces. The local roughness, measured as a function of window size r, shows a crossover at a characteristic length r_c, from a rapid increase with…
Geometric stress focusing, e.g. in a crumpled sheet, creates point-like vertices that terminate in a characteristic local crescent shape. The observed scaling of the size of this crescent is an open question in the stress focusing of…
In this paper, we deals with isoperimetric-type inequalities for closed convex curves in the Euclidean plane R^2. We derive a family of parametric inequalities involving the following geometric functionals associated to a given convex curve…
Spontaneous intervalley coherence is suspected in several different graphene multilayer systems, but is difficult to confirm because of a paucity of convenient experimental signatures. Here we suggest that magneto-conductance features…
In this paper, we investigate the geometric invariant properties of a normal curve on a smooth immersed surface under conformal transformation. We obtain an invariant-sufficient condition for the conformal image of a normal curve. We also…
We develop a new approach to the conformal geometry of embedded hypersurfaces by treating them as conformal infinities of conformally compact manifolds. This involves the Loewner--Nirenberg-type problem of finding on the interior a metric…
Graphene monolayers supported on oxide substrates have been demonstrated with superior charge mobility and thermal transport for potential device applications. Morphological corrugation can strongly influence the transport properties of the…
We propose, on the basis of our first principles density functional based calculations, a new isomer of graphane, in which the C-H bonds of a hexagon alternate in 3-up, 3-down fashion on either side of the sheet. This 2D puckered structure…
A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is carried out to identify the conditions for stability of a granular gas of rough hard spheres. The description is based on the results…
Surface roughness becomes relevant if typical length scales of the system are comparable to the scale of the variations as it is the case in microfluidic setups. Here, an apparent boundary slip is often detected which can have its origin in…
Interactions among electrons can give rise to striking collective phenomena when the kinetic energy of charge carriers is suppressed. One example is the fractional quantum Hall effect, in which correlations between electrons moving in two…
The surfaces of growing biological tissues, swelling gels, and compressed rubbers do not remain smooth, but frequently exhibit highly localized inward folds. We reveal the morphology of this surface folding in a novel experimental setup,…
We investigate a minimal model of the plastic deformation of amorphous materials. The material elements are assumed to exhibit ideally plastic behavior (J2 plasticity). Structural disorder is considered in terms of random variations of the…
A stochastic nonlinear electrical characteristic of graphene is reported. Abrupt current changes are observed from voltage sweeps between the source and drain with an on/off ratio up to 10^(3). It is found that graphene channel experience…
Recent Herschel observations have confirmed that filaments are ubiquitous in molecular clouds and suggest that irrespectively of the column density, there is a characteristic width of about 0.1 pc whose physical origin remains unclear. We…
The structural properties of graphs are usually characterized in terms of invariants, which are functions of graphs that do not depend on the labeling of the nodes. In this paper we study convex graph invariants, which are graph invariants…
There exist three conformers of hydrogenated graphene, referred to as chair-, boat-, or washboard-graphane. These systems have a perfect two-dimensional periodicity mapped onto the graphene scaffold, but they are characterized by a $sp^3$…
In this work, we study various properties of embedded hypersurfaces in $1+1+2$ decomposed spacetimes with a preferred spatial direction, denoted $e^{\mu}$, which are orthogonal to the fluid flow velocity of the spacetime and admit a proper…
Many examples of natural systems can be described by random Gaussian surfaces. Much can be learned by analyzing the Fourier expansion of the surfaces, from which it is possible to determine the corresponding Hurst exponent and consequently…
We present a detailed transmission electron microscopy and electron diffraction study of the thinnest possible membrane, a single layer of carbon atoms suspended in vacuum and attached only at its edges. Membranes consisting of two graphene…