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Let F be a codimension-one, C^2-foliation on a manifold M without boundary. In this work we show that if the Godbillon--Vey class GV(F) \in H^3(M) is non-zero, then F has a hyperbolic resilient leaf. Our approach is based on methods of…
Normal incidence ion irradiation at elevated temperatures, when amorphization is prevented, induces novel nanoscale patterns of crystalline structures on elemental semiconductors by a reverse epitaxial growth mechanism: on Ge surfaces…
An atomic-scale study utilizing scanning tunneling microscopy (STM) in ultrahigh vacuum (UHV) is performed on large single crystalline graphene grains synthesized on Cu foil by a chemical vapor deposition (CVD) method. After thermal…
We have used Ultrahigh Vacuum (UHV) Scanning tunneling microscopy (STM) to investigate the effect of thermal annealing of graphene grown by chemical vapour deposition (CVD) on a Cu(110) foil. We show that the annealing appears to induce a…
This short note modifies a reconstruction method by the author (Comm. PDE, 45(9):1118-1133, 2020), for reconstructing piecewise constant conductivities in the Calder\'on problem (electrical impedance tomography). In the former paper, a…
We give a new construction of the measure of maximal entropy for transitive Anosov flows through a method analogous to the construction of Patterson-Sullivan measures in negative curvature. In order to carry out our procedure we prove…
The purpose of this paper is to present a ``Cech-De Rham'' model for the cohomology of leaf spaces. This model lends itself to the construction of characteristic classes (in the cohomology of classifying spaces) by explicit geometrical…
An extension of the Burton-Cabrera-Frank model [Phil. Trans. R. Soc. London, Ser. A 243, 299 (1951)] including diffusion along steps and entropic step-step interaction is introduced. This extended model is successfully applied to simulate…
Uniform, mostly single-layer graphene with enhanced stability is demonstrated over Co film. The polycrystalline Co film deposited on a SiO2/Si substrate gives a continuous graphene layer that is easily transferred without the aid of any…
We provide a data structure for maintaining an embedding of a graph on a surface (represented combinatorially by a permutation of edges around each vertex) and computing generators of the fundamental group of the surface, in amortized time…
We reprove the $\lambda$-Lemma for finite dimensional gradient flows by generalizing the well-known contraction method proof of the local (un)stable manifold theorem. This only relies on the forward Cauchy problem. We obtain a rather…
We prove a rigidity property for mapping tori associated to minimal topological dynamical systems using tools from noncommutative geometry. More precisely, we show that under mild geometric assumptions, an orientation-preserving leafwise…
Refraction, traditionally viewed as a geometric event occurring at material interfaces, is now being re-examined through the lens of coherence. Recent studies in optics and photonics, including coherence tomography, Moire interference, and…
Graphite surfaces can be manipulated by several methods to create graphene structures of different shapes and sizes. Scanning tunneling microscopy (STM) can be used to create these structures either through mechanical contact between the…
We investigate two and three-dimensional shell-structured-inflatable froths, which can be constructed by a recursion procedure adding successive layers of cells around a germ cell. We prove that any froth can be reduced into a system of…
Suppose that $\mathcal F$ is a transversely oriented, codimension one foliation of a connected, closed, oriented 3-manifold. Suppose also that $\mathcal F$ has continuous tangent plane field and is {\sl taut}; that is, closed smooth…
We study the quasiclassical expansion associated with a complex curve. In a more specific context this is the 1/N expansion in U(N)-invariant matrix integrals. We compare two approaches, the CFT approach and the topological recursion, and…
We introduce a novel technique to generate Benders' cuts from a conic relaxation ("corner") derived from a basis of a higher-dimensional polyhedron that we aim to outer approximate in a lower-dimensional space. To generate facet-defining…
This paper provides a unified framework connecting dynamical systems with tools from topological data analysis and geometric topology and inspires new interactions among dynamical systems, topology, and nonlinear analysis. To this end, we…
We propose an innovative, easy-to-implement approach to synthesize large-area singlecrystalline graphene sheets by chemical vapor deposition on copper foil. This method doubly takes advantage of residual oxygen present in the gas phase.…