Related papers: Realistic pattern formations on surfaces by adding…
The eigenvalue problem of the Laplace-Beltrami operators on curved surfaces plays an essential role in the convergence analysis of the numerical simulations of some important geometric partial differential equations which involve this…
A random surface scattering in a one-mode waveguide is studied in the case when the surface profile has long-range correlations along the waveguide. Analytical treatment of this problem shows that with a proper choice of the surface, one…
Optical surface waves, highly localized modes bound to the surface of media, enable manipulation of light at nanoscale, thus impacting a wide range of areas in nanoscience. By applying metamaterials, artificially designed optical materials,…
In this work we explore the influence of random surface roughness on the cantilever sensitivity to respond to curvature changes induced by changes in surface stress. The roughness is characterized by the out-of-plane roughness amplitude w,…
We study the lubricated contact of sliding soft surfaces that are locally patterned but globally cylindrical, held together under an external normal force. The local patterns represent either naturally occurring surface roughness or…
Patterns on curved surfaces are ubiquitous, yet the influence of surface geometry on pattern dynamics remains elusive. We recently reported a new mechanism of pattern propagation in which a static pattern on a flat plane becomes a…
We construct algebraic surfaces with a large number of type A singularities. Bivariate polynomials presented in previous works for the construction of nodal surfaces and certain families of Belyi polynomials are used. In some cases explicit…
Moir\'e patterns, typically formed by overlaying two layers of two-dimensional materials, exhibit an effective long-range periodicity that depends on the short-range periodicity of each layer and their spatial misalignment. Here, we study…
The Laplace-Beltrami operator on (the surface of) a triaxial ellipsoid admits a sequence of real eigenvalues diverging to plus infinity. By introducing ellipsoidal coordinates, this eigenvalue problem for a partial differential operator is…
We consider pattern formation in periodically forced binary systems. In particular we focus on systems in which the two species are differentially forced, one being accelerated with respect to the other. Using a continuum model consisting…
Despite the growing demand for accurate surface normal estimation models, existing methods use general-purpose dense prediction models, adopting the same inductive biases as other tasks. In this paper, we discuss the inductive biases needed…
We investigate the statistical evidence for the use of `rough' fractional processes with Hurst exponent $H< 0.5$ for the modeling of volatility of financial assets, using a model-free approach. We introduce a non-parametric method for…
The scaling properties of the roughness of surfaces grown by two different processes randomly alternating in time, are addressed. The duration of each application of the two primary processes is assumed to be independently drawn from given…
The ability to create surface structures with precisely controlled chirality remains a major challenge in laser-matter interaction experiments. In this work, we theoretically study the interaction of vortex laser beams, characterized by…
Repetitive patterns are ubiquitous in natural and human-made objects, and can be created with a variety of tools and methods. Manual authoring provides unmatched degree of freedom and control, but can require significant artistic expertise…
Using polarization measurements in remote sensing and optical studies allows retrieving more information. We consider relationship between the reflection coefficients of plane and rough surfaces for linearly polarized waves. Certain…
We present an approach to robustly track the geometry of an object that deforms over time from a set of input point clouds captured from a single viewpoint. The deformations we consider are caused by applying forces to known locations on…
In the rough phase, the width of interfaces separating different phases of statistical systems increases logarithmically with the system size. This phenomenon is commonly described in terms of the capillary wave model, which deals with…
We introduce an arbitrary order, computationally efficient method to smooth corners on curves in the plane, as well as edges and vertices on surfaces in $\mathbb R^3$. The method is local, only modifying the original surface in a…
Conventional dynamic atomic force microscopy (AFM) can be extended to bimodal and multimodal AFM in which the cantilever is simultaneously excited at two ore more resonance frequencies. Such excitation schemes result in one additional…