Related papers: The three-dimensional statistical characterization…
We report on measurements of the local friction law at a multi-contact interface formed between a smooth rubber and statistically rough glass lenses, under steady state friction. Using contact imaging, surface displacements are measured,…
We study the fracture surface of three dimensional samples through a model for quasi-static fractures known as Born Model. We find for the roughness exponent a value of 0.5 expected for ``small length scales'' in microfracturing…
We define a class a metric spaces we call Brownian surfaces, arising as the scaling limits of random maps on general orientable surfaces with a boundary and we study the geodesics from a uniformly chosen random point. These metric spaces…
In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…
The notions of discrete conformality on triangle meshes have rich mathematical theories and wide applications. The related notions of discrete uniformizations on triangle meshes, suggest efficient methods for computing the uniformizations…
We study singularities and geometric properties of surfaces given by the singular loci of normal congruence of frontals with pure-frontal singular points. These surfaces consist of the normal ruled surface and focal surfaces of the initial…
This paper deals with finding surfaces in $\mathbb{R}^3$ which are as close as possible to being flat and span a given contour such that the contour is a geodesic on the sought surface. We look for a surface which minimizes the total…
A novel full-field surface profilometer using diffractive-based chromatic confocal microscopy and area-scan spectral sensing is developed. A normalized cross correlation algorithm was developed to establish a spectrum-depth response curve.…
We elucidate the geometric background of function-theoretic properties for the Gauss maps of several classes of immersed surfaces in three-dimensional space forms, for example, minimal surfaces in Euclidean three-space, improper affine…
Microscopic fringe projection profilometry is a powerful 3D measurement technique with a theoretical measurement accuracy better than one micron provided that the measured targets can be imaged with good fringe visibility. However,…
A marginally outer trapped hypersurface is a generalization of minimal hypersurfaces originated from general relativity. We show a curvature estimate for stable marginally outer trapped hypersurfaces up to the free boundary satisfying a…
We demonstrate a technique that allows highly surface sensitive imaging of nanostructures on planar surfaces over large areas, providing a new avenue for research in materials science, especially for \textit{in situ} applications. The…
The load-area relation of rough surfaces is of great interest in tribology. For elastic-plastic solids with strain hardening, an incremental model is adopted to analyze the contact of rough surfaces, in which the contact is modeled by…
Hypothesis Understanding wetting behavior is of great importance for natural systems and technological applications. The traditional concept of contact angle, a purely geometrical measure related to curvature, is often used for…
The paper studies 'good arrangements' (transversality properties) of collections of sets in a normed vector space near a given point in their intersection. We target primal (metric and slope) characterizations of transversality properties…
Providing dry solid contacts with on-demand macroscale frictional behaviour remains a formidable challenge in tribology, haptics or robotics. Metainterfaces created from surfaces with engineered asperity-based topographies can achieve such…
Developing effective descriptions of the microscopic dynamics of many physical phenomena can both dramatically enhance their computational exploration and lead to a more fundamental understanding of the underlying physics. Previously, an…
In this paper, we propose to employ a Gaussian map representation to estimate precise location and count of 3D surface features, addressing the limitations of state-of-the-art methods based on density estimation which struggle in presence…
We give a relationship that yields an effective geometric way of evaluating mean curvature of surfaces. The approach is reminiscent of the Gauss's contour based evaluation of intrinsic curvature. The presented formula may have a number of…
We study a random fiber bundle model with tips of the fibers placed on a graph having co-ordination number 3. These fibers follow local load sharing with uniformly distributed threshold strengths of the fibers. We have studied the critical…