Publication
How roughness emerges on natural and engineered surfaces
Abstract
Roughness, defined as unevenness of material surfaces, plays an important role in determining how engineering components or natural objects interact with other bodies and their environment. The emergence of fractal roughness on natural and engineered surfaces across a range of length scales suggests the existence of common processes and mechanisms for nucleation and evolution of roughness. In this article, we review recent advances in understanding the origins of roughness and topography evolution on natural and engineered surfaces and their connection with subsurface deformation mechanisms. Directions for future research toward understanding the origins of roughness on solid surfaces are discussed.
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Related concepts (33)
Connection form
In mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms. Historically, connection forms were introduced by Élie Cartan in the first half of the 20th century as part of, and one of the principal motivations for, his method of moving frames. The connection form generally depends on a choice of a coordinate frame, and so is not a tensorial object.
Connection (principal bundle)
In mathematics, and especially differential geometry and gauge theory, a connection is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. A principal G-connection on a principal G-bundle P over a smooth manifold M is a particular type of connection which is compatible with the action of the group G. A principal connection can be viewed as a special case of the notion of an Ehresmann connection, and is sometimes called a principal Ehresmann connection.
Connection (mathematics)
In geometry, the notion of a connection makes precise the idea of transporting local geometric objects, such as tangent vectors or tensors in the tangent space, along a curve or family of curves in a parallel and consistent manner. There are various kinds of connections in modern geometry, depending on what sort of data one wants to transport. For instance, an affine connection, the most elementary type of connection, gives a means for parallel transport of tangent vectors on a manifold from one point to another along a curve.
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