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The Snowball Earth hypothesis proposes that during one or more of Earth's icehouse climates, Earth's surface became entirely or nearly entirely frozen, sometime earlier than 650 Mya during the Cryogenian period. Proponents of the hypothesis argue that it best explains sedimentary deposits generally regarded as of glacial origin at tropical palaeolatitudes and other enigmatic features in the geological record. Opponents of the hypothesis contest the implications of the geological evidence for global glaciation and the geophysical feasibility of an ice- or slush-covered ocean and emphasize the difficulty of escaping an all-frozen condition. A number of unanswered questions remain, including whether the Earth was a full snowball, or a "slushball" with a thin equatorial band of open water.
A rotation is a circular movement of an object around a center of rotation. The geometric plane along which the rotation occurs is called the rotation plane, and the imaginary line extending from the center and perpendicular to the rotation plane is called the rotation axis. A three-dimensional object can always be rotated about an infinite number of rotation axes.
A drumlin, from the Irish word droimnín, first recorded in 1833, in the classical sense is an elongated hill in the shape of an inverted spoon or half-buried egg formed by glacial ice acting on underlying unconsolidated till or ground moraine. Clusters of drumlins create a landscape which is often described as having a 'basket of eggs topography'.
Sedimentary rocks are types of rock that are formed by the accumulation or deposition of mineral or organic particles at the Earth's surface, followed by cementation. Sedimentation is the collective name for processes that cause these particles to settle in place. The particles that form a sedimentary rock are called sediment, and may be composed of geological detritus (minerals) or biological detritus. The geological detritus originated from weathering and erosion of existing rocks, or from the solidification of molten lava blobs erupted by volcanoes. The geological detritus is transported to the place of deposition by water, wind, ice or mass movement, which are called agents of denudation. Biological detritus was formed by bodies and parts of dead aquatic organisms, as well as their fecal mass, suspended in water and slowly piling up on the floor of water bodies. Sedimentation may also occur as dissolved minerals precipitate from water solution.
The principal components of a collection of points in a real p-space are a sequence of direction vectors, where the vector is the direction of a line that best fits the data while being orthogonal to the first vectors. Here, a best-fitting line is defined as one that minimizes the average squared distance from the points to the line. These directions constitute an orthonormal basis in which different individual dimensions of the data are linearly uncorrelated. Principal component analysis (PCA) is the process of computing the principal components and using them to perform a change of basis on the data, sometimes using only the first few principal components and ignoring the rest.
In numerical analysis, one of the most important problems is designing efficient and stable algorithms for finding the eigenvalues of a matrix. These eigenvalue algorithms may also find eigenvectors.
In numerical analysis, inverse iteration is an iterative eigenvalue algorithm. It allows one to find an approximate eigenvector when an approximation to a corresponding eigenvalue is already known. The method is conceptually similar to the power method. It appears to have originally been developed to compute resonance frequencies in the field of structural mechanics.
In neuroscience, tractography is a 3D modeling technique used to visually represent nerve tracts using data collected by diffusion MRI. It uses special techniques of magnetic resonance imaging (MRI) and computer-based diffusion MRI. The results are presented in two- and three-dimensional images called tractograms.
Conglomerate is a clastic sedimentary rock that is composed of a substantial fraction of rounded to subangular gravel-size clasts. A conglomerate typically contain a matrix of finer grained sediments, such as sand, silt, or clay, which fills the interstices between the clasts. The clasts and matrix are typically cemented by calcium carbonate, iron oxide, silica, or hardened clay.
The Rössler attractor is the attractor for the Rössler system, a system of three non-linear ordinary differential equations originally studied by Otto Rössler. These differential equations define a continuous-time dynamical system that exhibits chaotic dynamics associated with the fractal properties of the attractor.
In differential geometry, the two principal curvatures at a given point of a surface are the eigenvalues of the shape operator at the point. They measure how the surface bends by different amounts in different directions at that point.
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by , is the factor by which the eigenvector is scaled.
Diffusion-weighted magnetic resonance imaging is the use of specific MRI sequences as well as software that generates images from the resulting data that uses the diffusion of water molecules to generate contrast in MR images. It allows the mapping of the diffusion process of molecules, mainly water, in biological tissues, in vivo and non-invasively. Molecular diffusion in tissues is not free, but reflects interactions with many obstacles, such as macromolecules, fibers, and membranes. Water molecule diffusion patterns can therefore reveal microscopic details about tissue architecture, either normal or in a diseased state. A special kind of DWI, diffusion tensor imaging (DTI), has been used extensively to map white matter tractography in the brain.
In mathematics, the structure tensor, also referred to as the second-moment matrix, is a matrix derived from the gradient of a function. It summarizes the predominant directions of the gradient in a specified neighborhood of a point, and the degree to which those directions are coherent. The structure tensor is often used in image processing and computer vision.
In linear algebra, eigendecomposition or sometimes spectral decomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors. Only diagonalizable matrices can be factorized in this way.
In sedimentology imbrication refers to a primary depositional fabric consisting of a preferred orientation of clasts such that they overlap one another in a consistent fashion, rather like a run of toppled dominoes. Imbrication is observed in conglomerates and some volcaniclastic deposits.
Fractional anisotropy (FA) is a scalar value between zero and one that describes the degree of anisotropy of a diffusion process. A value of zero means that diffusion is isotropic, i.e. it is unrestricted in all directions. A value of one means that diffusion occurs only along one axis and is fully restricted along all other directions. FA is a measure often used in diffusion imaging where it is thought to reflect fiber density, axonal diameter, and myelination in white matter. The FA is an extension of the concept of eccentricity of conic sections in 3 dimensions, normalized to the unit range.
Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is a matrix-free method for finding the largest eigenvalues and the corresponding eigenvectors of a symmetric positive definite generalized eigenvalue problem
Roundness is the degree of smoothing due to abrasion of sedimentary particles. It is expressed as the ratio of the average radius of curvature of the edges or corners to the radius of curvature of the maximum inscribed sphere.
A cobble is a clast of rock defined on the Udden–Wentworth scale as having a particle size of 64–256 millimeters (2.5–10.1 in), larger than a pebble and smaller than a boulder. Other scales define a cobble's size in slightly different terms. A rock made predominantly of cobbles is termed a conglomerate. Cobblestone is a building material based on cobbles.
References
- ↑ Graham, D., and Midgley, N., 2000. Earth Surface Processes and Landforms (25) pp 1473–1477
- ↑ Sneed, ED; Folk, RL (1958). "Pebbles in the lower Colorado River, Texas, a study of particle morphogenesis". Journal of Geology. 66 (2): 114–150. Bibcode:1958JG.....66..114S. doi:10.1086/626490.
- ↑ Knox-Robinson, Carl M; Gardoll, Stephen J (1998). "GIS-stereoplot: an interactive stereonet plotting module for ArcView 3.0 geographic information system". Computers & Geosciences. 24: 243–250. Bibcode:1998CG.....24..243K. doi:10.1016/S0098-3004(97)00122-2.
- ↑ Stereo32
- ↑ Benn, D., Evans, D., 2004. A Practical Guide to the study of Glacial Sediments. London: Arnold. pp 103–107