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A dyadic tensor T is an order-2 tensor formed by the tensor product ⊗ of two Cartesian vectors a and b, written T = a ⊗ b.Analogous to vectors, it can be written as a linear combination of the tensor basis e x ⊗ e x ≡ e xx, e x ⊗ e y ≡ e xy, ..., e z ⊗ e z ≡ e zz (the right-hand side of each identity is only an abbreviation, nothing more):
This is a list of models and meshes commonly used in 3D computer graphics for testing and demonstrating rendering algorithms and visual effects. Their use is important for comparing results, similar to the way standard test images are used in image processing .
This discussion of tensors so far assumes finite dimensionality of the spaces involved, where the spaces of tensors obtained by each of these constructions are naturally isomorphic. [ Note 2 ] Constructions of spaces of tensors based on the tensor product and multilinear mappings can be generalized, essentially without modification, to vector ...
This list of moment of inertia tensors is given for principal axes of each object.. To obtain the scalar moments of inertia I above, the tensor moment of inertia I is projected along some axis defined by a unit vector n according to the formula:
In machine learning, the term tensor informally refers to two different concepts (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data may be organized in a multidimensional array (M-way array), informally referred to as a "data tensor"; however, in the strict mathematical sense, a tensor is a multilinear mapping over a set of domain vector spaces to a range vector ...
The model was proposed by Ronald Rivlin in 1948 using invariants, though Mooney had already described a version in stretch form in 1940, and Wall had noted the equivalence in shear with the Hooke model in 1942. In contrast to linear elastic materials, the stress–strain curve of a neo-Hookean material is not linear. Instead, the relationship ...
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In the frame work of single-point closures (Reynolds-stress transport models = RSTM) still provide the best representation of flow physics. Due to numeric requirements an explicit formulation based on a low number of tensors is desirable and was already introduced originally most explicit algebraic stress models are formulated using a 10-term basis: