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where is the volume fraction of the fibers in the composite (and is the volume fraction of the matrix).. If it is assumed that the composite material behaves as a linear-elastic material, i.e., abiding Hooke's law = for some elastic modulus of the composite and some strain of the composite , then equations 1 and 2 can be combined to give
Vegard's law assumes that both components A and B in their pure form (i.e., before mixing) have the same crystal structure. Here, a A (1-x) B x is the lattice parameter of the solid solution, a A and a B are the lattice parameters of the pure constituents, and x is the molar fraction of B in the solid solution.
The shear viscosity (or viscosity, in short) of a fluid is a material property that describes the friction between internal neighboring fluid surfaces (or sheets) flowing with different fluid velocities.
This process is called raising the index. Raising and then lowering the same index (or conversely) are inverse operations, which is reflected in the metric and inverse metric tensors being inverse to each other (as is suggested by the terminology): = = =
The scalar triple product (also called the mixed product, box product, or triple scalar product) is defined as the dot product of one of the vectors with the cross product of the other two. Geometric interpretation
Sometimes multiplication and division are given equal precedence, or sometimes multiplication is given higher precedence than division; see § Mixed division and multiplication below. If each subtraction is replaced with addition of the opposite (additive inverse), then the associative and commutative laws of addition allow terms to be added in ...
Bond's theory and index brought a greater measure of openness to the calculations for selecting the type, size, and power ratings for ore milling equipment. [ 5 ] Bond was inducted with its first class into the National Mining Hall of Fame posthumously in 1988, [ 6 ] and received a Distinguished Achievement Medal by his alma mater, the Colorado ...
Weinberg angle θ W, and relation between couplings g, g ′, and e = g sin θ W.Adapted from Lee (1981). [1] The pattern of weak isospin, T 3, and weak hypercharge, Y W, of the known elementary particles, showing electric charge, Q, [a] along the Weinberg angle.