TL;DR: In this article, a method for treating a complex structure as an assemblage of distinct regions, or substructures, is presented using basic mass and stiffness matrices, together with conditions of geometrical compatibility along substructure boundaries.
Abstract: A method for treating a complex structure as an assemblage of distinct regions, or substructures, is presented. Using basic mass and stiffness matrices for the substructures, together with conditions of geometrical compatibility along substructure boundaries, the method employs two forms of generalized coordinates. Boundary generalized coordinates give displacements and rotations of points along substructure boundaries and are related to the displacement modes of the substructures known as "constraint modes." All constraint modes are generated by matrix operations from substructure input data. Substructure normal-mode generalized coordinates are related to free vibration modes of the substructures relative to completely restrained boundaries. The definition of substructure modes and the requirement of compatibility along substructure boundaries lead to coordinate transformation matrices that are employed in obtaining system mass and stiffness matrices from the mass and stiffness matrices of the substructures. Provision is made, through a RayleighRitz procedure, for reducing the total number of degrees of freedom of a structure while retaining accurate description of its dynamic behavior. Substructure boundaries may have any degree of redundancy. An example is presented giving a free vibration analysis of a structure having a highly indeterminate substructure boundary.
TL;DR: In this article, the authors studied the kinetics of the substructure evolution and its correspondence to the strain hardening evolution of an Fe-22 wt.% Mn-0.6 wt% C TWIP steel during tensile deformation by means of electron channeling contrast imaging (ECCI) combined with electron backscatter diffraction (EBSD).
TL;DR: In this paper, experimental constraints on possible lepton and quark substructure are analyzed and expressed in terms of a general formalism for describing composite particles in term of their constituents. But the authors do not consider the effect of the measured gyromagnetic ratios on the internal structure of light leptons.
Abstract: Experimental constraints on possible lepton and quark substructure are analyzed and expressed in terms of a general formalism for describing composite particles in terms of their constituents. In particular, the measured gyromagnetic ratios may very severely restrict possible internal structure of light leptons (electrons and muons) in some models. Simple expressions for hadronic $g$ values and electromagnetic radii are given in terms of their quarkgluon infinite-momentum-frame wave function. The contribution to the anomalous moment of a fermion due to internal structure is shown to vanish as the mass or inverse-size scale of the internal state becomes infinitely large.
TL;DR: In this article, single crystals of tin grown from the melt under a wide range of conditions are shown to exhibit a fibrous structure which manifests itself as parallel ridges ("corrugations") on the free surface o...
Abstract: Single crystals of tin grown from the melt under a wide range of conditions are shown to exhibit a fibrous structure which manifests itself as parallel ridges ("corrugations") on the free surface o...
TL;DR: In this paper, the authors argue that the discrepancy between observed and model-predicted flux ratios is due to substructure in the lens, and propose a strategy to model lens systems in which substructure is suspected.
Abstract: We discuss whether one should expect that multiply imaged QSOs can be understood with ‘simple’ lens models that contain only a few parameters. Whereas for many lens systems such simple mass models yield a remarkably good description of the observed properties, there are some systems which are notoriously difficult to understand quantitatively. We argue that at least in one case (B 1422+231) these difficulties are not (solely) due to a ‘wrong’ parametrization of the lens model, but that the discrepancy between observed and model-predicted flux ratios is due to substructure in the lens. As in microlensing for optical fluxes, such substructure can distort also the radio flux ratios predicted by ‘simple’ mass models, in particular for highly magnified images, without appreciably changing image positions. Substructure also does not change the time delay significantly, and therefore has little effect on the determination of the Hubble constant using time delays. We quantify these statements with several simple scenarios for substructure, and propose a strategy to model lens systems in which substructure is suspected.