A theory is presented that describes the time evolution of the diffraction properties of holographically formed thick phase gratings in ferroelectrics, particularly in iron-doped lithium niobate. The theory is based upon a model that relates the instantaneous electromagnetic fields in a grating to the refractive index in a manner consistent with the work of Young et al.; that is, the index modulation amplitude is proportional to the product of the amplitudes of the writing fields, while index maxima and intensity maxima are spatially shifted by some fraction of a fringe. The model leads to coupled nonlinear equations for the writing fields that are analogous to the linear equations of Kogelnik, and in certain limits, yield identical results. Closed-form solutions of the coupled nonlinear equations are found to describe the interaction between writing beams observed by Staebler and Amodei, as well as the time evolution of diffraction efficiency observed by Amodei et al. In conjunction with the latter experiment, the present theory affords a striking verification of the grating formation concepts of Young et al.

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Cellulosic webs, such as paper materials, are composed of an interwoven, bonded network of cellulose fibers. Strength-controlling parameters in these webs are influenced by constituent fibers and method of processing and manufacture. Instead of estimating the effect on tensile strength of each processing/manufacturing variable, this study modifies and compares the point stress criteria and average stress criteria models used to estimate defect-free (i.e., maximum possible) tensile strength and the inherent size of the cumulative effect of strength-limiting defects. The two major modifications to these models were to assume that defect-free tensile strength was unknown and that unnotched tensile strength was reduced by the presence of inherent defects. These modifications allow the calculation of inherent defect size and defect-free tensile strength by characterizing the tensile strength of the web in the presence of stress concentrations associated with holes of different radius. The models were applied to seven paper materials including lightweight, commercial papers, linerboards, and cylinder boards; estimated inherent defect sizes ranged from 0.1 to 1.5 mm. For most materials considered, defect size was larger in the 2-direction than the 1-direction. Actual measured tensile strengths ranged from 59% to over 95% of the estimated defect-free tensile strengths, σu.

The three-dimensional motion of asymmetric rigid fibers settling under gravity in a quiescent fluid was experimentally measured using a pair of cameras located on a movable platform. The particle motion typically consisted of an initial transient after which the particle approached a steady rate of rotation about an axis parallel to the acceleration of gravity, with its center of mass following a helical trajectory. Numerical and analytical methods were used to predict translational and angular velocities as well as the evolution of the fiber orientation as a function of time. A comparison of calculated and measured values shows that it is possible to quantitatively predict complex motions of particles that have highly asymmetric shape. The relations between particle shape and settling trajectory have potential applications for hydrodynamic characterization of fiber shapes and fiber separation.