A convolution-backprojection formula is deduced for direct reconstruction of a three-dimensional density function from a set of two-dimensional projections. The formula is approximate but has useful properties, including errors that are relatively small in many practical instances and a form that leads to convenient computation. It reduces to the standard fan-beam formula in the plane that is perpendicular to the axis of rotation and contains the point source. The algorithm is applied to a mathematical phantom as an example of its performance.

Magnetorheological elastomers consist of natural or synthetic rubber filled with micron-sized magnetizable particles. During curing of the elastomer, an applied magnetic field aligns the particles into chains. The shear modulus of the resulting cured material is sensitive to magnetic fields of several kOe magnitude. Such sensitivity to magnetic field makes these materials attractive for applications in automotive mounting components. At large fields (magnetic induction B>1 T), the Fe particles are completely magnetized or saturated. Calculations using finite element analysis show that for typical elastomers the increase in shear modulus due to interparticle magnetic forces at saturation is about 50% of the zero-field modulus. The optimum particle volume fraction for the largest fractional change in modulus at saturation is predicted to be 27%. Calculations of the zero-field shear modulus perpendicular to the chain axis indicate that it does not exceed the modulus of a filled elastomer with randomly dispersed particles of the same concentration.

Numerical and analytical models of magnetorheological fluid phenomena that account explicitly for the effects of magnetic nonlinearity and saturation are described. Finite-element analysis was used to calculate the field distribution in chains of magnetizable particles. The field-dependent stress required to shear the chains was then obtained using the Maxwell stress tensor. Three regimes are identified: at low applied fields, the stress increase quadratically, as expected from linear magnetostatics. In intermediate fields, the contact or polar regions of each particle saturate, reducing the rate of increase of the stress with increasing field. At high fields, the particles saturate completely, and the stress reaches its limiting value. Approximate analytical expressions for the yield stress and shear modulus in these regimes are also derived. The predictions of these models are compared to magnetorheological experiments in the literature and from our laboratory. These models predict successfully the magnitude of the stresses as well as their field dependence. They also suggest that particles comprised of materials with higher saturation magnetizations will exhibit the largest magnetorheological effects.

The interparticle forces and resulting shear stresses in a magnetorheological fluid are calculated. The field due to a linear chain of particles in a fixed average magnetic induction Bave is determined from a finite element analysis in which the nonlinearity and saturation of the particle magnetization are incorporated. The shear stresses are then computed from the field using Maxwell’s stress tensor. The stresses obtained for all but the lowest magnetic inductions are controlled by the saturation of the magnetization in the contact regions of each particle. Identifying the maximum shear stress as a function of shear strain with the yield stress gives values in agreement with results reported for typical fluids. For high magnetic inductions the yield stress plateaus due to the complete saturation of the particle magnetization; the stress scales as the square of the saturation magnetization in this regime.

Forces between particles aligned into chains by an applied electric field in an electrorheological (ER) fluid are calculated using finite-element techniques and, approximately, using a dipole approximation with local-field effects. Evaluation of the effective dielectric constant is emphasized and the shear modulus is derived from the shear dependence. For high-frequency (f≳0.1–1 kHz) applied electric fields, the forces and the modulus depend upon the dielectric constants of the suspending fluid and the dispersed particles. For low-frequency or dc electric fields, the conductivities of the components are dominant. These effects are treated within a Maxwell–Wagner approach. If the ratio of particle-to-fluid conductivities substantially exceeds the ratio of dielectric constants, a large enhancement of the modulus is found. Implications for the design of ER fluids are discussed briefly.

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Autoionization emission from transition metals: An electron stimulated analog of resonant photoemissionPhotoemission experiments on 3d transition metals are reviewed. The emphasis is on understanding the results of experiments, not on experimental details and methods. Extensive use is made of simple models. Much of the review pertains to resonances associated with the autoionization 3J/3d n + '-.3p 6 3d n -, + e and their implications for electronic structure.Nonresonant ultraviolet and x-ray photoemission spectroscopies are also discussed. Photoemission and photoabsorption of transition-metal atoms are discussed first. Results for Mn are described at length to establish the validity of the autoionization mechanism. The results from atomic spectroscopy are used to interpret experiments on solids. The role of atomiclike excitations in solids is examined. Compounds oftransition metals are analyzed in terms of ligandfield theory, which is shown to be inadequate. Newer theories involving configuration interaction are shown to agree better with experiment. Various mechanisms for the excitation of photoemission satellites are presented. In the metallic state, effects similar to those observed for the compounds occur. The existence of two-hound-hole final states is demonstrated. Their importance in Auger spectroscopy, valence-and core-emission satellites, and resonant photoemission is discussed. The effects of closely related electron correlations on the band structure are described.R25