Grand Jury - Irregularities in Function - Substitution of Grand Jurors

The Pennsylvania Supreme Court has held that the unprecedented substitution of six grand jurors one year after the original panel had been sworn and begun its work was prejudicial to the defendant and necessitated the invalidation of the investigating grand jury\u27s presentment and the subsequent indictment based on that presentment. Commonwealth v. Levinson, 389 A.2d 1062 (Pa. 1978)

On the effective properties of suspensions

Einstein's formula for the viscosity of dilute suspensions describes how rigid particles immersed in a Stokes-fluid increase its macroscopic viscosity in terms of the particle volume density ∅. However, up to now, a rigorous justification has only been obtained for dissipation functionals of the flow feld. In this thesis, a cloud of N spherical rigid particles of radius R suspended in a fluid of viscosity μ is considered. It is rigorously shown that the homogenized fluid in the regime NR3 → 0 as N → ∞ has, in accordance with Einstein's formula, the viscosityμ' = μ ( 1 + 5/2∅) to first order in ∅. This is done by establishing L∞ and Lpp estimates for the difference of the solution to the microscopic problem and the solution to the homogenized equation. Regarding the distribution of the particles, it is assumed that the particles are contained in some bounded region and are well separated in the sense that the minimal distance is comparable to the average one. The main tools for the proof are a dipole approximation of the flow feld of the suspension together with the so-called method of reflections and a coarse graining of the volume density. By a very close mathematical analogy to electrostatics a similar result, regarding Maxwell's formula for the conductivity of suspensions, is proven, namely that the conductivity of the homogenized material isη' = η (1 + 3∅) to first order in ∅

Non-existence of mean-field models for particle orientations in suspensions

We consider a suspension of spherical inertialess particles in a Stokes flow on the torus $\mathbb T^3$. The particles perturb a linear extensional flow due to their rigidity constraint. Due to the singular nature of this perturbation, no mean-field limit for the behavior of the particle orientation can be valid. This contrasts with widely used models in the literature such as the FENE and Doi models and similar models for active suspensions. The proof of this result is based on the study of the mobility problem of a single particle in a non-cubic torus, which we prove to exhibit a nontrivial coupling between the angular velocity and a prescribed strain.Comment: All comments welcom