Projection operator formalism and entropy

The entropy definition is deduced by means of (re)deriving the generalized non-linear Langevin equation using Zwanzig projector operator formalism. It is shown to be necessarily related to an invariant measure which, in classical mechanics, can always be taken to be the Liouville measure. It is not true that one is free to choose a ``relevant'' probability density independently as is done in other flavors of projection operator formalism. This observation induces an entropy expression which is valid also outside the thermodynamic limit and in far from equilibrium situations. The Zwanzig projection operator formalism therefore gives a deductive derivation of non-equilibrium, and equilibrium, thermodynamics. The entropy definition found is closely related to the (generalized) microcanonical Boltzmann-Planck definition but with some subtle differences. No ``shell thickness'' arguments are needed, nor desirable, for a rigorous definition. The entropy expression depends on the choice of macroscopic variables and does not exactly transform as a scalar quantity. The relation with expressions used in the GENERIC formalism are discussed

Local transient rheological behavior of concentrated suspensions

This paper reports experiments on the shear transient response of concentrated non-Brownian suspensions. The shear viscosity of the suspensions is measured using a wide-gap Couette rheometer equipped with a Particle Image Velocimetry (PIV) device that allows measuring the velocity field. The suspensions made of PMMA particles (31$\mu$m in diameter) suspended in a Newtonian index- and density-matched liquid are transparent enough to allow an accurate measurement of the local velocity for particle concentrations as high as 50%. In the wide-gap Couette cell, the shear induced particle migration is evidenced by the measurement of the time evolution of the flow profile. A peculiar radial zone in the gap is identified where the viscosity remains constant. At this special location, the local particle volume fraction is taken to be the mean particle concentration. The local shear transient response of the suspensions when the shear flow is reversed is measured at this point where the particle volume fraction is well defined. The local rheological measurements presented here confirm the macroscopic measurements of Gadala-Maria and Acrivos (1980). After shear reversal, the viscosity undergoes a step-like reduction, decreases slower and passes through a minimum before increasing again to reach a plateau. Upon varying the particle concentration, we have been able to show that the minimum and the plateau viscosities do not obey the same scaling law with respect to the particle volume fraction. These experimental results are consistent with the scaling predicted by Mills and Snabre (2009) and with the results of numerical simulation performed on random suspensions [Sierou and Brady (2001)]. The minimum seems to be associated with the viscosity of an isotropic suspension, or at least of a suspension whose particles do not interact through non-hydrodynamic forces, while the plateau value would correspond to the viscosity of a suspension structured by the shear where the non-hydrodynamic forces play a crucial role

UTD analysis of electromagnetic scattering by flat structures

The different scattering mechanisms that contribute to the radar cross of finite flat plates were identified and analyzed. The geometrical theory of diffraction, the equivalent current and the corner diffraction are used for this study. A study of the cross polarized field for a monopole mounted on a plate is presented, using novel edge wave mechanism in the analysis. The results are compared with moment method solutions as well as measured data

Horn antenna with v-shaped corrugated surface

Corrugated shape is easily machined for millimeter wave application and is better suited for folding antenna designs. Measured performance showed ""V'' corrugations and rectangular corrugations have nearly the same pattern beamwidth, gain, and impedance. Also, ""V'' corrugations have higher relative power loss

A case-control study of the effect of infant feeding on celiac disease

Aims: The aim of this study was to investigate the association between the duration of breast-feeding and the age at the first gluten introduction into the infant diet and the incidence and age at onset of celiac disease. Methods: In a case-control study, 143 children with celiac disease and 137 randomly recruited gender- and age-matched control children were administered a standardized questionnaire. Multivariate-adjusted odds ratios (OR) as estimates of the relative risk and corresponding 95% confidence intervals (95% CI) were calculated. Results: The risk of developing celiac disease decreased significantly by 63% for children breast-fed for more than 2 months (OR 0.37, 95% Cl 0.21-0.64) as compared with children breast-fed for 2 months or less. The age at first gluten introduction had no significant influence on the incidence of celiac disease (OR 0.72, 95% Cl 0.29-1.79 comparing first gluten introduction into infant diet >3 months vs. less than or equal to3 months). Conclusions: A significant protective effect on the incidence of celiac disease was suggested by the duration of breast-feeding (partial breastfeeding as well as exclusive breast-feeding). The data did not support an influence of the age at first dietary gluten exposure on the incidence of celiac disease. However, the age at first gluten exposure appeared to affect the age at onset of symptoms. Copyright (C) 2001 S. Karger AG, Basel