Thermodynamics and phase behavior of the lamellar Zwanzig model

Binary mixtures of lamellar colloids represented by hard platelets are studied within a generalization of the Zwanzig model for rods, whereby the square cuboids can take only three orientations along the $x$, $y$ or $z$ axes. The free energy is calculated within Rosenfeld's ''Fundamental Measure Theory'' (FMT) adapted to the present model. In the one-component limit, the model exhibits the expected isotropic to nematic phase transition, which narrows as the aspect ratio $\zeta=L/D$ ($D$ is the width and $L$ the thickness of the platelets) increases. In the binary case the competition between nematic ordering and depletion-induced segregation leads to rich phase behaviour.Comment: 9 pages, 6 figure

Random Phase Approximation and Extensions Applied to a Bosonic Field Theory

An application of a self-consistent version of RPA to quantum field theory with broken symmetry is presented. Although our approach can be applied to any bosonic field theory, we specifically study the $\phi^4$ theory in 1+1 dimensions. We show that standard RPA approach leads to an instability which can be removed when going to a superior version,i.e. the renormalized RPA. We present a method based on the so-called charging formula of the many electron problem to calculate the correlation energy and the RPA effective potential.Comment: 30 pages, LaTeX file, 10 figures included, final version accepted in EPJ

Screened electrostatic interactions between clay platelets

An effective pair potential for systems of uniformly charged lamellar colloids in the presence of an electrolytic solution of microscopic co- and counterions is derived. The charge distribution on the discs is expressed as a collection of multipole moments, and the tensors which determine the interactions between these multipoles are derived from a screened Coulomb potential. Unlike previous studies of such systems, the interaction energy may now be expressed for discs at arbitrary mutual orientation. The potential is shown to be exactly equivalent to the use of linearized Poisson-Boltzmann theory.Comment: 23 pages, 10 figures, created with Revtex. To appear in Molecular Physic

Conditional quantum state engineering in repeated 2-photon down conversion

The U(1,1) and U(2) transformations realized by three-mode interaction in the respective parametric approximations are studied in conditional measurement, and the corresponding non-unitary transformation operators are derived. As an application, the preparation of single-mode quantum states using an optical feedback loop is discussed, with special emphasis of Fock state preparation. For that example, the influence of non-perfect detection and feedback is also considered.Comment: 17 pages, 4 figures, using a4.st

Tolerance and Sensitivity in the Fuse Network

We show that depending on the disorder, a small noise added to the threshold distribution of the fuse network may or may not completely change the subsequent breakdown process. When the threshold distribution has a lower cutoff at a finite value and a power law dependence towards large thresholds with an exponent which is less than $0.16\pm0.03$, the network is not sensitive to the added noise, otherwise it is. The transition between sensitivity or not appears to be second order, and is related to a localization-delocalization transition earlier observed in such systems.Comment: 12 pages, 3 figures available upon request, plain Te

A universal velocity distribution of relaxed collisionless structures

Several general trends have been identified for equilibrated, self-gravitating collisionless systems, such as density or anisotropy profiles. These are integrated quantities which naturally depend on the underlying velocity distribution function (VDF) of the system. We study this VDF through a set of numerical simulations, which allow us to extract both the radial and the tangential VDF. We find that the shape of the VDF is universal, in the sense that it depends only on two things namely the dispersion (radial or tangential) and the local slope of the density. Both the radial and the tangential VDF's are universal for a collection of simulations, including controlled collisions with very different initial conditions, radial infall simulation, and structures formed in cosmological simulations.Comment: 13 pages, 6 figures; oversimplified analysis corrected; changed abstract and conclusions; significantly extended discussio

Burst avalanches in solvable models of fibrous materials

We review limiting models for fracture in bundles of fibers, with statistically distributed thresholds for breakdown of individual fibers. During the breakdown process, avalanches consisting of simultaneous rupture of several fibers occur, and the distribution $D(\Delta)$ of the magnitude $\Delta$ of such avalanches is the central characteristics in our analysis. For a bundle of parallel fibers two limiting models of load sharing are studied and contrasted: the global model in which the load carried by a bursting fiber is equally distributed among the surviving members, and the local model in which the nearest surviving neighbors take up the load. For the global model we investigate in particular the conditions on the threshold distribution which would lead to anomalous behavior, i.e. deviations from the asymptotics $D(\Delta) \sim \Delta^{-5/2}$, known to be the generic behavior. For the local model no universal power-law asymptotics exists, but we show for a particular threshold distribution how the avalanche distribution can nevertheless be explicitly calculated in the large-bundle limit.Comment: 28 pages, RevTeX, 3 Postscript figure

Investigation of Polymer–Plasticizer Blends as SH-SAW Sensor Coatings for Detection of Benzene in Water with High Sensitivity and Long-Term Stability

We report the first-ever direct detection of benzene in water at concentrations below 100 ppb (parts per billion) using acoustic wave (specifically, shear-horizontal surface acoustic wave, SH-SAW) sensors with plasticized polymer coatings. Two polymers and two plasticizers were studied as materials for sensor coatings. For each polymer–plasticizer combination, the influence of the mixing ratio of the blend on the sensitivity to benzene was measured and compared to commercially available polymers that were used for BTEX (benzene, toluene, ethylbenzene, and xylene) detection in previous work. After optimizing the coating parameters, the highest sensitivity and lowest detection limit for benzene were found for a 1.25 μm thick sensor coating of 17.5%-by-weight diisooctyl azelate-polystyrene on the tested acoustic wave device. The calculated detection limit was 45 ppb, with actual sensor responses to concentrations down to 65 ppb measured directly. Among the sensor coatings that showed good sensitivity to benzene, the best long-term stability was found for a 1.0 μm thick coating of 23% diisononyl cyclohexane-1,2-dicarboxylate-polystyrene, which was studied here because it is known to show no detectable leaching in water. The present work demonstrates that, by varying type of plasticizer, mixing ratio, and coating thickness, the mechanical and chemical properties of the coatings can be conveniently tailored to maximize analyte sorption and partial chemical selectivity for a given class of analytes as well as to minimize acoustic-wave attenuation in contact with an aqueous phase at the operating frequency of the sensor device