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

21 Layer troposphere-stratosphere climate model

The global climate model is extended through the stratosphere by increasing the vertical resolution and raising the rigid model top to the 0.01 mb (75 km) level. The inclusion of a realistic stratosphere is necessary for the investigation of the climate effects of stratospheric perturbations, such as changes of ozone, aerosols or solar ultraviolet irradiance, as well as for studying the effect on the stratosphere of tropospheric climate changes. The observed temperature and wind patterns throughout the troposphere and stratosphere are simulated. In addition to the excess planetary wave amplitude in the upper stratosphere, other model deficiences include the Northern Hemisphere lower stratospheric temperatures being 5 to 10 C too cold in winter at high latitudes and the temperature at 50 to 60 km altitude near the equator are too cold. Methods of correcting these deficiencies are discussed