Exchange Processes in a Channel with Two Vertical Emerged Obstructions

The flow around two vertical obstructions situated in a long open channel with lateral walls is simulated using Large Eddy Simulation (LES). The emerged obstructions (groynes) are oriented perpendicular to the channel side walls. The incoming channel flow is fully turbulent. The focus of the present paper is to examine the mass transfer between a contaminant situated initially in the (embayment) region between the obstructions and the main channel. The mass transfer is simulated using a passive (conserved) scalar transport equation. The scalar is introduced instantaneously inside the embayment. The eddy structures that populate the detached shear layer starting at the tip of the upstream obstruction and their interaction with the coherent structures inside the embayment area are shown to play an important role in the contaminant entrainment from the embayment area into the main channel. It is also found that the flow convected into the embayment from the region downstream of the second obstruction can substantially accelerate the removal of the contaminant from the embayment region. A detailed analysis of the contaminant flux variation in the top, middle and bottom layers inside the embayment region is carried out to better understand how the contaminant exits the embayment area, the role played by vertical motions within the embayment, and the effects induced by the presence of the bottom surface which delays the contaminant purging from the bottom layer. It is found that one half of the contaminant mass situated initially in the bottom third of the embayment volume is not leaving the embayment through the corresponding embayment–channel interface. The opposite is observed for the top third layer where the mass of contaminant leaving through the top interface area is 50% higher than the corresponding mass of contaminant initially situated in the top layer. This shows that the mass exchange is highly non-uniform over the depth and there is an overall contaminant flux within the embayment toward the free surface. The decay of contaminant mass within the embayment is calculated enabling estimation of a global 1D exchange coefficient based on dead-zone theory. It is found that though dead-zone models can relatively accurately describe the contaminant mass decay in time within the embayment, the mass exchange is not characterized by a unique value of the exchange coefficient over the whole length of the ejection process for the present geometry and flow conditions. Rather, two distinct phases of the decay process are identified. In the initial phase of decay over which about 68% of the total mass of contaminant leaves the embayment, the exchange coefficient is found to be about twice the value estimated for the final phase.     

Construction of modular branching functions from Bethe's equations in the 3-state Potts chain

We use the single-particle excitation energies and the completeness rules of the 3-state antiferromagnetic Potts chain, which have been obtained from Bethe's equation, to compute the modular invariant partition function. This provides a fermionic construction for the branching functions of theD ₄ representation ofZ ₄ parafermions which complements the bosonic constructions. It is found that there are oscillations in some of the correlations and a new connection with the field theory of the Lee-Yang edge is presented.     

Multiple scattering calculations of step contrast in REM images of the Si(001) surface

Simulations of reflection electron microscopy (REM) images of both monolayer and bilayer steps on the bulk-terminated Si(001) surface, for the case when the primary electron beam azimuth is directed parallel to the line of the step, are presented. The simulations employ our previously reported theory of REM image formation which uses a 2D Bloch wave formulation of dynamical (multiple scattering) elastic RHEED theory to calculate diffracted amplitudes propagating from the surface. The only step contrast mechanism considered here is phase contrast and this is sufficient to produce the characteristic “black-white” appearance observed experimentally. Defocusing of the simulated images is also discussed.     

Density functional theory of polymer-polymer phase separation behavior

Polyatomic density functional theory is applied to a binary polymer blend. The polymer reference interaction site model (PRISM) liquid state theory provides the homogeneous state correlation functions necessary for the application of density functional theory. An effective chi parameter can be recognized from the density functional expression; however, the phase separation criteria does not depend solely upon the chi parameter, rather it depends upon various combinations of the species-dependent direct correlation functions of the blend. The Flory-Huggins chi parameter along with the associated phase diagram is obtained when the monomer volumes of the blend species are equal and for a range of monomer-monomer attractive interactions. Calculations are performed both with and without the assumption of incompressibility. The density functional theory along with the PRISM determined “input” predict that an isotopic polymer blend shows an upper critical solution temperature (UCST) phenomena. © 1995 John Wiley & Sons, Inc.     

Inference for a class of partially observed point process models

This paper presents a simulation-based framework for sequential inference from partially and discretely observed point process models with static parameters. Taking on a Bayesian perspective for the static parameters, we build upon sequential Monte Carlo methods, investigating the problems of performing sequential filtering and smoothing in complex examples, where current methods often fail. We consider various approaches for approximating posterior distributions using SMC. Our approaches, with some theoretical discussion are illustrated on a doubly stochastic point process applied in the context of finance.     

Contracting convex hypersurfaces by curvature

We consider compact convex hypersurfaces contracting by functions of their curvature. Under the mean curvature flow, uniformly convex smooth initial hypersurfaces evolve to remain smooth and uniformly convex, and contract to points after finite time. The same holds if the initial data is only weakly convex or non-smooth, and the limiting shape at the final time is spherical. We provide a surprisingly large family of flows for which such results fail, by a variety of mechanisms: Uniformly convex hypersurfaces may become non-convex, and smooth ones may develop curvature singularities; even where this does not occur, non-uniformly convex regions and singular parts in the initial hypersurface may persist, including flat sides, ridges of infinite curvature, or ‘cylindrical’ regions where some of the principal curvatures vanish; such cylindrical regions may persist even if the speed is positive, and in such cases the hypersurface may even collapse to a line segment or higher-dimensional disc rather than to a point. We provide sufficient conditions for these various disasters to occur, and by avoiding these arrive at a class of flows for which arbitrary weakly convex initial hypersurfaces immediately become smooth and uniformly convex and contract to points.     

Sharp Recovery Bounds for Convex Demixing,with Applications

Demixing refers to the challenge of identifying two structured signals given only the sum of the two signals and prior information about their structures. Examples include the problem of separating a signal that is sparse with respect to one basis from a signal that is sparse with respect to a second basis, and the problem of decomposing an observed matrix into a low-rank matrix plus a sparse matrix. This paper describes and analyzes a framework, based on convex optimization, for solving these demixing problems, and many others. This work introduces a randomized signal model that ensures that the two structures are incoherent, i.e., generically oriented. For an observation from this model, this approach identifies a summary statistic that reflects the complexity of a particular signal. The difficulty of separating two structured, incoherent signals depends only on the total complexity of the two structures. Some applications include (1) demixing two signals that are sparse in mutually incoherent bases, (2) decoding spread-spectrum transmissions in the presence of impulsive errors, and (3) removing sparse corruptions from a low-rank matrix. In each case, the theoretical analysis of the convex demixing method closely matches its empirical behavior.     

Authentication of black cohosh (Actaea racemosa) dietary supplements based on chemometric evaluation of hydroxycinnamic acid esters and hydroxycinnamic acid amides

Analytical and Bioanalytical Chemistry - Ester and amide derivatives of hydroxycinnamic acids are found in black cohosh (Actaea racemosa) and other Actaea plants. These two compound groups were...     

On the maximum of the k-dependent susceptibility for fixed k and T > Tc

We study the maximum occuring in ${}_{\mathrm{x}}\text{(}\text{k}\text{, T)}$ for fixed k at a temperature T_max > T_c. We examine the predictions of both Ornstein-Zernike and ?-expansions for the position of this maximum. These are compared with the exact results fot the two-dimensional Ising model.