Suspension Flows in a Pipeline with Partial Phase Separation

The formulation of a model for the evolution of the flow of a solid-liquid mixture (coal-water) in a horizontal pipeline with partial phase separation is the aim of this work. Problems of instabilities due to complex eigenvalues, observed in previous models, seem to be completely solved in the present model, in which we give the genesis of the different terms written in the equations, coming from the natural definition of mass and momentum balance, and the consequent proof of well-posedness of the obtained PDE system with boundary-Cauchy data. The model describes a three-layer flow. Most of the material is carried by the upper layer, while the bottom layer consists of an immobile sediment. The intermediate layer grows to a maximum thickness and has the role of regulating the mass exchange between the extreme layers. In the last section we present some simulations for a particular choice of flow regime, and boundary-Cauchy data, that were suggested by experimental results provided by Snamprogetti (Fano, Italy).Comment: 29 pages, 7 figure

Notes on a 3-term Conjugacy Recurrence for the Iterative Solution of Symmetric Linear Systems

We consider a 3-term recurrence, namely CG_2step, for the iterative solution of symmetric linear systems. The new algorithm generates conjugate directions and extends some standard theoretical properties of the Conjugate Gradient (CG) method [10]. We prove the finite convergence of CG_2step, and we provide some error analysis. Then, we introduce preconditioning for CG_2step, and we prove that standard error bounds for the CG also hold for our proposal.Iterative methods, 3-term recurrences, Conjugate Gradient method, Error Analysis, Preconditioning

Optimal Regularity for a Class of Singular Abstract Parabolic Equations

A general class of singular abstract Cauchy problems is considered which naturally arises in applications to certain Free Boundary Problems. Existence of an associated evolution operator characterizing its solutions is established and is subsequently used to derive optimal regularity results. The latter are well known to be important basic tools needed to deal with corresponding nonlinear Cauchy Problems such as those associated to Free Boundary Problems

The scaling relations of early--type galaxies in clusters I. Surface photometry in seven nearby clusters

This is the first paper of a series investigating the scaling relations of early-type galaxies in clusters. Here we illustrate the multi-band imagery and the image reduction and calibration procedures relative to the whole sample of 22 clusters at 0.05 < z < 0.25. We also present the detailed surface photometry of 312 early-type galaxies in 7 clusters in the first redshift bin, z~0.025-0.075. We give for each galaxy the complete set of luminosity and geometrical profiles, and and a number of global, photometric and morphological parameters. They have been evaluated taking into account the effects of seeing. Internal consistency checks and comparisons with data in the literature confirm the quality of our analysis. These data, together with the spectroscopic ones presented in the second paper of the series, will provide the local calibration of the scaling relations.Comment: 36 pages, 13 figures, 7 tables, accepted for publication in A&

A Class of Preconditioners for Large Indefinite Linear Systems, as by-product of Krylov subspace Methods: Part I

We propose a class of preconditioners, which are also tailored for symmetric linear systems from linear algebra and nonconvex optimization. Our preconditioners are specifically suited for large linear systems and may be obtained as by-product of Krylov subspace solvers. Each preconditioner in our class is identified by setting the values of a pair of parameters and a scaling matrix, which are user-dependent, and may be chosen according with the structure of the problem in hand. We provide theoretical properties for our preconditioners. In particular, we show that our preconditioners both shift some eigenvalues of the system matrix to controlled values, and they tend to reduce the modulus of most of the other eigenvalues. In a companion paper we study some structural properties of our class of preconditioners, and report the results on a significant numerical experience.preconditioners; large indefinite linear systems; large scale nonconvex optimization; Krylov subspace methods

A Class of Preconditioners for Large Indefinite Linear Systems, as by-product of Krylov subspace Methods: Part II

In this paper we consider the parameter dependent class of preconditioners M(a,d,D) defined in the companion paper The latter was constructed by using information from a Krylov subspace method, adopted to solve the large symmetric linear system Ax = b. We first estimate the condition number of the preconditioned matrix M(a,d,D). Then our preconditioners, which are independent of the choice of the Krylov subspace method adopted, proved to be effective also when solving sequences of slowly changing linear systems, in unconstrained optimization and linear algebra frameworks. A numerical experience is provided to give evidence of the performance of M(a,d,D).preconditioners; large indefinite linear systems; large scale nonconvex optimization; Krylov subspace methods

Surface Photometry of Early-type Galaxies in the Hubble Deep Field

The detailed surface photometry of a sample of early-type galaxies in the Hubble Deep Field is presented as part of a long-term project aimed to settle strong observational constraints to the theories modelling the evolution of elliptical galaxies from the early stages. The sample has been extracted, in the V_606 band, from the catalog by Couch (1996). The analysis of the luminosity and geometrical profiles, carried out on 162 candidates obeying our provisional selection criteria, resulted in a list of 99 'bona fide' early-type galaxies, for which accurate total magnitudes and effective radii were computed. The comparison with the magnitudes given by Williams et al.(1996) indicates that the automated photometry tends to underestimate the total luminosity of the ellipticals. The luminosity profiles of most of galaxies in our sample follow fairly well the deVaucouleurs law (`Normal' profiles). However, a relevant fraction of galaxies, even following the deVaucouleurs law in the main body light distribution, exhibit in the inner region a flattening of the luminosity profile not attributable to the PSF (`Flat' profiles) or, in some cases, a complex (multi-nucleus) structure (`Merger' profiles). The average ellipticity of galaxies belonging to the `Flat' and `Merger' classes is found to be significantly higher than that of the `Normal' galaxies. Moreover, even taken into account the relevant uncertainty of the outer position angle profiles, the amount of isophotal twisting of HDF ellipticals turns out to be significantly larger with respect to that of the local samples.Comment: 22 pages, LaTeX with laa.sty and psfig.sty macros + 28 embedded postscript figures. To appear in Astronomy and Astrophysics Supp

Optical surface photometry of radio galaxies - II. Observations and data analysis

Optical imaging observations for 50 radio galaxies are presented. For each object isophotal contours, photometric profiles, structural parameters (position angle, ellipticity, Fourier coefficients), and total magnitudes are given. These observations, obtained in the Cousins R band, complement the data presented in a previous paper and are part of a larger project aimed at studying the optical properties of low redshift (z<0.12) radio galaxies (Govoni et al. 1999). Comments for each individual source are reported.Comment: 9 pages, plus 17 .gif figures, accepted by Astronomy and Astrophysics, Supplement Serie