Natural cement and monumental restoration

Natural cement, called "Roman” cement, was invented at the end of the 19th century and played an important role in the development of civil engineering works until the 1860s. More surprisingly, it was also used to restore historic buildings, such as gothic cathedrals. This paper deals with the mineralogy and the durability of natural cement in the particular case of the Bourges Cathedral in France. This study illustrates the interest of this material particularly adapted in stone repair or substitution. Contrary to traditional mortars, the present samples are made of neat cement paste, revealed by the absence of mineral additions as quartz or carbonate sand. Several combined techniques (SEM-EDS, TGA, XRD) were carried out to determine the composition of the hydraulic binder rich in calcium aluminate hydrates. The raw marl at the origin of the cement production contains oxidized pyrites which consist in a potential source of sulphate pollution of the surrounding limestone. The exposition of the cement in urban environment leads to some weathering features as atmospheric sulfation. Finally a petrophysical approach, based on water porosity, capillary sorption and compressive strength, has been performed to demonstrate the durability and the compatibility of natural cement applied as an historical building restoration morta

Random perfect lattices and the sphere packing problem

Motivated by the search for best lattice sphere packings in Euclidean spaces of large dimensions we study randomly generated perfect lattices in moderately large dimensions (up to d=19 included). Perfect lattices are relevant in the solution of the problem of lattice sphere packing, because the best lattice packing is a perfect lattice and because they can be generated easily by an algorithm. Their number however grows super-exponentially with the dimension so to get an idea of their properties we propose to study a randomized version of the algorithm and to define a random ensemble with an effective temperature in a way reminiscent of a Monte-Carlo simulation. We therefore study the distribution of packing fractions and kissing numbers of these ensembles and show how as the temperature is decreased the best know packers are easily recovered. We find that, even at infinite temperature, the typical perfect lattices are considerably denser than known families (like A_d and D_d) and we propose two hypotheses between which we cannot distinguish in this paper: one in which they improve Minkowsky's bound phi\sim 2^{-(0.84+-0.06) d}, and a competitor, in which their packing fraction decreases super-exponentially, namely phi\sim d^{-a d} but with a very small coefficient a=0.06+-0.04. We also find properties of the random walk which are suggestive of a glassy system already for moderately small dimensions. We also analyze local structure of network of perfect lattices conjecturing that this is a scale-free network in all dimensions with constant scaling exponent 2.6+-0.1.Comment: 19 pages, 22 figure

The structure of invariant tori in a 3D galactic potential

We study in detail the structure of phase space in the neighborhood of stable periodic orbits in a rotating 3D potential of galactic type. We have used the color and rotation method to investigate the properties of the invariant tori in the 4D spaces of section. We compare our results with those of previous works and we describe the morphology of the rotational, as well as of the tube tori in the 4D space. We find sticky chaotic orbits in the immediate neighborhood of sets of invariant tori surrounding 3D stable periodic orbits. Particularly useful for galactic dynamics is the behavior of chaotic orbits trapped for long time between 4D invariant tori. We find that they support during this time the same structure as the quasi-periodic orbits around the stable periodic orbits, contributing however to a local increase of the dispersion of velocities. Finally we find that the tube tori do not appear in the 3D projections of the spaces of section in the axisymmetric Hamiltonian we examined.Comment: 26 pages, 34 figures, accepted for publication in the International Journal of Bifurcation and Chao

Definition of an indicator assessing the impact of a dam on the downstream river landscape

The increasing number of water withdrawals in Alpine regions represents a significant threat to aquatic ecosystems and river landscape (riverscape). To assess their sustainability, the impacts on river ecological status and landscape features need to be quantified with appropriate indicators. However, assessment of landscape attributes is a complex challenge, due to the lack of standardized methods. Moreover, few metrics quantifying the impacts of water withdrawal on downstream riverscape perception are available in the scientific literature. In this paper, a new indicator, named Landscape Protection Level (LPL), aimed at assessing the effects of water withdrawals on the river landscape, is presented. The indicator has been developed in Aosta Valley (NW Italian Alps), where the river network is heavily exploited by hundreds of withdrawals for hydropower production and irrigation, and it has been included in a multi-criteria analysis (MCA) procedure to assess the sustainability of water withdrawal licenses in relation to different flow release scenarios. The LPL indicator is based on three parameters, Constraint Factor, Release Factor, and Visual Elements Factor, quantifying the presence of landscape protection constraints, the ratio of flow released downstream of the dam to the available river discharge, and the impact on the visual perception of the bypassed stretch, respectively. Its application in four real case studies of existing hydropower plants is presented and discussed in the paper, demonstrating the indicator applicability to assess both specific release values and flow release scenarios varying over the year. Results are analyzed by highlighting the main strengths and weaknesses of the indicator and proposing some suggestions for future improvements. In particular, the reactiveness of the indicator, the representativeness of the stakeholders’ interests, the transparency of the indicator calculation procedure, and the time required for data collection and processing are discussed. Finally, future activities aimed at further improving the indicator applicability and transferability to different river contexts are proposed

Boundary Limitation of Wavenumbers in Taylor-Vortex Flow

We report experimental results for a boundary-mediated wavenumber-adjustment mechanism and for a boundary-limited wavenumber-band of Taylor-vortex flow (TVF). The system consists of fluid contained between two concentric cylinders with the inner one rotating at an angular frequency $\Omega$. As observed previously, the Eckhaus instability (a bulk instability) is observed and limits the stable wavenumber band when the system is terminated axially by two rigid, non-rotating plates. The band width is then of order $\epsilon^{1/2}$ at small $\epsilon$ ($\epsilon \equiv \Omega/\Omega_c - 1$) and agrees well with calculations based on the equations of motion over a wide $\epsilon$-range. When the cylinder axis is vertical and the upper liquid surface is free (i.e. an air-liquid interface), vortices can be generated or expelled at the free surface because there the phase of the structure is only weakly pinned. The band of wavenumbers over which Taylor-vortex flow exists is then more narrow than the stable band limited by the Eckhaus instability. At small $\epsilon$ the boundary-mediated band-width is linear in $\epsilon$. These results are qualitatively consistent with theoretical predictions, but to our knowledge a quantitative calculation for TVF with a free surface does not exist.Comment: 8 pages incl. 9 eps figures bitmap version of Fig

The Distribution of Bar and Spiral Strengths in Disk Galaxies

The distribution of bar strengths in disk galaxies is a fundamental property of the galaxy population that has only begun to be explored. We have applied the bar/spiral separation method of Buta, Block, and Knapen to derive the distribution of maximum relative gravitational bar torques, Q_b, for 147 spiral galaxies in the statistically well-defined Ohio State University Bright Galaxy Survey (OSUBGS) sample. Our goal is to examine the properties of bars as independently as possible of their associated spirals. We find that the distribution of bar strength declines smoothly with increasing Q_b, with more than 40% of the sample having Q_b <= 0.1. In the context of recurrent bar formation, this suggests that strongly-barred states are relatively short-lived compared to weakly-barred or non-barred states. We do not find compelling evidence for a bimodal distribution of bar strengths. Instead, the distribution is fairly smooth in the range 0.0 <= Q_b < 0.8. Our analysis also provides a first look at spiral strengths Q_s in the OSU sample, based on the same torque indicator. We are able to verify a possible weak correlation between Q_s and Q_b, in the sense that galaxies with the strongest bars tend also to have strong spirals.Comment: Accepted for publication in the Astronomical Journal, August 2005 issue (LaTex, 23 pages + 11 figures, uses aastex.cls

Regularization of Linear Ill-posed Problems by the Augmented Lagrangian Method and Variational Inequalities

We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a standard source condition. Using the method of variational inequalities, we extend these results in this paper to convergence rates of lower order, both for the case of an a priori parameter choice and an a posteriori choice based on Morozov's discrepancy principle. In addition, our approach allows the derivation of convergence rates with respect to distance measures different from the Bregman distance. As a particular application, we consider sparsity promoting regularization, where we derive a range of convergence rates with respect to the norm under the assumption of restricted injectivity in conjunction with generalized source conditions of H\"older type

Structure of Disk Dominated Galaxies I. Bulge/Disk Parameters, Simulations, and Secular Evolution

(Abridged) A robust analysis of galaxy structural parameters, based on the modeling of bulge and disk brightnesses in the BVRH bandpasses, is presented for 121 face-on and moderately inclined late-type spirals. Each surface brightness (SB) profile is decomposed into a sum of a generalized Sersic bulge and an exponential disk. The reliability and limitations of our bulge-to-disk (B/D) decompositions are tested with extensive simulations of galaxy brightness profiles (1D) and images (2D). Galaxy types are divided into 3 classes according to their SB profile shapes; Freeman Type-I and Type-II, and a third ``Transition'' class for galaxies whose profiles change from Type-II in the optical to Type-I in the infrared. We discuss possible interpretations of Freeman Type-II profiles. The Sersic bulge shape parameter for nearby Type-I late-type spirals shows a range between n=0.1-2 but, on average, the underlying surface density profile for the bulge and disk of these galaxies is adequately described by a double-exponential distribution. We confirm a coupling between the bulge and disk with a scale length ratio r_e/h=0.22+/-0.09, or h_bulge/h_disk=0.13+/-0.06 for late-type spirals, in agreement with recent N-body simulations of disk formation and models of secular evolution. This ratio increases from ~0.20 for late-type spirals to ~0.24 for earlier types. The similar scaling relations for early and late-type spirals suggest comparable formation and/or evolution scenarios for disk galaxies of all Hubble types.Comment: 78 pages with 23 embedded color figures + tables of galaxy structural parameters. Accepted for publication in the Astrophysical Journal. The interested reader is strongly encouraged to ignore some of the low res figures within; instead, download the high resolution version from http://www.astro.ubc.ca/people/courteau/public/macarthur02_disks.ps.g