The thermodynamics and roughening of solid-solid interfaces

The dynamics of sharp interfaces separating two non-hydrostatically stressed solids is analyzed using the idea that the rate of mass transport across the interface is proportional to the thermodynamic potential difference across the interface. The solids are allowed to exchange mass by transforming one solid into the other, thermodynamic relations for the transformation of a mass element are derived and a linear stability analysis of the interface is carried out. The stability is shown to depend on the order of the phase transition occurring at the interface. Numerical simulations are performed in the non-linear regime to investigate the evolution and roughening of the interface. It is shown that even small contrasts in the referential densities of the solids may lead to the formation of finger like structures aligned with the principal direction of the far field stress.Comment: (24 pages, 8 figures; V2: added figures, text revisions

Scale Free Cluster Distributions from Conserving Merging-Fragmentation Processes

We propose a dynamical scheme for the combined processes of fragmentation and merging as a model system for cluster dynamics in nature and society displaying scale invariant properties. The clusters merge and fragment with rates proportional to their sizes, conserving the total mass. The total number of clusters grows continuously but the full time-dependent distribution can be rescaled over at least 15 decades onto a universal curve which we derive analytically. This curve includes a scale free solution with a scaling exponent of -3/2 for the cluster sizes.Comment: 4 pages, 3 figure

Comparing the temperatures of galaxy clusters from hydro-N-body simulations to Chandra and XMM-Newton observations

Theoretical studies of the physical processes guiding the formation and evolution of galaxies and galaxy clusters in the X-ray are mainly based on the results of numerical hydrodynamical N-body simulations, which in turn are often directly compared to X-ray observations. Although trivial in principle, these comparisons are not always simple. We demonstrate that the projected spectroscopic temperature of thermally complex clusters obtained from X-ray observations is always lower than the emission-weighed temperature, which is widely used in the analysis of numerical simulations. We show that this temperature bias is mainly related to the fact that the emission-weighted temperature does not reflect the actual spectral properties of the observed source. This has important implications for the study of thermal structures in clusters, especially when strong temperature gradients, like shock fronts, are present. Because of this bias, in real observations shock fronts appear much weaker than what is predicted by emission-weighted temperature maps, and may even not be detected. This may explain why, although numerical simulations predict that shock fronts are a quite common feature in clusters of galaxies, to date there are very few observations of objects in which they are clearly seen. To fix this problem we propose a new formula, the spectroscopic-like temperature function, and show that, for temperature larger than 3 keV, it approximates the spectroscopic temperature better than few per cent, making simulations more directly comparable to observations.Comment: Submitted for publication in MNRAS; 15 pages, 10 color figures and 13 BW figures,mn2e.cls. High resolution figures available here: http://people.roma2.infn.it/~mazzotta/preprints/mazzotta.pd

Diffusion, Fragmentation and Coagulation Processes: Analytical and Numerical Results

We formulate dynamical rate equations for physical processes driven by a combination of diffusive growth, size fragmentation and fragment coagulation. Initially, we consider processes where coagulation is absent. In this case we solve the rate equation exactly leading to size distributions of Bessel type which fall off as $\exp(-x^{3/2})$ for large $x$-values. Moreover, we provide explicit formulas for the expansion coefficients in terms of Airy functions. Introducing the coagulation term, the full non-linear model is mapped exactly onto a Riccati equation that enables us to derive various asymptotic solutions for the distribution function. In particular, we find a standard exponential decay, $\exp(-x)$, for large $x$, and observe a crossover from the Bessel function for intermediate values of $x$. These findings are checked by numerical simulations and we find perfect agreement between the theoretical predictions and numerical results.Comment: (28 pages, 6 figures, v2+v3 minor corrections

Weak-Lensing Halo Numbers and Dark-Matter Profiles

Integral measures of weak gravitational lensing by dark-matter haloes, like the aperture mass, are sensitive to different physical halo properties dependent on the halo mass density profile. For isothermal profiles, the relation between aperture mass and virial mass is steeper than for haloes with the universal NFW profile. Consequently, the halo mass range probed by the aperture mass is much wider for NFW than for isothermal haloes. We use recent modifications to the Press-Schechter mass function in CDM models normalised to the local abundance of rich clusters, to predict the properties of the halo sample expected to be accessible with the aperture mass technique. While ~10 haloes should be detected per square degree if the haloes have NFW profiles, their number density is lower by approximately an order of magnitude if they have isothermal profiles. These results depend only very mildly on the cosmological background model. We conclude that counts of haloes with a significant weak-lensing signal are a powerful discriminator between different dark-matter profiles.Comment: submitted to A&

Discrepant Mass Estimates in the Cluster of Galaxies Abell 1689

We present a new mass estimate of a well-studied gravitational lensing cluster, Abell 1689, from deep Chandra observations with a total exposure of 200 ks. Within r=200 h-1 kpc, the X-ray mass estimate is systematically lower than that of lensing by 30-50%. At r>200 h-1 kpc, the mass density profiles from X-ray and weak lensing methods give consistent results. The most recent weak lensing work suggest a steeper profile than what is found from the X-ray analysis, while still in agreement with the mass at large radii. Previous studies have suggested that cooler small-scale structures can bias X-ray temperature measurements or that the northern part of the cluster is disturbed. We find these scenarios unlikely to resolve the central mass discrepancy since the former requires 70-90% of the space to be occupied by these cool structures and excluding the northern substructure does not significantly affect the total mass profiles. A more plausible explanation is a projection effect. We also find that the previously reported high hard-band to broad-band temperature ratio in A1689, and many other clusters observed with Chandra, may be resulting from the instrumental absorption that decreases 10-15% of the effective area at ~1.75 keV.Comment: 18 pages, 15 figures. ApJ accepte

Morphology of two dimensional fracture surface

We consider the morphology of two dimensional cracks observed in experimental results obtained from paper samples and compare these results with the numerical simulations of the random fuse model (RFM). We demonstrate that the data obey multiscaling at small scales but cross over to self-affine scaling at larger scales. Next, we show that the roughness exponent of the random fuse model is recovered by a simpler model that produces a connected crack, while a directed crack yields a different result, close to a random walk. We discuss the multiscaling behavior of all these models.Comment: slightly revise

XMM−NewtonXMM-Newton Ω\Omega project: III. Gas mass fraction shape in high redshift clusters

We study the gas mass fraction, $f\_{\rm gas},$ behavior in $XMM-Newton$ $\Omega$ project. The typical $f\_{\rm gas}$ shape of high redshift galaxy clusters follows the global shape inferred at low redshift quite well. This result is consistent with the gravitational instability picture leading to self similar structures for both the dark and baryonic matter. However, the mean $f\_{\rm gas} in distant clusters shows some differences to local ones, indicating a departure from strict scaling. This result is consistent with the observed evolution in the luminosity-temperature relation. We quantitatively investigate this departure from scaling laws. Within the local sample we used, a moderate but clear variation of the amplitude of the gas mass fraction with temperature is found, a trend that weakens in the outer regions. These variations do not explain departure from scaling laws of our distant clusters. An important implication of our results is that the gas fraction evolution, a test of the cosmological parameters, can lead to biased values when applied at radii smaller than the virial radius. From our$XMM$ clusters, the apparent gas fraction at the virial radius is consistent with a non-evolving universal value in a high matter density model and not with a concordance.Comment: Accepted, A&A, in pres

Eurasian Reindeer Pastoralism in a Changing Climate: Indigenous Knowledge and NASA Remote Sensing

It is intended that Reindeer Mapper/EALAT will be able to provide reindeer herders with an efficient tool for managing the real-time movements and migrations of their herds through enabling improved efficiency in linking different members of the herder settlements or communities and providing real-time local, satellite or other data (e.g., ice melt in lakes and rivers, weather events), thus enabling real time adjustments to herd movements to avoid problems such as changing weather/climate conditions, freeze-thaw "lock-out" problems, or take advantage of availability of better pasturelands along migration routes. The system is being designed to incorporate local data to allow users to bring their own data into the system for analysis in addition to the data provided by the system itself. With the local information of the population, up to date environmental data and habitat characteristics, the system could generate maps depicting important features of interest for reindeer managers. One of the products derived from the planned Reindeer Mapper system will be a web-based graphic display that allows analysts to quickly pinpoint areas of interest such as those with large concentrations of reindeer and provide surrounding environmental information. The system could be automatically updated with near-real-time information such as hourly precipitation and snowfall rate and accumulation, daily surface and air temperatures, and vegetation cover conditions. The system could bring attention to the proximity of human and animal populations as part of the need for control response. A local GIS will bring these many layers together with several supporting models, showing only a straightforward graphic of the real-time situation in the field. Because the system proposed will be operating in the Internet environment, it should be virtually accessible from any network computers and wireless remote access from the field. The International Center for Reindeer Husbandry in Kautokeino, Norway, is providing regional and international coordination of and access to data sets and expertise, and will act as overall clearinghouse for EALAT information