A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems

In the present paper we give a proof of Nekhoroshev's theorem, which is concerned with an exponential estimate for the stability times in nearly integrable Hamiltonian systems. At variance with the already published proof, which refers to the case of an unperturbed Hamiltonian having the generic property of steepness, we consider here the particular case of a convex unperturbed Hamiltonian. The corresponding simplification in the proof might be convenient for an introduction to the subject.     

On the non-linear ‘squeezing’ effects around circular tunnels

An analysis is presented of the non-linear creep effects around a deep circular tunnel driven in ‘squeezing’ ground. The time-dependent behaviour of the geotechnical medium is described by means of a simple viscoplastic rheological model capable of approximating primary, secondary and tertiary creep behaviours. It is shown that tertiary creep can be allowed for by providing a suitable law governing the variation of some material parameters (such as viscosity) with stresses and strains. The basic operations of the ‘evolutive’ procedure adopted for time integration are outlined. Along each time integration step, quadratic variations of the stress and strain fields and linear variations of the material parameters are assumed. The results of various finite element analyses are presented concerning both lined and unlined cases. For the lined cases, the influence of the liner stiffness and of the time elapsed between the end of excavation and the liner installation is considered.     

A nonlinear programming analysis of unconfined steady-state seepage

A finite element, variable mesh analysis of unconfined steady-state seepage problems is presented based on a nonlinear programming algorithm. It is shown that the minimization of an objective function which merely represents a measure of the total flux leaving or entering the mesh at the free surface nodes (except those that belong also to pervious boundaries) does not permit a unique definition of the free surface geometry. This problem, which is apparently related to the numerical instabilities often met when using variable mesh approaches, can be eliminated by adding to the objective function a term representing a sort of overall ‘regularity’ condition for the shape of the free surface. The modified solution procedure turns out to be stable and able to provide meaningful results for practical problems even when rather coarse meshes are adopted.     

Flow in coronal loops with a mass source

This research studies the flow of plasma inside a coronal loop in which an injection of plasma through the lateral surface is permitted. The flow is assumed steady and polytropic. The problem covers two cases: (a) upflow at one footpoint, downflow at the other; (b) downflow at both footpoints. The first case can be shown to be quite similar to that of a mass-conserving flow with variable cross section; the second, instead, is characterized by solutions with a different type of topology; its main new feature is the obvious fact that all the solutions pass through a single point going from negative to positive velocities. In this second case the density ratio between footpoints and top can be much smaller than in a mass conserving flow. This can explain some properties of observed loops.     

Selection criteria for linear regression models to estimate individual tree biomasses in the Atlantic Rain Forest,Brazil

Background

Biomass models are useful for several purposes, especially for quantifying carbon stocks and dynamics in forests. Selecting appropriate equations from a fitted model is a process which can involves several criteria, some widely used and others used to a lesser extent. This study analyzes six selection criteria for models fitted to six sets of individual biomass collected from woody indigenous species of the Tropical Atlantic Rain Forest in Brazil. Six models were examined and the respective fitted equations evaluated by the residual sum of squares, adjusted coefficient of determination, absolute and relative estimates of the standard error of estimate, and Akaike and Schwartz (Bayesian) information criteria. The aim of this study was to analyze the numeric behavior of these model selection criteria and discuss the ease of interpretation of them. The importance of residual analysis in model selection is stressed.

Results

The adjusted coefficient of determination (\( R^{2}_{adj.} \)) and the standard error of estimate in percentage (Syx%) are relative model selection criteria and are not affected by sample size and scale of the response variable. The sum of squared residuals (SSR), the absolute standard error of estimate (Syx), the Akaike information criterion and the Schwartz information criterion, in turn, depend on these quantities. The best fit model was always the same within a given data set regardless the model selection criteria considered (except for SSR in two cases), indicating they tend to converge to a common result. However, such criteria are not always closely related across different data sets. General model selection criteria are indicative of the average goodness of fit, but do not capture bias and outlier effects. Graphical residual analysis is a useful tool to this detection and must always be used in model selection.

Conclusions

It is concluded that the criteria for model selection tend to lead to a common result, regardless their mathematical formulation and statistical significance. Relative measures of goodness of fitting are easier to interpret than the absolute ones. Careful graphical residual analysis must always be used to confirm the performance of the models.

     

Fluid–rock interactions associated with regional tectonics and basin evolution

An integrated approach consisting of fracture analysis, petrography, carbon, oxygen and strontium‐isotope analyses, as well as fluid‐inclusion micro‐thermometry, led to a better understanding of the evolution of fluid–rock interactions and diagenesis of the Upper Permian to Upper Triassic carbonates of the United Arab Emirates. The deposited carbonates were first marked by extensive early dolomitization. During progressive burial, the carbonates were affected by dolomite recrystallization as well as precipitation of vug and fracture‐filling dolomite, quartz and calcite cements. After considerable burial during the Middle Cretaceous, sub‐vertical north–south oriented fractures (F1) were cemented by dolomite derived from mesosaline to hypersaline fluids. Upon the Late Cretaceous maximum burial and ophiolite obduction, sub‐vertical east–west fractures (F2) were cemented by dolomite (Dc2) and saddle dolomite (Ds) derived from hot, highly saline fluids. Then, minor quartz cement has precipitated in fractures from hydrothermal brines. Fluid‐inclusion analyses of the various diagenetic phases imply the involvement of increasingly hot (200°C) saline brines (20 to 23% NaCl eq.). Through one‐dimensional burial history numerical modelling, the maximum temperatures reached by the studied rocks are estimated to be in the range of 160 to 200°C. Tectonically‐driven flux of hot fluids and associated diagenetic products are interpreted to have initiated during the Late Cretaceous maximum burial and lasted until the Oligocene–Miocene compressional tectonics and related uplift. The circulation of such hydrothermal brines led to partial dissolution of dolomites (Dc2 and Ds) and to precipitation of hydrothermal calcite C1 in new (mainly oriented north–south; F3) and pre‐existing, reactivated fractures. The integration of the obtained data confirms that the diagenetic evolution was controlled primarily by the interplay of the burial thermal evolution of the basin and the regional tectonic history. Hence, this contribution highlights the impacts of regional tectonics and basin history on diagenetic processes, which may subsequently affect reservoir properties.     

Hillslope-to-valley transition morphology: New opportunities from high resolution DTMs

The search for the optimal spatial scale for observing landforms to understand physical processes is a fundamental issue in geomorphology. Topographic attributes derived from Digital Terrain Models (DTMs) such as slope, curvature and drainage area provide a basis for topographic analyses. The slope–area relationship has been used to distinguish diffusive (hillslope) from linear (valley) processes, and to infer dominant sediment transport processes. In addition, curvature is also useful in distinguishing the dominant landform process. Recent topographic survey techniques such as LiDAR have permitted detailed topographic analysis by providing high-quality DTMs. This study uses LiDAR-derived DTMs with a spatial scale between 1 and 30 m in order to find the optimal scale for observation of dominant landform processes in a headwater basin in the eastern Italian Alps where shallow landsliding and debris flows are dominant. The analysis considered the scaling regimes of local slope versus drainage area, the spatial distribution of curvature, and field observations of channel head locations. The results indicate that: i) hillslope-to-valley transitions in slope–area diagrams become clearer as the DTM grid size decreases due to the better representation of hillslope morphology, and the topographic signature of valley incision by debris flows and landslides is also best displayed with finer DTMs; ii) regarding the channel head distribution in the slope–area diagrams, the scaling regimes of local slope versus drainage area obtained with grid sizes of 1, 3, and 5 m are more consistent with field data; and iii) the use of thresholds of standard deviation of curvature, particularly at the finest grid size, were proven as a useful and objective methodology for recognizing hollows and related channel heads.     

Surface heat fluxes and thermohaline variability in the Ross Sea and in Terra Nova Bay polynya

The Ross Sea is an important area for the ventilation of the deep layers of the Southern Ocean (e.g. [Jacobs, S.S., Fairbanks, R.G., Horibe, Y., 1985. Origin and evolution of water masses near the Antarctic continental margin: evidence from H218O/H216O ratios in seawater. In: Jacobs, S.S. (Ed.), Oceanology of the Antarctic Continental Shelf. Antarctic Research Series, vol. 43. pp. 59–85; Orsi, A.H., Johnson, G.C., Bullister, J.L., 1999. Circulation, mixing, and the production of Antarctic bottom water. Progress in Oceanography 109, 43–55]). These processes are driven by the atmospheric forcing which, at high latitude, plays a key role in the formation and thickness of sea ice. In order to investigate the effect of the atmospheric forcing variability at different time scales, we analysed the surface heat budget over the Ross Sea continental shelf and in Terra Nova Bay (TNB) polynya, using analyses for the period 1990–2006 provided by European Centre for Medium-range Weather Forecast (ECMWF). This study was also performed using thermohaline data collected within the activities of Climatic Long-term Interaction for the mass-balance in Antarctica project of the Italian National Programme for Antarctic Research for the summer periods from 1994 until 2001.The annual average of the heat budget over the continental shelf of the Ross Sea estimated in the period 1990–2006 shows an interannual variability ranging between −97 and −123 W m⁻². Assuming that the heat loss must be compensated by the sensible heat carried by the Circumpolar Deep Water we estimated its transport (3.1 Sv) and its variability (0.2 Sv). Similarly in the TNB polynya the heat loss reaches its maximum in 2003 (−313 W m⁻²) and its minimum (−58 W m⁻²) in 1996. The related production of sea ice and the High Salinity Shelf Water (HSSW) were also estimated. The HSSW production switched from the lowest values during the first 10 years of the investigated period (1990–2000) to the highest values for the remaining period (2001–2006).The thermohaline characteristics of the water column in TNB show a general decrease in salinity with a superimposed variability. Comparison between the estimated HSSW production and the salinity observed within the TNB water column show similar tendency in the last years after 2002, while during the period 1995–1998 the behaviour is different. Our hypothesis concern a possible role of the CDW inflow in the TNB area and our results could be explained by a different contribution of CDW transport and HSSW production to the salt content within the water column.     

Synthetic ANaB(Na x Li1 − x Mg1)CMg5Si8O22(OH)2 (with x = 0.6, 0.2 and 0) P21/m amphiboles at high pressure: a synchrotron infrared study

The high-pressure behavior of three synthetic amphiboles crystallized with space group P2₁/m at room conditions in the system Li₂O–Na₂O–MgO–SiO₂–H₂O has been studied by in situ synchrotron infrared absorption spectroscopy. The amphiboles have compositions ^ANa ^B(Na _x Li_1 − x Mg₁) ^CMg₅ Si₈ O₂₂(OH)₂ with x = 0.6, 0.2 and 0.0, respectively. The high-P experiments up to 32 GPa were carried out on the U2A beamline at Brookhaven National Laboratory (NY, USA) using a diamond anvil cell under non-hydrostatic or quasi-hydrostatic conditions. The two most intense absorption bands in the OH-stretching infrared spectra can be assigned to two non-equivalent O–H dipoles in the P2₁/m structure, bonded to the same local environment ^M1M3Mg₃–OH–^ANa, and pointing toward two differently kinked tetrahedral rings. In all samples these bands progressively merge to give a unique symmetrical absorption with increasing pressure, suggesting a change in symmetry from P2₁/m to C2/m. The pressure at which the transition occurs appears to be linearly correlated to the aggregate B-site dimension. The infrared spectra collected for amphibole ^B(Na_0.2Li_0.8Mg₁) in the frequency range 50 to 1,400 cm⁻¹ also show a series of changes with increasing pressure. The data reported here support the inference of Iezzi et al. (Am Miner 91:479–482, 2006a) regarding a new high-pressure amphibole polymorph.     

Seasonal changes in runoff generation in a small forested mountain catchment

This study aimed to investigate the seasonal variability of runoff generation processes, the sources of stream water, and the controls on the contribution of event water to streamflow for a small forested catchment in the Italian pre‐Alps. Hydrometric, isotopic, and electrical conductivity data collected between August 2012 and August 2013 revealed a marked seasonal variability in runoff responses. Noticeable differences in runoff coefficients and hydrological dynamics between summer and fall/spring rainfall events were related to antecedent moisture conditions and event size. Two‐component and three‐component hydrograph separation and end‐member mixing analysis showed an increase in event water contributions to streamflow with event size and average rainfall intensity. Event water fractions were larger during dry conditions in the summer, suggesting that stormflow generation in the summer consisted predominantly of direct channel precipitation and some saturated overland flow from the riparian zone. On the contrary, groundwater and hillslope soil water contributions dominated the streamflow response during wet conditions in fall. Seasonal differences were also noted between event water fractions computed based on isotopic and electrical conductivity data, likely because of the dilution effect during the wetter months. Copyright © 2014 John Wiley & Sons, Ltd.