Simultaneous identification of parameter,initial condition,and boundary condition in groundwater modelling

In this paper, we perform an inverse method to simultaneously estimate aquifer parameters, initial condition, and boundary conditions in groundwater modelling. The parameter estimation is extended to a complete inverse problem that makes the calibrated groundwater flow model more realistic. The adjoint state method, the gradient search method, and the least square error algorithm are combined to build the optimization procedure. Horizontal two‐dimensional groundwater flow in a confined aquifer is exemplified to demonstrate the correlation between unknowns, the contribution of observation, as well as the suitability of applying the inverse method. The correlation analysis shows the connection between storage coefficient and initial condition. Besides, transmissivity and boundary conditions are also highly correlated. More observations at different location and time are necessary to provide sufficient information. A time series of unsteady head is requested for estimation of storage coefficient and initial condition. Observation near boundary is very effective for boundary condition estimation. The observation at pumping well mostly contributes to the estimation of transmissivity. According to all observations, it is possible to identify parameters, initial condition, and boundary condition simultaneously. Furthermore, the results not only illustrate the traditional assumption of known boundary condition but also initial condition, which may cause an incorrect estimation. Copyright © 2009 John Wiley & Sons, Ltd.     

Bayesian analysis of stage–fall–discharge models for gauging stations affected by variable backwater

Parsimonious stage–fall–discharge rating curve models for gauging stations subject to backwater complications are developed from simple hydraulic theory. The rating curve models are compounded in order to allow for possible shifts in the hydraulics when variable backwater becomes effective. The models provide a prior scientific understanding through the relationship between the rating curve parameters and the hydraulic properties of the channel section under study. This characteristic enables prior distributions for the rating curve parameters to be easily elicited according to site‐specific information and the magnitude of well‐known hydraulic quantities. Posterior results from three Norwegian and one American twin‐gauge stations affected by variable backwater are obtained using Markov chain Monte Carlo simulation techniques. The case studies demonstrate that the proposed Bayesian rating curve assessment is appropriate for developing rating procedures for gauging stations that are subject to variable backwater. Copyright © 2009 John Wiley & Sons, Ltd.     

Early solar system aqueous activity: K isotope evidence from Allende

The alkali element K is moderately volatile and fluid mobile; thus, it can be influenced by both primary processes (evaporation and recondensation) in the solar nebula and secondary processes (thermal and aqueous alteration) in the parent body. Since these primary and secondary processes would induce different isotopic fractionations, K isotopes could become a potential tracer to distinguish them. Using recently developed methods with improved precision (0.05‰, 95% confidence interval), we systematically measured the K isotopic compositions and major/trace elemental compositions of chondritic components (18 chondrules, 3 CAIs, 2 matrices, and 5 bulks) in the carbonaceous chondrite fall Allende. Among all the components analyzed in this study, CAIs, which formed initially under high‐temperature conditions in the solar nebula and were dominated by nominally K‐free refractory minerals, have the highest K₂O content (average 0.53 wt%) and have K isotope compositions most enriched in heavy isotopes (δ⁴¹K: ?0.30 to ?0.25‰). Such an observation is consistent with previous petrologic studies that show CAIs in Allende have undergone alkali enrichment during metasomatism. In contrast, chondrules contain lower K₂O content (0.003–0.17 wt%) and generally lighter K isotope compositions (δ⁴¹K: ?0.87‰ to ?0.24‰). The matrix and bulks are nearly identical in K₂O content and K isotope compositions (0.02–0.05 wt%; δ⁴¹K: ?0.62 to ? 0.46‰), which are, as expected, right in the middle of CAIs and chondrules. This strongly indicates that most of the chondritic components of Allende suffered aqueous alteration and their K isotopic compositions are the ramification of Allende parent‐body processing instead of primary nebular signatures. Nevertheless, we propose the small K isotope fractionations observed (< 1‰) among Allende components are likely similar to the overall range of K isotopic fractionation that occurred in nebular environment. Furthermore, the K isotope compositions seen in the components of Allende in this study are consistent with MC‐ICP‐MS analyses of the components in ordinary chondrites, which also show an absence of large (10‰) isotope fractionations. This is not expected as evaporation experiments in nebular conditions suggest there should be large K isotopic fractionations. Nevertheless, possible nebular processes such as chondrules back exchanging with ambient gas when they formed could explain this lack of large K isotopic variation.     

The evolution of the z distribution of normal neutron stars in the Galaxy

Under the two initial 1‐D one parameter velocity distribution forms (one is normal, the other is exponential), the z direction scale height evolution of normal neutron stars in the Galaxy is studied by numerical simulation. We do statistics for the cases at different time segments, also do statistics for the cumulative cases made of each time segment. The results show in the cumulative cases the evolution curves of the scale heights are smoother than in the each time segment, i.e., the cumulation improve the signal‐to‐noise ratio. Certainly the evolution cases are different at different Galactic disk locations, which also have very large difference from the average cases in the whole disk. In the initial stages of z evolution of normal neutron stars, after the beginning transient states, the cumulative scale heights increase linearly with time, and the cumulative scale height increasing rates have linear relationship with the initial velocity distribution parameters, which have larger fluctuation in the vicinity of the Sun than in the whole disk. We utilize the linear relationship of the cumulative scale height increasing rates vs. the initial velocity distribution parameters in the vicinity of the Sun to make comparison with the observation near the Sun. The results show if there is no magnetic decay, then the deserved initial velocity parameters are obvious lower than the present well known results from some authors; whereas if introducing magnetic decay, for the 1‐D normal case we can make consistence among concerning results using magnetic decay time values which are supported by some authors, while for the 1‐D exponential case the results show the lackness of young pulsar samples in the larger z in the vicinity of the Sun (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

European Solar Telescope: Progress status

In this paper, the present status of the development of the design of the European Solar Telescope is described. The telescope is devised to have the best possible angular resolution and polarimetric performance, maximizing the throughput of the whole system. To that aim, adaptive optics and multi‐conjugate adaptive optics are integrated in the optical path. The system will have the possibility to correct for the diurnal variation of the distance to the turbulence layers, by using several deformable mirrors, conjugated at different heights. The present optical design of the telescope distributes the optical elements along the optical path in such a way that the instrumental polarization induced by the telescope is minimized and independent of the solar elevation and azimuth. This property represents a large advantage for polarimetric measurements. The ensemble of instruments that are planned is also presented (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A complex variable solution for stress and displacement field around a lined circular tunnel at great depth

By applying the series expansion technique in the complex variable method established by Muskhelishvili, the plane elasticity problem for the stress and displacement field around a lined circular tunnel in conjunction with the consideration of misfit and interaction between the liner and the surrounding geomaterial is dealt with. The tunnel is assumed to be driven in a homogeneous and isotropic geomaterial. The coefficients in the Laurent series expansion of the stress functions are determined. The complex potentials in the liner and the surrounding geomaterial are explicitly derived, respectively. As an example, the case of a lined circular tunnel located in an isotropic initial stress field but subjected to uniform internal pressure is numerically considered. Numerical results indicate that the installation of tunnel liner can reduce the influences of the tunnel excavation on the in situ displacement and stress fields. However, the relative thickness and rigidity of the liner should be in an appropriate range. In addition, the effect of the tunnel excavation upon the displacement field is more significant than that upon the stress field. As far as the stress field in the surrounding geomaterial is concerned, when the ratio between the cover depth of tunnel and the tunnel radius is larger than 5, the results for the stress field in the paper are applicable. When the ratio between the tunnel depth and the tunnel radius is larger than 20, the results are applicable for the displacement field. Copyright © 2008 John Wiley & Sons, Ltd.     

Vertical amplitude reduction of Rayleigh waves by a row of piles in a poroelastic half‐space

A row of rigid piles is addressed as the countermeasures for isolating Rayleigh waves in a poroelastic half‐space. The complex characteristic equations for Rayleigh waves are derived via Biot's theory and their existence conditions are given. The piles are modeled as Euler–Bernoulli beams with longitudinal displacements and the diffracted field by each pile is constructed only with Rayleigh waves. Six infinite linear systems of algebraic equations are obtained in terms of the equilibrium of forces and continuity of displacements at the pile–soil interfaces. The systems are subsequently solved in the complex least‐squares sense. The influence of certain pile and soil characteristics such as the permeability of poroelastic soil, spacing between the piles and length of the piles on the isolating performance of a pile barrier is investigated. Computed results show that the permeability of poroelastic soil displays a significant effect on the vertical amplitude reduction of Rayleigh waves. Copyright © 2009 John Wiley & Sons, Ltd.     

Non‐equilibrium concepts lead to a unified explanation of the formation of chondrules and chondrites

Abstract— Calculations of the formation of seven types of chondrules in Semarkona from a gas of solar composition were performed with the FACT computer program to predict the chemistries of oxides (including silicates), developed by the authors and their colleagues. The constrained equilibrium theory was used in the calculations with two nucleation constraints suggested by nucleation theory. The first constraint was the blocking of Fe and other metal gaseous atoms from condensing to form solids or liquids because of very high surface free energies and high surface tensions of the solid and liquid metals, respectively. The second constraint was the blocking of the condensation of solids and the formation of metastable liquid oxides (including silicates) well below their liquidus temperatures. Our laboratory experiments suggested subcooling of type IIA chondrule compositions of 400 degrees or more below the liquidus temperature. The blocking of iron leads to a supersaturation of Fe atoms, so that the partial pressure of Fe (p_Fe) is larger than the partial pressure at equilibrium (p_Fe(eq)). The supersaturation ratio S = p_Fe/p_Fe(eq) becomes larger than 1 and increases rapidly with a decrease in temperature. This drives the reaction Fe + H₂O ? H₂ + FeO to the right. With S = 100, the activity of FeO in the liquid droplet is 100 times as large as the value at equilibrium. The FeO activities are a function of temperature and provide relative average temperatures of the crystallization of chondrules. Our calculations for the LL3.0 chondrite Semarkona and our study of some non‐equilibrium effects lead to accurate representations of the compositions of chondrules of types IA, IAB, IB, IIA, IIAB, IIB, and CC. Our concepts readily explain both the variety of FeO concentrations in the different chondrule types and the entire process of chondrule formation. Our theory is unified and could possibly explain the formation of chondrules in all chondritic meteorites as well as provide a simple explanation for the complex chemistries of chondrites, and especially for type 3 chondrites.