The method of fundamental solutions for free surface Stefan problems

In this paper, free surface problems of Stefan-type for the parabolic heat equation are investigated using the method of fundamental solutions. The additional measurement necessary to determine the free surface could be a boundary temperature, a heat flux or an energy measurement. Both one- and two-phase flows are investigated. Numerical results are presented and discussed.

An iterative method based on boundary integrals for elliptic Cauchy problems in semi-infinite domains

In this study, we investigate the problem of reconstruction of a stationary temperature field from given temperature and heat flux on a part of the boundary of a semi-infinite region containing an inclusion. This situation can be modelled as a Cauchy problem for the Laplace operator and it is an ill-posed problem in the sense of Hadamard. We propose and investigate a Landweber-Fridman type iterative method, which preserve the (stationary) heat operator, for the stable reconstruction of the temperature field on the boundary of the inclusion. In each iteration step, mixed boundary value problems for the Laplace operator are solved in the semi-infinite region. Well-posedness of these problems is investigated and convergence of the procedures is discussed. For the numerical implementation of these mixed problems an efficient boundary integral method is proposed which is based on the indirect variant of the boundary integral approach. Using this approach the mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing that stable and accurate reconstructions of the temperature field on the boundary of the inclusion can be obtained also in the case of noisy data. These results are compared with those obtained with the alternating iterative method.

Population lensing vs thermal lensing in Yb:YAG rods and disks

The induced lenses in the Yb:YAG rods and disks end-pumped by a Gaussian beam were analyzed both analytically and numerically. The thermally assisted mechanisms of the lens formation were considered to include: the conventional volume thermal index changes ("dn/dT"), the bulging of end faces, the photoelastic effect, and the bending (for a disk). The heat conduction equations (with an axial heat flux for a disk and a radial heat flux for a rod), and quasi-static thermoelastic equations (in the plane-stress approximation with free boundary conditions) were solved to find the thermal lens power. The population rate equation with saturation (by amplified spontaneous emission or an external wave) was examined to find the electronic lens power in the active elements.

Prediction of welding distortion in butt joint of thin plates

This paper investigates distortions and residual stresses induced in butt joint of thin plates using Metal Inert Gas welding. A moving distributed heat source model based on Goldak's double-ellipsoid heat flux distribution is implemented in Finite Element (FE) simulation of the welding process. Thermo-elastic-plastic FE methods are applied to modelling thermal and mechanical behaviour of the welded plate during the welding process. Prediction of temperature variations, fusion zone and heat affected zone as well as longitudinal and transverse shrinkage, angular distortion, and residual stress is obtained. FE analysis results of welding distortions are compared with existing experimental and empirical predictions. The welding speed and plate thickness are shown to have considerable effects on welding distortions and residual stresses. © 2009 Elsevier Ltd. All rights reserved.

Ecohydrology, evapotranspiration and hydrogeochemistry of carbonate mangrove wetlands

Coastal environments can be highly susceptible to environmental changes caused by anthropogenic pressures and natural events. Both anthropogenic and natural perturbations may directly affect the amount and the quality of water flowing through the ecosystem, both in the surface and subsurface and can subsequently, alter ecological communities and functions. The Florida Everglades and the Sian Ka'an Biosphere Reserve (Mexico) are two large ecosystems with an extensive coastal mangrove ecotone that represent a historically altered and pristine environment, respectively. Rising sea levels, climate change, increased water demand, and salt water intrusion are growing concerns in these regions and underlies the need for a better understanding of the present conditions. The goal of my research was to better understand various ecohydrological, environmental, and hydrogeochemical interactions and relationships in carbonate mangrove wetlands. A combination of aqueous geochemical analyses and visible and near-infrared reflectance data were employed to explore relationships between surface and subsurface water chemistry and spectral biophysical stress in mangroves. Optical satellite imagery and field collected meteorological data were used to estimate surface energy and evapotranspiration and measure variability associated with hurricanes and restoration efforts. Furthermore, major ionic and nutrient concentrations, and stable isotopes of hydrogen and oxygen were used to distinguish water sources and infer coastal groundwater discharge by applying the data to a combined principal component analysis-end member mixing model. Spectral reflectance measured at the field and satellite scales were successfully used to estimate surface and subsurface water chemistry and model chloride concentrations along the southern Everglades. Satellite imagery indicated that mangrove sites that have less tidal flushing and hydrogeomorphic heterogeneity tend to have more variable evapotranspiration and soil heat flux in response to storms and restoration. Lastly, water chemistry and multivariate analyses indicated two distinct fresh groundwater sources that discharge to the phosphorus-limited estuaries and bays of the Sian Ka'an Biopshere Reserve; and that coastal groundwater discharge was an important source for phosphorus. The results of the study give us a better understanding of the ecohydrological and hydrogeological processes in carbonate mangrove environments that can be then be extrapolated to similar coastal ecosystems in the Caribbean.

Last Interglacial synthesis of high-latitude temperature: temperature anomalies and associated errors for 4 time slices

The Last Interglacial (LIG, 129-116 thousand of years BP, ka) represents a test bed for climate model feedbacks in warmer-than-present high latitude regions. However, mainly because aligning different palaeoclimatic archives and from different parts of the world is not trivial, a spatio-temporal picture of LIG temperature changes is difficult to obtain. Here, we have selected 47 polar ice core and sub-polar marine sediment records and developed a strategy to align them onto the recent AICC2012 ice core chronology. We provide the first compilation of high-latitude temperature changes across the LIG associated with a coherent temporal framework built between ice core and marine sediment records. Our new data synthesis highlights non-synchronous maximum temperature changes between the two hemispheres with the Southern Ocean and Antarctica records showing an early warming compared to North Atlantic records. We also observe warmer than present-day conditions that occur for a longer time period in southern high latitudes than in northern high latitudes. Finally, the amplitude of temperature changes at high northern latitudes is larger compared to high southern latitude temperature changes recorded at the onset and the demise of the LIG. We have also compiled four data-based time slices with temperature anomalies (compared to present-day conditions) at 115 ka, 120 ka, 125 ka and 130 ka and quantitatively estimated temperature uncertainties that include relative dating errors. This provides an improved benchmark for performing more robust model-data comparison. The surface temperature simulated by two General Circulation Models (CCSM3 and HadCM3) for 130 ka and 125 ka is compared to the corresponding time slice data synthesis. This comparison shows that the models predict warmer than present conditions earlier than documented in the North Atlantic, while neither model is able to produce the reconstructed early Southern Ocean and Antarctic warming. Our results highlight the importance of producing a sequence of time slices rather than one single time slice averaging the LIG climate conditions.

Multi-year weather data in the remote semi-arid to arid mountain region of the Saharan flank of the Atlas Mountains

In 2001, a weather and climate monitoring network was established along the temperature and aridity gradient between the sub-humid Moroccan High Atlas Mountains and the former end lake of the Middle Drâa in a pre-Saharan environment. The highest Automated Weather Stations (AWS) was installed just below the M'Goun summit at 3850 m, the lowest station Lac Iriki was at 450 m. This network of 13 AWS stations was funded and maintained by the German IMPETUS (BMBF Grant 01LW06001A, North Rhine-Westphalia Grant 313-21200200) project and since 2011 five stations were further maintained by the GERMAN DFG Fennec project (FI 786/3-1), this way some stations of the AWS network provided data for almost 12 years from 2001-2012. Standard meteorological variables such as temperature, humidity, and wind were measured at an altitude of 2 m above ground. Other meteorological variables comprise precipitation, station pressure, solar irradiance, soil temperature at different depths and for high mountain station snow water equivalent. The stations produced data summaries for 5-minute-precipitation-data, 10- or 15-minute-data and a daily summary of all other variables. This network is a unique resource of multi-year weather data in the remote semi-arid to arid mountain region of the Saharan flank of the Atlas Mountains. The network is described in Schulz et al. (2010) and its further continuation until 2012 is briefly discussed in Redl et al. (2015, doi:10.1175/MWR-D-15-0223.1) and Redl et al. (2016, doi:10.1002/2015JD024443).