Determining the temperature from incomplete boundary data

An iterative procedure for determining temperature fields from Cauchy data given on a part of the boundary is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. A convergence proof of this method in a weighted L2-space is included, as well as a stopping criteria for the case of noisy data. Moreover, a solvability result in a weighted Sobolev space for a parabolic initial boundary value problem of second order with mixed boundary conditions is presented. Regularity of the solution is proved. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Asymptotic Property of Eigenvalues and Eigenfunctions of the Laplace Operator in Domain with a Perturbed Boundary

2000 Mathematics Subject Classification: 35J05, 35C15, 44P05

Anti-Periodic Boundary Value Problem for Impulsive Fractional Integro Differential Equations

MSC 2010: 34A37, 34B15, 26A33, 34C25, 34K37

Crack Theory with Singularities at the Boundary

2002 Mathematics Subject Classification: 35S15, 35J70, 35J40, 38J40

Two-phase flow analogy as an effective boundary condition for modelling liquids at atomistic resolution

A hybrid Molecular Dynamics/Fluctuating Hydrodynamics framework based on the analogy with two-phase hydrodynamics has been extended to dynamically tracking the feature of interest at all-atom resolution. In the model, the hydrodynamics description is used as an effective boundary condition to close the molecular dynamics solution without resorting to standard periodic boundary conditions. The approach is implemented in a popular Molecular Dynamics package GROMACS and results for two biomolecular systems are reported. A small peptide dialanine and a complete capsid of a virus porcine circovirus 2 in water are considered and shown to reproduce the structural and dynamic properties compared to those obtained in theory, purely atomistic simulations, and experiment.

Carbon and nitrogen stable isotopic patterns in South Florida coastal ecosystems: Modern and paleoceanographic perspectives

Long term management plans for restoration of natural flow conditions through the Everglades increase the importance of understanding potential nutrient impacts of increased freshwater delivery on coastal biogeochemistry. The present study sought to increase understanding of the coastal marine system of South Florida under modern conditions and through the anthropogenic changes in the last century, on scales ranging from individual nutrient cycle processes to seasonal patterns in organic material (OM) under varying hydrodynamic regime, to century scale analysis of sedimentary records. In all applications, carbon and nitrogen stable isotopic compositions of OM were examined as natural recorders of change and nutrient cycling in the coastal system. ^ High spatial and temporal variability in stable isotopic compositions were observed on all time scales. During a transient phytoplankton bloom, δ 15N values suggested nitrogen fixation as a nutrient source supporting enhanced productivity. Seasonally, particulate organic material (POM) from ten sites along the Florida Reef Tract and in Florida Bay demonstrated variable fluctuations dependent on hydrodynamic setting. Three separate intra-annual patterns were observed, yet statistical differences were observed between groupings of Florida Bay and Atlantic Ocean sites. The POM δ 15N values ranged on a quarterly basis by 7‰, while δ 13C varied by 22‰. From a sediment history perspective, four cores collected from Florida Bay further demonstrated the spatial and temporal variability of the system in isotopic composition of bulk OM over time. Source inputs of OM varied with location, with terrestrial inputs dominating proximal to Everglades freshwater discharge, seagrasses dominating in open estuary cores, and a marine mixture of phytoplankton and seagrass in a core from the boundary zone between Florida Bay and the Gulf of Mexico. Significant shifts in OM geochemistry were observed coincident with anthropogenic events of the 20th century, including railroad and road construction in the Florida Keys and Everglades, and also the extensive drainage changes in Everglades hydrology. The sediment record also preserved evidence of the major hurricanes of the last century, with excursions in geochemical composition coincident with Category 4-5 storms. ^

Development of an enhanced hydro-geochemical model to address mercury-speciation fate and transport in aquatic environments

An awareness of mercury (Hg) contamination in various aquatic environments around the world has increased over the past decade, mostly due to its ability to concentrate in the biota. Because the presence and distribution of Hg in aquatic systems depend on many factors (e.g., pe, pH, salinity, temperature, organic and inorganic ligands, sorbents, etc.), it is crucial to understand its fate and transport in the presence of complexing constituents and natural sorbents, under those different factors. An improved understanding of the subject will support the selection of monitoring, remediation, and restoration technologies. The coupling of equilibrium chemical reactions with transport processes in the model PHREEQC offers an advantage in simulating and predicting the fate and transport of aqueous chemical species of interest. Thus, a great variety of reactive transport problems could be addressed in aquatic systems with boundary conditions of specific interest. Nevertheless, PHREEQC lacks a comprehensive thermodynamic database for Hg. Therefore, in order to use PHREEQC to address the fate and transport of Hg in aquatic environments, it is necessary to expand its thermodynamic database, confirm it and then evaluate it in applications where potential exists for its calibration and continued validation. The objectives of this study were twofold: 1) to develop, expand, and confirm the Hg database of the hydrogeochemical PHREEQC to enhance its capability to simulate the fate of Hg species in the presence of complexing constituents and natural sorbents under different conditions of pH, redox, salinity and temperature; and 2) to apply and evaluate the new database in flow and transport scenarios, at two field test beds: Oak Ridge Reservation, Oak Ridge, TN and Everglades National Park, FL, where Hg is present and is of much concern. Overall, this research enhanced the capability of the PHREEQC model to simulate the coupling of the Hg reactions in transport conditions. It also demonstrated its usefulness when applied to field situations.

Isotopic data of atmospheric methane from EDML and Vostok ice cores over a full glacial cycle

The response of natural CH4 sources to climate changes will be an important factor to consider as concentrations of this potent greenhouse gas continue to increase. Polar ice cores provide the means to assess this sensitivity in the past and have shown a close connection between CH4 levels and northern hemisphere temperature variability over the last glacial cycle. However, the contribution of the various CH4 sources and sinks to these changes is still a matter of debate. Contemporaneous stable CH4 isotope records in ice cores provide additional boundary conditions for assessing changes in the CH4 sources and sinks. Here we present new ice core CH4 isotope data covering the last 160,000 years, showing a clear decoupling between CH4 loading and carbon isotopic variations over most of the record. We suggest that d13CH4 variations were not dominated by a change in the source mix but rather by climate- and CO2-related ecosystem control on the isotopic composition of the methane precursor material, especially in seasonally inundated wetlands in the tropics. In contrast, relatively stable d13CH4 intervals occurred during large CH4 loading changes concurrently with past climate changes implying that most CH4 sources (most notably tropical wetlands) responded simultaneously.

Theoretical modeling and experimental validation of fluid-loaded micro rectangular plates

This paper presents a theoretical model on the vibration analysis of micro scale fluid-loaded rectangular isotropic plates, based on the Lamb's assumption of fluid-structure interaction and the Rayleigh-Ritz energy method. An analytical solution for this model is proposed, which can be applied to most cases of boundary conditions. The dynamical experimental data of a series of microfabricated silicon plates are obtained using a base-excitation dynamic testing facility. The natural frequencies and mode shapes in the experimental results are in good agreement with the theoretical simulations for the lower order modes. The presented theoretical and experimental investigations on the vibration characteristics of the micro scale plates are of particular interest in the design of microplate based biosensing devices. Copyright © 2009 by ASME.

Carbon and Nitrogen Stable Isotopic Patterns in South Florida Coastal Ecosystems: Modern and Paleoceanographic Perspectives

Long term management plans for restoration of natural flow conditions through the Everglades increase the importance of understanding potential nutrient impacts of increased freshwater delivery on coastal biogeochemistry. The present study sought to increase understanding of the coastal marine system of South Florida under modern conditions and through the anthropogenic changes in the last century, on scales ranging from individual nutrient cycle processes to seasonal patterns in organic material (OM) under varying hydrodynamic regime, to century scale analysis of sedimentary records. In all applications, carbon and nitrogen stable isotopic compositions of OM were examined as natural recorders of change and nutrient cycling in the coastal system. High spatial and temporal variability in stable isotopic compositions were observed on all time scales. During a transient phytoplankton bloom, ä15N values suggested nitrogen fixation as a nutrient source supporting enhanced productivity. Seasonally, particulate organic material (POM) from ten sites along the Florida Reef Tract and in Florida Bay demonstrated variable fluctuations dependent on hydrodynamic setting. Three separate intra-annual patterns were observed, yet statistical differences were observed between groupings of Florida Bay and Atlantic Ocean sites. The POM ä15N values ranged on a quarterly basis by 7‰, while ä13C varied by 22‰. From a sediment history perspective, four cores collected from Florida Bay further demonstrated the spatial and temporal variability of the system in isotopic composition of bulk OM over time. Source inputs of OM varied with location, with terrestrial inputs dominating proximal to Everglades freshwater discharge, seagrasses dominating in open estuary cores, and a marine mixture of phytoplankton and seagrass in a core from the boundary zone between Florida Bay and the Gulf of Mexico. Significant shifts in OM geochemistry were observed coincident with anthropogenic events of the 20th century, including railroad and road construction in the Florida Keys and Everglades, and also the extensive drainage changes in Everglades hydrology. The sediment record also preserved evidence of the major hurricanes of the last century, with excursions in geochemical composition coincident with Category 4-5 storms.

(Fig. 1D, 3E) Sea surface temperature and alkenone C37:4 for sediment core MD01-2444 during the penultimate glaciation

Past glacials can be thought of as natural experiments in which variations in boundary conditions influenced the character of climate change. However, beyond the last glacial, an integrated view of orbital- and millennial-scale changes and their relation to the record of glaciation has been lacking. Here, we present a detailed record of variations in the land-ocean system from the Portuguese margin during the penultimate glacial and place it within the framework of ice-volume changes, with particular reference to European ice-sheet dynamics. The interaction of orbital- and millennial-scale variability divides the glacial into an early part with warmer and wetter overall conditions and prominent climate oscillations, a transitional mid-part, and a late part with more subdued changes as the system entered a maximum glacial state. The most extreme event occurred in the mid-part and was associated with melting of the extensive European ice sheet and maximum discharge from the Fleuve Manche river. This led to disruption of the meridional overturning circulation, but not a major activation of the bipolar seesaw. In addition to stadial duration, magnitude of freshwater forcing, and background climate, the evidence also points to the influence of the location of freshwater discharges on the extent of interhemispheric heat transport.

GIS technologies and spatial organization patterns among hunter-gatherers: an archaeological case study from Southern Patagonia (southern South America)

This paper discusses some aspects of hunter-gatherer spatial organization in southern South Patagonia, in later times to 10,000 cal yr BP. Various methods of spatial analysis, elaborated with a Geographic Information System (GIS) were applied to the distributional pattern of archaeological sites with radiocarbon dates. The shift in the distributional pattern of chronological information was assessed in conjunction with other lines of evidence within a biogeographic framework. Accordingly, the varying degrees of occupation and integration of coastal and interior spaces in human spatial organization are explained in association with the adaptive strategies hunter-gatherers have used over time. Both are part of the same human response to changes in risk and uncertainty variability in the region in terms of resource availability and environmental dynamics.

Monitoring and model updating of an FRP pedestrian truss bridge

This paper presents the results of a real bridge field experiment, carried out on a fiber reinforced polymer (FRP) pedestrian truss bridge of which nodes are reinforced with stainless steel plates. The aim of this paper is to identify the dynamic parameters of this bridge by using both conventional techniques and a model updating algorithm. In the field experiment, the bridge was instrumented with accelerometers at a number of locations on the bridge deck, recording both vertical and transverse vibrations. It was excited via jump tests at particular locations along its span and the resulting acceleration signals are used to identify dynamic parameters, such as the bridge mode shape, natural frequency and damping constant. Pedestrianinduced vibrations are also measured and utilized to identify dynamic parameters of the bridge. For a complete analysis of the bridge, a numerical model of the FRP bridge is created whose properties are calibrated utilizing a model updating algorithm. Comparable frequencies and mode shapes to those from the experiment were obtained by the FE models considering the reinforcement by increasing elastic modulus at every node of the bridge by stainless steel plate. Moreover, considering boundary conditions at both ends as fixed in the model resulted in modal properties comparable/similar to those from the experiment. This study also demonstrated that the effect of reinforcement and boundary conditions must be properly considered in an FE model to analyze real behavior of the FRP bridge.

Parameterization of quasigeostrophic eddies in primitive equation ocean models

A parameterization of mesoscale eddy fluxes in the ocean should be consistent with the fact that the ocean interior is nearly adiabatic. Gent and McWilliams have described a framework in which this can be approximated in L-coordinate primitive equation models by incorporating the effects of eddies on the buoyancy field through an eddy-induced velocity. It is also natural to base a parameterization on the simple picture of the mixing of potential vorticity in the interior and the mixing of buoyancy at the surface. The authors discuss the various constraints imposed by these two requirements and attempt to clarify the appropriate boundary conditions on the eddy-induced velocities at the surface. Quasigeostrophic theory is used as a guide to the simplest way of satisfying these constraints.

Unfolding Operator Method for Thin Domains with a Locally Periodic Highly Oscillatory Boundary

We analyze the behavior of solutions of the Poisson equation with homogeneous Neumann boundary conditions in a two-dimensional thin domain which presents locally periodic oscillations at the boundary. The oscillations are such that both the amplitude and period of the oscillations may vary in space. We obtain the homogenized limit problem and a corrector result by extending the unfolding operator method to the case of locally periodic media.