Two new integral transforms and their applications

<p>This thesis is in two parts. In Part I the independent variable �� in the trigonometric form of Legendre's equation is extended to the range ( -���, ���). The associated spectral representation is an infinite integral transform whose kernel is the analytic continuation of the associated Legendre function of the second kind into the complex ��-plane. This new transform is applied to the problems of waves on a spherical shell, heat flow on a spherical shell, and the gravitational potential of a sphere. In each case the resulting alternative representation of the solution is more suited to direct physical interpretation than the standard forms.</p> <p>In Part II separation of variables is applied to the initial-value problem of the propagation of acoustic waves in an underwater sound channel. The Epstein symmetric profile is taken to describe the variation of sound with depth. The spectral representation associated with the separated depth equation is found to contain an integral and a series. A point source is assumed to be located in the channel. The nature of the disturbance at a point in the vicinity of the channel far removed from the source is investigated.</p>

Coastal management measures for the lower Maumee Watershed, Lake Erie

In January 2006 the Maumee Remedial Action Plan (RAP) Committee submitted a State II Watershed Restoration Plan for the Maumee River Great Lakes Area of Concern (AOC) area located in NW Ohio to the State of Ohio for review and endorsement (MRAC, 2006). The plan was created in order to fulfill the requirements, needs and/or use of five water quality programs including: Ohio Department of Natural Resources (DNR) Watershed Coordinator Program; Ohio EPA Great Lakes RAP Program; Ohio DNR Coastal Non-point Source Pollution Control Program; Ohio EPA Total Maximum Daily Load Program; and US Fish & Wildlife Service Natural Resources Damage Program. The plan is intended to serve as a comprehensive regional management approach for all jurisdictions, agencies, organizations, and individuals who are working to restore the watershed, waterways and associated coastal zone. The plan includes: background information and mapping regarding hydrology, geology, ecoregions, and land use, and identifies key causes and sources for water quality concerns within the six 11-digit hydrological units (HUCs), and one large river unit that comprise the Maumee AOC. Tables were also prepared that contains detailed project lists for each major watershed and was organized to facilitate the prioritization of research and planning efforts. Also key to the plan and project tables is a reference to the Ohio DNR Coastal Management Measures that may benefit from the implementation of an identified project. This paper will examine the development of the measures and their importance for coastal management and watershed planning in the Maumee AOC. (PDF contains 4 pages)

Oxygen, carbon and hydrogen isotope studies of contact metamorphism

<p>The O¹⁸/O¹⁶, C¹³/C¹², and D/H ratios have been determined for rocks and coexisting minerals from several granitic plutons and their contact metamorphic aureoles in northern Nevada, eastern California, central Colorado, and Texas, with emphasis on oxygen isotopes. A consistent order of O¹⁸/O¹⁶, C¹³/C¹², and D/H enrichment in coexisting minerals, and a correlation between isotopic fractionations among coexisting mineral pairs are in general observed, suggesting that mineral assemblages tend to approach isotopic equilibrium during contact metamorphism. In certain cases, a correlation is observed between oxygen isotopic fractionations of a mineral pair and sample distance from intrusive contacts. Isotopic temperatures generally show good agreement with heat flow considerations. Based on the experimentally determined quartz-muscovite O¹⁸/O¹⁶ fractionation calibration curve, temperatures are estimated to be 525 to 625��C at the contacts of the granitic stocks studied.</p> <p>Small-scale oxygen isotope exchange effects between intrusive and country rock are observed over distances of 0.5 to 3 feet on both sides of the contacts; the isotopic gradients are typically 2 to 3 per mil per foot. The degree of oxygen isotopic exchange is essentially identical for different coexisting minerals. This presumably occurred through a diffusion-controlled recrystallization process. The size of the oxygen isotope equilibrium systems in the small-scale exchanged zones vary from about 1.5 cm to 30 cm. A xenolith and a re-entrant of country rock projecting into on intrusive hove both undergone much more extensive isotopic exchange (to hundreds of feet); they also show abnormally high isotopic temperatures. The marginal portions of most plutons have unusually high O¹⁸/O¹⁶ ratios compared to "normal" igneous rocks, presumably due to large-scale isotopic exchange with meta-sedimentary country rocks when the igneous rocks were essentially in a molten state. The isotopic data suggest that outward horizontal movement of H₂O into the contact metamorphic aureoles is almost negligible, but upward movement of H₂O may be important. Also, direct influx and absorption of water from the country rock may be significant in certain intrusive stocks.</p> <p>Except in the exchanged zones, the O¹⁸/O¹⁶ ratios of pelitic rocks do not change appreciably during contact metamorphism, even in the cordierite and sillimanite grades; this is in contrast to regional metamorphic rocks which commonly decrease in O¹⁸ with increasing grade. Low O¹⁸/O¹⁶ and C¹³/C¹² ratios of the contact metamorphic marbles generally correlate well with the presence of calc-silicate minerals, indicating that the CO₂ liberated during metamorphic decarbonation reactions is enriched in both O¹⁸ and C¹³ relative to the carbonates.</p> <p>The D/H ratios of biotites in the contact metamorphic rocks and their associated intrusions show a geographic correlation that is similar to that shown by the D/H ratios of meteoric surface waters, perhaps indicating that meteoric waters were present in the rocks during crystallization of the biotites.</p>

Part I - The radiation of elastic waves from a spherical cavity in a half space. Part II - Precision determination of focal depths and epicenters of earthquakes.

<p>Part I: The dynamic response of an elastic half space to an explosion in a buried spherical cavity is investigated by two methods. The first is implicit, and the final expressions for the displacements at the free surface are given as a series of spherical wave functions whose coefficients are solutions of an infinite set of linear equations. The second method is based on Schwarz's technique to solve boundary value problems, and leads to an iterative solution, starting with the known expression for the point source in a half space as first term. The iterative series is transformed into a system of two integral equations, and into an equivalent set of linear equations. In this way, a dual interpretation of the physical phenomena is achieved. The systems are treated numerically and the Rayleigh wave part of the displacements is given in the frequency domain. Several comparisons with simpler cases are analyzed to show the effect of the cavity radius-depth ratio on the spectra of the displacements.</p> <p>Part II: A high speed, large capacity, hypocenter location program has been written for an IBM 7094 computer. Important modifications to the standard method of least squares have been incorporated in it. Among them are a new way to obtain the depth of shocks from the normal equations, and the computation of variable travel times for the local shocks in order to account automatically for crustal variations. The multiregional travel times, largely based upon the investigations of the United States Geological Survey, are confronted with actual traverses to test their validity.</p> <p>It is shown that several crustal phases provide control enough to obtain good solutions in depth for nuclear explosions, though not all the recording stations are in the region where crustal corrections are considered. The use of the European travel times, to locate the French nuclear explosion of May 1962 in the Sahara, proved to be more adequate than previous work.</p> <p>A simpler program, with manual crustal corrections, is used to process the Kern County series of aftershocks, and a clearer picture of tectonic mechanism of the White Wolf fault is obtained.</p> <p>Shocks in the California region are processed automatically and statistical frequency-depth and energy depth curves are discussed in relation to the tectonics of the area.</p>

Infiltration of fine and coarse sand into an open-work gravel bed

The siltation of an experimental gravel bed, with three grades of sand moving in suspension and as bedload, was examined. The rate of infiltration of sand into the void space of the gravel was determined under differing conditions of discharge, water depth, and velocity (jointly expressed as variation in the Froude Number) and suspended sediment concentration. The downstream reduction in siltation from the point source was also examined.

High frequency wave propagation in the earth: theory and observation

<p>The wave-theoretical analysis of acoustic and elastic waves refracted by a spherical boundary across which both velocity and density increase abruptly and thence either increase or decrease continuously with depth is formulated in terms of the general problem of waves generated at a steady point source and scattered by a radially heterogeneous spherical body. A displacement potential representation is used for the elastic problem that results in high frequency decoupling of P-SV motion in a spherically symmetric, radially heterogeneous medium. Through the application of an earth-flattening transformation on the radial solution and the Watson transform on the sum over eigenfunctions, the solution to the spherical problem for high frequencies is expressed as a Weyl integral for the corresponding half-space problem in which the effect of boundary curvature maps into an effective positive velocity gradient. The results of both analytical and numerical evaluation of this integral can be summarized as follows for body waves in the crust and upper mantle:</p> <p>1) In the special case of a critical velocity gradient (a gradient equal and opposite to the effective curvature gradient), the critically refracted wave reduces to the classical head wave for flat, homogeneous layers.</p> <p>2) For gradients more negative than critical, the amplitude of the critically refracted wave decays more rapidly with distance than the classical head wave.</p> <p>3) For positive, null, and gradients less negative than critical, the amplitude of the critically refracted wave decays less rapidly with distance than the classical head wave, and at sufficiently large distances, the refracted wave can be adequately described in terms of ray-theoretical diving waves. At intermediate distances from the critical point, the spectral amplitude of the refracted wave is scalloped due to multiple diving wave interference.</p> <p>These theoretical results applied to published amplitude data for P-waves refracted by the major crustal and upper mantle horizons (the Pg, P*, and Pn travel-time branches) suggest that the 'granitic' upper crust, the 'basaltic' lower crust, and the mantle lid all have negative or near-critical velocity gradients in the tectonically active western United States. On the other hand, the corresponding horizons in the stable eastern United States appear to have null or slightly positive velocity gradients. The distribution of negative and positive velocity gradients correlates closely with high heat flow in tectonic regions and normal heat flow in stable regions. The velocity gradients inferred from the amplitude data are generally consistent with those inferred from ultrasonic measurements of the effects of temperature and pressure on crustal and mantle rocks and probable geothermal gradients. A notable exception is the strong positive velocity gradient in the mantle lid beneath the eastern United States (2 x 10^-3 sec^-1), which appears to require a compositional gradient to counter the effect of even a small geothermal gradient.</p> <p>New seismic-refraction data were recorded along a 800 km profile extending due south from the Canadian border across the Columbia Plateau into eastern Oregon. The source for the seismic waves was a series of 20 high-energy chemical explosions detonated by the Canadian government in Greenbush Lake, British Columbia. The first arrivals recorded along this profile are on the Pn travel-time branch. In northern Washington and central Oregon their travel time is described by T = ��/8.0 + 7.7 sec, but in the Columbia Plateau the Pn arrivals are as much as 0.9 sec early with respect to this line. An interpretation of these Pn arrivals together with later crustal arrivals suggest that the crust under the Columbia Plateau is thinner by about 10 km and has a higher average P-wave velocity than the 35-km-thick, 62-km/sec crust under the granitic-metamorphic terrain of northern Washington. A tentative interpretation of later arrivals recorded beyond 500 km from the shots suggests that a thin 8.4-km/sec horizon may be present in the upper mantle beneath the Columbia Plateau and that this horizon may form the lid to a pronounced low-velocity zone extending to a depth of about 140 km.</p>

Scattering by two degenerate anisotropic modes in square-lattice dielectric photonic crystals

We systematically investigate the square-lattice dielectric photonic crystals that have been used to demonstrate flat slab imaging experimentally. A right-handed Bloch mode is found in the left-handed frequency region by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Using the multiple scattering theory, numerical simulations demonstrate that the left-handed mode and the right-handed mode are excited simultaneously by a point source and result in two kinds of transmitted waves. Impacted by the evanescent waves, superposition of these transmitted waves brings on complicated near field distributions such as the so-called imaging and its disappearance.

The Status of Eelgrass, Zostera marina, as Bay Scallop Habitat: Consequences for the Fishery in the Western Atlantic

Zostera marina is a member of a widely distributed genus of seagrasses, all commonly called eelgrass. The reported distribution of eelgrass along the east coast of the United States is from Maine to North Carolina. Eelgrass inhabits a variety of coastal habitats, due in part to its ability to tolerate a wide range of environmental parameters. Eelgrass meadows provide habitat, nurseries, and feeding grounds for a number of commercially and ecologically important species, including the bay scallop, Argopecten irradians. In the early 1930���s, a marine event, termed the ���wasting disease,��� was responsible for catastrophic declines in eelgrass beds of the coastal waters of North America and Europe, with the virtual elimination of Z. marina meadows in the Atlantic basin. Following eelgrass declines, disastrous losses were documented for bay scallop populations, evidence of the importance of eelgrass in supporting healthy scallop stocks. Today, increased turbidity arising from point and non-point source nutrient loading and sediment runoff are the primary threats to eelgrass along the Atlantic coast and, along with recruitment limitation, are likely reasons for the lack of recovery by eelgrass to pre-1930���s levels. Eelgrass is at a historical low for most of the western Atlantic with uncertain prospects for systematic improvement. However, of all the North American seagrasses, eelgrass has a growth rate and strategy that makes it especially conducive to restoration and several states maintain ongoing mapping, monitoring, and restoration programs to enhance and improve this critical resource. The lack of eelgrass recovery in some areas, coupled with increasing anthropogenic impacts to seagrasses over the last century and heavy fishing pressure on scallops which naturally have erratic annual quantities, all point to a fishery with profound challenges for survival.

Protocols for conducting dolphin capture-release health assessment studies

Marine mammals, such as dolphins, can serve as key indicator species in coastal areas by reflecting the effects of natural and anthropogenic stressors. As such they are often considered sentinels of environmental and ecosystem health (Bossart 2006; Wells et al. 2004; Fair and Becker 2000). The bottlenose dolphin is an apex predator and a key component of many estuarine environments in the southeastern United States (Woodward-Clyde Consultants 1994; SCDNR 2005). Health assessments of dolphins are especially critical in areas where populations are depleted, show signs of epidemic disease and/or high mortality and/or where habitat is being altered or impacted by human activities. Recent assessments of environmental conditions in the Indian River Lagoon, Florida (IRL) and the estuarine waters surrounding Charleston, South Carolina (CHS) highlight the need for studies of the health of local bottlenose dolphins. While the condition of southeastern estuaries was rated as fair in the National Coastal Condition Report (U.S. EPA 2001), it was noted that the IRL was characterized by poorer than expected benthic communities, significant sediment toxicity and increased nutrient concentrations. Similarly, portions of the CHS estuary have sediment concentrations of aliphatic aromatic hydrocarbons, select inorganic metals, and some persistent pesticides far in excess of reported bioeffect levels (Hyland et al. 1998). Long-term trends in water quality monitoring and recent scientific research suggest that waste load assimilation, non-point source runoff impacts, contaminated sediments, and toxic pollutants are key issues in the CHS estuary system. Several ���hot spots��� with high levels of heavy metals and organic compounds have been identified (Van Dolah et al. 2004). High concentrations of anthropogenic trace metals, polychlorinated biphenyls (PCB���s) and pesticides have been found in the sediments of Charleston Harbor, as well as the Ashley and Cooper Rivers (Long et al. 1998). Two superfund sites are located within the CHS estuary and the key contaminants of concern associated with these sites are: polycyclic aromatic hydrocarbons (PAH), lead, chromium, copper, arsenic, zinc and dioxin. Concerns related to the overall health of IRL dolphins and dermatologic disease observed in many dolphins in the area (Bossart et al. 2003) initiated an investigation of potential factors which may have impacted dolphin health. From May-August 2001, 35 bottlenose dolphins died in the IRL during an unusual mortality event (MMC 2003). Many of these dolphins were diagnosed with a variety of skin lesions including proliferative ulcerative dermatitis due to protozoa and fungi, dolphin pox and a vesicular dermatopathy of unknown etiology (Bossart et al. 2003). Multiple species from fish to dolphins in the IRL system have exhibited skin lesions of various known and unknown etiologies (Kane et al. 2000; Bossart et al. 2003; Reif et al. 2006). On-going photo-identification (photo-ID) studies have documented skin diseases in IRL dolphins (Mazzoil et al. 2005). In addition, up to 70% of green sea turtles in the IRL exhibit fibropapillomas, with the highest rates of occurrence being seen in turtles from the southern IRL (Hirama 2001).

Flux and sources of nutrients in the Mississippi-Atchafalaya River Basin: Topic 3 Report for the Integrated Assessment on Hypoxia in the Gulf of Mexico.

Ths report addresses the following two questions: 1) What are the loads (flux) of nutrients transported from the Mississippi-Atchafalaya River Basin to the Gulf of Mexico, and where do they come from within the basin? 2) What is the relative importance of specific human activities, such as agriculture, point-source discharges, and atmospheric deposition in contributing to these loads? These questions were addressed by first estimating the flux of nutrients from the Mississippi-Atchafalaya River Basin and about 50 interior basins in the Mississippi River system using measured historical streamflow and water quality data. Annual nutrient inputs and outputs to each basin were estimated using data from the National Agricultural Statistics Service, National Atmospheric Deposition Program, and point-source data provided by the USEPA. Next, a nitrogen mass balance was developed using agricultural statistics, estimates of nutrient cycling in agricultural systems, and a geographic information system. Finally, multiple regression models were developed to estimate the relative contributions of the major input sources to the flux of nitrogen and phosphorus to the Gulf of Mexico.

Gulf of Mexico tidal creeks serve as sentinel habitats for assessing the impact of coastal development on ecosystem health

A study was conducted, in association with the Alabama and Mississippi National Estuarine Research Reserves (NERRs) in the Gulf of Mexico (GoM) as well as the Georgia, South Carolina, and North Carolina NERRs in the Southeast (SE), to evaluate the impacts of coastal development on tidal creek sentinel habitats, including potential impacts to human health and well-being. Uplands associated with Southeast and Gulf of Mexico tidal creeks, and the salt marshes they drain, are popular locations for building homes, resorts, and recreational facilities because of the high quality of life and mild climate associated with these environments. Tidal creeks form part of the estuarine ecosystem characterized by high biological productivity, great ecological value, complex environmental gradients, and numerous interconnected processes. This research combined a watershed-level study integrating ecological, public health and human dimension attributes with watershed-level land cover data. The approach used for this research was based upon a comparative watershed and ecosystem approach that sampled tidal creek networks draining developed watersheds (e.g., suburban, urban, and industrial) as well as undeveloped sites (Holland et al. 2004, Sanger et al. 2008). The primary objective of this work was to define the relationships between coastal development with its concomitant land cover changes, and non-point source pollution loading and the ecological and human health and wellbeing status of tidal creek ecosystems. Nineteen tidal creek systems, located along the Southeastern United States coast from southern North Carolina to southern Georgia, and five Gulf of Mexico systems from Alabama and Mississippi were sampled during summer (June-August) 2005, 2006 (SE) and 2008 (GoM). Within each system, creeks were divided into two primary segments based upon tidal zoning: intertidal (i.e., shallow, narrow headwater sections) and subtidal (i.e., deeper and wider sections), and watersheds were delineated for each segment. In total, we report findings on 29 intertidal and 24 subtidal creeks. Indicators sampled throughout each creek included water quality (e.g., dissolved oxygen, salinity, nutrients, chlorophyll-a levels), sediment quality (e.g., characteristics, contaminant levels including emerging contaminants), pathogen and viral indicators (e.g., fecal coliform, enterococci, F+ coliphages, F- coliphages), and abundance and tissue contamination of biological resources (e.g., macrobenthic and nektonic communities, shellfish tissue contaminants). Tidal creeks have been identified as a sentinel habitat to assess the impacts of coastal development on estuarine areas in the southeastern US. A conceptual model for tidal creeks in the southeastern US identifies that human alterations (stressors) of upland in a watershed such as increased impervious cover will lead to changes in the physical and chemical environment such as microbial and nutrient pollution (exposures), of a receiving water body which then lead to changes in the living resources (responses). The overall objective of this study is to evaluate the applicability of the current tidal creek classification framework and conceptual model linking tidal creek ecological condition to potential impacts of development and urban growth on ecosystem value and function in the Gulf of Mexico US in collaboration with Gulf of Mexico NERR sites. The conceptual model was validated for the Gulf of Mexico US tidal creeks. The tidal creek classification system developed for the southeastern US could be applied to the Gulf of Mexico tidal creeks; however, some differences were found that warrant further examination. In particular, pollutants appeared to translate further downstream in the Gulf of Mexico US compared to the southeastern US. These differences are likely the result of the morphological and oceanographic differences between the two regions. Tidal creeks appear to serve as sentinel habitats to provide an early warning of the ensuing harm to the larger ecosystem in both the Southeastern and Gulf of Mexico US tidal creeks.

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On a classical problem of acoustic wave scattering by a free vortex: Numerical modelling

The scattering of sound from a point source by a Rankine vortex is investigated numerically by solving the Euler equations with the novel high-resolution CABARET method. For several Mach numbers of the vortex, the time-average amplitudes of the scattered field obtained from the numerical modeling are compared with the theoretical scaling laws' predictions. Copyright �� 2009 by Sergey Karabasov.

Transient flows in enclosures: A generalised approach for modelling the effects of geometry, heat gains and wind

Transient flows in a confined ventilated space induced by a buoyancy source of time-varying strength and an external wind are examined. The space considered has varying cross-sectional area with height. A generalised theoretical model is proposed to investigate the flow dynamics following the activation of an external wind and an internal source of buoyancy. To investigate the effect of geometry, we vary the angle of the wall inclination of a particular geometry in which a point source of constant buoyancy is activated in the absence of wind. Counter-intuitively the ventilation is worse and lower airflow rates are established for geometries of increasing cross-sectional areas with height. We investigate the effect of the source buoyancy strength by comparing two cases: (1) when the buoyancy input is constant and (2) when the buoyancy input gradually increases over time so that after a finite time the total buoyancy inputs for (1) and (2) are identical. The rate at which the source heat gains are introduced has a significant role on the flow behaviour as we find that, in case (2), a warmer layer and a more pronounced overshoot are obtained than in case (1). The effect of assisting and opposing wind on the transient ventilation of an enclosure of constant cross-sectional area with height and constant heat gains is examined. A Froude number Fr is used to define the relative strengths of the buoyancy-induced and wind-induced velocities and five different transient states and their associated critical Fr are identified. �� 2010 Elsevier Ltd.

Thermal stratification produced by plumes and jets in enclosed spaces

The airflow and thermal stratification produced by a localised heat source located at floor level in a closed room is of considerable practical interest and is commonly referred to as a 'filling box'. In rooms with low aspect ratios H/R ��� 1 (room height H to characteristic horizontal dimension R) the thermal plume spreads laterally on reaching the ceiling and a descending horizontal 'front' forms separating a stably stratified, warm upper region from cooler air below. The stratification is well predicted for H/R ��� 1 by the original filling box model of Baines and Turner (J. Fluid. Mech. 37 (1968) 51). This model represents a somewhat idealised situation of a plume rising from a point source of buoyancy alone-in particular the momentum flux at the source is zero. In practical situations, real sources of heating and cooling in a ventilation system often include initial fluxes of both buoyancy and momentum, e.g. where a heating system vents warm air into a space. This paper describes laboratory experiments to determine the dependence of the 'front' formation and stratification on the source momentum and buoyancy fluxes of a single source, and on the location and relative strengths of two sources from which momentum and buoyancy fluxes were supplied separately. For a single source with a non-zero input of momentum, the rate of descent of the front is more rapid than for the case of zero source momentum flux and increases with increasing momentum input. Increasing the source momentum flux effectively increases the height of the enclosure, and leads to enhanced overturning motions and finally to complete mixing for highly momentum-driven flows. Stratified flows may be maintained by reducing the aspect ratio of the enclosure. At these low aspect ratios different long-time behaviour is observed depending on the nature of the heat input. A constant heat flux always produces a stratified interior at large times. On the other hand, a constant temperature supply ultimately produces a well-mixed space at the supply temperature. For separate sources of momentum and buoyancy, the developing stratification is shown to be strongly dependent on the separation of the sources and their relative strengths. Even at small separation distances the stratification initially exhibits horizontal inhomogeneity with localised regions of warm fluid (from the buoyancy source) and cool fluid. This inhomogeneity is less pronounced as the strength of one source is increased relative to the other. Regardless of the strengths of the sources, a constant buoyancy flux source dominates after sufficiently large times, although the strength of the momentum source determines whether the enclosure is initially well mixed (strong momentum source) or stably stratified (weak momentum source). �� 2001 Elsevier Science Ltd. All rights reserved.