7,421 research outputs found

    A Novel Method of Solution for the Fluid Loaded Plate

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    We study the Cauchy problem associated with the equations governing a fluid loaded plate formulated on either the line or the half-line. We show that in both cases the problem can be solved by employing the unified approach to boundary value problems introduced by on of the authors in the late 1990s. The problem on the full line was analysed by Crighton et. al. using a combination of Laplace and Fourier transforms. The new approach avoids the technical difficulty of the a priori assumption that the amplitude of the plate is in Ldt1(R+)L^1_{dt}(R^+) and furthermore yields a simpler solution representation which immediately implies the problem is well-posed. For the problem on the half-line, a similar analysis yields a solution representation, but this formula involves two unknown functions. The main difficulty with the half-line problem is the characterisation of these two functions. By employing the so-called global relation, we show that the two functions can be obtained via the solution of a complex valued integral equation of the convolution type. This equation can be solved in closed form using the Laplace transform. By prescribing the initial data η0\eta_0 to be in H3(R+)H^3(R^+), we show that the solution depends continuously on the initial data, and hence, the problem is well-posed.Comment: 17 pages, 3 figures. Minor adjustments made to the introductio

    Using Revealed and Stated Preference Data to Estimate the Scope and Access Benefits Associated with Cave Diving

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    In a single-site travel cost model framework, revealed and stated preference data are jointly estimated to provide the first use value estimate associated with recreational cave diving. Focusing on one of Florida’s first magnitude springs, we estimate average per-person per-trip use values of approximately 165,generatingannualcavedivingusevaluesinexcessof165, generating annual cave diving use values in excess of 1,150. Further, in an investigation of potential site quality changes, we find that divers are sensitive to scope effects with an additional cave system increasing annual per-person use values by approximately 130,whileimprovedaccessyieldsanadditional130, while improved access yields an additional 57 in per-person annual consumer surplus. Finally, three additional model specifications are estimated and indicate that divers use different travel cost preferences when assessing their revealed and stated preference trip counts but a single preference structure to evaluate site quality changes. Key Words: Revealed and Stated Behavior; Scope Effects; Access; Travel Cost Preferences

    Measuring the Willingness to Pay for Fresh Water Cave Diving

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    Fresh water springs are unique natural resources that are contained within public lands across the United States. Natural resource management on public lands generates many interesting policy issues as the competing goals of conservation, recreational opportunity provision, and revenue generation often clash. As demand for recreational cave diving sites increases, the paper provides natural resource site managers with the first statistical estimate of divers’ willingness to pay to dive fresh water cave and cavern systems. Using a contingent valuation model approach and correcting for hypothetical bias, we find that divers’ median willingness to pay for cave diving opportunities at the site of interest is approximately $68 per dive. Model results also provide evidence of diver sensitivity with respect to scope as individuals are willing to pay more for dives that are higher in quality. Key Words: Contingent Valuation Model; Willingness to Pay; Cave Diving; Scope Sensitivity

    Modeling plan-form deltaic response to changes in fluvial sediment supply

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    This study focuses on the effects of changes in fluvial sediment supply on the plan-form shape of wave-dominated deltas. We apply a one-line numerical shoreline model to calculate shoreline evolution after (I) elimination and (II) time-periodic variation of fluvial input. Model results suggest four characteristic modes of wave-dominated delta development after abandonment. The abandonment mode is determined by the pre-abandonment downdrift shoreline characteristics and wave climate (which are, in turn, determined by previous delta evolution). For asymmetrical deltas experiencing shoreline instability on the downdrift flank, time-periodic variation in fluvial input influences the evolution of downdrift-migrating sandwaves. The frequency and magnitude of the riverine "forcing" can initiate a pattern that migrates away from the river mouth, interacting with the development of shoreline sandwaves. Model results suggest that long-period signals in fluvial delivery can be shredded by autogenic sand waves, whereas shorter-term riverine fluctuations can dominate the signal of the autogenic sandwaves. The insights provided by these exploratory numerical experiments provide a set of hypotheses that can be further tested using natural examples
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