Prediction of wave height based on half-cycle excursion analysis

This paper presents a method to evaluate statistical properties of half-cycle excursions including extreme values. The probability density function for half-cycle excursions for an arbitrarily given wave spectrum is developed based on the Gaussian assumption. The results of numerical computations carried out using wave data obtained during hurricane Camille show that the half-cycle probability density function agrees well with the histogram constructed from the data. The extreme wave height for design consideration computed with risk parameter 0.01 is approximately 20% greater than the observed extreme height.     

A new concept of a hull form to improve wave response characteristics for marine construction barges

The object of the new hull form is to provide a single hull which possesses long natural periods of roll and heave and has substantially reduced motion response amplitudes in very high sea states. Model tests and preliminary estimates indicated that the new hull form can be designed for roll and heave motions nearly equivalent to those of much larger semisubmersible units.All existing conventional marine construction barges have rectangular cross section hull. The new hull form consists of a system of upper side tanks and lower side tanks added onto a rectangular cross section hull. The upper tanks and lower tanks form longitudinal troughs on the port and starboard sides. Structural grillage of any open type is to connect the upper and lower tanks at the side of the vessel. Figure 1 indicates a profile and a typical transverse section of the new hull form. The new hull comprises the concept of reduced water plane area which is turn results in low transverse metacentric height and low tons per in. immersion. The novel features of combining low GM_T and low TPI with extremely heavy damping and added mass of the entrained water characteristics result in very long natural periods of roll and heave and considerably small rolling and heaving amplitudes in high sea states. The open side shell plating on the side of the vessel functions to dissipate wave energy at the side of the vessel which would have otherwise been transmitted to the vessel and caused the vessel to respond. This paper presents the conceptual foundation and outline of the new hull form. Model test results are presented and implemented. Also presented is the design philosophy.     

Intrinsic orbital coordinates on a Hamiltonian surface

A reversible dynamical system with two degrees-of-freedom is reduced to a second-order, Hamiltonian system under a change of independent variable. In certain circumstances, the reduced order system may be integrated following an orthogonal curvilinear transformation from Cartesian x,y to intrinsic orbital coordinates , . Solutions for the orbit position and true time variables are expressed by: % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiabg2 % da9iaadAgacaGGOaGaeqOVdGNaaiilaiabeE7aOjaacMcacaGGSaGa % aeiiaiaadMhacqGH9aqpcaWGNbGaaiikaiabe67a4jaacYcacqaH3o % aAcaGGPaGaaiilaiaabccacaWGKbGaamiDaiabg2da9iabgglaXoaa % dmaabaWaaSaaaeaacaWGibWaa0baaKqaahaacqaH+oaEaeaacaqGYa % aaaOGaam4raiabgUcaRiaadIeadaqhaaqcbaCaaiabeE7aObqaaiaa % ikdaaaGccaWGfbaabaGaaGOmaiaacIcacaWGibGaey4kaSIaamyvai % aacMcaaaaacaGLBbGaayzxaaWaaWbaaSqabKqaGhaacaaIXaGaai4l % aiaaikdaaaGccaWGKbGaeqiXdqhaaa!6498! \[ x = f(\xi ,\eta ),{\rm{ }}y = g(\xi ,\eta ),{\rm{ }}dt = \pm \left[ {\frac{{_\xi ^{\rm{2}} {\ie} + _\eta ^2 }}{{2( + U)}}} \righ \]1446 1040 where U is the potential function, and z is the new independent variable. The functions f, g may be expressed by quadratures when the metric coefficients {\er},{\ie} are specified. Two second-order, partial differential equations specify {\er}, {\ie} and Hamiltonian {\tH}. Auxiliary conditions are needed because the solutions are underdetermined. For example, both sets of curvilinear coordinate lines are orbits when certain dynamical compatibility conditions between U and {\ie} (or {\er}) are satisfied. Alternatively, when orbits cross the parametric curves, the auxiliary condition {\er} = {\ie} specifies a conformal transformation, and the partial differential equation for {\tH} may be reduced to an ordinary differential equation for the orbit curve. In either case, integrability is guaranteed for Lionville dynamical systems. Specific applications are presented to illustrate direct solution for the orbit (e.g., two fixed centers) and inverse solution for the potential.     

Stratigraphy of total metals in PIRLA sediment cores

Sediment cores from 30 low-alkalinity lakes in northern New England (NE), New York (NY), the northern Great Lakes States (NGLS) of Minnesota, Michigan, and Wisconsin, and Florida (FL) have been dated by ²¹⁰Pb and analyzed for water and organic content, eight major elements (Al, Ti, Fe, Mn, Ca, Mg, Na, K) plus four trace metals (Pb, Zn, Cu, and V). Variations in the percentages of major elements through time are dominated by long-term independent variations in the abundance of SiO₂, FeO, and to a lesser extent Ca and Al. Additional variations are caused by varying proportions of inorganic matter. Major variations in chemistry are generally unrelated to documented distrubances in the watersheds; most disturbances are minor fires or selective logging.Accelerated accumulation of Pb from atmospheric sources into sediment first occurs in sediment dated between 1800 and 1850 in NY and NE, slightly later in the NGLS region, and about 1900 in FL. Modern accumulation rates in all areas are comparable (ca. 1 to 4 g cm^–2 yr^–1). Accumulation rates of Pb in some lakes have declined significantly from 1975 to 1985. Atmospheric deposition of anthropogenic Zn and Cu is also indicated by generally increasing accumulation rates in sediment cores, but the record is not as clear nor are chemical profiles in all lakes parallel to the trends in atmospheric emissions inferred on the basis of fossil fuel consumption, smelting, and other industrial activities. Inter-lake variations in profiles of Cu and Zn are large. Vanadium accumulation rates increase by the 1940s in NY and NE, but not until the 1950s in the NGLS region. This timing correlates with regional trends in the combustion of fuel oil, a major source of atmospheric V.Acidification of some of the lakes is suggested by decreases in the concentration and accumulation rates of Mn, Ca, and Zn in recent sediment, relative to other elements of catchment origin. The decreases generally occur slightly before the onset of acidification as indicated by diatoms. Increased sediment accumulation rates for Fe may indicate the acidification of watershed soils. The use of the accumulation rate of TiO₂ as an indicator of rates of erosion and for normalization of trace metal accumulation rates is in question for lakes where the flux of TiO₂ from the atmosphere varies and is a significant fraction of the total flux of TiO₂ to the sediment.This is the thirteenth of a series of papers to be published by this journal which is a contribution of the Paleoecological Investigation of Recent Lake Acidification (PIRLA) project. Drs. D. F. Charles and D. R. Whitehead are guest editors for this series.     

Composition-Induced Variations in SIMS Instrumental Mass Fractionation during Boron Isotope Ratio Measurements of Silicate Glasses

An analytical artefact is reported here related to differences in instrumental mass fractionation between NIST SRM glasses and natural geological glasses during SIMS boron isotope determinations. The data presented demonstrated an average 3.4‰ difference between the NIST glasses and natural basaltic to rhyolitic glasses mainly in terms of their sputtering-induced fractionation of boron isotopes. As no matrix effect was found among basaltic to rhyolitic glasses, instrumental mass fractionation of most natural glass samples can be corrected by using appropriate glass reference materials. In order to confirm the existence of the compositionally induced variations in boron SIMS instrumental mass bias, the observed offset in SIMS instrumental mass bias has been independently reproduced in two laboratories and the phenomenon has been found to be stable over a period of more than one year. This study highlights the need for a close match between the chemical composition of the reference material and the samples being investigated.     

Photochemistry and Vertical Transport in Io's Atmosphere and Ionosphere

We present an updated model for the photochemistry of Io's atmosphere and ionosphere and use this model to investigate the sensitivity of the chemical structure to vertical transport rates. SO₂is assumed to be the dominant atmospheric gas, with minor molecular sodium species such as Na₂S or Na₂O released by sputtering or venting from the surface. Photochemical products include SO, O₂, S, O, Na, NaO, NaS, and Na₂. We consider both “thick” and “thin” SO₂atmospheres that encompass the range allowed by recent HST and millimeter-wave observations, and evaluate the possibility that O₂and/or SO may be significant minor dayside constituents and therefore likely dominant nightside gases. The fast reaction between S and O₂limits the column abundance of O₂to ∼10⁴less than that calculated by Kumar (J. Geophys. Res.87, 1677–1684, 1982; 89(A9), 7399–7406, 1984) for a pure sulfur/oxygen atmosphere. If a significant source of NaO₂or Na₂O were supplied by the surface and mixed rapidly upward, then oxygen liberated in the chemical reactions which also liberate free Na would provide an additional source of O₂. Fast eddy mixing will enhance the transport of molecular sodium species to the exobase, in addition to increasing the vertical transport rate of ions. Ions produced in the atmosphere will be accelerated by the reduced corotation electric field penetrating the atmosphere. These ions experience collisions with the neutral gas, leading to enhanced vertical ion diffusion. The dominant ion, Na⁺, is lost primarily by charge exchange with Na₂O and/or Na₂S in the lower atmosphere and by diffusion through the ionopause in the upper atmosphere. The atmospheric column abundance of SO, O₂, and the upper atmosphere escape rates of Na, S, O, and molecular sodium species are all strong functions of the eddy mixing rate. Most atmospheric escape, including that of molecular sodium species, probably occurs from the low density “background” SO₂atmosphere, while a localized high density “volcanic” SO₂atmosphere can yield an ionosphere consistent with that detected by the Pioneer 10 spacecraft.     

Commentary and critique of “accounting for mineral resources: Issues and BEA's initial estimates”

The Bureau of Economic Analysis (BEA), U.S. Department of Commerce, in keeping with broad international efforts to green national gross domestic product (GDP) accounts, has attempted to create satellite accounts for mineral depletion. The present paper criticizes the BEA's unit rent measure of resource depletion, which is based upon Hotelling's pure theory of exhaustion. Following a thorough criticism of Hotelling's theory as a real-world model of mineral prices, practical issues related to the treatment of recycling, exploration, definition of reserves/resources, and their valuation/exploitation are introduced. For crude oil and natural gas and the nonfuel minerals, specific application problems of joint products and residuals complicate BEA's assumptions and efforts.     

Cordierite-garnet-sillimanite-quartz equilibrium: I. New experimental calibration in the system FeO−Al2O3−SiO2−H2O and certain P-T-X H2O relations

The equilibrium in which hydrous Fe-cordierite breaks down to almandine, sillimanite, quartz, and water was previously experimentally determined by Richardson (1968) and Holdaway and Lee (1977) using QMF buffer and by Weisbrod (1973) using QIF buffer. All these studies yielded similar results — a negative dP/dT slope for the equilibrium curve. However, based on theoretical arguments, Martignole and Sisi (1981), and based on Fe-Mg partitioning experiments on coexisting cordierite and garnet in equilibrium with sillimanite and quartz, Aranovich and Podlesskii (1983) suggested that this equilibrium curve has a positive dP/dT slope and its position depends on the water content of the equilibrium cordierite. We have redetermined this equilibrium using a much improved tecnique of detecting reaction direction, and cordierite starting material that contained virtually no hercynite. Hercynite was present as a contaminant in the cordierites of previous experimental studies and possibly reacted with quartz during the experimental runs to expand the apparent stability field of Fe-cordierite. We synthesized Fe-cordierite from reagent grade oxides at 710°C and 2 kbar (using QMF buffer) with two intermediate stages of grinding and mixing. The cordierite has a unit cell volume of 1574.60 ų (molar volume=23.706 J/bar) and no Fe³⁺ as indicated by X-ray diffraction and room temperature Mössbauer studies respectively. Reaction direction was concluded by noting20% change of the ratios of intensities of two key X-ray diffraction peaks of cordierite and almandine. Our results show that the four-phase equilibrium curve passes through the points 2.1 kbar, 650°C and 2.5 kbar, 750°C. This disagrees with all previous experimental studies. H₂O in the Fe-cordierite, equilibrated at 2.2 kbar and 700°C and determined by H-extraction line in the stable isotope laboratory, is 1.13 wt% (n=0.41 moles). H₂O content of pure Mg-cordierite equilibrated under identical conditions and determined by thermogravimentric conditions and determined by thermogravimetric analysis is 1.22 wt% (n=0.40). Similar determinations on Fe-cordierite and Mg-cordierite equilibrated at 2.0 kbar and 650°C show 1.27 wt% (n=0.46) and 1.47 wt% (n=0.48) of H₂O respectively. Thus, H₂O content appears to be independent of Fe/Mg ratio in cordierite, a conclusion which supports previous experimental determinations. The experimentally determined equilibrium curve represents conditions of P_H2O=P_total. From this we calculated the anhydrous curve representing equilibrium under conditions of X _H2O ^V =0.0. A family of calculated equilibrium curves of constant n _H2O ^Cord cut the experimentally determined curve at a very small angle indicating a slight variation in n _H2O ^Cord in cordierite in equilibrium with almandine, sillimanite, and quartz under the conditions of constant X _H2O ^V . Ancther set of calculated equilibrium curves, each representing constant a _H2O ^V demonstrate that the slopes of the curves vary with X _H2O ^V , and are all positive in the full range of 0.0X _H2O ^V 1.0.     

Crystallization processes in an artificial magma: variations in crystal shape,growth rate and composition with melt cooling history

A large (4.8 m³, 1.3x10⁷ g) artificial mafic melt with a bulk composition similar to that of a basalt (but with a high CaO content of 17 wt%) was generated during a demonstration of in situ vitrification and was allowed to cool naturally. During the melting process, convection was vigorous, resulting in a chemically and thermally homogeneous melt body. Once heating was complete, the cooling rate was rapid with the temperature dropping from 1500°C to 500°C in 6 days within the interior of the 3 m diameter, 1.5 m thick body. A 20 h period of constant temperature (1140°C) observed during colling was the result of latent heat released by widespread crystallization. The final crystalline assemblage consists of diopsidic to hedenbergitic pyroxene and anorthitic feldspar, with a subordinate amount of potassic feldspar, plus a small amount of evolved glass. The compositions and proportions of phases agree well with those predicted by the MELTS thermodynamic model. Thermal and textural evidence suggest that convection within the melt ceased coincident with formation of the first crystals. Textural investigation of core samples reveals large (up to 1 cm in length) acicular diopsidic pyroxenes in a matrix of smaller feldspar and zoned pyroxene crystals (500 m in length). Crystal shape and pyroxene composition vary as a function of position within the solidified body, as a function of cooling rate. Both crystal size and degree of crystallinity are highest in the central, most slowly-cooled parts of the rock. Crystal shape is characterized by tabular, equilibrium-growth forms in the slowly-cooled areas, grading to highly skeletal, dendritic forms at the rapidly-cooled edges of the body. The pyroxene crystals are dominantly homogeneous diopside, but crystals are characterized by thin Fe-rich hedenbergitic rims. These rims were deposited when Mg in the melt was depleted by diopside growth, and melt temperature had cooled sufficiently to allow Fe-rich pyroxene growth. Crystal growth rates can be calculated based on thermal behavior of the melt, reinforced by thermodynamic modelling, and are determined to be between 10^-7 and 10^-8 cm/s in the central part of the melt. These estimates agree well with growth rates in natural systems with similar cooling rates. Pyroxene crystals that formed at a higher cooling rates are characterized by higher Al and lower Mg contents relative to tabular equilibrium crystalline forms, presumably as a result of disequilibrium melt compositions at the crystal-melt interface.New Mexico Bureau of Mines and Mineral Resources, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA