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.     

The scattering mean free path in the Uranian atmosphere

New measurements of the equivalent widths of the 4-0 S(0) and S(1) H₂ quadrupole lines in the Uranian spectrum have been obtained using high dispersion (4.12 Å/mm) image-tube spectrography. The measured equivalent widths are $\text{62 ± 19}\text{m}\text{A}\text{?}\text{and}\text{58 ± 13}\text{m}\text{A}\text{?}$ for the S(0) and S(1) lines, respectively. Curve-of-growth analysis in terms of a reflecting layer model yields an H₂ column-density of 780_?330⁺⁹⁴⁰km amagat and a temperature of 78_?24⁺⁸⁰°K. Interpretation using a semi-infinite, homogeneous, isotropically scattering model for line formation yields a scattering mean free path at λ6400 Å of 550 ± 250 km amagat. Quoted errors for both the H₂ column-density and the scattering mean free path include the effect of uncertainty in the choice of atmospheric temperature. The results are discussed in terms of current models for the Uranian atmosphere.     

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.     

Concentrations of unsubstituted polynuclear aromatic hydrocarbons in bay mussels (Mytilus edulis) from Oregon, USA

Concentrations of fifteen unsubstituted polynuclear aromatic hydrocarbons (PNAH) were measured in Mytilus edulis from two sites in Yaquina Bay, Oregon, USA, during 1979–1980. There were significant differences in PNAH levels between the two populations. The average total concentration in mussels inhabiting the more industrialized bayfront was 986·2 μg/kg compared with 273·9 μg/kg in mussels from a more remote site across the bay. Substantial differences were found in the concentrations of different PNAH in M. edulis examined during this study. The smaller more water soluble, compounds were concentrated to one or two orders of magnitude above the larger, less soluble PNAH.     

Particulate flux in the water column overlying Santa Monica Basin

Fluxes of particulate carbon, nitrogen, phytoplankton pigments, biogenic silica and dry mass were measured using free-floating and moored sediment trap arrays in the Santa Monica Basin during the period from October 1985 to August 1990 as part of the California Basin Study (CaBS) Program. In field testing for potential sources of sediment trap biases, we found little significant or consistent difference in rate estimates between short-term drifting traps and long-term moored traps, between preserved and unpreserved traps in short-term experiments, between different preservatives (mercury or formalin) in long-term experiments, between different designs of small cylindrical traps, and between deep-moored cylindrical traps and large conical traps. We did, however, find that sediment trap samples collected and analyzed on 0.45 μm silver filters gave estimates of carbon and nitrogen fluxes about 25% higher than samples collected on GF/F glass-fiber filters. Concurrent trap deployments at two stations 18km apart revealed low mesoscale variability in flux estimates. Seasonal patterns in carbon and nitrogen flux were not evident in our data, but strong seasonality, with spring maxima and summer minima, were observed for fluxes of phaeopigments and biogenic silica out of the euphotic zone.Time-averaged rates of particulate flux for long-term trap deployments from January to August 1990, were 121, 18.8, 1.5, 67 and 633mg m⁻²d⁻¹ at 110–135m for carbon, nitrogen, phaeopigment, biogenic silica and mass, respectively. Flux estimates to the basin floor (835–860m) were 50, 6.5, 0.64, 41.6 and 575mg m⁻²d⁻¹ for the same parameters. The former estimates are constrained by and in good agreement with independent assessments of new production from nitrate uptake in the euphotic zone. The latter agree with rates previously inferred from the sedimentary record using ²¹⁰Pb as a tracer. In addition, the difference in carbon estimates in the water column between the euphotic zone and the basin floor is consistent with the requirements for bacterial growth and metabolism at intermediate depths as measured by the thymidine method.     

Water fluxes through the Cretan Arc Straits, Eastern Mediterranean Sea: March 1994 to June 1995

Five research cruises were undertaken incorporating ADCP sections along the Cretan Arc Straits and CTD surveys covering the entire area of the Straits and the Cretan Sea. In addition, six moorings (with 15 current meters) were deployed within the Straits, which monitored flows in the surface (50 m), intermediate (250 m), and deep (50 m from the bottom) layers. The ADCP, CM, and CTD datasets enable the derivation of water transports through the Cretan Arc Straits to be assessed. Flow structure through the Cretan Arc Straits is not the typical flow regime with a surface inflow and deep outflow, instead there is a persistent deep outflow of Cretan Deep Water (CDW) (σ_θ>29.2) with an annual mean of ˜0.6 Sv, through the Antikithira and Kassos Straits at depths below 400 m and 500 m, respectively. CDW outflowing transports are higher (˜0.8 Sv) in April–June, and lower (˜0.3 Sv) in October–December. Within the upper water layer (0–˜400 m), the transport and the water exchanges through the Straits are controlled by local circulation features, which weaken substantially below 200 m. The Asia Minor Current (AMC) influences the Rhodes and the Karpathos Straits, resulting in a net inflow of water. In contrast, the Mirtoan/West Cretan Cyclone influences the Antikithira and Kithira Straits, where there is a net outflow. In the Kassos Strait, there is a complex interaction between the East Cretan Cyclone, the Ierapetra Anticyclone and the westward extension of the Rhodes Gyre, which results in a variable flow regime. There is a net inflow in autumn and early winter, and a switch to a net outflow in early spring and summer. The total inflow and outflow, throughout all of the Straits, ranged from ˜2 to ˜3.5 Sv, with higher values in autumn and early winter and lower in summer. The AMC carries ˜2 Sv of inflow through the Rhodes and Karpathos Straits, and this accounts for 60–80% of the total inflow. About 10–15% of the total outflow is of CDW, and a further 45–70% occurs through the upper 400 m of the Kithira and Antikithira Straits. The Kassos Strait exhibits a net inflow of ˜0.7 Sv in autumn and early winter, with a net outflow of ˜0.5 Sv in early spring and summer.     

Building and Testing an <Emphasis Type="Italic">a priori</Emphasis> Geophysical Model for Western Eurasia and North Africa

We construct and evaluate a new three-dimensional model of crust and upper mantle structure in Western Eurasia and North Africa (WENA) extending to 700 km depth and having 1° parameterization. The model is compiled in an a priori fashion entirely from existing geophysical literature, specifically, combining two regionalized crustal models with a high-resolution global sediment model and a global upper mantle model. The resulting WENA1.0 model consists of 24 layers: water, three sediment layers, upper, middle, and lower crust, uppermost mantle, and 16 additional upper mantle layers. Each of the layers is specified by its depth, compressional and shear velocity, density, and attenuation (quality factors, Q _P and Q _S ). The model is tested by comparing the model predictions with geophysical observations including: crustal thickness, surface wave group and phase velocities, upper mantle _n velocities, receiver functions, P-wave travel times, waveform characteristics, regional 1-D velocities, and Bouguer gravity. We find generally good agreement between WENA1.0 model predictions and empirical observations for a wide variety of independent data sets. We believe this model is representative of our current knowledge of crust and upper mantle structure in the WENA region and can successfully be used to model the propagation characteristics of regional seismic waveform data. The WENA1.0 model will continue to evolve as new data are incorporated into future validations and any new deficiencies in the model are identified. Eventually this a priori model will serve as the initial starting model for a multiple data set tomographic inversion for structure of the Eurasian continent.