PetroPlot: A plotting and data management tool set for Microsoft Excel

PetroPlot is a 4000-line software code written in Visual Basic for the spreadsheet program Excel that automates plotting and data management tasks for large amount of data. The major plotting functions include: automation of large numbers of multiseries XY plots; normalized diagrams (e.g., spider diagrams); replotting of any complex formatted diagram with multiple series for any other axis parameters; addition of customized labels for individual data points; and labeling flexible log scale axes. Other functions include: assignment of groups for samples based on multiple customized criteria; removal of nonnumeric values; calculation of averages/standard deviations; calculation of correlation matrices; deletion of nonconsecutive rows; and compilation of multiple rows of data for a single sample to single rows appropriate for plotting. A cubic spline function permits curve fitting to complex time series, and comparison of data to the fits. For users of Excel, PetroPlot increases efficiency of data manipulation and visualization by orders of magnitude and allows exploration of large data sets that would not be possible making plots individually. The source codes are open to all users

A hydrous melting and fractionation model for mid-ocean ridge basalts: Application to the Mid-Atlantic Ridge near the Azores

The major element, trace element, and isotopic composition of mid-ocean ridge basalt glasses affected by the Azores hotspot are strongly correlated with H2O content of the glass. Distinguishing the relative importance of source chemistry and potential temperature in ridge-hotspot interaction therefore requires a comprehensive model that accounts for the effect of H2O in the source on melting behavior and for the effect of H2O in primitive liquids on the fractionation path. We develop such a model by coupling the latest version of the MELTS algorithm to a model for partitioning of water among silicate melts and nominally anhydrous minerals. We find that much of the variation in all major oxides except TiO2 and a significant fraction of the crustal thickness anomaly at the Azores platform are explained by the combined effects on melting and fractionation of up to ~700 ppm H2O in the source with only a small thermal anomaly, particularly if there is a small component of buoyantly driven active flow associated with the more H2O-rich melting regimes. An on-axis thermal anomaly of ~35°C in potential temperature explains the full crustal thickness increase of ~4 km approaching the Azores platform, whereas a ≥75°C thermal anomaly would be required in the absence of water or active flow. The polybaric hydrous melting and fractionation model allows us to solve for the TiO2, trace element and isotopic composition of the H2O-rich component in a way that self-consistently accounts for the changes in the melting and fractionation regimes resulting from enrichment, although the presence and concentration in the enriched component of elements more compatible than Dy cannot be resolved

Origins of chemical diversity of back-arc basin basalts: a segment-scale study of the Eastern Lau Spreading Center

We report major, trace, and volatile element data on basaltic glasses from the northernmost segment of the Eastern Lau Spreading Center (ELSC1) in the Lau back-arc basin to further test and constrain models of back-arc volcanism. The zero-age samples come from 47 precisely collected stations from an 85 km length spreading center. The chemical data covary similarly to other back-arc systems but with tighter correlations and well-developed spatial systematics. We confirm a correlation between volatile content and apparent extent of melting of the mantle source but also show that the data cannot be reproduced by the model of isobaric addition of water that has been broadly applied to back-arc basins. The new data also confirm that there is no relationship between mantle temperature and the wet melting productivity. Two distinct magmatic provinces can be identified along the ELSC1 axis, a southern province influenced by a “wet component” with strong affinities to arc volcanism and a northern province influenced by a “damp component” intermediate between enriched mid-ocean ridge basalts (E-MORB) and arc basalts. High–field strength elements and rare earth elements are all mobilized to some extent by the wet component, and the detailed composition of this component is determined. It differs in significant ways from the Mariana component reported by E. Stolper and S. Newman (1994), particularly by having lower abundances of most elements relative to H_(2)O. The differences can be explained if the slab temperature is higher for the Mariana and the source from which the fluid is derived is more enriched. The ELSC1 damp component is best explained by mixing between the wet component and an E-MORB-like component. We propose that mixing between water-rich fluids and low-degree silicate melts occurs at depth in the subduction zone to generate the chemical diversity of the ELSC1 subduction components. These modified sources then rise independently to the surface and melt, and these melts mix with melts of the background mantle from the ridge melting regime to generate the linear data arrays characteristic of back-arc basalts. The major and trace element framework for ELSC1, combined with different slab temperatures and compositions for difference convergent margins, may be able to be applied to other back-arc basins around the globe

Space Charge Limited 2-d Electron Flow between Two Flat Electrodes in a Strong Magnetic Field

An approximate analytic solution is constructed for the 2-d space charge limited emission by a cathode surrounded by non emitting conducting ledges of width Lambda. An essentially exact solution (via conformal mapping) of the electrostatic problem in vacuum is matched to the solution of a linearized problem in the space charge region whose boundaries are sharp due to the presence of a strong magnetic field. The current density growth in a narrow interval near the edges of the cathode depends strongly on Lambda. We obtain an empirical formula for the total current as a function of Lambda which extends to more general cathode geometries.Comment: 4 pages, LaTex, e-mail addresses: [email protected], [email protected]

Origins of Chemical Diversity of Back-Arc Basin Basalts: A Segment-Scale Study of the Eastern Lau Spreading Center

We report major, trace, and volatile element data on basaltic glasses from the northernmost segment of the Eastern Lau Spreading Center (ELSC1) in the Lau back-arc basin to further test and constrain models of back-arc volcanism. The zero-age samples come from 47 precisely collected stations from an 85 km length spreading center. The chemical data covary similarly to other back-arc systems but with tighter correlations and well-developed spatial systematics. We confirm a correlation between volatile content and apparent extent of melting of the mantle source but also show that the data cannot be reproduced by the model of isobaric addition of water that has been broadly applied to back-arc basins. The new data also confirm that there is no relationship between mantle temperature and the wet melting productivity. Two distinct magmatic provinces can be identified along the ELSC1 axis, a southern province influenced by a wet component with strong affinities to arc volcanism and a northern province influenced by a damp component intermediate between enriched mid-ocean ridge basalts (E-MORB) and arc basalts. High field strength elements and rare earth elements are all mobilized to some extent by the wet component, and the detailed composition of this component is determined. It differs in significant ways from the Mariana component reported by E. Stolper and S. Newman (1994), particularly by having lower abundances of most elements relative to $H_2O$. The differences can be explained if the slab temperature is higher for the Mariana and the source from which the fluid is derived is more enriched. The ELSC1 damp component is best explained by mixing between the wet component and an E-MORB-like component. We propose that mixing between water-rich fluids and low-degree silicate melts occurs at depth in the subduction zone to generate the chemical diversity of the ELSC1 subduction components. These modified sources then rise independently to the surface and melt, and these melts mix with melts of the background mantle from the ridge melting regime to generate the linear data arrays characteristic of back-arc basalts. The major and trace element framework for ELSC1, combined with different slab temperatures and compositions for difference convergent margins, may be able to be applied to other back-arc basins around the globe.Earth and Planetary Science

Transport across nanogaps using semiclassically consistent boundary conditions

Charge particle transport across nanogaps is studied theoretically within the Schrodinger-Poisson mean field framework and the existence of limiting current investigated. It is shown that the choice of a first order WKB wavefunction as the transmitted wave leads to self consistent boundary conditions and gives results that are significantly different in the non-classical regime from those obtained using a plane transmitted wave. At zero injection energies, the quantum limiting current density, J_c, is found to obey the local scaling law J_c ~ (V_g)^alpha/(D)^{5-2alpha} with the gap separation D and voltage V_g. The exponent alpha > 1.1 with alpha --> 3/2 in the classical regime of small de Broglie wavelengths. These results are consistent with recent experiments using nanogaps most of which are found to be in a parameter regime where classical space charge limited scaling holds away from the emission dominated regime.Comment: 4 pages, 4 ps figure

Diffusion-limited reactions and mortal random walkers in confined geometries

Motivated by the diffusion-reaction kinetics on interstellar dust grains, we study a first-passage problem of mortal random walkers in a confined two-dimensional geometry. We provide an exact expression for the encounter probability of two walkers, which is evaluated in limiting cases and checked against extensive kinetic Monte Carlo simulations. We analyze the continuum limit which is approached very slowly, with corrections that vanish logarithmically with the lattice size. We then examine the influence of the shape of the lattice on the first-passage probability, where we focus on the aspect ratio dependence: Distorting the lattice always reduces the encounter probability of two walkers and can exhibit a crossover to the behavior of a genuinely one-dimensional random walk. The nature of this transition is also explained qualitatively.Comment: 18 pages, 16 figure

On the formation/dissolution of equilibrium droplets

We consider liquid-vapor systems in finite volume $V\subset\R^d$ at parameter values corresponding to phase coexistence and study droplet formation due to a fixed excess $\delta N$ of particles above the ambient gas density. We identify a dimensionless parameter $\Delta\sim(\delta N)^{(d+1)/d}/V$ and a \textrm{universal} value \Deltac=\Deltac(d), and show that a droplet of the dense phase occurs whenever \Delta>\Deltac, while, for \Delta<\Deltac, the excess is entirely absorbed into the gaseous background. When the droplet first forms, it comprises a non-trivial, \textrm{universal} fraction of excess particles. Similar reasoning applies to generic two-phase systems at phase coexistence including solid/gas--where the ``droplet'' is crystalline--and polymorphic systems. A sketch of a rigorous proof for the 2D Ising lattice gas is presented; generalizations are discussed heuristically.Comment: An announcement of a forthcoming rigorous work on the 2D Ising model; to appear in Europhys. Let

Dynamic Scaling of an Adsorption-Diffusion Process on Fractals

A dynamic scaling of a diffusion process involving the Langmuir type adsorption is studied. We find dynamic scaling functions in one and two dimensions and compare them with direct numerical simulations, and we further study the dynamic scaling law on fractal surfaces. The adsorption-diffusion process obeys the fracton dynamics on the fractal surfaces.Comment: 9 pages, 7 figure

Sr-Nd-Pb-Hf isotope results from ODP Leg 187: Evidence for mantle dynamics of the Australian-Antarctic Discordance and origin of the Indian MORB source

New high precision PIMMS Hf and Pb isotope data for 14–28 Ma basalts recovered during ODP Leg 187 are compared with zero-age dredge samples from the Australian-Antarctic Discordance (AAD). These new data show that combined Nd-Hf isotope systematics can be used as an effective discriminant between Indian and Pacific MORB source mantle domains. In particular, Indian mantle is displaced to lower εNd and higher εHf ratios compared to Pacific mantle. As with Pb isotope plots, there is almost no overlap between the two mantle types in Nd-Hf isotope space. On the basis of our new Nd-Hf isotope data, we demonstrate that Pacific MORB-source mantle was present near the eastern margin of the AAD from as early as 28 Ma, its boundary with Indian MORB-source mantle coinciding with the eastern edge of a basin-wide arcuate depth anomaly that is centered on the AAD. This observation rules out models requiring rapid migration of Pacific MORB mantle into the Indian Ocean basin since separation of Australia from Antarctica. Although temporal variations in isotopic composition can be discerned relative to the fracture zone boundary of the modern AAD at 127°E, the distribution of different compositional groups appears to have remained much the same relative to the position of the residual depth anomaly for the past 30 m.y. Thus significant lateral flow of mantle along the ridge axis toward the interface appears unlikely. Instead, the dynamics that maintain both the residual depth anomaly and the isotopic boundary between Indian and Pacific mantle are due to eastward migration of the Australian and Antarctic plates over a stagnated, but slowly upwelling, slab oriented roughly orthogonal to the ridge axis. Temporal and spatial variations in the compositions of Indian MORB basalts within the AAD can be explained by progressive displacement of shallower Indian MORB-source mantle by deeper mantle having a higher εHf composition ascending ahead of the upwelling slab. Models for the origin of the distinctive composition of the Indian MORB-source based on recycling of a heterogeneous enriched component that consist of ancient altered ocean crust plus<10% pelagic sediment are inconsistent with Nd-Hf isotope systematics. Instead, the data can be explained by a model in which Indian mantle includes a significant proportion of material that was processed in the mantle wedge above a subduction zone and was subsequently mixed back into unprocessed upper mantle