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]

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

Modes of Growth in Dynamic Systems

Regardless of a system's complexity or scale, its growth can be considered to be a spontaneous thermodynamic response to a local convergence of down-gradient material flows. Here it is shown how growth can be constrained to a few distinct modes that depend on the availability of material and energetic resources. These modes include a law of diminishing returns, logistic behavior and, if resources are expanding very rapidly, super-exponential growth. For a case where a system has a resolved sink as well as a source, growth and decay can be characterized in terms of a slightly modified form of the predator-prey equations commonly employed in ecology, where the perturbation formulation of these equations is equivalent to a damped simple harmonic oscillator. Thus, the framework presented here suggests a common theoretical under-pinning for emergent behaviors in the physical and life sciences. Specific examples are described for phenomena as seemingly dissimilar as the development of rain and the evolution of fish stocks.Comment: 16 pages, 6 figures, including appendi

Mantle Source Variations beneath the Eastern Lau Spreading Center and the Nature of Subduction Components in the Lau Basin-Tonga Arc System

New high-density sampling of the Eastern Lau Spreading Center provides constraints on the processes that affect the mantle wedge beneath a back-arc environment, including the effect of the subduction input on basalt petrogenesis and the change in subduction input with distance from the Tonga arc. We obtained trace element and Pb-Sr-Nd isotopic compositions of 64 samples distributed between 20.2 degree S and 22.3 degree S with an average spacing of ~3.6 km. The trace element and isotope variations do not vary simply with distance from the arc and reflect variations in the mantle wedge composition and the presence of multiple components in the subduction input. The mantle wedge composition varies form north to south, owing to the southward migration of Indian-like mantle, progressively replacing the initially Pacific-like mantle wedge. The mantle wedge compositions also require an enriched mid-ocean ridge basalt-like trace element enrichment that has little effect on isotope ratios, suggesting recent low-degree melt enrichment events. The composition of the subduction input added to the mantle wedge is geographically variable and mirrors the changes observed in the Tonga arc island lavas. The combination of the back-arc and arc data allows identification of several components contributing to the subduction input. These are a fluid derived from the altered oceanic crust with a possible sedimentary contribution, a pelagic sediment partial melt, and, in the southern Lau basin, a volcaniclastic sediment partial melt. While on a regional scale, there is a rough decrease in subduction influence with the distance from the arc, on smaller scales, the distribution of the subduction input reflects different mechanisms of the addition of the subduction input to a variable mantle wedge.Earth and Planetary Science

Enriched Basalts at Segment Centers: The Lucky Strike (37°17′N) and Menez Gwen (37°50′N) Segments of the Mid‐Atlantic Ridge

Basalts from the Mid-Atlantic Ridge change progressively in composition with increasing distance from the Azores platform. Study of the Lucky Strike and Menez Gwen segments reveals much complexity in the gradient. Both segments contain only basalts enriched relative to normal mid-oceanic ridge basalt, but in two distinct groups. Moderately enriched basalts occur throughout the segments, with proximal Menez Gwen enriched relative to Lucky Strike. Highly enriched basalts occur at segment centers. Incompatible element ratios of the highly enriched basalts exceed those of the Azores platform, while isotopic compositions are less enriched. These observations can be explained by a low-degree melt of garnet-bearing Azores mantle added to mantle depleted by previous melt extraction. Melting this “metasomatized” mantle produces lavas that match the enriched samples. The Azores gradient cannot be explained by simple two-component mixing; rather, it reflects recent melt extraction and addition processes related to southward flow of the Azores plume. The Azores gradient also permits tests of segmentation models. Central supply models predict step functions in chemical compositions between segments. Within-segment gradients require vertical supply. Central supply is supported by robust central volcanoes, thicker crust at segment centers, and a step function in isotopes between the segments. The lava diversity at segment centers, however, requires batches of distinct magma that are preserved through melting and melt delivery. Within-segment gradients in moderately incompatible element ratios support a component of multiple supply. The data suggest partial homogenization of magma within a segment and preferential melt focusing to segment centers with some vertical transport.Earth and Planetary Science

Development of a thermal ionizer as ion catcher

An effective ion catcher is an important part of a radioactive beam facility that is based on in-flight production. The catcher stops fast radioactive products and emits them as singly charged slow ions. Current ion catchers are based on stopping in He and H$_2$ gas. However, with increasing intensity of the secondary beam the amount of ion-electron pairs created eventually prevents the electromagnetic extraction of the radioactive ions from the gas cell. In contrast, such limitations are not present in thermal ionizers used with the ISOL production technique. Therefore, at least for alkaline and alkaline earth elements, a thermal ionizer should then be preferred. An important use of the TRI$\mu$P facility will be for precision measurements using atom traps. Atom trapping is particularly possible for alkaline and alkaline earth isotopes. The facility can produce up to 10$^9$ s$^{-1}$ of various Na isotopes with the in-flight method. Therefore, we have built and tested a thermal ionizer. An overview of the operation, design, construction, and commissioning of the thermal ionizer for TRI$\mu$P will be presented along with first results for $^{20}$Na and $^{21}$Na.Comment: 10 pages, 4 figures, XVth International Conference on Electromagnetic Isotope Separators and Techniques Related to their Applications (EMIS 2007

Arsenite sorption and co-precipitation with calcite

Sorption of As(III) by calcite was investigated as a function of As(III) concentration, time and pH. The sorption isotherm, i.e. the log As(III) vs. log [As(OH)3 degrees / Assat] plot is S-shaped and has been modelled on an extended version of the surface precipitation model. At low concentrations, As(OH)3 degrees is adsorbed by complexation to surface Ca surface sites, as previously described by the X-ray standing wave technique. The inflexion point of the isotherm, where As(OH)3 degrees is limited by the amount of surface sites (ST), yields 6 sites nm-2 in good agreement with crystallographic data. Beyond this value, the amount of sorbed arsenic increases linearly with solution concentration, up to the saturation of arsenic with respect to the precipitation of CaHAsO3(s). The solid solutions formed in this concentration range were examined by X-ray and neutron diffraction. The doped calcite lattice parameters increase with arsenic content while c/a ratio remains constant. Our results made on bulk calcite on the atomic displacement of As atoms along [0001] direction extend those published by Cheng et al., (1999) on calcite surface. This study provides a molecular-level explanation for why As(III) is trapped by calcite in industrial treatments.Comment: 9 page

Mechanical tuning of the evaporation rate of liquid on crossed fibers

We investigate experimentally the drying of a small volume of perfectly wetting liquid on two crossed fibers. We characterize the drying dynamics for the three liquid morphologies that are encountered in this geometry: drop, column and a mixed morphology, in which a drop and a column coexist. For each morphology, we rationalize our findings with theoretical models that capture the drying kinetics. We find that the evaporation rate depends significantly on the liquid morphology and that the drying of liquid column is faster than the evaporation of the drop and the mixed morphology for a given liquid volume. Finally, we illustrate that shearing a network of fibers reduces the angle between them, changes the morphology towards the column state, and so enhances the drying rate of a volatile liquid deposited on it

Thermodynamically Consistent Force Field for Molecular Dynamics Simulations of Alkaline-Earth Carbonates and Their Aqueous Speciation

In recent years atomistic simulations have become increasingly important in providing molecular insight to complement experiments. Even for the seemingly simple case of ion-pair formation a detailed atomistic picture of the structure and relative stability of the contact, solvent-shared and solvent-separated ion pairs can only be readily achieved by computer simulation. Here a new force field parametrization for the alkaline-earth carbonate interactions in water has been developed by fitting against experimental thermodynamic and structural data. We demonstrate that the present force field can accurately reproduce the dynamics and thermodynamics of the ions in solution, which is the key to producing quantitatively accurate data that can be compared against experiment