A gravitational kinetic theory for planetesimals

An analytical theory is developed for the velocity evolution of nonaccreting planetesimal populations, based on the Boltzmann and Fokker-Planck equations. Adapting Shkarofsky's calculation of plasma viscosities, the rate of increase in random velocities due to gravitational encounters between planetesimals of equal mass is found to be one-third to one-half Safronov's result. Comparison with Wetherill's numerical experiments suggests that the Fokker-Planck equation underestimates the effectiveness of encounters and that Safronov's value is approximately correct. For populations of nonuniform sizes, the Fokker-Planck equation indicates an efficient redistribution of energy from the largest bodies to the smaller ones. By conserving angular momentum, the rate of radial spreading of orbits is also derived.     

Phase relationships in Buchan facies series pelitic assemblages: calculations with application to andalusite-staurolite parageneses in the Mount Lofty Ranges,South Australia

Low-pressure, medium- to high-temperature (Buchan-type) regional metamorphism of pelitic rocks in the Mount Lofty Ranges, South Australia, is defined by the development of biotite, staurolite-andalusite, fibrolite, prismatic sillimanite and migmatite zones. K-feldspar makes its first appearance in the prismatic sillimanite zone and here we restrict our discussion to lower grade assemblages containing prograde muscovite, concentrating particularly on well-developed andalusitestaurolite parageneses. In general, the spatial distribution and mineral chemical variation of these assemblages accord with the predictions of petrogenetic grids and P-T and T-X _Fe pseudo-sections constructed from the internally consistent data set of Holland and Powell (1990) in the system KFMASH, assuming a(H₂O) 1, although analysed white mica compositions are systematically more aluminous than predicted. Importantly, the stability ranges of most critical assemblages predicted by these grids and pseudo-sections coincide closely with P-T estimates calculated using the data set of Holland and Powell (1990) from the Mount Lofty Ranges assemblages. With the exception of Mn in garnet and Zn in one staurolite-cordierite-muscovite assemblage non-KFMASH components do not significantly appear to have affected the stability ranges of the observed assemblages. An apparent local reversal in isograd zonation in which andalusite first appears down-grade of staurolite suggests a metamorphic field gradient concave towards the temperature axis and, together with evidence for essentially isobaric heating of individual rocks, is consistent with the exposures representing an oblique profile through a terrain in which heat was dissipated from intrusive bodies at discrete structural levels.Mineral abbreviations used in figures als Al₂SiO₅ phase - bi biotite - chl chlorite - ky kyanite - ph phengite - sill sillimanite - and andalusite - cd cordieritc - gt garnet - mu muscovite - q quartz - st staurolite     

STAMP: spatial–temporal analysis of moving polygons

Research questions regarding temporal change in spatial patterns are increasingly common in geographical analysis. In this research, we explore and extend an approach to the spatial–temporal analysis of polygons that are spatially distinct and experience discrete changes though time. We present five new movement events for describing spatial processes: displacement, convergence, divergence, fragmentation and concentration. Spatial–temporal measures of events for size and direction are presented for two time periods, and multiple time periods. Size change metrics are based on area overlaps and a modified cone-based model is used for calculating polygon directional relationships. Quantitative directional measures are used to develop application specific metrics, such as an estimation of the concentration parameter for a von Mises distribution, and the directional rate of spread. The utility of the STAMP methods are demonstrated by a case study on the spread of a wildfire in northwestern Montana.      

Evacuees’ information sources and reentry decision making in the aftermath of Hurricane Ike

In the aftermath of a hurricane, local emergency managers need to communicate reentry plans to households that might be scattered over multiple counties or states. To better understand evacuees’ households’ reliance on different information sources at the time they decided to return home, this study collected data on reentry after Hurricane Ike. The results from a survey of 340 evacuating households indicated that there was low compliance with official reentry plans and that none of the information sources produced greater compliance with official reentry plans. Nonetheless, there were significant changes in the utilization of different sources of emergency information over the course of an evacuation but local news media remained the most common sources throughout the event. There also were significant differences in the relative importance of different sources of reentry information, with people relying most on information from peers. In summary, local authorities need to identify more effective ways to communicate with evacuees that have relocated to distant communities and to motivate them to comply with official reentry plans.     

A three-dimensional,iterative mapping procedure for the implementation of an ionosphere-magnetosphere anisotropic Ohm’s law boundary condition in global magnetohydrodynamic simulations

The mathematical formulation of an iterative procedure for the numerical implementation of an ionosphere-magnetosphere (IM) anisotropic Ohm’s law boundary condition is presented. The procedure may be used in global magnetohydrodynamic (MHD) simulations of the magnetosphere. The basic form of the boundary condition is well known, but a well-defined, simple, explicit method for implementing it in an MHD code has not been presented previously. The boundary condition relates the ionospheric electric field to the magnetic field-aligned current density driven through the ionosphere by the magnetospheric convection electric field, which is orthogonal to the magnetic field B, and maps down into the ionosphere along equipotential magnetic field lines. The source of this electric field is the flow of the solar wind orthogonal to B. The electric field and current density in the ionosphere are connected through an anisotropic conductivity tensor which involves the Hall, Pedersen, and parallel conductivities. Only the height-integrated Hall and Pedersen conductivities (conductances) appear in the final form of the boundary condition, and are assumed to be known functions of position on the spherical surface R=R₁ representing the boundary between the ionosphere and magnetosphere. The implementation presented consists of an iterative mapping of the electrostatic potential , the gradient of which gives the electric field, and the field-aligned current density between the IM boundary at R=R₁ and the inner boundary of an MHD code which is taken to be at R₂>R₁. Given the field-aligned current density on R=R₂, as computed by the MHD simulation, it is mapped down to R=R₁ where it is used to compute by solving the equation that is the IM Ohm’s law boundary condition. Then is mapped out to R=R₂, where it is used to update the electric field and the component of velocity perpendicular to B. The updated electric field and perpendicular velocity serve as new boundary conditions for the MHD simulation which is then used to compute a new field-aligned current density. This process is iterated at each time step. The required Hall and Pedersen conductances may be determined by any method of choice, and may be specified anew at each time step. In this sense the coupling between the ionosphere and magnetosphere may be taken into account in a self-consistent manner.