20,250 research outputs found
Bi-Lipschitz geometry of weighted homogeneous surface singularities
We show that a weighted homogeneous complex surface singularity is metrically
conical (i.e., bi-Lipschitz equivalent to a metric cone) only if its two lowest
weights are equal. We also give an example of a pair of weighted homogeneous
complex surface singularities that are topologically equivalent but not
bi-Lipschitz equivalent.Comment: 5 pages. Added result that nonhomogeneous cyclic quotients are not
conica
Pressure Calculation in Polar and Charged Systems using Ewald Summation: Results for the Extended Simple Point Charge Model of Water
Ewald summation and physically equivalent methods such as particle-mesh
Ewald, kubic-harmonic expansions, or Lekner sums are commonly used to calculate
long-range electrostatic interactions in computer simulations of polar and
charged substances. The calculation of pressures in such systems is
investigated. We find that the virial and thermodynamic pressures differ
because of the explicit volume dependence of the effective, resummed Ewald
potential. The thermodynamic pressure, obtained from the volume derivative of
the Helmholtz free energy, can be expressed easily for both ionic and rigid
molecular systems. For a system of rigid molecules, the electrostatic energy
and the forces at the atom positions are required, both of which are readily
available in molecular dynamics codes. We then calculate the virial and
thermodynamic pressures for the extended simple point charge (SPC/E) water
model at standard conditions. We find that the thermodynamic pressure exhibits
considerably less system size dependence than the virial pressure. From an
analysis of the cross correlation between the virial and thermodynamic
pressure, we conclude that the thermodynamic pressure should be used to drive
volume fluctuations in constant-pressure simulations.Comment: RevTeX, 19 pages, 2 EPS figures; in press: Journal of Chemical
Physics, 15-August-199
The Roughness Properties of Small Ice-Bearing Craters at the South Pole of the Moon: Implications for Accessing Fresh Water Ice in Future Surface Operations
The lunar poles provide a fascinating thermal environment capable of cold-trapping water ice on geologic timescales [1]. While there have been many observations indicating the presence of water ice at the lunar surface [e.g., 24], it is still not clear when this ice was delivered to the Moon. The timing of volatile dep-osition provides important constraints on the origin of lunar ice because different delivery mechanisms have been active at different times throughout lunar history. We previously found that some small (<10 km) cra-ters at the south pole of the Moon have morphologies suggestive of relatively young ages, on the basis of crisp crater rims [5]. These craters are too small to date with robust cratering statistics [5], but the possibility of ice in young craters is intriguing because it suggests that there is some recent and perhaps ongoing mechanism that is delivering or redistributing water to polar cold traps. Therefore, understanding if these small, ice-bear-ing craters are indeed young is essential in understand-ing the age and source of volatiles on the Moon. Here we take a new approach to understand the ages of these small polar cold traps: analyzing the roughness properties of small ice-bearing craters. It is well under-stood that impact crater properties (e.g., morphology, rock abundance, and roughness) evolve with time due to a variety of geologic and space-weathering processes [611]. Topographic roughness is a measurement of the local deviation from the mean topography, providing a measurement of surface texture, and is a powerful tool for evaluating surface evolution over geologic time [e.g., 1114]. In this study we analyze the roughness of southern lunar craters (40S90S) from all geologic eras, and determine how the roughness of small (<10 km) ice-bearing craters compare. We discuss the implications of the ages of ice-bearing south polar craters, and potential strategies for accessing fresh ice on the Moon
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