Erosion versus construction: The origin of Venusian channels

Lava channels are a common feature in the volcanic regions of the Moon, and have now been observed on Venus. There has been much debate about the origin of lunar channels as to whether they are the result of erosional (either thermal or mechanical) or constructional processes. It is necessary to determine the criteria to distinguish between the different types of channels. The clearest evidence is that the presence of levees indicates that the channel experienced a constructional phase for a period. One example of a channel of this type in the southeast region of Aphrodite Terra appears to show both erosional and constructional characteristics. It is approximately 700 km long with an average width of about 1 km. It drops a distance of 700 m from beginning to end, which means that the average slope is 0.06 degrees. Its source may have been a graben situated at the northwest end of the channel. It appears to have different origins along its length. The lack of levees near the source suggests that the channel is erosional in this region. The presence of levees indicates that a constructional phase has occurred. These are formed by lava repeatedly splashing over the channel sides and solidifying. Evidence of levees is seen further away from the source. However, the presence of levees does not mean that the lava was not also eroding and deepening the channel. Thus, in conclusion, our example channel is very sinuous and there is evidence of erosion. There may also have been overflow here. In its middle reaches it roofs over and has the characteristics of a lava tube. In the lower reaches there is strong evidence for the presence of levees indicating construction. On Earth, limited amounts of erosion may occur in basaltic lava channels, although not nearly on the same scale as on the planets just mentioned. For lava erosion on Earth to occur to a comparable extent, excessive eruption times are required. However, low-viscosity komatiite lava may erode to a larger extent and there is direct evidence that carbonatite lava erodes when the underlying strata is also carbonatite. Previously, it has always been assumed that for thermal erosion to occur the flow must be turbulent. Recent findings indicate that this may be a false assumption and that laminar flow may be effective in eroding the substrate

Geodesic Flow on the Normal Congruence of a Minimal Surface

We study the geodesic flow on the normal line congruence of a minimal surface in ${\Bbb{R}}^3$ induced by the neutral K\"ahler metric on the space of oriented lines. The metric is lorentz with isolated degenerate points and the flow is shown to be completely integrable. In addition, we give a new holomorphic description of minimal surfaces in ${\Bbb{R}}^3$ and relate it to the classical Weierstrass representation.Comment: AMS-LATEX 8 pages 2, figure

Virtual Structure Constants as Intersection Numbers of Moduli Space of Polynomial Maps with Two Marked Points

In this paper, we derive the virtual structure constants used in mirror computation of degree k hypersurface in CP^{N-1}, by using localization computation applied to moduli space of polynomial maps from CP^{1} to CP^{N-1} with two marked points. We also apply this technique to non-nef local geometry O(1)+O(-3)->CP^{1} and realize mirror computation without using Birkhoff factorization.Comment: 10 pages, latex, a minor change in Section 4, English is refined, Some typing errors in Section 3 are correcte

SuperIdentity: fusion of identity across real and cyber domains

Under both benign and malign circumstances, people now manage a spectrum of identities across both real-world and cyber domains. Our belief, however, is that all these instances ultimately track back for an individual to reflect a single ‘SuperIdentity’. This paper outlines the assumptions underpinning the SuperIdentity Project, describing the innovative use of data fusion to incorporate novel real-world and cyber cues into a rich framework appropriate for modern identity. The proposed combinatorial model will support a robust identification or authentication decision, with confidence indexed both by the level of trust in data provenance, and the diagnosticity of the identity factors being used. Additionally, the exploration of correlations between factors may underpin the more intelligent use of identity information so that known information may be used to predict previously hidden information. With modern living supporting the ‘distribution of identity’ across real and cyber domains, and with criminal elements operating in increasingly sophisticated ways in the hinterland between the two, this approach is suggested as a way forwards, and is discussed in terms of its impact on privacy, security, and the detection of threa

The orbit rigidity matrix of a symmetric framework

A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides a matrix representation for fully symmetric infinitesimal flexes, and fully symmetric stresses of symmetric frameworks. The orbit matrix is a true analog of the standard rigidity matrix for general frameworks, and its analysis gives important insights into questions about the flexibility and rigidity of classes of symmetric frameworks, in all dimensions. With this narrower focus on fully symmetric infinitesimal motions, comes the power to predict symmetry-preserving finite mechanisms - giving a simplified analysis which covers a wide range of the known mechanisms, and generalizes the classes of known mechanisms. This initial exploration of the properties of the orbit matrix also opens up a number of new questions and possible extensions of the previous results, including transfer of symmetry based results from Euclidean space to spherical, hyperbolic, and some other metrics with shared symmetry groups and underlying projective geometry.Comment: 41 pages, 12 figure

Small oscillations and the Heisenberg Lie algebra

The Adler Kostant Symes [A-K-S] scheme is used to describe mechanical systems for quadratic Hamiltonians of $\mathbb R^{2n}$ on coadjoint orbits of the Heisenberg Lie group. The coadjoint orbits are realized in a solvable Lie algebra $\mathfrak g$ that admits an ad-invariant metric. Its quadratic induces the Hamiltonian on the orbits, whose Hamiltonian system is equivalent to that one on $\mathbb R^{2n}$. This system is a Lax pair equation whose solution can be computed with help of the Adjoint representation. For a certain class of functions, the Poisson commutativity on the coadjoint orbits in $\mathfrak g$ is related to the commutativity of a family of derivations of the 2n+1-dimensional Heisenberg Lie algebra $\mathfrak h_n$. Therefore the complete integrability is related to the existence of an n-dimensional abelian subalgebra of certain derivations in $\mathfrak h_n$. For instance, the motion of n-uncoupled harmonic oscillators near an equilibrium position can be described with this setting.Comment: 17 pages, it contains a theory about small oscillations in terms of the AKS schem

Lunar elemental composition and ivestigations with D-CIXS x-ray mapping spectrometer on SMART-1

The D-CIXS Compact X-ray Spectrometer on ESA SMART-1 successfully launched in Sept 2003 can derive 45 km resolution images of the Moon with a spectral resolution of 185 eV, providing the first high-resolution global map of rock forming element abundances

Some comparisons of impact craters on Mercury and the Moon

Although the general morphologies of fresh mercurian and lunar craters are remarkably similar, comparisons of ejecta deposits, interior structures, and changes in morphology with size reveal important differences between the two populations of craters. The differences are attributable to the different gravity fields in which the craters were formed and have significant implications for the interpretation of cratering processes and their effects on all planetary bodies