Water on Mars: Clue to accretional history

Geological evidence for large amounts of water at the Martian surface appears to be in conflict with geochemical evidence from SNC meteorites that suggests that the Mars mantle is dry and should have lost almost all of its initially large inventory of water during accretion. Here, several possibilities are suggested as to how the apparently conflicting data from two sources may be reconciled. The considerations examined indicate that several plausible explanations for the apparent conflict between geochemical evidence of little water on Mars and geologic evidence of abundant water. One possible conclusion is that Mars has a primitive volatile-rich crust that has been partly overplated with young, dry, mantle-derived volcanoes of which we have samples in the SNC meteorites

Kinematic Self-Similar Cylindrically Symmetric Solutions

This paper is devoted to find out cylindrically symmetric kinematic self-similar perfect fluid and dust solutions. We study the cylindrically symmetric solutions which admit kinematic self-similar vectors of second, zeroth and infinite kinds, not only for the tilted fluid case but also for the parallel and orthogonal cases. It is found that the parallel case gives contradiction both in perfect fluid and dust cases. The orthogonal perfect fluid case yields a vacuum solution while the orthogonal dust case gives contradiction. It is worth mentioning that the tilted case provides solution both for the perfect as well as dust cases.Comment: 22 pages, accepted for publication in Int. J. of Mod. Phys.

Volcanic features of Hawaii. A basis for comparison with Mars

Despite the difference in size Martian and Hawaiian volcanoes have numerous characteristics in common. Specific features such as lava channels, collapsed lava tubes, levees and flow fronts, all very common in Hawaii, are also abundant on the flanks of some of the Martian volcanoes. Striking differences also exist, such as the apparent lack of radial rift zones on some Martian volcanoes and the paucity of cinder and spatter cones. Some of the best photographs of Martian and Hawaiian volcanic features are presented. Descriptive legends are provided for each picture. An overview of the geological processes and structures depicted is included

Vortex macroscopic superpositions in ultracold bosons in a double-well potential

We study macroscopic superpositions in the orbital rather than the spatial degrees of freedom, in a three-dimensional double-well system. We show that the ensuing dynamics of $N$ interacting excited ultracold bosons, which in general requires at least eight single-particle modes and ${N+7 \choose N}$ Fock vectors, is described by a surprisingly small set of many-body states. An initial state with half the atoms in each well, and purposely excited in one of them, gives rise to the tunneling of axisymmetric and transverse vortex structures. We show that transverse vortices tunnel orders of magnitude faster than axisymmetric ones and are therefore more experimentally accessible. The tunneling process generates macroscopic superpositions only distinguishable by their orbital properties and within experimentally realistic times.Comment: 9 pages, 6 figure

The fine structure of asset returns: an empirical investigation

We investigate the importance of diffusion and jumps in a new model for asset returns. In contrast to standard models, we allow for jump components displaying finite or infinite activity and variation. Empirical investigations of time series indicate that index dynamics are devoid of a diffusion component, which may be present in the dynamics of individual stocks. This leads to the conjecture, confirmed on options data, that the risk-neutral process should be free of a diffusion component. We conclude that the statistical and risk-neutral processes for equity prices are pure jump processes of infinite activity and finite variation

Options on realized variance and convex orders

Realized variance option and options on quadratic variation normalized to unit expectation are analysed for the property of monotonicity in maturity for call options at a fixed strike. When this condition holds the risk-neutral densities are said to be increasing in the convex order. For Leacutevy processes, such prices decrease with maturity. A time series analysis of squared log returns on the S&P 500 index also reveals such a decrease. If options are priced to a slightly increasing level of acceptability, then the resulting risk-neutral densities can be increasing in the convex order. Calibrated stochastic volatility models yield possibilities in both directions. Finally, we consider modeling strategies guaranteeing an increase in convex order for the normalized quadratic variation. These strategies model instantaneous variance as a normalized exponential of a Leacutevy process. Simulation studies suggest that other transformations may also deliver an increase in the convex order

Evolution of a Primordial Black Hole Population

We reconsider in this work the effects of an energy absorption term in the evolution of primordial black holes (hereafter PBHs) in the several epochs of the Universe. A critical mass is introduced as a boundary between the accreting and evaporating regimes of the PBHs. We show that the growth of PBHs is negligible in the Radiation-dominated Era due to scarcity of energy density supply from the expanding background, in agreement with a previous analysis by Carr and Hawking, but that nevertheless the absorption term is large enough for black holes above the critical mass to preclude their evaporation until the universe has cooled sufficiently. The effects of PBH motion are also discussed: the Doppler effect may give rise to energy accretion in black-holes with large peculiar motions relative to background. We discuss how cosmological constraints are modified by the introduction of the critical mass since that PBHs above it do not disturb the CMBR. We show that there is a large range of admissible masses for PBHs above the critical mass but well below the cosmological horizon. Finally we outline a minimal kinetic formalism, solved in some limiting cases, to deal with more complicated cases of PBH populationsComment: RevTex file, 8 pp., 3 .ps figures available upon request from [email protected]

Shopping for food: lessons from a London borough

Purpose – This paper aims to measure access to food in an inner London borough. Design/methodology/approach – There were six phases, which included designing food baskets, consultation with local residents and a shop survey. Recognising the cultural make-up of the borough food baskets and menus were developed for four key communities, namely: White British, Black Caribbean, Turkish, and Black African. Three areas were identified for the study and shopping hubs identified with a 500-metre radius from a central parade of shops. Findings – The findings paint an intricate web of interactions ranging from availability in shops to accessibility and affordability being key issues for some groups. It was found that in the areas studied there was availability of some key healthy items, namely fresh fruit and vegetables, but other items such as: fresh meat and poultry, fish, lower fat dairy foods, high fibre pasta and brown rice were not available. Access was found to be defined, by local people, as more extensive than just physical distance to/from shops – for many shopping was made more difficult by having to use taxis and inconvenient buses. Small shops were important in delivering healthy food options to communities in areas of deprivation and were judged to offer a better range and more appropriate food than the branches of the major supermarket chains. Research limitations/implications – The importance of monitoring the impact of shops and shop closures on healthy food availability is emphasised. From a policy perspective the findings suggest that approaches based on individual agency need to be balanced with upstream public health nutrition approaches in order to influence the options available. Originality/value – The paper is arguably the first to examine and dissect the issue of food availability and accessibility in the inner London borough in question, especially in the light of its proposed redevelopment for the London Olympics in 2012