Fermion Zero Modes in Odd Dimensions

We study the zero modes of the Abelian Dirac operator in any odd dimension. We use the stereographic projection between a $(2n-1)$ dimensional space and a $(2n-1)$ sphere embedded in a $2n$ dimensional space. It is shown that the Dirac operator with a gauge field of uniform field strengths in $S^{2n-1}$ has symmetries of SU($n$)$\times$U(1) which is a subgroup of SO($2n$). Using group representation theory, we obtain the number of fermion zero modes, as well as their explicit forms, in a simple way.Comment: 14 page

Formation of "Chemically Pure" Magnetite from Mg-Fe-Carbonates Implications for the Exclusively Inorganic Origin of Magnetite and Sulfides in Martian Meteorite ALH84001

Magnetite and sulfides in the black rims of carbonate globules in Martian meteorite ALH84001 have been studied extensively because of the claim by McKay et al. that they are biogenic in origin. However, exclusively inorganic (abiotic) processes are able to account for the occurrence of carbonate-sulfide-magnetite assemblages in the meteorite. We have previously precipitated chemically zoned and sulfide-bearing carbonate globules analogous to those in ALH84001 (at less than or equal to 150 C) from multiple fluxes of variable-composition Ca-Mg-Fe-CO2-S-H2O solutions. Brief heating of precipitated globules to approx. 470 C produced magnetite and pyrrhotite within the globules by thermal decomposition of siderite and pyrite, respectively. We have also shown that morphology of magnetite formed by inorganic thermal decomposition of Fe-rich carbonate is similar to the morphology of so-called biogenic magnetite in the carbonate globules of ALH84001. Magnetite crystals in the rims of carbonate globules in ALH84001 are chemically pure [Note: "Chemically pure" is defined here as magnetite with Mg at levels comparable or lower than Mg detected by [8] in ALH84001 magnetite]. A debate continues on whether or not chemically pure magnetite can form by the thermal decomposition of mixed Mg-Fe-carbonates that have formed under abiotic conditions. Thomas-Keprta et al. argue that it is not possible to form Mg-free magnetite from Mg-Fe-carbonate based on thermodynamic data. We previously suggested that chemically pure magnetite could form by the thermal decomposition of relatively pure siderite in the outer rims of the globules. Mg-Fe-carbonates may also thermally decompose under conditions conducive for formation of chemically pure magnetite. In this paper we show through laboratory experiments that chemically pure magnetite can form by an inorganic process from mixed Mg-Fe-carbonates

Global Anomalies and Anyons in 1+1 Dimensions

We consider the analog in one spatial dimension of the Bose-Fermi transmutation for planar systems. A quantum mechanical system of a spin 1/2 particle coupled to an abelian gauge field, which is classically invariant under gauge transformations and charge conjugation is studied. It is found that unless the flux enclosed by the particle orbits is quantized, and the spin takes a value $n+ 1/2$, at least one of the two symmetries would be anomalous. Thus, charge conjugation invariance and the existence of abelian instantons simultaneously force the particles to be either bosons or fermions, but not anyons.Comment: Changed title. To be published in Physics Letters

Lithologies Making Up CM Carbonaceous Chondrites and Their Link to Space Exposure Ages

Chondrite parent bodies are among the first large bodies to have formed in the early Solar System, and have since remained almost chemically unchanged having not grown large enough or quickly enough to undergo differentiation. Their major nonvolatile elements bear a close resemblance to the solar photosphere. Previous work has concluded that CM chondrites fall into at least four distinct space exposure age groups (0.1 megaannus, 0.2 megaannus, 0.6 megaannus and 2.0 megaannus), but the meaning of these groupings is unclear. It is possible that these meteorites came from different parent bodies which broke up at different times, or instead came from the same parent body which underwent multiple break-up events, or a combination of these scenarios

Lithologies Making Up CM Carbonaceous Chondrites and Their Link to Space Exposure Ages

Chondrite parent bodies are among the first large bodies to have formed in the early Solar System, and have since remained almost chemically unchanged having not grown large enough or quickly enough to undergo differentiation. Their major nonvolatile elements bear a close resemblance to the solar photosphere. Previous work has concluded that CM chondrites fall into at least four distinct space exposure age groups (0.1 Ma, 0.2 Ma, 0.6 Ma and >2.0 Ma), but the meaning of these groupings is unclear. It is possible that these meteorites came from different parent bodies which broke up at different times, or instead came from the same parent body which underwent multiple break-up events, or a combination of these scenarios

The Present Habitability Potential of Gale Crater: What We Have Learned So Far From Mars Science Laboratory

The Mars Science Laboratory mission has comprehensively interrogated the surface environment of Mars as it explores Gale Crater. Both chemical and physical attributes of the present environment have been measured over the course of the mission, enabling us to compare the present state of the martian surface with the environmental requirements of prokaryotic microbes. While this approach does not exclude the possibility of martian life that may have evolved to adapt to the present conditions, it is advantageous in that it allows us to evaluate environmental requirements of known life and also provide insight into the likelihood of forward contamination by Earth organisms with the comparison of their environmental requirements with the measured attributes of the environment at Gale Crater. We have already modeled a paleoenvironment with high habitability potential (HP) based upon chemistry, mineralogy and other geological evidence such as sedimentary structures and larger scale geomorphology [1]. In this report, we turn our attention to the present HP of the Yellowknife Bay area, including the importance of the physical environmental metrics such as atmospheric pressure, air and ground temperature, ionizing radiation, wind speed and direction, slope, etc

Mineralogy and Elemental Composition of Wind Drift Soil at Rocknest, Gale Crater

The Mars Science Laboratory rover Curiosity has been exploring Mars since August 5, 2012, conducting engineering and first-time activities with its mobility system, arm, sample acquisition and processing system (SA/SPaH-CHIMRA) and science instruments. Curiosity spent 54 sols at a location named "Rocknest," collecting and processing five scoops of loose, unconsolidated materials ("soil") acquired from an aeolian bedform (Fig. 1). The Chemistry and Mineralogy (CheMin) instrument analyzed portions of scoops 3, 4, and 5, to obtain the first quantitative mineralogical analysis of Mars soil, and to provide context for Sample Analysis at Mars (SAM) measurements of volatiles, isotopes and possible organic materials

The Rehabilitation Effectiveness for Activities for Life (REAL) study: a national programme of research into NHS inpatient mental health rehabilitation services across England

Background: The REAL (Rehabilitation Effectiveness for Activities for Life) research programme, funded by the National Institute for Heath Research (NIHR) from 2009 to 2015, investigated NHS mental health rehabiliation services across England. The users of these services are people with longer-term, complex mental health problems, such as schizophrenia, who have additional problems that complicate recovery. Although only around 10% of people with severe mental illness require inpatient rehabilitation, because of the severity and complexity of their problems they cost 25–50% of the total mental health budget. Despite this, there has been little research to help clinicians and commissioners to plan and deliver effective treatments and services. This research aimed to address this gap. Methods: The programme had four phases. (1) A national survey, using quantitative and qualitative methods, was used to provide a detailed understanding of the scope and quality of NHS mental health rehabilitation services in England and the characteristics of those who use them. (2) We developed a training intervention for staff of NHS inpatient mental health rehabilitation units to facilitate service users’ activities. (3) The clinical effectiveness and cost-effectiveness of the staff training programme was evaluated through a cluster randomised controlled trial involving 40 units that scored below average on our quality assessment tool in the national survey. A qualitative process evaluation and a realistic evaluation were carried out to inform our findings further. (4) A naturalistic cohort study was carried out involving 349 service users of 50 units that scored above average on our quality assessment tool in the national survey, who were followed up over 12 months. Factors associated with better clinical outcomes were investigated through exploratory analyses. Results: Most NHS trusts provided inpatient mental health rehabilitation services. The quality of care provided was higher than that in similar facilities across Europe and was positively associated with service users’ autonomy. Our cluster trial did not find our staff training intervention to be clinically effective [coefficient 1.44, 95% confidence interval (CI) –1.35 to 4.24]; staff appeared to revert to previous practices once the training team left the unit. Our realistic review suggested that greater supervision and senior staff support could help to address this. Over half of the service users in our cohort study were successfully discharged from hospital over 12 months. Factors associated with this were service users’ activity levels [odds ratio (OR) 1.03, 95% CI 1.01 to 1.05] and social skills (OR 1.13, 95% CI 1.04 to 1.24), and the ‘recovery’ orientation of the unit (OR 1.04, 95% CI 1.00 to 1.08), which includes collaborative care planning with service users and holding hope for their progress. Quality of care was not associated with costs of care. A relatively small investment (£67 per service user per month) was required to achieve the improvement in everyday functioning that we found in our cohort study. Conclusions: People who require inpatient mental health rehabilitation are a ‘low-volume, high-needs’ group. Despite this, these services are able to successfully discharge most to the community within 18 months. Our results suggest that this may be facilitated by recovery-orientated practice that promotes service users’ activities and social skills. Further research is needed to identify effective interventions that enhance such practice to deliver these outcomes. Our research provides evidence that NHS inpatient mental health rehabilitation services deliver high-quality care that successfully supports service users with complex needs in their recovery. Main limitation: Our programme included only NHS, non-secure, inpatient mental health rehabilitation services. Trial registration: Current Controlled Trials ISRCTN25898179. Funding: The NIHR Programme Grants for Applied Research programme

CM Carbonaceous Chondrite Lithologies and Their Space Exposure Ages

The CMs are the most commonly falling C chondrites, and therefore may be a major component of C-class asteroids, the targets of several current and future space missions. Previous work [1] has concluded that CM chondrites fall into at least four distinct cosmic ray space exposure (CRE) age groups (0.1 million years, 0.2 million years, 0.6 million years and greater than 2.0 million years), an unusually large number, but the meaning of these groupings is unclear. It is possible that these meteorites came from different parent bodies which broke up at different times, or instead came from the same parent body which underwent multiple break-up events, or a combination of these scenarios, or something else entirely. The objective of this study is to investigate the diversity of lithologies which make up CM chondrites, in order to determine whether the different exposure ages correspond to specific, different CM lithologies, which permit us to constrain the history of the CM parent body(ies). We have already reported significant petrographic differences among CM chondrites [2-4]. We report here our new results