A geochemical and petrological study of the tertiary minor intrusions of Rhum, northwest Scotland

The Rhum minor intrusion suite is petrographically and compositionally variable, the majority of the basic rocks are aphyric dolerites but olivine phyric (picritic) and plagioclase phyric (big feldspar) dolerites are also present. In addition, several medium to coarse grained gabbro and peridotite plugs occur. Intermediate rocks are not abundant and acid dykes are rare. The basic and intermediate intrusions occur in a variety of structural environments all over the island, the gabbros and peridotites are generally emplaced as plugs in the northern and southern Torridonian tracts, while the few acid dykes are usually closely associated with the plutonic acid rocks. Twelve classes of dolerite (Groups 1-12) and five classes of gabbro have been distinguished on geochemical and petrographic grounds. The suite as a whole is characterised by high MgO levels when compared with rocks of analogous differentiation in other Tertiary suites of North-West Britain, Several of the group 1 picrites are believed to have existed as mafic liquids with 15-20 wt% MgO at high crustal levels. In addition the basic members (dolerite groups 2 to 4) and several of the gabbros are characterised by higher Ni and Cr and lower Al(_2)O(_3) than comparable British Tertiary rocks. Discriminant Function analysis of the compositional variation within the basic members of the Rhum minor intrusion suite has shown that the majority of these rocks are completely transitional between alkali olivine basalt and tholeiite basalt and contrast with the mildly alkaline Skye Main Lava Series and the mildly tholeiitic Ardnamurchan cone sheets. In contrast, the dolerite groups 5 and 6 are very similar to some of the Skye magma types and consequently are believed to be outlying members of the Skye regional dyke swarm. Of the intermediate rocks, the dolerite groups 8 and 9 and the gabbroic differentiates are tholeiitic in affinity and the dolerite groups 10 to 12 are alkalic in affinity. Detailed field and geochemical investigation has shown there is a progression from tholeiitic basic magmas to high MgO more alkalic composition with time. Despite the known presence of a large upper crustal magma chamber on Rhum, the geochemical variation of the majority of the basic rocks is cottatible with processes operating below 15 km within the lower crust, or in the upper mantle at depths up to 80 km. In contrast the big feldspar (group 7) dolerites and the magmas which gave rise to the peridotite plugs are believed to have been tapped from a high level crustal magma chamber. In addition the divergence towards more extreme alkalic and tholeiitic compositions in the intermediate rocks coupled with their general porphyritic nature and their major oxide and trace element variation suggests that they are the product of low pressure fractionation processes

Unbounded-error One-way Classical and Quantum Communication Complexity

This paper studies the gap between quantum one-way communication complexity $Q(f)$ and its classical counterpart $C(f)$, under the {\em unbounded-error} setting, i.e., it is enough that the success probability is strictly greater than 1/2. It is proved that for {\em any} (total or partial) Boolean function $f$, $Q(f)=\lceil C(f)/2 \rceil$, i.e., the former is always exactly one half as large as the latter. The result has an application to obtaining (again an exact) bound for the existence of $(m,n,p)$-QRAC which is the $n$-qubit random access coding that can recover any one of $m$ original bits with success probability $\geq p$. We can prove that $(m,n,>1/2)$-QRAC exists if and only if $m\leq 2^{2n}-1$. Previously, only the construction of QRAC using one qubit, the existence of $(O(n),n,>1/2)$-RAC, and the non-existence of $(2^{2n},n,>1/2)$-QRAC were known.Comment: 9 pages. To appear in Proc. ICALP 200

Participatory cotton breeding for organic and low input farming in Central India

Up to 80% of world’s organic cotton is produced in India. However, involved producers are facing increased difficulties to find suitable cultivars. Few hybrids selected for high input farming and genetically-modified (GM) cotton, which is explicitly excluded in organic farming, are presently dominating the Indian seed market. In addition farmers have lost their traditional knowledge on seed production and hybrid seed needs to be purchased each season

Transport in Almost Integrable Models: Perturbed Heisenberg Chains

The heat conductivity kappa(T) of integrable models, like the one-dimensional spin-1/2 nearest-neighbor Heisenberg model, is infinite even at finite temperatures as a consequence of the conservation laws associated with integrability. Small perturbations lead to finite but large transport coefficients which we calculate perturbatively using exact diagonalization and moment expansions. We show that there are two different classes of perturbations. While an interchain coupling of strength J_perp leads to kappa(T) propto 1/J_perp^2 as expected from simple golden-rule arguments, we obtain a much larger kappa(T) propto 1/J'^4 for a weak next-nearest neighbor interaction J'. This can be explained by a new approximate conservation law of the J-J' Heisenberg chain.Comment: 4 pages, several minor modifications, title change

Fractional Operators, Dirichlet Averages, and Splines

Fractional differential and integral operators, Dirichlet averages, and splines of complex order are three seemingly distinct mathematical subject areas addressing different questions and employing different methodologies. It is the purpose of this paper to show that there are deep and interesting relationships between these three areas. First a brief introduction to fractional differential and integral operators defined on Lizorkin spaces is presented and some of their main properties exhibited. This particular approach has the advantage that several definitions of fractional derivatives and integrals coincide. We then introduce Dirichlet averages and extend their definition to an infinite-dimensional setting that is needed to exhibit the relationships to splines of complex order. Finally, we focus on splines of complex order and, in particular, on cardinal B-splines of complex order. The fundamental connections to fractional derivatives and integrals as well as Dirichlet averages are presented

1/f spectrum and memory function analysis of solvation dynamics in a room-temperature ionic liquid

To understand the non-exponential relaxation associated with solvation dynamics in the ionic liquid 1-ethyl-3-methylimidazolium hexafluorophosphate, we study power spectra of the fluctuating Franck-Condon energy gap of a diatomic probe solute via molecular dynamics simulations. Results show 1/f dependence in a wide frequency range over 2 to 3 decades, indicating distributed relaxation times. We analyze the memory function and solvation time in the framework of the generalized Langevin equation using a simple model description for the power spectrum. It is found that the crossover frequency toward the white noise plateau is directly related to the time scale for the memory function and thus the solvation time. Specifically, the low crossover frequency observed in the ionic liquid leads to a slowly-decaying tail in its memory function and long solvation time. By contrast, acetonitrile characterized by a high crossover frequency and (near) absence of 1/f behavior in its power spectra shows fast relaxation of the memory function and single-exponential decay of solvation dynamics in the long-time regime.Comment: 10 pages, 4 figure

The Sizes of 1720 MHz OH Masers: VLBA and MERLIN Observations of the Supernova Remnants W44 and W28

We have used the NRAO Very Long Baseline Array (VLBA) to image OH(1720 MHz) masers in the supernova remnants W28 and W44 at a resolution of 40 mas. We also used MERLIN to observe the same OH(1720 MHz) masers in W44 at a resolution of 290 x 165 mas. All the masers are resolved by these VLBA and MERLIN observations. The measured sizes range from 50 to 180 mas and yield brightness temperature estimates from 0.3--20 x 10**8 K. We investigate whether these measured angular sizes are intrinsic and hence originate as a result of the physical conditions in the supernova remnant shock, or whether they are scatter broadened sizes produced by the turbulent ionized gas along the line of sight. While the current data on the temporal and angular broadening of pulsars, masers and extragalactic soures toward W44 and W28 can be understood in terms of scattering, we cannot rule out that these large sizes are intrinsic. Recent theoretical modeling by Lockett et al. suggests that the physical parameters in the shocked region are indicative of densities and OH abundances which lead to estimates of sizes as large as what we measure. If the sizes and structure are intrinsic, then the OH(1720 MHz) masrs may be more like the OH(1612 MHz) masers in circumstellar shells than OH masers associated with HII regions. At two locations in W28 we observe the classical S-shapes in the Stokes V profiles caused by Zeeman splitting and use it to infer magnetic fields of order 2 milliGauss.Comment: 24 pages, 6 figures, accepted by Ap

The Formaldehyde Masers in Sgr B2: Very Long Baseline Array and Very Large Array Observations

Observations of two of the formaldehyde (H2CO) masers (A and D) in Sgr B2 using the VLBA+Y27 (resolution ~0.01") and the VLA (resolution ~9") are presented. The VLBA observations show compact sources (<10 milliarcseconds, <80 AU) with brightness temperatures >10^8 K. The maser sources are partially resolved in the VLBA observations. The flux densities in the VLBA observations are about 1/2 those of the VLA; and, the linewidths are about 2/3 of the VLA values. The applicability of a core-halo model for the emission distribution is demonstrated. Comparison with earlier H2CO absorption observations and with ammonia (NH3) observations suggests that H2CO masers form in shocked gas. Comparison of the integrated flux densities in current VLA observations with those in previous observations indicates that (1) most of the masers have varied in the past 20 years, and (2) intensity variations are typically less than a factor of two compared to the 20-year mean. No significant linear or circular polarization is detected with either instrument.Comment: 20 pages, 3 figures, 5 tables, accepted to Ap

The Detection of Outflows in the IR-Quiet Molecular Core NGC 6334 I(North)

We find strong evidence for outflows originating in the dense molecular core NGC 6334 I(North): a 1000 Msol molecular core distinguished by its lack of HII regions and mid-IR emission. New observations were obtained of the SiO 2-1 and 5-4 lines with the SEST 15-m telescope and the H2 (1-0) S(1) line with the ESO 2.2-m telescope. The line profiles of the SiO transitions show broad wings extending from -50 to 40 km/s, and spatial maps of the line wing emission exhibit a bipolar morphology with the peaks of the red and blue wing separated by 30". The estimated mass loss rate of the outflow is comparable to those for young intermediate to high-mass stars. The near-IR images show eight knots of H2 emission. Five of the knots form a linear chain which is displaced from the axis of the SiO outflow; these knots may trace shock excited gas along the path of a second, highly collimated outflow. We propose that I(N) is a rare example of a molecular core in an early stage of cluster formation.Comment: 4 pages, LaTeX, 3 ps figures, accepted by ApJ

The Remarkable Mid-Infrared Jet of Massive Young Stellar Object G35.20-0.74

The young massive stellar object G35.20-0.74 was observed in the mid-infrared using T-ReCS on Gemini South. Previous observations have shown that the near infrared emission has a fan-like morphology that is consistent with emission from the northern lobe of a bipolar radio jet known to be associated with this source. Mid-infrared observations presented in this paper show a monopolar jet-like morphology as well, and it is argued that the mid-infrared emission observed is dominated by thermal continuum emission from dust. The mid-infrared emission nearest the central stellar source is believed to be directly heated dust on the walls of the outflow cavity. The hydroxyl, water, and methanol masers associated with G35.20-0.74 are spatially located along these mid-infrared cavity walls. Narrow jet or outflow cavities such as this may also be the locations of the linear distribution of methanol masers that are found associated with massive young stellar objects. The fact that G35.20-0.74 has mid-infrared emission that is dominated by the outflow, rather than disk emission, is a caution to those that consider mid-infrared emission from young stellar objects as only coming from circumstellar disks.Comment: Accepted for publication in ApJ Letters; 4 pages; 2 figures; a version with full resolution images is available here: http://www.ctio.noao.edu/~debuizer