812 research outputs found
Paragenesis of multiple platinum-group mineral populations in Shetland ophiolite chromitite: 3D X-ray tomography and in situ Os isotopes
Chromitite from the Harold’s Grave locality in the mantle section of the Shetland ophiolite complex is extremely enriched in Ru, Os and Ir, at µg/g concentrations. High-resolution X-ray computed tomography on micro-cores from these chromitites was used to determine the location, size, distribution and morphology of the platinum-group minerals (PGM). There are five generations of PGM in these chromitites. Small (average 5 µm in equivalent sphere diameter, ESD) euhedral laurites, often with Os-Ir alloys, are totally enclosed in the chromite and are likely to have formed first by direct crystallisation from the magma as the chromite crystallised. Also within the chromitite there are clusters of larger (50 µm ESD) aligned elongate crystals of Pt-, Rh-, Ir-, Os- and Ru-bearing PGM that have different orientations in different chromite crystals. These may have formed either by exsolution, or by preferential nucleation of PGMs in boundary layers around particular growing chromite grains. Thirdly there is a generation of large (100 µm ESD) composite Os-Ir-Ru-rich PGM that are all interstitial to the chromite grains and sometimes form in clusters. It is proposed that Os, Ir and Ru in this generation were concentrated in base metal sulfide droplets that were then re-dissolved into a later sulfide-undersaturated magma, leaving PGM interstitial to the chromite grains. Fourthly there is a group of almost spherical large (80 µm ESD) laurites, hosting minor Os-Ir-Ru-rich PGM that form on the edge or enclosed in chromite grains occurring in a sheet crosscutting a chromitite layer. These may be hosted in an annealed late syn- or post magmatic fracture. Finally a few of the PGM have been deformed in localised shear zones through the chromitites. The vast majority of the PGM – including small PGM enclosed within chromite, larger interstitial PGM and elongate aligned PGM – have Os isotope compositions that give Re-depletion model ages approximately equal to the age of the ophiolite at ∼492 Ma. A number of other PGM – not confined to a single textural group – fall to more or less radiogenic values, with four PGM giving anomalously unradiogenic Os corresponding to an older age of ∼1050 Ma. The 187Os/188Os isotopic ratios for PGM from Cliff and Quoys, from the same ophiolite section, are somewhat more radiogenic than those at Harold’s Grave. This may be due to a distinct mantle source history or possibly the assimilation of radiogenic crustal Os
Smectic ordering in liquid crystal - aerosil dispersions I. X-ray scattering
Comprehensive x-ray scattering studies have characterized the smectic
ordering of octylcyanobiphenyl (8CB) confined in the hydrogen-bonded silica
gels formed by aerosil dispersions. For all densities of aerosil and all
measurement temperatures, the correlations remain short range, demonstrating
that the disorder imposed by the gels destroys the nematic (N) to smectic-A
(SmA) transition. The smectic correlation function contains two distinct
contributions. The first has a form identical to that describing the critical
thermal fluctuations in pure 8CB near the N-SmA transition, and this term
displays a temperature dependence at high temperatures similar to that of the
pure liquid crystal. The second term, which is negligible at high temperatures
but dominates at low temperatures, has a shape given by the thermal term
squared and describes the static fluctuations due to random fields induced by
confinement in the gel. The correlation lengths appearing in the thermal and
disorder terms are the same and show strong variation with gel density at low
temperatures. The temperature dependence of the amplitude of the static
fluctuations further suggests that nematic susceptibility become suppressed
with increasing quenched disorder. The results overall are well described by a
mapping of the liquid crystal-aerosil system into a three dimensional XY model
in a random field with disorder strength varying linearly with the aerosil
density.Comment: 14 pages, 13 figure
Hydrogen-bonded Silica Gels Dispersed in a Smectic Liquid Crystal: A Random Field XY System
The effect on the nematic to smectic-A transition in octylcyanobiphenyl (8CB)
due to dispersions of hydrogen-bonded silica (aerosil) particles is
characterized with high-resolution x-ray scattering. The particles form weak
gels in 8CB creating a quenched disorder that replaces the transition with the
growth of short range smectic correlations. The correlations include thermal
critical fluctuations that dominate at high temperatures and a second
contribution that quantitatively matches the static fluctuations of a random
field system and becomes important at low temperatures.Comment: 10 pages, 4 postscript figures as separate file
No Dynamics in the Extremal Kerr Throat
Motivated by the Kerr/CFT conjecture, we explore solutions of vacuum general
relativity whose asymptotic behavior agrees with that of the extremal Kerr
throat, sometimes called the Near-Horizon Extreme Kerr (NHEK) geometry. We
argue that all such solutions are diffeomorphic to the NHEK geometry itself.
The logic proceeds in two steps. We first argue that certain charges must
vanish at all times for any solution with NHEK asymptotics. We then analyze
these charges in detail for linearized solutions. Though one can choose the
relevant charges to vanish at any initial time, these charges are not
conserved. As a result, requiring the charges to vanish at all times is a much
stronger condition. We argue that all solutions satisfying this condition are
diffeomorphic to the NHEK metric.Comment: 42 pages, 3 figures. v3: minor clarifications and correction
Information-Geometric Indicators of Chaos in Gaussian Models on Statistical Manifolds of Negative Ricci Curvature
A new information-geometric approach to chaotic dynamics on curved
statistical manifolds based on Entropic Dynamics (ED) is proposed. It is shown
that the hyperbolicity of a non-maximally symmetric 6N-dimensional statistical
manifold M_{s} underlying an ED Gaussian model describing an arbitrary system
of 3N degrees of freedom leads to linear information-geometric entropy growth
and to exponential divergence of the Jacobi vector field intensity, quantum and
classical features of chaos respectively.Comment: 8 pages, final version accepted for publicatio
Optimal estimation of qubit states with continuous time measurements
We propose an adaptive, two steps strategy, for the estimation of mixed qubit
states. We show that the strategy is optimal in a local minimax sense for the
trace norm distance as well as other locally quadratic figures of merit. Local
minimax optimality means that given identical qubits, there exists no
estimator which can perform better than the proposed estimator on a
neighborhood of size of an arbitrary state. In particular, it is
asymptotically Bayesian optimal for a large class of prior distributions.
We present a physical implementation of the optimal estimation strategy based
on continuous time measurements in a field that couples with the qubits.
The crucial ingredient of the result is the concept of local asymptotic
normality (or LAN) for qubits. This means that, for large , the statistical
model described by identically prepared qubits is locally equivalent to a
model with only a classical Gaussian distribution and a Gaussian state of a
quantum harmonic oscillator.
The term `local' refers to a shrinking neighborhood around a fixed state
. An essential result is that the neighborhood radius can be chosen
arbitrarily close to . This allows us to use a two steps procedure by
which we first localize the state within a smaller neighborhood of radius
, and then use LAN to perform optimal estimation.Comment: 32 pages, 3 figures, to appear in Commun. Math. Phy
A Derivation of Three-Dimensional Inertial Transformations
The derivation of the transformations between inertial frames made by
Mansouri and Sexl is generalised to three dimensions for an arbitrary direction
of the velocity. Assuming lenght contraction and time dilation to have their
relativistic values, a set of transformations kinematically equivalent to
special relativity is obtained. The ``clock hypothesis'' allows the derivation
to be extended to accelerated systems. A theory of inertial transformations
maintaining an absolute simultaneity is shown to be the only one logically
consistent with accelerated movements. Algebraic properties of these
transformations are discussed. Keywords: special relativity, synchronization,
one-way velocity of light, ether, clock hypothesis.Comment: 16 pages (A5), Latex, one figure, to be published in Found. Phys.
Lett. (1997
On the Computational Complexity of Measuring Global Stability of Banking Networks
Threats on the stability of a financial system may severely affect the
functioning of the entire economy, and thus considerable emphasis is placed on
the analyzing the cause and effect of such threats. The financial crisis in the
current and past decade has shown that one important cause of instability in
global markets is the so-called financial contagion, namely the spreading of
instabilities or failures of individual components of the network to other,
perhaps healthier, components. This leads to a natural question of whether the
regulatory authorities could have predicted and perhaps mitigated the current
economic crisis by effective computations of some stability measure of the
banking networks. Motivated by such observations, we consider the problem of
defining and evaluating stabilities of both homogeneous and heterogeneous
banking networks against propagation of synchronous idiosyncratic shocks given
to a subset of banks. We formalize the homogeneous banking network model of
Nier et al. and its corresponding heterogeneous version, formalize the
synchronous shock propagation procedures, define two appropriate stability
measures and investigate the computational complexities of evaluating these
measures for various network topologies and parameters of interest. Our results
and proofs also shed some light on the properties of topologies and parameters
of the network that may lead to higher or lower stabilities.Comment: to appear in Algorithmic
Relativistic nuclear recoil corrections to the energy levels of hydrogen-like and high lithium like atoms in all orders in
The relativistic nuclear recoil corrections to the energy levels of
low-laying states of hydrogen-like and high lithium-like atoms in all
orders in are calculated. The calculations are carried out using the
B-spline method for the Dirac equation.
For low the results of the calculation are in good agreement with the
-expansion results. It is found that the nuclear recoil
contribution, additional to the Salpeter's one, to the Lamb shift () of
hydrogen is . The total nuclear recoil correction to the energy
of the transition in lithium-like uranium
constitutes and is largely made up of QED contributions.Comment: 19 pages, latex, accepted for publication in Phys. Rev.
Ecological Invasion, Roughened Fronts, and a Competitor's Extreme Advance: Integrating Stochastic Spatial-Growth Models
Both community ecology and conservation biology seek further understanding of
factors governing the advance of an invasive species. We model biological
invasion as an individual-based, stochastic process on a two-dimensional
landscape. An ecologically superior invader and a resident species compete for
space preemptively. Our general model includes the basic contact process and a
variant of the Eden model as special cases. We employ the concept of a
"roughened" front to quantify effects of discreteness and stochasticity on
invasion; we emphasize the probability distribution of the front-runner's
relative position. That is, we analyze the location of the most advanced
invader as the extreme deviation about the front's mean position. We find that
a class of models with different assumptions about neighborhood interactions
exhibit universal characteristics. That is, key features of the invasion
dynamics span a class of models, independently of locally detailed demographic
rules. Our results integrate theories of invasive spatial growth and generate
novel hypotheses linking habitat or landscape size (length of the invading
front) to invasion velocity, and to the relative position of the most advanced
invader.Comment: The original publication is available at
www.springerlink.com/content/8528v8563r7u2742
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