313 research outputs found
Calculation of the energetics of water incorporation in majorite garnet
Interpretation of lateral variations in upper mantle seismic wave speeds requires constraints on the relationship between elasticity and water concentration at high pressure for all major mantle minerals, including the garnet component. We have calculated the structure and energetics of charge-balanced hydrogen substitution into tetragonal MgSiO3 majorite up to P = 25 GPa using both classical atomistic simulations and complementary first-principles calculations. At the pressure conditions of Earth’s transition zone, hydroxyl groups are predicted to be bound to Si vacancies (o) as the hydrogarnet defect, [oSi+4OHO]X, at the Si2 tetrahedral site or as the [oMg+2OHO]X defect at the octahedral Mg3 site. The hydrogarnet defect is more favorable than the [oMg+2OHO]X defect by 0.8–1.4 eV/H at 20 GPa. The presence of 0.4 wt% Al2O3 substituted into the octahedral sites further increases the likelihood of the hydrogarnet defect by 2.2–2.4 eV/H relative to the [oMg+2OHO]X defect at the Mg3 site. OH defects affect the seismic ratio, R = dlnvs/dlnvp, in MgSiO3 majorite (?R = 0.9–1.2 at 20 GPa for 1400 ppm wt H2O) differently than ringwoodite at high pressure, yet may be indistinguishable from the thermal dlnvs/dlnvp for ringwoodite. The incorporation of 3.2 wt% Al2O3 also decreases R(H2O) by ~0.2–0.4. Therefore, to accurately estimate transition zone compositional and thermal anomalies, hydrous majorite needs to be considered when interpreting seismic body wave anomalies in the transition zone
Topological stability of broken symmetry on fuzzy spheres
We study the spontaneous symmetry breaking of O(3) scalar field on a fuzzy
sphere . We find that the fluctuations in the background of topological
configurations are finite. This is in contrast to the fluctuations around a
uniform configuration which diverge, due to Mermin-Wagner-Hohenberg-Coleman
theorem, leading to the decay of the condensate. Interesting implications of
enhanced topological stability of the configurations are pointed out.Comment: Version to appear in MPLA, 9 pages, 6 figure
Monte Carlo approach to nonperturbative strings -- demonstration in noncritical string theory
We show how Monte Carlo approach can be used to study the double scaling
limit in matrix models. As an example, we study a solvable hermitian one-matrix
model with the double-well potential, which has been identified recently as a
dual description of noncritical string theory with worldsheet supersymmetry.
This identification utilizes the nonperturbatively stable vacuum unlike its
bosonic counterparts, and therefore it provides a complete constructive
formulation of string theory. Our data with the matrix size ranging from 8 to
512 show a clear scaling behavior, which enables us to extract the double
scaling limit accurately. The ``specific heat'' obtained in this way agrees
nicely with the known result obtained by solving the Painleve-II equation with
appropriate boundary conditions.Comment: 15 pages, 10 figures, LaTeX, JHEP3.cls; references added, typos
correcte
Spontaneous symmetry breakdown in fuzzy spheres
We study and analyse the questions regarding breakdown of global symmetry on
noncommutative sphere. We demonstrate this by considering a complex scalar
field on a fuzzy sphere and isolating Goldstone modes. We discuss the role of
nonlocal interactions present in these through geometrical considerations.Comment: 8 pages, 7 figure
Growth rates, stable oxygen isotopes (δ^18O), and strontium (Sr/Ca) composition in two species of Pacific sclerosponges (Acanthocheatetes wellsi and Astrosclera willeyana) with δ^18O calibration and application to paleoceanography
The isotopic and elemental composition of sclerosponge skeletons is used to reconstruct paleoceanographic records. Yet few studies have systematically examined the natural variability in sclerosponge skeletal δ^(18)O, growth, and Sr/Ca, and how that may influence the interpretation of sclerosponge proxy records. Here, we analyzed short records in seven specimens of Acanthocheatetes wellsi (high-Mg calcite, 21 mol% Mg) from Palau, four A. wellsi (high-Mg calcite, 21 mol% Mg) from Saipan, and three Astrosclera willeyana (aragonite) sclerosponges from Saipan, as well as one long record in an A. wellsi specimen from Palau spanning 1945–2001.5. In Saipan, species-specific and mineralogical effects appear to have a negligible effect on sclerosponge δ^(18)O, facilitating the direct comparison of δ^(18)O records between species at a given location. At both sites, A. wellsi δ^(18)O and growth rates were sensitive to environmental conditions, but Sr/Ca was not sensitive to the same conditions. High-resolution δ^(18)O analyses confirmed this finding as both A. wellsi and A. willeyana deposited their skeleton in accordance with the trends in isotopic equilibrium with seawater, though with a 0.27‰ offset in the case of A. willeyana. In the high-Mg-calcite species A. wellsi, Mg may be interfering with Sr incorporation into the skeleton. On multidecadal timescales, A. wellsi sclerosponge δ^(18)O in Palau tracked the Southern Oscillation Index variability post-1977, but not pre-1977, coincident with the switch in the Pacific Decadal Oscillation (PDO) at ~1976. This suggests that water mass circulation in the region is influenced by El Niño— Southern Oscillation variability during positive PDO phases, but not during negative ones
Numerical simulations of a non-commutative theory: the scalar model on the fuzzy sphere
We address a detailed non-perturbative numerical study of the scalar theory
on the fuzzy sphere. We use a novel algorithm which strongly reduces the
correlation problems in the matrix update process, and allows the investigation
of different regimes of the model in a precise and reliable way. We study the
modes associated to different momenta and the role they play in the ``striped
phase'', pointing out a consistent interpretation which is corroborated by our
data, and which sheds further light on the results obtained in some previous
works. Next, we test a quantitative, non-trivial theoretical prediction for
this model, which has been formulated in the literature: The existence of an
eigenvalue sector characterised by a precise probability density, and the
emergence of the phase transition associated with the opening of a gap around
the origin in the eigenvalue distribution. The theoretical predictions are
confirmed by our numerical results. Finally, we propose a possible method to
detect numerically the non-commutative anomaly predicted in a one-loop
perturbative analysis of the model, which is expected to induce a distortion of
the dispersion relation on the fuzzy sphere.Comment: 1+36 pages, 18 figures; v2: 1+55 pages, 38 figures: added the study
of the eigenvalue distribution, added figures, tables and references, typos
corrected; v3: 1+20 pages, 10 eps figures, new results, plots and references
added, technical details about the tests at small matrix size skipped,
version published in JHE
Twisted Covariant Noncommutative Self-dual Gravity
A twisted covariant formulation of noncommutative self-dual gravity is
presented. The formulation for constructing twisted noncommutative Yang-Mills
theories is used. It is shown that the noncommutative torsion is solved at any
order of the -expansion in terms of the tetrad and some extra fields of
the theory. In the process the first order expansion in for the
Pleba\'nski action is explicitly obtained.Comment: 23+1 pages, no figures, corrected typos, references and Appendix B is
adde
Probing the fuzzy sphere regularisation in simulations of the 3d \lambda \phi^4 model
We regularise the 3d \lambda \phi^4 model by discretising the Euclidean time
and representing the spatial part on a fuzzy sphere. The latter involves a
truncated expansion of the field in spherical harmonics. This yields a
numerically tractable formulation, which constitutes an unconventional
alternative to the lattice. In contrast to the 2d version, the radius R plays
an independent r\^{o}le. We explore the phase diagram in terms of R and the
cutoff, as well as the parameters m^2 and \lambda. Thus we identify the phases
of disorder, uniform order and non-uniform order. We compare the result to the
phase diagrams of the 3d model on a non-commutative torus, and of the 2d model
on a fuzzy sphere. Our data at strong coupling reproduce accurately the
behaviour of a matrix chain, which corresponds to the c=1-model in string
theory. This observation enables a conjecture about the thermodynamic limit.Comment: 31 pages, 15 figure
Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives
We generalise the construction of fuzzy CP^N in a manner that allows us to
access all noncommutative equivariant complex vector bundles over this space.
We give a simplified construction of polarization tensors on S^2 that
generalizes to complex projective space, identify Laplacians and natural
noncommutative covariant derivative operators that map between the modules that
describe noncommuative sections. In the process we find a natural
generalization of the Schwinger-Jordan construction to su(n) and identify
composite oscillators that obey a Heisenberg algebra on an appropriate Fock
space.Comment: 34 pages, v2 contains minor corrections to the published versio
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