2,002 research outputs found
Circum-Arctic mantle structure and long-wavelength topography since the Jurassic
The circum-Arctic is one of the most tectonically complex regions of the world, shaped by a history of ocean basin opening and closure since the Early Jurassic. The region is characterized by contemporaneous large-scale Cenozoic exhumation extending from Alaska to the Atlantic, but its driving force is unknown. We show that the mantle flow associated with subducted slabs of the South Anuyi, Mongol-Okhotsk, and Panthalassa oceans have imparted long-wavelength deflection on overriding plates. We identify the Jurassic-Cretaceous South Anuyi slab under present-day Greenland in seismic tomography and numerical mantle flow models. Under North America, we propose the âFarallonâ slab results from Andean-style ocean-continent convergence around ~30°N and from a combination of ocean-continent and intraoceanic subduction north of 50°N. We compute circum-Arctic dynamic topography through time from subduction-driven convection models and find that slabs have imparted on average <1â16âm/Myr of dynamic subsidence across the region from at least 170âMa to ~50âMa. With the exception of Siberia, the main phase of circum-Arctic dynamic subsidence has been followed either by slowed subsidence or by uplift of <1â6âm/Myr on average to present day. Comparing these results to geological inferences suggest that subduction-driven dynamic topography can account for rapid Middle to Late Jurassic subsidence in the Slave Craton and North Slope (respectively, <15 and 21âm/Myr, between 170 and 130âMa) and for dynamic subsidence (<7âm/Myr, ~170â50âMa) followed by dynamic uplift (<6âm/Myr since 50âMa) of the Barents Sea region. Combining detailed kinematic reconstructions with geodynamic modeling and key geological observations constitutes a powerful tool to investigate the origin of vertical motion in remote regions
Quantum affine Cartan matrices, Poincare series of binary polyhedral groups, and reflection representations
We first review some invariant theoretic results about the finite subgroups
of SU(2) in a quick algebraic way by using the McKay correspondence and quantum
affine Cartan matrices. By the way it turns out that some parameters
(a,b,h;p,q,r) that one usually associates with such a group and hence with a
simply-laced Coxeter-Dynkin diagram have a meaningful definition for the
non-simply-laced diagrams, too, and as a byproduct we extend Saito's formula
for the determinant of the Cartan matrix to all cases. Returning to invariant
theory we show that for each irreducible representation i of a binary
tetrahedral, octahedral, or icosahedral group one can find a homomorphism into
a finite complex reflection group whose defining reflection representation
restricts to i.Comment: 19 page
A new structural relaxation pathway of low-density amorphous ice
Low-density amorphous ice (LDA) is involved in critical cosmological
processes and has gained prominence as one of the at least two distinct
amorphous forms of ice. Despite these accolades, we still have an incomplete
understanding of the structural diversity that is encompassed within the LDA
state and the dynamic processes that take place upon heating LDA. Heating the
high-pressure ice VIII phase at ambient pressure is a remarkable example of
temperature-induced amorphisation yielding LDA. We investigate this process in
detail using X-ray diffraction and Raman spectroscopy, and show that the LDA
obtained from ice VIII is structurally different from the more 'traditional'
states of LDA which are approached upon thermal annealing. This new structural
relaxation pathway involves an increase of structural order on the intermediate
range length scale. In contrast with other LDA materials the local structure is
more ordered initially and becomes slightly more disordered upon annealing. We
also show that the cascade of phase transitions upon heating ice VIII at
ambient pressure includes the formation of ice IX which may be connected with
the structural peculiarities of LDA from ice VIII. Overall, this study shows
that LDA is a structurally more diverse material than previously appreciated.Comment: 12 pages, 5 figure
Lyashko-Looijenga morphisms and submaximal factorisations of a Coxeter element
When W is a finite reflection group, the noncrossing partition lattice NCP_W
of type W is a rich combinatorial object, extending the notion of noncrossing
partitions of an n-gon. A formula (for which the only known proofs are
case-by-case) expresses the number of multichains of a given length in NCP_W as
a generalised Fuss-Catalan number, depending on the invariant degrees of W. We
describe how to understand some specifications of this formula in a case-free
way, using an interpretation of the chains of NCP_W as fibers of a
Lyashko-Looijenga covering (LL), constructed from the geometry of the
discriminant hypersurface of W. We study algebraically the map LL, describing
the factorisations of its discriminant and its Jacobian. As byproducts, we
generalise a formula stated by K. Saito for real reflection groups, and we
deduce new enumeration formulas for certain factorisations of a Coxeter element
of W.Comment: 18 pages. Version 2 : corrected typos and improved presentation.
Version 3 : corrected typos, added illustrated example. To appear in Journal
of Algebraic Combinatoric
A Robust Solution Procedure for Hyperelastic Solids with Large Boundary Deformation
Compressible Mooney-Rivlin theory has been used to model hyperelastic solids,
such as rubber and porous polymers, and more recently for the modeling of soft
tissues for biomedical tissues, undergoing large elastic deformations. We
propose a solution procedure for Lagrangian finite element discretization of a
static nonlinear compressible Mooney-Rivlin hyperelastic solid. We consider the
case in which the boundary condition is a large prescribed deformation, so that
mesh tangling becomes an obstacle for straightforward algorithms. Our solution
procedure involves a largely geometric procedure to untangle the mesh: solution
of a sequence of linear systems to obtain initial guesses for interior nodal
positions for which no element is inverted. After the mesh is untangled, we
take Newton iterations to converge to a mechanical equilibrium. The Newton
iterations are safeguarded by a line search similar to one used in
optimization. Our computational results indicate that the algorithm is up to 70
times faster than a straightforward Newton continuation procedure and is also
more robust (i.e., able to tolerate much larger deformations). For a few
extremely large deformations, the deformed mesh could only be computed through
the use of an expensive Newton continuation method while using a tight
convergence tolerance and taking very small steps.Comment: Revision of earlier version of paper. Submitted for publication in
Engineering with Computers on 9 September 2010. Accepted for publication on
20 May 2011. Published online 11 June 2011. The final publication is
available at http://www.springerlink.co
Long-term stability of TES satellite radiance measurements
The utilization of Tropospheric Emission Spectrometer (TES) Level 2 (L2) retrieval products for the purpose of assessing long term changes in atmospheric trace gas composition requires knowledge of the overall radiometric stability of the Level 1B (L1B) radiances. The purpose of this study is to evaluate the stability of the radiometric calibration of the TES instrument by analyzing the difference between measured and calculated brightness temperatures in selected window regions of the spectrum. The Global Modeling and Assimilation Office (GMAO) profiles for temperature and water vapor and the Real-Time Global Sea Surface Temperature (RTGSST) are used as input to the Optimal Spectral Sampling (OSS) radiative transfer model to calculate the simulated spectra. The TES reference measurements selected cover a 4-year period of time from mid 2005 through mid 2009 with the selection criteria being; observation latitudes greater than â30° and less than 30°, over ocean, Global Survey mode (nadir view) and retrieved cloud optical depth of less than or equal to 0.01. The TES cloud optical depth retrievals are used only for screening purposes and no effects of clouds on the radiances are included in the forward model. This initial screening results in over 55 000 potential reference spectra spanning the four year period. Presented is a trend analysis of the time series of the residuals (observation minus calculations) in the TES 2B1, 1B2, 2A1, and 1A1 bands, with the standard deviation of the residuals being approximately equal to 0.6 K for bands 2B1, 1B2, 2A1, and 0.9 K for band 1A1. The analysis demonstrates that the trend in the residuals is not significantly different from zero over the 4-year period. This is one method used to demonstrate that the relative radiometric calibration is stable over time, which is very important for any longer term analysis of TES retrieved products (L2), particularly well-mixed species such as carbon dioxide and methane
Interacting Multiple Try Algorithms with Different Proposal Distributions
We propose a new class of interacting Markov chain Monte Carlo (MCMC)
algorithms designed for increasing the efficiency of a modified multiple-try
Metropolis (MTM) algorithm. The extension with respect to the existing MCMC
literature is twofold. The sampler proposed extends the basic MTM algorithm by
allowing different proposal distributions in the multiple-try generation step.
We exploit the structure of the MTM algorithm with different proposal
distributions to naturally introduce an interacting MTM mechanism (IMTM) that
expands the class of population Monte Carlo methods. We show the validity of
the algorithm and discuss the choice of the selection weights and of the
different proposals. We provide numerical studies which show that the new
algorithm can perform better than the basic MTM algorithm and that the
interaction mechanism allows the IMTM to efficiently explore the state space
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