50 research outputs found
On a correspondence between quantum SU(2), quantum E(2) and extended quantum SU(1,1)
In a previous paper, we showed how one can obtain from the action of a
locally compact quantum group on a type I-factor a possibly new locally compact
quantum group. In another paper, we applied this construction method to the
action of quantum SU(2) on the standard Podles sphere to obtain Woronowicz'
quantum E(2). In this paper, we will apply this technique to the action of
quantum SU(2) on the quantum projective plane (whose associated von Neumann
algebra is indeed a type I-factor). The locally compact quantum group which
then comes out at the other side turns out to be the extended SU(1,1) quantum
group, as constructed by Koelink and Kustermans. We also show that there exists
a (non-trivial) quantum groupoid which has at its corners (the duals of) the
three quantum groups mentioned above.Comment: 35 page
Enhancing proton mobility in polymer electrolyte membranes : lessons from molecular dynamic simulation
Typical proton-conducting polymer electrolyte membranes (PEM) for fuel cell applications consist of a perfluorinated polymeric backbone and side chains with SO3H groups. The latter dissociate upon sufficient water uptake into SO3- groups on the chains and protons in the aqueous subphase, which percolates through the membrane. We report here systematic molecular dynamics simulations of proton transport through the aqueous subphase of wet PEMs. The simulations utilize a recently developed simplified version (Walbran, A.; Kornyshev, A. A. J. Chem. Phys. 2001, 114, 10039) of an empirical valence bond (EVB) model, which is designed to describe the structural diffusion during proton transfer in a multiproton environment. The polymer subphase is described as an excluded volume for water, in which pores of a fixed slab-shaped geometry are considered. We study the effects on proton mobility of the charge delocalization inside the SO3- groups, of the headgroup density (PPM "equivalent weight"), and of the motion of headgroups and side chains. We analyze the correlation between the proton mobility and the degree of proton confinement in proton-carrying clusters near SO3- parent groups. We have found and rationalized the following factors that facilitate the proton transfer: (i) charge delocalization within the SO3- groups, (ii) fluctuational motions of the headgroups and side chains, and (iii) water content
Modeling of proton transfer in polymer electrolyte membranes on different time and length scales
Polymer electrolyte membranes (PEMs) are key component materials in fuel cell technology. Understanding the relationship between the elementary acts of proton transport and the operation of the entire cell on different time and length scales is therefore particularly rewarding. We discuss the results of recent atomistic computer simulations of proton transport in porous PEMs. Different models cover the range from individual local proton hops to diffusion processes with polymer mobility included
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Hydro-frac monitoring using ground time-domain electromagnetics
As motivation for considering new electromagnetic techniques for hydraulic fracture monitoring, we develop a simple financial model for the net present value offered by geophysical characterization to reduce the error in stimulated reservoir volume calculations. This model shows that even a 5% improvement in stimulated reservoir volume for a 1 billion barrel (bbl) field results in over 1 billion U.S. dollars (US100/bbl. oil and US50/bbl. oil. The application of conductivity upscaling, often used in electromagnetic modeling to reduce mesh size and thus simulation runtimes, is shown to be inaccurate for the high electrical contrasts needed to represent steel-cased wells in the earth. Fine-scale finite-difference modeling with 12.22-mm cells to capture the steel casing and fractures shows that the steel casing provides a direct current pathway to a created fracture that significantly enhances the response compared with neglecting the steel casing. We consider conductively enhanced proppant, such as coke-breeze-coated sand, and a highly saline brine solution to produce electrically conductive fractures. For a relatively small frac job at a depth of 3 km, involving 5,000 bbl. of slurry and a source midpoint to receiver separation of 50 m, the models show that the conductively enhanced proppant produces a 15% increase in the electric field strength (in-line with the transmitter) in a 10-Ωm background. In a 100-Ωm background, the response due to the proppant increases to 213%. Replacing the conductive proppant by brine with a concentration of 100,000-ppm NaCl, the field strength is increased by 23% in the 100-Ωm background and by 2.3% in the 10-Ωm background. All but the 100,000-ppm NaCl brine in a 10-Ωm background produce calculated fracture-induced electric field increases that are significantly above 2%, a value that has been demonstrated to be observable in field measurements. © 2015 European Association of Geoscientist
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Deep learning multiphysics network for imaging CO2 saturation and estimating uncertainty in geological carbon storage
Multiphysics inversion exploits different types of geophysical data that often complement each other and aims to improve overall imaging resolution and reduce uncertainties in geophysical interpretation. Despite the advantages, traditional multiphysics inversion is challenging because it requires a large amount of computational time and intensive human interactions for preprocessing data and finding trade-off parameters. These issues make it nearly impossible for traditional multiphysics inversion to be applied as a real-time monitoring tool for geological carbon storage. In this paper, we present a deep learning (DL) multiphysics network for imaging CO2 saturation in real time. The multiphysics network consists of three encoders for analysing seismic, electromagnetic and gravity data and shares one decoder for combining imaging capabilities of the different geophysical data for better predicting CO2 saturation. The network is trained on pairs of CO2 label models and multiphysics data so that it can directly image CO2 saturation. We use the bootstrap aggregating method to enhance the imaging accuracy and estimate uncertainties associated with CO2 saturation images. Using realistic CO2 label models and multiphysics data derived from the Kimberlina CO2 storage model, we evaluate the performance of the deep learning multiphysics network and compare its imaging results to those from the deep learning single-physics networks. Our modelling experiments show that the deep learning multiphysics network for seismic, electromagnetic, and gravity data not only improves the imaging accuracy but also reduces uncertainties associated with CO2 saturation images. Our results also suggest that the deep learning multiphysics network for the non-seismic data (i.e., electromagnetic and gravity) can be used as an effective low-cost monitoring tool in between regular seismic monitoring