moment maps
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2021 ◽  
Vol 281 (3) ◽  
pp. 109039
Author(s):  
Raúl Quiroga-Barranco ◽  
Armando Sánchez-Nungaray

Annals of PDE ◽  
2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Tristan C. Collins ◽  
Shing-Tung Yau

Author(s):  
B Riaz ◽  
M N Machida

Abstract We present ALMA 12CO (2-1), 13CO (2-1), C18O (2-1) molecular line observations of a very young proto-brown dwarf system, ISO-OPH 200. We have conducted physical+chemical modelling of the complex internal structure for this system using the core collapse simulations for brown dwarf formation. The model at an age of ∼6000 yr can provide a good fit to the observed kinematics, spectra, and reproduce the complex structures seen in the moment maps. Results from modelling indicate that 12CO emission is tracing an extended (∼1000 au) molecular outflow and a bright shock knot, 13CO is tracing the outer (∼1000 au) envelope/pseudo-disc, and C18O is tracing the inner (∼500 au) pseudo-disc. The source size of ∼8.6 au measured in the 873μm image is comparable to the inner Keplerian disc size predicted by the model. A 3D model structure of ISO-OPH 200 suggests that this system is viewed partially through a wide outflow cavity resulting in a direct view of the outflow and a partial view of the envelope/pseudo-disc. We have argued that ISO-OPH 200 has been mis-classified as a Class Flat object due to the unusual orientation. The various signatures of this system, notably, the young ∼616 yr outflow dynamical age and high outflow rate (∼1 × 10−7 M⊙ yr−1), silicate absorption in the 10$\rm{\mu m}$ mid-infrared spectrum, pristine ISM-like dust in the envelope/disc, comparable sizes of the extended envelope and outflow, indicate that ISO-OPH 200 is an early Class 0 stage system formed in a star-like mechanism via gravitational collapse of a very low-mass core.


2021 ◽  
Vol 13 (3) ◽  
pp. 471
Author(s):  
Kaiyu Zhang ◽  
Xikai Fu ◽  
Xiaolei Lv ◽  
Jili Yuan

Building change detection using remote sensing images is essential for various applications such as urban management and marketing planning. However, most change detection approaches can only detect the intensity or type of change. The aim of this study is to dig for more change information from time-series synthetic aperture radar (SAR) images, such as the change frequency and the change moments. This paper proposes a novel multitemporal building change detection framework that can generate change frequency map (CFM) and change moment maps (CMMs) from multitemporal SAR images. We first give definitions of CFM and CMMs. Then we generate change feature using four proposed generators. After that, a new cosegmentation method combining raw images and change feature is proposed to divide time-series images into changed and unchanged areas separately. Secondly, the proposed cosegmentation and the morphological building index (MBI) are combined to extract changed building objects. Then, the logical conjunction between the cosegmentation results and the binarized MBI is performed to recognize every moment of change. In the post-processing step, we use fragment removal to increase accuracy. Finally, we propose a novel accuracy assessment index for CFM. We call this index average change difference (ACD). Compared to the traditional multitemporal change detection methods, our method outperforms other approaches in terms of both qualitative results and quantitative indices of ACD using two TerraSAR-X datasets. The experiments show that the proposed method is effective in generating CFM and CMMs.


2021 ◽  
Vol 26 (none) ◽  
Author(s):  
Anton Alekseev ◽  
Elizaveta Arzhakova ◽  
Daria Smirnova

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Anthony Ashmore ◽  
Charles Strickland-Constable ◽  
David Tennyson ◽  
Daniel Waldram

Abstract We analyse the geometry of generic Minkowski $$ \mathcal{N} $$ N = 1, D = 4 flux compactifications in string theory, the default backgrounds for string model building. In M-theory they are the natural string theoretic extensions of G2 holonomy manifolds. In type II theories, they extend the notion of Calabi-Yau geometry and include the class of flux backgrounds based on generalised complex structures first considered by Graña et al. (GMPT). Using E7(7) × ℝ+ generalised geometry we show that these compactifications are characterised by an SU(7) ⊂ E7(7) structure defining an involutive subbundle of the generalised tangent space, and with a vanishing moment map, corresponding to the action of the diffeomorphism and gauge symmetries of the theory. The Kähler potential on the space of structures defines a natural extension of Hitchin’s G2 functional. Using this framework we are able to count, for the first time, the massless scalar moduli of GMPT solutions in terms of generalised geometry cohomology groups. It also provides an intriguing new perspective on the existence of G2 manifolds, suggesting possible connections to Geometrical Invariant Theory and stability.


Author(s):  
Zhihui Li ◽  
Charles C Steidel ◽  
Max Gronke ◽  
Yuguang Chen

Abstract We present new observations of Lyman-α (Lyα) Blob 1 (LAB1) in the SSA22 protocluster region (z = 3.09) using the Keck Cosmic Web Imager (KCWI) and Keck Multi-object Spectrometer for Infrared Exploration (MOSFIRE). We have created a narrow-band Lyα image and identified several prominent features. By comparing the spatial distributions and intensities of Lyα and Hβ, we find that recombination of photo-ionized H i gas followed by resonant scattering is sufficient to explain all the observed Lyα/Hβ ratios. We further decode the spatially-resolved Lyα profiles using both moment maps and radiative transfer modeling. By fitting a set of multiphase, ‘clumpy’ models to the observed Lyα profiles, we manage to reasonably constrain many parameters, namely the H i number density in the inter-clump medium (ICM), the cloud volume filling factor, the random velocity and outflow velocity of the clumps, the H i outflow velocity of the ICM and the local systemic redshift. Our model has successfully reproduced the diverse Lyα morphologies, and the main results are: (1) The observed Lyα spectra require relatively few clumps per line-of-sight as they have significant fluxes at the line center; (2) The velocity dispersion of the clumps yields a significant broadening of the spectra as observed; (3) The clump bulk outflow can also cause additional broadening if the H i in the ICM is optically thick; (4) The H i in the ICM is responsible for the absorption feature close to the Lyα line center.


Author(s):  
Kael Dixon

AbstractWe study toric nearly Kähler manifolds, extending the work of Moroianu and Nagy. We give a description of the global geometry using multi-moment maps. We then investigate polynomial and radial solutions to the toric nearly Kähler equation.


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