scholarly journals Conformal transformation with multiple scalar fields and geometric property of field space with Einstein-like solutions

2021 ◽  
Vol 104 (6) ◽  
Author(s):  
Yong Tang ◽  
Yue-Liang Wu
Keyword(s):  
Conformal Transformation ◽  
Geometric Property ◽  
Scalar Fields

On the construction of orthogonal curvilinear grids for regional oceanic modeling: algorithm and user guide

2020 ◽  
Vol 48 (4) ◽  
pp. 45-111
Author(s):  
A. F. Shepetkin
Keyword(s):  
Inverse Problem ◽  
Numerical Solution ◽  
Elliptic Problem ◽  
Software Package ◽  
Conformal Transformation ◽  
Iterative Procedure ◽  
Geometric Shape ◽  
Curvilinear Grids ◽  
Grid Points ◽  
Grid Nodes

A new algorithm for constructing orthogonal curvilinear grids on a sphere for a fairly general geometric shape of the modeling region is implemented as a “compile-once - use forever” software package. It is based on the numerical solution of the inverse problem by an iterative procedure -- finding such distribution of grid points along its perimeter, so that the conformal transformation of the perimeter into a rectangle turns this distribution into uniform one. The iterative procedure itself turns out to be multilevel - i.e. an iterative loop built around another, internal iterative procedure. Thereafter, knowing this distribution, the grid nodes inside the region are obtained solving an elliptic problem. It is shown that it was possible to obtain the exact orthogonality of the perimeter at the corners of the grid, to achieve very small, previously unattainable level of orthogonality errors, as well as make it isotropic -- local distances between grid nodes about both directions are equal to each other.

scholarly journals New AdS4 vacua in dyonic ISO(7) gauged supergravity

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Nikolay Bobev ◽  
Thomas Fischbacher ◽  
Fridrik Freyr Gautason ◽  
Krzysztof Pilch
Keyword(s):  
Scalar Fields ◽  
Global Symmetry ◽  
Supergravity Theory

Abstract We identify 219 AdS4 solutions in four-dimensional dyonically gauged ISO(7) $$ \mathcal{N} $$ N = 8 supergravity and present some of their properties. One of the new solutions preserves $$ \mathcal{N} $$ N = 1 supersymmetry and provides a rare explicit example of an AdS4 vacuum dual to a 3d SCFT with no continuous global symmetry. There are also two new non-supersymmetric solutions for which all 70 scalar fields in the supergravity theory have masses above the BF bound. All of these AdS4 solutions can be uplifted to massive type IIA supergravity. Motivated by this we present the low lying operator spectra of the dual 3d CFTs for all known supersymmetric AdS4 solutions in the theory and organize them into superconformal multiplets.

scholarly journals Geometric property-based convolutional neural network for indoor object detection

2021 ◽  
Vol 18 (1) ◽  
pp. 172988142199332
Author(s):  
Xintao Ding ◽  
Boquan Li ◽  
Jinbao Wang
Keyword(s):  
Neural Network ◽  
Object Detection ◽  
Convolutional Neural Network ◽  
Geometric Property ◽  
Ground Truth ◽  
Geometric Constraints ◽  
Depth Information ◽  
Training Set ◽  
Object Knowledge ◽  
The Mean

Indoor object detection is a very demanding and important task for robot applications. Object knowledge, such as two-dimensional (2D) shape and depth information, may be helpful for detection. In this article, we focus on region-based convolutional neural network (CNN) detector and propose a geometric property-based Faster R-CNN method (GP-Faster) for indoor object detection. GP-Faster incorporates geometric property in Faster R-CNN to improve the detection performance. In detail, we first use mesh grids that are the intersections of direct and inverse proportion functions to generate appropriate anchors for indoor objects. After the anchors are regressed to the regions of interest produced by a region proposal network (RPN-RoIs), we then use 2D geometric constraints to refine the RPN-RoIs, in which the 2D constraint of every classification is a convex hull region enclosing the width and height coordinates of the ground-truth boxes on the training set. Comparison experiments are implemented on two indoor datasets SUN2012 and NYUv2. Since the depth information is available in NYUv2, we involve depth constraints in GP-Faster and propose 3D geometric property-based Faster R-CNN (DGP-Faster) on NYUv2. The experimental results show that both GP-Faster and DGP-Faster increase the performance of the mean average precision.

scholarly journals Symmetry and unification from soft theorems and unitarity

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Clifford Cheung ◽  
Zander Moss
Keyword(s):  
Symmetry Algebra ◽  
Scalar Fields ◽  
Particle Interactions ◽  
Massive Scalar ◽  
Coset Space ◽  
Dimensional Theory ◽  
Finite Spectrum ◽  
Physical Constraints ◽  
High Energies ◽  
Zero Condition

Abstract We argue that symmetry and unification can emerge as byproducts of certain physical constraints on dynamical scattering. To accomplish this we parameterize a general Lorentz invariant, four-dimensional theory of massless and massive scalar fields coupled via arbitrary local interactions. Assuming perturbative unitarity and an Adler zero condition, we prove that any finite spectrum of massless and massive modes will necessarily unify at high energies into multiplets of a linearized symmetry. Certain generators of the symmetry algebra can be derived explicitly in terms of the spectrum and three-particle interactions. Furthermore, our assumptions imply that the coset space is symmetric.

scholarly journals A discussion on Lorentz preserving scalar fields in Lorentz violating theory

2012 ◽  
Vol 405 ◽  
pp. 012015
Author(s):  
O Ganguly ◽  
D Gangopadhyay ◽  
P Majumdar
Keyword(s):  
Scalar Fields

scholarly journals Correlation between small-scale velocity and scalar fluctuations in a turbulent channel flow

2009 ◽  
Vol 627 ◽  
pp. 1-32 ◽  
Author(s):  
HIROYUKI ABE ◽  
ROBERT ANTHONY ANTONIA ◽  
HIROSHI KAWAMURA
Keyword(s):  
Strain Rate ◽  
Channel Flow ◽  
Dissipation Rate ◽  
Compressive Strain ◽  
Outer Region ◽  
Turbulent Channel Flow ◽  
Scalar Fields ◽  
Scalar Dissipation ◽  
Small Scale ◽  
Scalar Dissipation Rate

Direct numerical simulations of a turbulent channel flow with passive scalar transport are used to examine the relationship between small-scale velocity and scalar fields. The Reynolds number based on the friction velocity and the channel half-width is equal to 180, 395 and 640, and the molecular Prandtl number is 0.71. The focus is on the interrelationship between the components of the vorticity vector and those of the scalar derivative vector. Near the wall, there is close similarity between different components of the two vectors due to the almost perfect correspondence between the momentum and thermal streaks. With increasing distance from the wall, the magnitudes of the correlations become smaller but remain non-negligible everywhere in the channel owing to the presence of internal shear and scalar layers in the inner region and the backs of the large-scale motions in the outer region. The topology of the scalar dissipation rate, which is important for small-scale scalar mixing, is shown to be associated with the organized structures. The most preferential orientation of the scalar dissipation rate is the direction of the mean strain rate near the wall and that of the fluctuating compressive strain rate in the outer region. The latter region has many characteristics in common with several turbulent flows; viz. the dominant structures are sheetlike in form and better correlated with the energy dissipation rate than the enstrophy.

scholarly journals Constructing Carrollian CFTs

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Nishant Gupta ◽  
Nemani V. Suryanarayana
Keyword(s):  
Scalar Fields ◽  
Higher Dimensions ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Relativistic Limit ◽  
Conformal Field ◽  
Local Symmetries ◽  
Derivatives Of ◽  
Special Case

Abstract We construct classical theories for scalar fields in arbitrary Carroll spacetimes that are invariant under Carrollian diffeomorphisms and Weyl transformations. When the local symmetries are gauge fixed these theories become Carrollian conformal field theories. We show that generically there are at least two types of such theories: one in which only time derivatives of the fields appear and the other in which both space and time derivatives appear. A classification of such scalar field theories in three (and higher) dimensions up to two derivative order is provided. We show that only a special case of our theories arises in the ultra-relativistic limit of a covariant parent theory.

scholarly journals Plebański-Demiański solutions in quadratic gravity with conformally coupled scalar fields

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
Adolfo Cisterna ◽  
Anibal Neira-Gallegos ◽  
Julio Oliva ◽  
Scarlett C. Rebolledo-Caceres
Keyword(s):  
Scalar Fields ◽  
Quadratic Gravity
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