scholarly journals Topological correlators and surface defects from equivariant cohomology

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Rodolfo Panerai ◽  
Antonio Pittelli ◽  
Konstantina Polydorou
Keyword(s):  
Quantum Mechanics ◽  
Equivariant Cohomology ◽  
Surface Defects ◽  
Star Product ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional System ◽  
The Novel ◽  
One Dimensional ◽  
Dual Quantum

Abstract We find a one-dimensional protected subsector of $$ \mathcal{N} $$ N = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S3. Then, we apply it to the novel case of S2× S1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncom- mutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general $$ \mathcal{N} $$ N = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

On the Recovery of 3D Spatial Statistics of Particles from 1D Measurements: Implications for Airborne Instruments

2014 ◽  
Vol 31 (10) ◽  
pp. 2078-2087 ◽  
Author(s):  
Michael L. Larsen ◽  
Clarissa A. Briner ◽  
Philip Boehner
Keyword(s):  
Point Processes ◽  
Pair Correlation ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional System ◽  
Cloud Droplets ◽  
Sampling Variability ◽  
One Dimensional ◽  
Natural Sampling ◽  
The One

Abstract The spatial positions of individual aerosol particles, cloud droplets, or raindrops can be modeled as a point processes in three dimensions. Characterization of three-dimensional point processes often involves the calculation or estimation of the radial distribution function (RDF) and/or the pair-correlation function (PCF) for the system. Sampling these three-dimensional systems is often impractical, however, and, consequently, these three-dimensional systems are directly measured by probing the system along a one-dimensional transect through the volume (e.g., an aircraft-mounted cloud probe measuring a thin horizontal “skewer” through a cloud). The measured RDF and PCF of these one-dimensional transects are related to (but not, in general, equal to) the RDF/PCF of the intrinsic three-dimensional systems from which the sample was taken. Previous work examined the formal mathematical relationship between the statistics of the intrinsic three-dimensional system and the one-dimensional transect; this study extends the previous work within the context of realistic sampling variability. Natural sampling variability is found to constrain substantially the usefulness of applying previous theoretical relationships. Implications for future sampling strategies are discussed.

scholarly journals AdS2 × S2 × CY2 solutions in Type IIB with 8 supersymmetries

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Yolanda Lozano ◽  
Carlos Nunez ◽  
Anayeli Ramirez
Keyword(s):  
Quantum Mechanics ◽  
Riemann Surface ◽  
Central Charge ◽  
Global Solutions ◽  
Infinite Family ◽  
Dimensional System ◽  
One Dimensional

Abstract We present a new infinite family of Type IIB supergravity solutions preserving eight supercharges. The structure of the space is AdS2 × S2 × CY2 × S1 fibered over an interval. These solutions can be related through double analytical continuations with those recently constructed in [1]. Both types of solutions are however dual to very different superconformal quantum mechanics. We show that our solutions fit locally in the class of AdS2 × S2 × CY2 solutions fibered over a 2d Riemann surface Σ constructed by Chiodaroli, Gutperle and Krym, in the absence of D3 and D7 brane sources. We compare our solutions to the global solutions constructed by Chiodaroli, D’Hoker and Gutperle for Σ an annulus. We also construct a cohomogeneity-two family of solutions using non-Abelian T-duality. Finally, we relate the holographic central charge of our one dimensional system to a combination of electric and magnetic fluxes. We propose an extremisation principle for the central charge from a functional constructed out of the RR fluxes.

Mine Impact Burial Prediction From One to Three Dimensions

2008 ◽  
Vol 62 (1) ◽  
Author(s):  
Peter C. Chu
Keyword(s):  
Three Dimensional ◽  
Time History ◽  
Three Dimensions ◽  
Vertical Position ◽  
Burial Depth ◽  
Prediction Errors ◽  
Two Dimensional ◽  
Dimensional Model ◽  
One Dimensional ◽  
Dimensional Models

The Navy’s mine impact burial prediction model creates a time history of a cylindrical or a noncylindrical mine as it falls through air, water, and sediment. The output of the model is the predicted mine trajectory in air and water columns, burial depth/orientation in sediment, as well as height, area, and volume protruding. Model inputs consist of parameters of environment, mine characteristics, and initial release. This paper reviews near three decades’ effort on model development from one to three dimensions: (1) one-dimensional models predict the vertical position of the mine’s center of mass (COM) with the assumption of constant falling angle, (2) two-dimensional models predict the COM position in the (x,z) plane and the rotation around the y-axis, and (3) three-dimensional models predict the COM position in the (x,y,z) space and the rotation around the x-, y-, and z-axes. These models are verified using the data collected from mine impact burial experiments. The one-dimensional model only solves one momentum equation (in the z-direction). It cannot predict the mine trajectory and burial depth well. The two-dimensional model restricts the mine motion in the (x,z) plane (which requires motionless for the environmental fluids) and uses incorrect drag coefficients and inaccurate sediment dynamics. The prediction errors are large in the mine trajectory and burial depth prediction (six to ten times larger than the observed depth in sand bottom of the Monterey Bay). The three-dimensional model predicts the trajectory and burial depth relatively well for cylindrical, near-cylindrical mines, and operational mines such as Manta and Rockan mines.

A 16-connected three-dimensional hydrogen-bonding network in tetrakis(4-aminopyridinium) perylene-3,4,9,10-tetracarboxylate octahydrate

2014 ◽  
Vol 70 (7) ◽  
pp. 668-671 ◽  
Author(s):  
Zhi-Hui Zhang ◽  
Jin-Long Wang ◽  
Ning Gao ◽  
Ming-Yang He
Keyword(s):  
Hydrogen Bonding ◽  
Hydrogen Bonds ◽  
Linear Chain ◽  
Three Dimensional ◽  
Organic Salt ◽  
Water Molecules ◽  
The Novel ◽  
One Dimensional ◽  
Connected Node ◽  
Hydrogen Bonding Network

The novel title organic salt, 4C5H7N2+·C24H8O84−·8H2O, was obtained from the reaction of perylene-3,4,9,10-tetracarboxylic acid (H4ptca) with 4-aminopyridine (4-ap). The asymmetric unit contains half a perylene-3,4,9,10-tetracarboxylate (ptca4−) anion with twofold symmetry, two 4-aminopyridinium (4-Hap+) cations and four water molecules. Strong N—H...O hydrogen bonds connect each ptca4−anion with four 4-Hap+cations to form a one-dimensional linear chain along the [010] direction, decorated by additional 4-Hap+cations attached by weak N—H...O hydrogen bonds to the ptca4−anions. Intermolecular O—H...O interactions of water molecules with ptca4−and 4-Hap+ions complete the three-dimensional hydrogen-bonding network. From the viewpoint of topology, each ptca4−anion acts as a 16-connected node by hydrogen bonding to six 4-Hap+cations and ten water molecules to yield a highly connected hydrogen-bonding framework. π–π interactions between 4-Hap+cations, and between 4-Hap+cations and ptca4−anions, further stabilize the three-dimensional hydrogen-bonding network.

Diffraction of Electrons by Two and Three Mutually Orthogonal Standing Light Waves

1975 ◽  
Vol 53 (2) ◽  
pp. 157-164 ◽  
Author(s):  
F. Ehlotzky
Keyword(s):  
Electron Scattering ◽  
Light Wave ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional Problem ◽  
One Dimensional ◽  
Standing Light Wave ◽  
Light Waves ◽  
The One ◽  
Rectangular Lattices

The one-dimensional problem of electron scattering by a standing light wave, known as the Kapitza–Dirac effect, is shown to be easily extendable to two and three dimensions, thus showing all characteristics of diffraction of electrons by simple two- and three-dimensional rectangular lattices.

One-Dimensional Periodic Potential in Quantum Mechanics

2010 ◽  
Vol 3 (2) ◽  
pp. 99-107
Author(s):  
Vladimir K. Ignatovich
Keyword(s):  
Mathematical Method ◽  
Quantum Mechanics ◽  
Periodic Potential ◽  
Three Dimensional ◽  
Periodic Systems ◽  
Periodic Media ◽  
One Dimensional

An elegant mathematical method is demonstrated with the help of simplest one-dimensional problems of quantum mechanics. This method is then applied to calculation of scattering on one-dimensional periodic systems. Generalization of the method for calculation of scattering in three dimensional periodic media and for spinor particles is pointed out.

INSTANTONS AND SPHALERONS IN SKYRMED WEINBERG–SALAM MODELS AND GRASSMANNIAN MODELS

2000 ◽  
Vol 15 (02) ◽  
pp. 251-264
Author(s):  
F. BRAU ◽  
V. BRIHAYE ◽  
D. H. TCHRAKIAN
Keyword(s):  
Higgs Doublet ◽  
Three Dimensions ◽  
Dimensional System ◽  
One Dimensional ◽  
Yang Mills ◽  
Pure Gauge ◽  
Static Solutions ◽  
The One ◽  
Matter Fields

Several Lagrangians describing the SU(2) Yang–Mills (YM) field interacting with matter are considered, which support both instantons (in four Euclidean dimensions) and sphaleron (in three dimensions, static) solutions. The matter fields are the complex Higgs doublet for the Weinberg–Salam (WS) model, and a (2 × 4) Grassmannian model. These Lagrangians feature Skyrme-like extensions to enable the existence of the instantons, which decay as pure gauge at infinity. For two of these models, we have numerically integrated the one-dimensional system arising from the imposition of radial ansatz.

A Unified Correction Method for the Acoustic Refraction (UCMAR) Caused by a Three Dimensional Shear Layer

2019 ◽  
Vol 105 (5) ◽  
pp. 732-742
Author(s):  
Lican Wang ◽  
Rongqian Chen ◽  
Yancheng You ◽  
Wenjun Wu ◽  
Ruofan Qiu
Keyword(s):  
Wind Tunnel ◽  
Temperature Gradient ◽  
Shear Layer ◽  
Ray Tracing ◽  
Three Dimensional ◽  
Correction Method ◽  
Three Dimensions ◽  
Acceptable Solution ◽  
One Dimensional ◽  
Planar Shear

The acoustic refraction induced by the shear layer in an open-jet wind tunnel causes a source shift when estimating the source location with beamforming. Traditional correction methods of the shear layer refraction are achieved through a computational eff ort or limited using one-dimensional or planar shear layer. In this paper, the unified correction method for acoustic refraction (UCMAR) is suitable for the three dimensions that covers several traditional forms. Meanwhile, the UCMAR can consider more general configurations, such as the temperature gradient on both sides of the shear layer and the off -axis source in a circular wind tunnel. These configurations are validated through a ray tracing technique and a benchmark example. In addition, the principle of time reverse is integrated with UCMAR. This results in a reverse UCMAR, which can quickly attain an acceptable solution.

Propagation of Low Frequency Elastic Disturbances in a Three-Dimensional Composite Material

1975 ◽  
Vol 42 (1) ◽  
pp. 159-164 ◽  
Author(s):  
W. Kohn
Keyword(s):  
Secular Equation ◽  
Displacement Vector ◽  
Three Dimensional ◽  
Low Frequency ◽  
Three Dimensions ◽  
Low Frequencies ◽  
One Dimensional ◽  
Coupled Partial Differential Equations ◽  
Constant Coefficients ◽  
The Mean

This paper is a generalization to three dimensions of an earlier study for one-dimensional composites. We show here that in the limit of low frequencies the displacement vector ui(r,t) can be written in the form ui (r,t) = (∂ij + vijl (r) ∂/∂xl + …) Uj (r,t). Here Uj (r,t) is a slowly varying vector function of r and t which describes the mean displacement of each cell of the composite. Its components satisfy a set of three coupled partial differential equations with constant coefficients. These coefficients are obtainable from the three-by-three secular equation which yields the low-lying normal mode frequencies, ω(k). Information about local strains is contained in the function vijl(r), which is characteristic of static deformations, and is discussed in detail. Among applications of this method is the structure of the head of a pulse propagating in an arbitrary direction.

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